Matematicas_en_SAT_Informe_Ford_Sarah_Richards_Agosto_25

Improving Maths Education in Rural Honduras

A research study on maths teaching and learning in the Sistema de Aprendizaje Tutorial (SAT)

Sarah Richards, Consultant

August 2010

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This report is dedicated to the Baha’i youth of Iran.

They have been denied access to higher education for decades,

and are beacons of hope, compassion and fortitude.

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Contents Acknowledgements .......................................................................................................................................................... 5

Executive Summary ....................................................................................................................................................... 6

Background ...................................................................................................................................................................... 11

Objectives .......................................................................................................................................................................... 13

Methodology .................................................................................................................................................................... 13

Limitations of the study .............................................................................................................................................. 13

Creating an atmosphere of consultation .............................................................................................................. 15

In the classroom ........................................................................................................................................................ 15

Improving the educational value of classroom talk ................................................................................... 17

General Training and consultation skills ........................................................................................................ 19

The use of questions and answers .......................................................................................................................... 20

Allowing time for reflection ................................................................................................................................. 20

Questions: increasing participation .................................................................................................................. 20

Questioning: a formative assessment tool ..................................................................................................... 21

Tutor/student questions ....................................................................................................................................... 22

Three ways of working ................................................................................................................................................ 22

The use of tutor/student presentations of work ......................................................................................... 23

Working in small groups........................................................................................................................................ 25

Peer teaching and ‘social loafing’ .................................................................................................................. 25

A forgotten method? .......................................................................................................................................... 26

Individual work: the third force ......................................................................................................................... 27

Thinking time ........................................................................................................................................................ 27

Formative Assessment: fine tuning acompanimiento ..................................................................................... 28

Taking responsibility for learning .......................................................................................................................... 28

Unsupervised working ........................................................................................................................................... 29

Homework ................................................................................................................................................................... 29

Formative assessment helps students take responsibility for learning ............................................ 29

Tools and Representations ........................................................................................................................................ 30

The importance of the texts.................................................................................................................................. 30

Multiple representations ....................................................................................................................................... 31

Updating and revision of texts ............................................................................................................................ 33

Guías de Aprendizaje y Evaluación (Ciclo Común) ..................................................................................... 35

Practical application of maths ............................................................................................................................. 37

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Statistics ....................................................................................................................................................................... 37

Linking SAT and community maths .................................................................................................................. 38

Evaluation ......................................................................................................................................................................... 38

Community Evaluation ........................................................................................................................................... 39

Evaluation – testing and retesting..................................................................................................................... 40

Maths: a problematic part of the program ..................................................................................................... 40

Percentages of retakes for 2008 ......................................................................................................................... 40

Comparing SAT performance with the government system .................................................................. 41

Tutors and mathematics: knowledge, attitudes and beliefs about teaching and learning ..................... 42

Tutor attitudes to maths: the positive results of training ........................................................................ 42

Building on an apprenticeship of observation.............................................................................................. 44

Theory- based practice ........................................................................................................................................... 45

Maintaining positivity: getting unstuck ........................................................................................................... 45

Tutor knowledge ....................................................................................................................................................... 46

Basic mathematical operations ......................................................................................................................... 47

The transition to Bachillerato ......................................................................................................................... 48

Preparing for training .................................................................................................................................................. 50

To study or not to study texts .............................................................................................................................. 50

Maintaining the quality of maths training ........................................................................................................... 50

The Training................................................................................................................................................................ 50

Supporting tutors’ development of practice in the field........................................................................... 51

The role of the field assessor .................................................................................................................................. 51

Institutional links .......................................................................................................................................................... 52

Conclusions ....................................................................................................................................................................... 55

References ........................................................................................................................................................................ 60

Appendix 1: Observations: maths trainings .................................................................................................. 62

Appendix 2 – Summary of the field assessors’ session observations ................................................. 63

Appendix 3: Summary of field assessors comments on classroom observations (not monthly

reports) ......................................................................................................................................................................... 66

Appendix 4: Questionnaire Survey .................................................................................................................... 69

Appendix 5: Additional comments of the tutors on the questionnaire .............................................. 77

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Acknowledgements

This report was made possible through grant number 1070-0932 from the Ford Foundation.

I would also like to acknowledge the assistance of all those currently involved in the

implementation of SAT-Honduras who gave their time and professional assistance during

this investigation, including the Executive Director of Bayan Association, Ing Soheil Dooki,

for his sustained encouragement; the mathematics coordinator, Ing Ruhollah Sayyáh, for his

fine example and patient, good humoured support; and the many other people, tutors, field

assistants, coordinators and administrative staff who all gave generously of their time,

inspired me by their dedication, and treated me with great kindness. This report would have

been impossible without them and I am very grateful. In addition, I am very grateful to Dr

Chris Martin (ex Ford Foundation) and Prof Diana Coben for helping identify the need for

this research, and for their useful ideas on how to undertake it, to Prof Malcolm Swan for

his valuable comments, to my colleagues at Abingdon & Witney College for their warm

support and the granting of extended leave and finally, a very heartfelt thank you to Dr

Michael Richards for his editing and wise advice.

The views and opinions expressed in the report, as well as any errors, are those of the

consultant1 and do not necessarily represent those of the Asociación Bayán or the Ford

Foundation.

1 Consultant qualifications include: BSc in Psychology (Open University, UK), Post Graduate Certificate in Education (Oxford University), MA in Education (Oxford Brookes University) and SAT Tutor (Impulsor level). Experience in education includes 20 years teaching and teacher training/mentoring in England, Malawi, Ghana, Mexico and Honduras. The consultant has delivered workshops/papers at various international conferences/training events in England, Ireland, Scotland, USA and Mexico. In 2002, she was on the final evaluation team of the UK Department for International Development (DFID) project to establish SAT on the north coast of Honduras (1997-2002). [email protected]

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Executive Summary

The Sistema de Aprendizaje Tutorial (SAT) is an interdisciplinary secondary school program

designed to provide a high quality and appropriate education in rural areas. The quality of

the Honduran SAT program has been nationally and internationally acknowledged. In

Honduras, SAT is implemented in a partnership of the Ministry of Education and four NGOs.

Asociación Bayán’s responsibilities include: philosophical guidance; the adaption and

updating of educational materials; implementation of the curriculum; all training; and

monitoring and evaluation of the educational processes.

Asociación Bayán and the Ford Foundation commissioned this report to:

Investigate tutor training for maths and the impact that this has on the mathematical

understanding and pedagogy of the tutors.

Assess other aspects of SAT affecting the development of the students’

mathematical capacity in the classroom.

Make recommendation to improve the effectiveness of the maths component in

SAT, with particular reference to tutor training.

It is further stated that the results of the study will be made available to the educational

community so that they can be of use to other educational programs, both national and

international.

It would be difficult and counterproductive to attempt to completely separate the maths

component, especially as regards the pedagogic aspects, from the overall SAT program,

in view of some of the generic pedagogic challenges faced. Therefore some more

general analysis of the learning process and challenges in SAT is in order.

In a little over a decade SAT has expanded dramatically from about a hundred students

to nearly eight thousand. This rapid expansion is a remarkable achievement made

possible by the energy and sacrifice of a dedicated team of people, and has involved the

formidable challenge of training about 700 tutors (there is a high turnover rate) and 80

field advisors and coordinators. One of the key challenges to maintaining the quality of

SAT is that it is based on several assumptions that are notoriously difficult to change,

about the purpose of education and learning processes which underpin the whole SAT

methodology, but which the trainees, despite a rigorous selection process, often do not

initially share. The most critical assumptions are that:

tutors and students are co-workers committed to individually and collaboratively

developing their spiritual, practical and intellectual capacities and service-orientated

attitudes;

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the learning process is most effective when it is active, participatory and applied to

solve real life problems;

the role of the tutor is to guide and accompany students on their developmental

journey - this is very different from the role of a traditional ‘transmission’ orientated

teacher.

A new type of educator is required, ‘con una amplia visión, no solo de los aspectos

educativos, sino también de lo relacionado a la gestión comunitaria y desarrollo

social.’2

The tutors, who are often without a sound maths education themselves3, face the daunting

task of enabling poorly prepared students4 to access, and succeed with, a curriculum that is

much more conceptually challenging (and necessarily so) than they have themselves

experienced. It is therefore unsurprising that maths has been the most problematic area of

SAT since the beginning of the program5.

It is an indication of the

fundamentally sound nature

of the training that almost all

the questioned tutors

reported that their own

maths had benefitted

significantly, and that they

had a more positive attitude

towards maths as a result of

their training with SAT. The

vast majority of the tutors

reported enjoying teaching

maths, and felt they

understood the material well enough to explain it to their students. A major contributing

factor to this success is the inclusive and collaborative learning environment created in most

of the trainings, and, very significantly, field reports and observations indicate this is almost

always replicated in the SAT classrooms.

The strong emphasis on the practical applications of maths, conceptual understanding and the integrated nature of the curriculum appears to be profoundly motivating for both tutors

2 ‘A broad vision of not only of education but also of the promotion of social and community development’

(taken from the introduction to Aprender Enseñando, the SAT teacher training text). . 3 Honduras was reported to have the worst maths education in Central America in the Informe de Progreso

Educativo de Honduras. (2005). Programa de Promoción de la Reforma Educativa en América Latina y Caribe (PREAL). Washington, DC/Chile: Inter-American Dialogue/Corporación de Investigación y Desarrollo 4 Rural schools are more likely to have several grades in one classroom and experience much more frequent

teacher absences than urban schools. 5 If students score less than 60% in an end of module test they have to retake it. In 2009, the percentage

retaking maths was 45% compared to a 16% average for the other four areas of SAT.

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and students, but during observations of trainings it was apparent that some key aspects of the SAT methodology are not being implemented, or are only being partially implemented. These are the aspects of the methodology that are most associated with effective maths pedagogy according to international research.

The neglected activities include ones that are strongly associated with conceptual development, increasing classroom participation, taking ownership of the learning process, and assisting teachers in assessing and responding to student learning. For example, activities explicitly recommended in the SAT texts, but not seen in 195 hours of training/classroom observations, are:

Individual work followed by small group work, in which each student in turn should explain/justify their method of resolving a problem or explaining a concept to the other members of the group

Use of the SAT Learning and Evaluation Guides

The SAT texts are innovative,

engaging and generally very

supportive to the learner, but they

sometimes assume a knowledge

and understanding of maths, and

its associated pedagogy, which

tutors have not yet developed. It

may be that many tutors are

satisfied with their delivery of the

curriculum because they are

unaware of the more challenging

aspects of the SAT methodology,

and the concomitant need for

greater conceptual understanding.

Many key teaching staff have therefore identified as an urgent need the development of

additional materials and activities which can enable the tutors and students to overcome

the deficiencies of their previous education. There is a strong commitment by SAT

coordinators to do this. A more complete utilisation of the SAT methodology may reduce

the need for additional materials, although some important (according to recent research

and international good practice for effective maths teaching) tools/activities should be

considered in terms of their potential to significantly enhance the learning process in SAT.

Teaching staff are very aware of the need to focus more on conceptual development and

pedagogy, but find that this is very difficult due to the severe time constraints of the current

training schedules. The more careful planning of training could help with this, but there is

also a need to increase (carefully selected) field support staff capacity to deliver more

specialist maths training in small, local trainings, and to mentor tutors. The process of

training maths specialists has begun and two trainings have taken place.

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Interviews revealed that most tutors are also studying for undergraduate degrees, and are

taking classes on education. But no linking of university studies and SAT, and very limited

reference to SAT educational theory, was observed during the trainings, apart from during

the initial training. A greater understanding of the theoretical underpinnings of the SAT

methodology, its relationship to wider educational theory, and how these relate to their

own beliefs and practices would significantly help tutors to more fully implement the SAT

methodology, and to become more reflective and effective practitioners (this finding is

supported by educational research literature).

The rapid expansion of SAT has placed Asociación Bayán under considerable stress, and all

the interviewed coordinators expressed serious concerns about maintaining quality.

Inconsistencies in data collection on field activities (although there are plans to produce a

manual), serious archiving problems,6 and the lack of effective fora for discussing concerns,

are (in the consultant’s view) are impacting Asociación Bayán’s capacity to address these

issues. It is vital that such constraints are urgently addressed.

It is clear that the quality of the tutors as effective teachers is the key to the success of the

SAT program. The high turnover rate of tutors7 means that the SAT trainings have to be very

effective. It is vital that tutors experience the full SAT methodology while in training,

understand the reasons for it, and are supported in their adoption of participatory teaching

practices. Therefore the most important recommendations of this consultancy report are

that:

Activities which are a part of the SAT methodology, but which have only partially

been adopted, or have not been adopted, are fully implemented, unless

consultation with FUNDAEC identifies them as being no longer appropriate.

Priority is given to building the capacity of:

o trainers to use the SAT methodology fully;

o the field assessors to be able to ‘accompany’ the tutors in the development

of their general pedagogic skills;

o carefully selected maths field support staff to be able to effectively support

the tutors in the development of their maths pedagogy/knowledge.

Effective fora for the consultation of pedagogical and other educational issues are

established.

Tutors are mentored in order to help develop their capacities to reflect on their

practice, and to be able to systematically experiment with small changes (action

research).

Relevant insights, techniques and tools originating outside SAT, particularly those

associated with increased classroom participation, conceptual development and

‘formative assessment’, are identified and considered for adoption and adaptation,

6 See Limitations: page 13/14

7 See Background: paragraph 5

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since (according to the consultant’s experience and relevant research literature)

these have the potential to significantly enhance key aspects of the SAT

pedagogy/curriculum.

The collection and analysis of field data and feedback is systematised and

standardised (where appropriate), and archiving systems are improved.

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Introduction

Background

The Sistema de Aprendizaje Tutorial (SAT) was developed in Colombia in the 1970s to

provide a good quality and appropriate secondary education in rural areas. The curriculum

is interdisciplinary and focused on developing students’ spiritual, moral, practical and

intellectual potential in order that they can, along with other community members, take

charge of their own autonomous and sustainable development (Box 1). The quality of SAT

has been nationally and internationally

acknowledged8.

In Honduras, SAT is implemented in a partnership

of the Ministry of Education and four NGOs,

including Asociación Bayán. Asociación Bayán,

among other services, provides: philosophical and

pedagogical guidance, including curriculum

development; all the training; monitoring and

evaluation; and adapts or updates SAT texts in

consultation with the founding NGO of SAT, the

Foundation for the Application and Teaching of

Sciences (FUNDAEC), Colombia.

SAT’s dramatic expansion from about a hundred

students to about eight thousand in a little over a

decade has presented the formidable challenge of

inducting and training over 700 new tutors, as

well as about 80 field advisors and coordinators.

The SAT philosophy and pedagogy is a new and

challenging paradigm for the majority, because

most Hondurans, especially those from poorer

backgrounds, have mainly experienced the

‘transmission’ or ‘empty container’ method of

teaching (UNDP, 2009a). It is widely recognised

that teachers tend to adopt the style of teaching

8 A 2005 Ministry of Education report on education in Honduras noted that: "SAT .... through the

development of contents relevant to the aspirations and real needs of the rural population, has shown

itself to be adapted to the special conditions of rural people." In 2002, SAT-Colombia received a Club of

Budapest “Change the World – Best Practice Award”; and in 2008 Asociación Bayán was invited to

present SAT-Honduras as a ‘best practice’ sustainable development case study at the UN Commission for

Sustainable Development (CSD-16) meeting.

Box 1

The search for a valid rural

education implies changes in

the relationships between

many of the elements of the

educational system - time,

space, students, teachers,

school, and the community.

For example, the relationship

between the students and the

professors in the programs of

FUNDAEC is one of co-workers

embarked on an enterprise of

great importance - the search

for the path of development

of their people. The student is

not considered an empty

container to be filled drop by

drop but a mine of hidden

talents and potential that

need to be discovered,

perfected, and directed

toward the service of others.

Source: Arbab el al (1988)

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that they have experienced as students (Schwille & Dembele, 2007).

However SAT has been able to achieve some significant positive changes in teaching style.

This is probably because of its strong philosophical base, and the fact that the training

already has some elements known to increase active teaching methods, such as systematic

training over a long period and support by peers in the field (Wiliam, 2006).

On the other hand SAT and Asociación Bayán have also faced the challenge of a high

turnover rate of tutors, which is to be expected in a rapidly expanding program. From 2000

to 2008 just over 500 tutors were trained, and about 20% left after an average 2.4 years.

The high turnover rate is partly due to the understandable tendency for tutors,

most of whom are undergraduates, to look for a secure job after completing their degree.

Those still in SAT average about 2 years of service9. This is problematic in that research

shows that experience is a key factor in improved teacher performance (Chingos &

Peterson, 2010; Wiliam, 2007); the short average length of tutor service also increases the

pressure on tutor training to be particularly effective.

The SAT methodology (Box 2) is largely inspired by

the Baha’i Writings, in which consultation is

conceptualised as the collaborative search for truth

and the process by which decisions are made for

community action. The criteria for consultation are

demanding and include (italicised phrases are from

the Bahá’í writings10): ‘purity of motive‘; an

atmosphere of ‘love and harmony’; objectivity or

detachment; ‘courtesy’; ‘absolute freedom’ of

expression; and the responsibility of all to give an

opinion supported by logical arguments rather than

personal emotions.

In SAT there is great emphasis on the quality of the textbooks and tutors. The textbooks are

fundamental to the methodology, and are designed to be worked through systematically by

the students, accompanied and helped, where necessary, by their tutor. This is very

different to normal Honduran practice in which the teacher stands at the front and teaches,

and the students listen. The SAT texts, through a series of thought provoking questions,

explanations and graded activities, develop key concepts, skills (intellectual and practical)

and attitudes so that students can become independent and rigorous mathematical

thinkers, and accurate, efficient practitioners.

9 Tutor data was only available up to 2008 so average length of service could have changed.

10 For example, ‘Should any one oppose, he must on no account feel hurt for not until matters are fully

discussed can the right way be revealed. The shining spark of truth cometh forth only after the clash of differing opinions.’ (Abdu’l Baha, cited in Shoghi Effendi, 1922).

Box 2

The method of teaching,

reflected in the design of

textbooks, is one of raising

questions and trying to find

answers in an atmosphere of

consultation between

teachers and students.

Source: Arbab et al (1988)

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There is substantial research evidence that teachers have a major influence on student

achievement; students with the best teachers learn at twice the rate of those with average

teachers (Rivkin, 2005). Asociación Bayán, in consultation with the Ford Foundation, has

identified or hypothesised that improving the level of maths teaching would have a

substantial impact both on overall academic progress and the running of small businesses,

agricultural and community projects. For these reasons Asociación Bayán and The Ford

Foundation commissioned this study and report.

Objectives

To investigate tutor training for maths, and the impact that this has on the

mathematical understanding and pedagogy of the tutors.

To report on other aspects of SAT affecting development of the students’

mathematical capacity in the classroom.

To make recommendations to improve the effectiveness of the maths component in

SAT, with particular reference to tutor training.

Methodology

Semi-structured interviews with coordinators, field advisors and tutors (Appendix 1)

Observations of maths and general training (156 hours), SAT lessons (15 attended in

the Departments of Atlantida, Colon and Santa Barbara) and a range of meetings,

including coordinator meetings (Appendix 1)

Participatory observation, including that derived from conducting tutor training in

maths11 and English, and providing support to other trainers/coordinators

Questionnaire surveys, focusing on tutor experience and attitudes to maths learning

and teaching (applied to 190 tutors of whom 133 responded (70%), adapted from

proven questionnaires by Swan (2006) and a seminal study by Fennema & Sherman

(1976) as translated by Ignacio et al (2006) (Appendix 4)

Review of documents: SAT Texts; Tutors’ worked Texts; Field Assessor Observation

Reports and Monthly Reports; Asociación Bayán Nacional Profiles; data on tutor

length of service; one Asociación Bayán internal report; and reports to donors (see

below).

Limitations of the study

The paucity of reports: after repeated requests for any report which contained

references of any sort to education, I was advised that due to hard disc failures and

archiving problems only the following reports were available: 2010 January Informe

de Actividades; the Perfiles Nacionales for 2010 (Block 1), 2008 (Blocks 2 & 3) and

11 Maths: 4 hours, English: 12 hours

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2009 (incomplete due to the coup); and three reports to donors12, two for 2007 (Jan

– June and July – Dec) and one for 2004-2006.13

SAT students were not consulted in this study, partly since the three year Hewlett

study by the Universities of Berkely, New York, Wellesley College (USA) and the

National Pedagogic University (Honduras) will contain an in-depth impact analysis of

student achievement and experience for the first two years of study14.

I decided that it was beyond the scope of this report to analyse the interactions

between mathematics and other curriculum areas, economic activities and

community development (in SAT these process are all integrated). It is however

hoped that this report will contribute to a holistic reflection on the SAT program.

The Asociación Bayán plans to review working conditions and practices and

therefore these are not addressed in this report.

12 Reports:

Scaling up the System of Tutorial Learning (SAT) as an alternative education program tackling rural poverty and gender inequity in Honduras:01:07:04-30:06:06 (No:1045-0688)

Building Sustainable Livelihoods through Agriculture 01.01.07:31.07.07 (CIDA)

Fortaleciendo la Candidación del Programa Educativa Rural SAT en Intibucá, La Paz y Comayagua. Junior 07 – Dec 07 (IBIS)

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There is very little documentation of SAT’s development in Honduras; this, combined with the loss of many key reports means that the opportunity for Association Bayán to reflect on its experience and for other organisations to benefit from them is seriously diminished. When the innovative nature and success of the program is taken into account this is a significant loss. 14

2007 (Draft proposal) 4 mains goals were: 1) To develop and apply appropriate measures of secondary school quality; 2) To evaluate the impact of SAT on treated communities, particularly student participants; 3) To explain the impact (or lack thereof) of the SAT program; 4) To extract lessons for the scaling-up of SAT in Latin America and expansion to new countries.

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Findings

SAT is implemented by a dedicated team that

believes strongly in its value and is committed to its

sustainable development. Although many senior

staff said that SAT’s rapid expansion has made it

difficult to maintain the high standard of training

achieved in earlier years, the vast majority of tutors

report that the maths training has had a significant

positive impact on them (Box 3) and that it

prepares them well for teaching. This report finds

that the maths tutor training is basically sound, but

that senior staff concerns are valid and there is an

urgent need to address them for quality to be

maintained and improved.

Creating an atmosphere of consultation

In the classroom

In the major recent Human Development report of Honduras by UNDP (2009a), which

focused on youth issues and contains a major survey of Honduran youth attitudes (UNDP,

2009b), Honduran youth responded that, after poverty, their greatest problem was

violence, principally feuds and fights. The SAT centres are located in communities where

family feuds are common and therefore can be a

difficult environment in which to develop an

‘atmosphere of consultation’.

In interviews with first year tutors and other tutors

recalling their first year, frequent mention was

made of the difficulties and sustained effort

required to establish and maintain classroom

norms of respect and collaboration. The majority

appear to achieve it; in the Field Assessor reports,

the boxes for: ‘Se observa un ambiente alegre y de

motivación en el grupo’15 and ‘Se observa respeto

hacia las opiniones de los compañeros’16 were

ticked 96% of the time (Appendix 2). This is a

15 ‘A happy and motivated atmosphere was observed.’ 16 ‘Students were respectful of one another’s opinions.’

Box 4

The class worked in small interacting

groups for two hours and then, during

the recess, most of the centre’s

seventy students played football

together with vigour and good

humour. The tutors were unable to

explain how the students formed their

teams - age, sex and community did

not appear to be factors.

Observation: March 2010

Box 3

En SAT la experiencia en matemática

es fascinante porque aprendes a

desarrollar tu propio concepto y te

pones a utilizar tu lógica matemática

que a veces esta muy dormida en

problemas de la vida diaria y te llevas

a resolver esos problemas de la vida

diaria.

Source: SAT tutor comment on

questionnaire

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Box 5

When a student in one group was

undergoing chemotherapy and not

robust enough to leave the house so

his SAT group met in his home during

his treatment and convalescence. Two

years later he is studying Bachillerato

with the same group.

A first year tutor realised at the

beginning of the year that the low

literacy levels of some of his students

would impede their progress so he

gave extra classes every Saturday for

the first block.

A tutor accompanied a group of his

students on the two hour walk to their

community and stayed for the night in

order to get to know their families and

experience their daily journey.

Parents, students and tutor worked

together, bringing sand from the river

so that they could build a new

classroom.

Source: observation Oct 2008 & April

2010, coordinator interview May 2010

tutor interview with video evidence May

2010.

yes/no Box, but judging by additional comments

(Appendix 4), they appear to be using fairly

similar indicators17 and, in most of the sixteen

classes observed, there was a collaborative,

purposeful and cheerful atmosphere (Box 4).

Tutors remain with the same students for up to

six years, and are responsible for academic

progress and pastoral support. It seems, from

interviews and conversations with tutors and co-

ordinators that most tutors demonstrate

commitment to, and develop strong bonds of

affection for, their students (Box 5). The fact that

they often go to considerable trouble to get to

know their home circumstances, provide extra

help and are active with their students in

community projects (Appendix 3) also contributes

to the generally united classroom atmosphere.

It was noticeable that although some assessor

monthly reports were fuller and franker than

others, most contained observations about the

learning environment that could usefully be

reflected on.

It is recommended that:

1. Asociación Bayán continues to build

on these good foundations by

continuing to reflect and

experiment with ways of further

developing ‘an atmosphere of consultation.’

17 Example of monthly reports were received from 8 out of 12 regions and observation reports on 36 tutors completed by 8 assessors. This represents less than 1% of the tutors it and cannot be considered representative.

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Improving the educational value of classroom

talk

Asking probing questions in order to consult on

them is at the heart of SAT methodology (Box 6).

This approach is supported by wide body of

research showing the value of discussion in the

learning process (Anthony & Walshaw, 2009).

Given the constant talking observed in SAT

classrooms, and the vital role that tutors

think this plays in learning,18 it is essential

to note that the evidence indicates that

some types of discussion are much more

productive than others (Box 7).

The concept of ‘consultation’ is far more

complex than that of ‘exploratory talk’

(Box 7), but they share common

characteristics, and developing

tutor/student capacity for ‘exploratory

talk’ can be considered as contributing to

the creation of ‘an atmosphere of

consultation’.

The whole-group discussions observed in

the trainings and classes were almost

exclusively of the ‘cumulative talk’ type.

The better trainers sometimes tried to

facilitate ‘exploratory’ discussions, with

some success, but generally it seemed as

though the trainers needed further

guidance in how to promote ‘exploratory

talk.’19 For example, it was observed that

in the tutor trainings, tutors rarely built on previous contributions by themselves or others

and this was never observed in a classroom.

18

86% of tutors reported (in the questionnaire survey) that their students usually learnt through discussion. 19

It may be that assessors (and tutors) have different conceptions of what it means to take part in a discussion. For example in the Informes de Visita (Appendix 2) in response to ‘Durante su estadia en el aula cuantos participantes vio opinar’ the reported percentage of students ranged from 100% to 6%. It was noticeable that assessors tended to give a similar estimate for all their observations. It may be that some assessors count giving an answer as ‘opinar’ while others require justification or elaboration as well.

Box 6

Un proceso en el cual se tiene como

referencia el método científico: el

grupo explora, identifica problemas,

formula interrogantes e hipótesis,

consigue información, experimenta,

descubre, crea modelos, aplica,

explica y plantea nuevas preguntas …

Source: Valcarcel & Correa (1995)

Box 7

Mercer (1995,2000) has described in some

depth the types of interaction that promote

effective and ineffective learning. In particular

he demonstrates the superiority of exploratory

talk over disputational and cumulative talk.

Exploratory talk consists of critical and

constructive exchanges, where challenges are

justified and alternative ideas are offered.

Disputational talk consists of disagreement

and individualised decision making. This is

characterised by short exchanges consisting of

assertions and counter-assertions. In

cumulative talk speakers build positively but

uncritically on what each of the others has

said. This is most typically characterised by

repetitions, confirmations and elaborations. In

short the most helpful talk appears to be that

where the participants work on and elaborate

each other’s reasoning in a collaborative rather

than a competitive atmosphere. Exploratory

talk enables reasoning to become audible and

knowledge becomes publicly accountable. -my

italics-

Source: Swan (2006:87)

18

Box 9

Entonces en general SAT tiene un desafío y es

justamente ayudar a sus participantes a pensar

más. Este es el problema. El Doctor Gustavo

Correa decía si tan solo logramos a ayudar a

los jóvenes pensar es un gran logro (¿). Porque

están acostumbrados que le profesor les digan

todo y ellos toman notas y cuando toman

examen es muy literal y entonces en SAT les

ponen difícil porque les está preguntando a

cado rato ‘¿Y Usted que piense y porque es

falso, y porque es verdadero, cual es la

justificación?’

Source: coordinator interview Abril 2010

The texts offer many opportunities for activities

associated with conceptual development, but most

tutors seemed unaware of them. This is indicated by

the fact that, although discussions which involved

sustained reasoning (photograph) were rarely

observed.20 96% of tutors reported that usually ‘mis

estudiantes realizan todos los ejercicios del texto de

matematicas’.21 Most exercises are diligently done,

but it was also observed that opportunities to probe

and extend conceptual understanding and analytical

capacity are lost (Box 8). Developing student

conceptual

understandin

g and capacity to think analytically is internationally

acknowledged to be challenging. Trainers are

aware of the difficulties (Box 9) and keen to

develop this key aspect of SAT methodology.


2. Tutors are explicitly taught the

characteristics of ‘exploratory talk’, provided

opportunities to develop these skills, and

mentored in facilitating appropriate kinds of

‘exploratory talk’ in the classroom.

3. Topics where tutors regularly experience difficulties are identified before training so that

questions, reflection, activities and discussion can be carefully planned.

4. Opportunities for developing mathematical thinking are clearly identified during training,

and appropriate activities are clearly demonstrated.

20 Trainers frequently asked students a question in order to probe understanding but discussions based around these answers were very rare. 21 ‘My students do all the exercises in the maths’ textbook’.

Box 8

It was clearly explained how to record

a quantity in different bases. The

tutors then constructed tables to

show how quantities were

represented in bases 2 – 10 (some

used beans to model the bases).

Students worked in small groups and,

with the help of the trainer, nearly all

had completed the table by the end of

the session. No time was given at the

end of the session for observations,

questions and the forming

generalisations related to the activity

Source: Observation May 2010

19

5. Tutors should have a written record (e.g., training handouts) to support classroom practice

and/or training in the taking of pedagogical notes, since inspection of many tutor texts

revealed that tutors very rarely take pedagogical notes22.

General Training and consultation skills

The process of developing an ‘atmosphere of consultation’ (Arbab, 1988) clearly transcends

subject areas; it is the foundation of the SAT methodology. The thrice yearly, two week

trainings are seen by coordinators as the key to raising tutor awareness of the qualities and

attitudes necessary to create a transformative learning environment.

Five different trainers were observed delivering Aprender Enseñando. It is clearly desirable

that trainers contribute creatively to the course content and method of delivery, but the

style of facilitation and content of the orientation varied to such a degree that tutors cannot

be considered to have received the same training. In some of the trainings there was an

open and accepting atmosphere, and tutors appeared to speak freely, but in others there

was little opportunity for the tutors to express their thoughts, and on one occasion an

opinion (valid in my view) was dismissed as incorrect. It is important that tutors have

substantial and varied experience of an ‘atmosphere of consultation’, particularly during

their early training; otherwise it is harder for them to develop such an atmosphere, in far

more challenging circumstances, in their own classes.


6. Aprender Enseñando is used to develop consultation skills and its delivery is

collaboratively planned so that tutors have a comparable experience.

22

A quick inspection of approximately 60 tutor texts revealed that some tutors never take pedagogical notes, even when it is recommended that they do. For example on one occasion after a very clear analogy and diagram was used by a trainer to clarify a concept it was suggested that a note was made of this. Subsequent inspection of the books revealed that only 15/21 tutors had done this and that the notes, when taken, were often very brief. When note taking is not suggested pedagogical notes are very rare. On one occasion tutors were provided with paper to make additional notes and glue to stick this into their books. This increased the quantity and legibility of notes.

20

The use of questions and answers

Allowing time for reflection

The questions in the texts have many purposes,

among them bringing to the student’s attention

something that s/he may not have considered

before (Box 10). The student may not be

expected to say or write anything immediately

after this reflection, but the act of doing it aids

learning, encourages independent thinking, and

enriches subsequent discussion. There is

evidence that a slight pause between asking a

question, even the simplest one, and a

student/tutor being required to answer, increases

participation (Hodgen & Wiliam, 2006). It was

observed that some trainers allowed time for reflection while others did not.


7. Trainers allow time between questions

and responses, and discuss the reasons for

doing this with the tutors.

Questions: increasing participation

It was observed that a large number of

questions are asked by the trainers/tutors.

Almost always, in both training and classes,

either a particular person is nominated to

answer (sometimes before the question is

asked) or it is addressed to the whole group,

and someone shouts out the answer. This

means that, although most tutors/students

contribute in most sessions, a vocal minority

tends to dominate.


8. Trainers/tutors are taught a range of techniques for increasing tutor/student

participation when answering questions.

Box 10

No se trata de entregar conceptos

totalmente elaborados, sino de

plantear preguntas y situaciones que

ayudan al estudiante a precisar ideas

en las cuales posiblemente no se

había detenido a pensar. ¿Cómo se

llego a nociones como punto, recta,

plano? ¿ Qué relaciones hay entre

ellas?

¿Para qué sirven esas ideas?

Source: Bosquejo General: El Espacio y Sus

Elementos.

21

Box 11

Practice in classrooms is formative to

the extent that evidence about

student achievement is elicited,

interpreted and used by teachers,

learners or their peers to make

decisions about the next steps in

instruction that are likely to be better,

or better founded, than decisions

made in the absence of the evidence

that was elicited.

Source: Black & Wiliam (2009)

Questioning: a formative assessment tool

There is strong research evidence that improving

formative assessment (Box 11) is the most

effective way of raising student performance

(Hattie & Timberley, 2007). Questioning can be a

good formative assessment tool if the teacher

asks appropriate questions, listens to the

answers, and builds on the information gained.

Student answers sometimes require probing and

reflecting on in order to understand what is

meant and to expose underlying assumptions

which may be impeding progress. This can take

time, but is essential for building up clear

communication. It was observed that some

trainers are much more skilled than others in this

process.

The SAT tutors seemed unaware of the power of

using student errors to explore and develop

conceptual understanding, as is shown by the fact

that 90% of the tutors in the questionnaire

reported that they tried to teach so that the

students did not make mistakes. Many of the

questions in the SAT texts are designed to

develop understanding; exploring mathematical

ideas, making mistakes and subsequently

analysing and rectifying them is an important part

of this process (Box 12).


9. Tutors are supported and mentored in the didactic use of questions and ‘error

analysis’ as a formative assessment tool; this includes being informed of the utility

of this approach;, experiencing it in training; knowing where it is most appropriate;

and being mentored in developing these skills by field assessor accompanimiento.

10. Students are encouraged to experiment, take risks, make mistakes, identify and

correct them. This would facilitate exploratory talk.

Box 12

Es necesario tener lápiz, papel y

borrador en mano, no para copiar,

sino para resolver personalmente

todos y cada uno de los ejercicios,

corriendo el riesgo de cometer

errores, de tomar caminos esquivados

y asumiendo también la

responsabilidad de revisar, corregir y

de proponer soluciones originales y

creativas.

Source: Bosquejo General: Manejo de

Variables, Unidad 1

22

Tutor/student questions

Developing student capacity to form probing questions is an important part of the SAT

methodology23. There are two ways this happens:

Firstly, students are specifically asked to make up a problem for other students to solve.

92% of the tutors reported that ‘aprendo mucho inventando nuevos problemas’24. Creating

problems or questions often requires more complex processing of the concepts than

responding to a readymade question. This type of activity assists in the internalisation and

development of concepts (Swan, 2006); the form and content of a student-made question

gives insights into understanding, and so can be used for formative assessment. Also being

able to create mathematical problems is a useful skill for tutors to acquire so that they can

provide students with additional examples, and support them in forming their own

problems.

Secondly, there are questions that originate from the students’ own engagement with the

topic and/or development processes. In the trainings for maths specialists25 it was observed

that participants asked questions about mathematical reasoning and representations, but in

the normal trainings and classes almost all the questions made by tutors/students referred

to algorithmic procedures as opposed to more substantial conceptual or community

development issues.


11. Activities where question formation is explicitly asked for or which lend

themselves to this are clearly identified in the trainings to help tutors more fully

utilise the texts.

12. Trainers experiment with using small group work as a way of encouraging the

formation of more reflective student questions, and encourage tutors to do the

same.

Three ways of working

The tutor guide Aprender Enseñando (Dooki & Arias, 2007) is studied by tutors in their first

training. It is a basic introduction that divides SAT pedagogy into three parts: Lectura

comentada; Estudio en pequeños grupos; y Estudio individual.26 In the field assessor report

form (Appendix 3) it is made explicit that lessons are expected to be a combination of these

23 El estudiante aprenda a plantearse el mismo los problemas, buscar los datos y encontrar las respuestas

(Bosquejo General, Suma y Resta)

24 I learn a lot inventing new problems

25 The maths coordinator is building up a team of maths specialist who will support other tutors, run the micro

centres (local, short trainings given when the need arises) and the best will deliver training. So far about 24 have attended a training, eight either have a maths degree or are near completing one 26

‘Reading and discussion’, ‘Small group work’ and ‘Individual work’

23

three groups: ‘Usa tanto la lectura comentada como trabajo en grupo y lectura individual?’27

is one of the criteria of a good class. All except one of the tutors (out of 29)28 were reported

by field assessors to be doing this. The three methods are explained quite generally in the

tutor guide, so that it is likely that each assessor/tutor/trainer has a different understanding

of what these terms mean.

In interviews and meetings it was clearly demonstrated that the SAT coordinators are deeply

committed to improving the pedagogy of SAT, and would like to have more time to reflect

on experience and initiate change. Each of the three methods above has an important

contribution to make towards creating an atmosphere of consultation but it is possible that,

as they are only described very generally, that staff members have very different

conceptualisations as to their principal characteristics. So it would be fruitful if assessors,

coordinators and tutors were given time to discuss what each one of the methods means to

them and a richer conceptualisation is attained. If this does not happen it could be

damaging, particularly in the case of trainers, if individual assumptions about the methods

cause a departure from the core SAT methodology.


13. Sufficient time is allowed for this at coordinator meetings for consultation on

pedagogy.

The use of tutor/student presentations of work

In about a third of the observed

classes, one or two students were

invited to the board to

demonstrate their calculations.

The student would, usually

silently, write up the procedure

and answer. The tutor or another

student would comment if there

was a mistake in the working out

and/or the final answer.

Use of the board followed a similar

pattern in the trainings. Some trainers had more tutor demonstrations than others, but the

main purpose of the activity was almost always to check the correct use of an algorithm. In

smaller groups the whole group would, sometimes animatedly, join in with the calculation,

but with larger groups there was less participation. Quite often it would become an

27 ‘Equal amounts of whole group reading and commenting on text (combined doing related activities), small group work and individual work.’ 28

6 observations received no comment for this category

24

exchange between the trainer and tutor (both with their backs to the group), the trainer

trying to plug a hole in the tutor’s understanding or of the algorithm.

Checking algorithms in this

way is time consuming.

Also 23% of tutors

reported finding it

stressful. This might not be

too concerning as long as it

is not humiliating, which it

appeared to be

sometimes.

Tutor whiteboard

presentations should be

used as a stimulus for discussion when a variety of responses are valid, and these can also

be compared and evaluated. Presentations, such as

that illustrated in the photograph (a tutor is telling

colleagues how he explains factorisation), can help

weaker members of the group because peers often

use more accessible language than the teacher. But in

order to be effective, the tutor presentations need to

be clearly delivered and allow sufficient time to

develop discussions and follow-up questions. It would

also be better to have fewer presentations, but for

them to be well thought out and closely analysed. The

aim should be to move towards analysing

mathematical methods and approaches and their

practical applications rather than practising

algorithms (Box 13).


14. More efficient methods to check answers and

correct procedures (e.g., use of small

individual white boards, peer checking, etc.)

be used in the trainings and classes instead of

whole class presentations by individual students/tutors.

15. Student/tutor presentations of work are used as the basis for discussions.

16. Appropriate activities are identified beforehand and adequate time allocated for

them.

Box 13

Effective teachers encourage their

students to explain and justify their

solutions. They ask them to take

and defend positions against the

contrary mathematical claims of

other students. They scaffold

student attempts to examine

conjectures, disagreements and

counterargument ... as attention

shifts from procedural rules to

making sense of maths ... students

become less preoccupied with

finding the answers and more with

the thinking that leads to the

answers.

Source: Anthony & Walshaw (2009):19

25

Working in small groups

Peer teaching and ‘social

loafing’

Peer teaching is

encouraged in SAT, for

example, 78%29 of tutors

reported other tutors

asking them for help with

maths. There is strong

research evidence to support peer teaching. In an internationally acclaimed meta-study

(Hattie, 1999) it was found to have an above average impact on student achievement, and

to be more effective than homework in improving student performance. With a peer, as

opposed to a teacher, people often feel more relaxed, more able to ask questions, request

clarification, try out something new and risk making mistakes. This complements the SAT

philosophy that the whole group should move forward together, and no one should be left

behind.

In small groups those who are more advanced gain by explaining and supporting their peers

as this helps them consolidate their

own knowledge. This contrasts with

whole group work when those who are

already proficient can be bored by

trainers/tutors revisiting material, as

was seen during the whole class

checking of algorithms. It was observed

that in the trainings the tutors almost

always work in unchanging friendship

groups of two to four people, and on

almost every occasion the exercises are

done collaboratively. However it was

also observed that occasionally more

‘social loafing’ than peer teaching or

collaborative group work took place. It is also well known that constant group work can

encourage passivity and dependency.

Another observed problem of constant collaboration was that struggling tutors were not

always identified and given the help they needed. For example, in the training for El

Sistema de Numeracion Decimal, a tutor was observed after the lesson copying out a table

29 First year tutors (who had not yet taught maths/completed training) were asked not to respond to this question. Of the other tutors 28% failed to respond.

26

of numbers made with different bases. When asked about the table, she could not express

any of the given numbers using a binary or any other base. Her textbook was correct, but it

is probable that her teaching of this section would have been unsatisfactory (appropriate

support, was of course, given to the tutor).

The observed small group working was usually informal and unstructured; on only a few

occasions was a group given a task that they were expected to provide feedback on as a

group. Therefore the focus of the group/pair activity tended to be on each person filling in

their textbook, sometimes with one member of the group playing the role of a transmission-

based teacher, and occasionally with the weaker tutors just copying out the answers.


17. Tutors are given clear criteria of how to assess their own and others’ work, and

guidelines are written on how to peer teach/accompany a tutor/student without

creating dependency (perhaps using the Guias de Aprendizaje y Evaluaciόn)

18. Tutors/students are encouraged to work in different groups.

19. Tutors/students capacity to work in groups is developed by using different types of

group work and providing opportunities for analysis of the effectiveness and

inclusivity of the group work.

20. Tutors experience and reflect on a range of techniques for improving group work

(see below)

21. Tutors are made more accountable for their progress in the trainings (e.g., a test at

the beginning and end) and/or tutors’ texts are formally reviewed before the end

of the training (this was a goal in the October 2008 Perfíl Nacional but not

observed in the maths trainings).

A forgotten method?

The following explicit instruction appears in the text Fracciones y Porcentajes (6.4): ‘para

revisar los ejercicios, formen grupos de 4 estudiantes y cado uno explique a los compañeros

de grupo como resolvió uno de los ejercicios’30.

Similar instructions appear in many other places in

this and various other texts. The instruction implies

that the students have done the exercise on their

own, have had time to reflect on it, and then that

each student should verbalise their understanding

of the exercise and explain it in a small group. It

appears to be vital part of the methodology (Box

14) and the effectiveness of this technique is also

strongly recognised in the literature, for example:

30 “Revise your answers in groups of four, each person explaining how s/he did one of the exercises.”

Box 14

‘los momentos más importantes de

cada lesión son los dedicados a

explicar a los compañeros la forma

cada uno resolvió los ejercicios’

Source Destrezas Algebraicas

En la Vida Rural:303

27

‘In small supportive groups students learn how to make conjectures and engage in

mathematical argumentation and validation’ (Anthony & Walshaw, 2009).

In spite of the explicit guidance to use it, this method was never observed. In the Teacher’s

Guide for this text there is no mention of a different review method having being

introduced, and therefore it can be assumed that it remains a key SAT method as developed

by FUNDAEC but it appears not to have been adopted in SAT-Honduras.


22. SAT Text instructions, and specifically this one, are implemented, unless

consultation with FUNDAEC reveals a method is no longer regarded as appropriate.

23. Recommended activities/methods, if not explicit in the text, are clearly explained

to the tutors.

Individual work: the third force

Thinking time

The SAT texts are full of questions. Some of the questions are to draw the students’

attention to a concept or aspect of a concept of which he/she might be unaware and which

is about to be developed in the text. The student is expected to reflect (briefly) on the

question before reading on. Students are also sometimes explicitly told to work through an

exercise independently. Independent working is an essential part of learning, as explained

in a recent overview of international research on effective maths pedagogy: ‘Teachers

should ensure that all students are given opportunities to think and work quietly by

themselves when they are not required to process the varied and sometimes conflicting

perspectives of others’ (Anthony & Walshaw, 2009).

28

In the tutor questionnaire, 88%31 reported that ‘mis estudiantes realizan los ejercicios por sí

mismo y consultan a sus compañeros de vez en cuando’. It was observed that there were

short periods of spontaneous independent working (2–5 minutes) in most SAT classes, but

that this rarely happened in the trainings. The limited time for training was given as the

reason. This is however a false economy since (according to research) it impedes learning,

creativity and independent thinking, as well as making it harder to assess tutor progress.

Not using this method in training gives tutors the impression that independent working is of

less value than group work.


24. Sufficient time should be allocated for ‘independent working’ in the trainings.

25. The reasons why independent working is important should be presented and

discussed in the trainings.

Formative Assessment: fine tuning acompanimiento32

In most trainings and classrooms there is a clearly visible interest and concern about the

progress of each tutor/student, and teaching is adapted in response to this. Interviews with

tutors resulted in many examples of the considerable effort expended in acompanimiento,

or accompanying each student on their developmental journey.

Improving formative assessment skills would greatly assist trainers/tutors in their

acompanimiento because the systematic use of a wider range of techniques would improve

the quality of the information obtained about teaching/learning, and thus make more

attuned adjustments possible. Many of these techniques are suggested in the texts but are

not, as yet, being fully used.


26. A range of formative assessment techniques is used; those in the texts are

identified and, where necessary, additional ones are introduced and

trainers/tutors/students are supported in developing their capacity to use them.

Taking responsibility for learning

It is expected that SAT students will ‘dejan de ser observadores pasivos de hechos y

circunstancias para convertirse en personas activas en la exploración de caminos de

mejoramiento personal y comunitario’33(Valcarcel & Lizcano, 1995:6). This is achieved

slowly by the acquisition of new habits and attitudes. One of the key attitudes/habits that 31

99% responded to question 32

An analogy that is used for both the tutors’ and assessors’ role is that of a person who ‘accompanies’ another on their educational journey. 33

Stop being passive observers of events and become active in the search for new ways of changing oneself and the community for the better.

29

Box 15

Yo prefería que hagamos las tareas en

el aula porque así yo los miro que

trabajan realmente. Si les doy un

trabajo y se encuentra a un amigo que

ya está en secundo y lo ayuda? Hacen

la mayoría del trabajo dentro del aula.

Yo les doy cosas para hacer en la casa

que yo se que pueden hacer.

Source: Interview with first year tutor

whose group had no retakes in first

module. May 2010

need to be developed in order to achieve this paradigm shift is taking responsibility for

one’s own learning. Tutors identified this as their second most important priority when

working with the students34 (Appendix 3).

Unsupervised working

During the tutor training periods SAT groups are often left unsupervised. Twelve tutors

were asked what their students were doing during this two week period. Only one replied

that they were not doing a SAT related activity. The others either had special tasks (e.g.

reading a book together and doing a report) or were working on the group agricultural plot.

No independent maths work was reported, apart from revising for tests. The tutors were

confident that the unsupervised work would be done.

On two occasions35 the tutor was absent and the class was observed working collaboratively

with their maths textbooks. And just as impressively, in

all the maths classes observed student discussions

focused on the maths. Once or twice a tutor urged

students to work faster, but it was never necessary to

ask a student to return to the task.

Homework

Coordinators and assessors reported that in some

groups the assigned homework was not done or if it

was done, copying was widespread, while in other

groups homework was well done and appeared to be

having an impact on learning. The texts emphasise the

importance of fluency, speed and accuracy when

calculating as well as conceptual understanding.

Homework can be very useful in developing the later (Box 15)


27. Tutors are given opportunities to share good practice on homework (and other

aspects of practice) e.g., trainings, micro-centres, tutor meetings, bulletin, website.

Formative assessment helps students take responsibility for learning

It is easier for students to be responsible for their own learning when they know what they

are supposed to be learning and the criteria for success, and when they are given clear

guidance on what they have to do to improve their performance. It is suggested in

Aprender Enseñando that the Guías de Aprendizaje y Evaluación should be studied closely by

34

When asked to allocate 100% between six possible priorities (appendix 4) the two highest scoring ones were: ‘Motivarse y tomar responsabilidad sobre su propio aprendizaje’ (mean: 24%) and ‘Utilizar la matemática para explorar y describir el mundo y resolver problemas de su vida cotidiana’ (mean: 32%). 35

Observations made during a previous visit, October 2008

30

Box 16

Effective teachers draw on a range of

representations to support their

students’ mathematical development.

These include the number system

itself, algebraic symbolism, graphs,

diagrams, models, equations,

notations, images, analogies,

metaphors, stories, textbooks and

technology. Such tools provide

vehicles for representation,

communication, reflection and

argumentation. They are most

effective when they cease to be

external aids, instead becoming

integral parts of students’

mathematical reasoning. As tools

become increasingly invested with

meaning, they become increasingly

useful for furthering learning.

Source: Summary of research findings

Anthony & Walshaw (2009)

tutors and students together as a way of

evaluating learning, but at no time was this

observed in either the trainings or classes.


28. The use of the Guias de Apprendizaje y

Evaluación as a formative assessment

tool is investigated, or students are given

other means to help them monitor their

progress.

Tools and Representations

If the metaphor for the learner is a ‘mine rich in

gems to be discovered and polished’ rather than

‘an empty pot to be filled’, then appropriate

‘tools’ (Box 16) are needed.

The importance of the texts

In her seminal study Ma (1999) found that the

most effective Chinese primary school teachers

developed a ‘profound understanding of

fundamental mathematics’ (PUFM) after

becoming teachers, and that this understanding

continued to develop throughout their careers (in contrast to US teachers who usually do

not develop PUFM). When interviewed, the teachers with PUFM attributed this to: teaching

more than one grade and intensive study of the teaching materials both independently and

with colleagues (Ma, 1999). This is good news for SAT in that tutors teach different grades,

and the texts are studied as part of the training and so there is a good basis on which to

build.

31

Box 18

On turning to page 232 El Espacio y sus Elementos at a micro centro

with four students. There was a murmur of recognition when

Pythagorus was mentioned. With a little prompting of one another

they recited, in unison: ‘the square of the hypotenuse is equal to ..’

When asked what that meant, someone said: ‘a squared plus b

squared ..’

And when asked what that meant, no one could offer an explanation.

The trainer drew a diagram drawn on the whiteboard showing the

sides squared and demonstrated how the squares of the two sides

were equal to the square on the hypotenuse. The tutors expressed

pleasure at the insight that this diagram gave them and said that now

they could understand the diagram in the text.

Source: Observation March 2010

Multiple representations

It is international good practice, as in SAT, to view

the learner as an active participant in the learning

process. It is widely agreed that each person

constructs his/her own understanding by

interpreting and internalising new information and

experiences. An implication of this is that the

more complex and varied is the experience of a

concept, the more ‘concrete’ or real it is to the

learner (Box 17).

Some of the texts have rich and varied

representations of concepts (e.g., El Sistema

Decimal), while others (e.g. Manejo de Variables

Unidad 1) assume a familiarity or ‘internalisation’

of algebraic symbolism which tutors appear not to

have developed (as shown by the errors made).

The better trainers use analogies, examples and

sometimes objects (e.g., a pair of scales when

explaining equations), but it is likely that many of

the tutors do not subsequently use these as very

few take notes about pedagogy.

In other texts, there are several situations in which

tutor/student

knowledge or

understanding is

assumed which they

do not yet have (Box

18). The act of

constructing a

representation and

experimenting with it

makes a concept

more ‘concrete’.

These sorts of

activities are

recommended in the

text but were rarely

observed in the

Box 17

I now offer a new perspective from which to expand our understanding of the concrete. The more connections

we make between an object and other objects the more concrete it becomes

for us. The richer the set of representations of the object, the more ways we have of interacting

with it, the more concrete it is for us. Concreteness, then, is that property which measures the degree of our

relatedness to the object, (the richness of our representations,

interactions, connections with the object), how close we are to it, or, if

you will, the quality of our relationship with the object.

Concreteness is not a property of an object but rather a property of a

person’s relationship to an object. Concepts that were hopelessly

abstract at one time can become concrete for us if we get into the ‘right

relationship’ with them.

Source: Wilensky (1991)

32

trainings. The reason given for this was lack of time.

Perhaps some of these issues stem from the fact that the texts were written for Columbia

where the standard of maths education is higher. In Honduras is it necessary to provide

varied representations at secondary level to make up for educational deficiencies at the

primary level (in the photograph students are doing an exercise on multiples

representations with algebra36) Many coordinators and tutors identified extra materials as

an urgent necessity.


29. Tutors are informed of the

utility/theory of multiple

representations and related

activities in the text are clearly

identified.

30. The texts are analysed with

tutors to identify where extra

representations and tools are

needed, and these developed in

collaboration with the tutors. (The

Maths Coordinator has for many years wanted to address this concern and in June

2010 Asociación Bayán submitted a proposal to Irish Aid for funding).

31. When the representations are physical they should, as far as possible be made

with locally available and sustainable/recycled materials (e.g. photographs:

representing the difference between (3 + 2 )2 and 32 + 22 using bottle tops and

seeds to represent the decimal system)

36

Activity taken from The Standard Units developed by Malcolm Swan, Susan Wall & others

33

Updating and revision of texts

The texts are innovative and engaging. The maths

is integrated with the other core SAT areas,

communication, technology, science and most

importantly, service to the community. The

constant application of the maths to worthwhile

practical applications is motivating. This is

demonstrated by the vast majority of tutors37

reporting that studying with SAT had made them

feel much more positively about maths and

generally giving the practical nature of the texts as

one of the reasons. However there are some

concerns:

Most coordinators interviewed

spontaneously complained about the

number of errors in the texts because they

undermine tutor/student confidence in the

texts38. Some of the information is out of

date, and therefore now incorrect. For

example, in Matematicas 1 Conjuntos y Numeros, (revised by Asociación Bayán in

2008), the number of species is given as about a million. Current estimates are

between two and one hundred million (an interesting fact in itself) and no mention is

made of the rate at which species are judged to be disappearing.

Other opportunities to engage tutors and students with current issues are missed.

Examples of this are: the balance between using animals for economic gain and

humane treatment, and the limitations of double entry book keeping e.g. it does not

record the social or environmental cost/benefits. In Para Salvar las Barreras it is

suggested that additional material is introduced where appropriate but this was

rarely observed.

The study and practice of maths offers many opportunities for the development of a

range of attitudes/qualities/skills, for example patience, perseverance, courage,

attention to detail, etc. Trainers/tutors rarely referred to this. These are sometimes

mentioned in the Guides to Learning and Evaluation and in the introductions to the

texts, as in Box 19. This example is from the second year of Bachillerato but it would

be beneficial to give more emphasis to attitudinal development from the first

text/guide.

37

Percentage 38

For example in Manejo de Variables: Unidad 2 (adapted and contextualised by Asociación Bayán 2004) there are at least 14 typographic errors, while some are minor (e.g. omission of question marks) six could impede understanding (e.g. incorrect answer)

Box 19

Lo mismo que las otras unidades hay

un énfasis en el desarrollo de

actitudes positivas, como las

siguientes: compromiso personal en el

aprendizaje proprio y del grupo;

satisfacción por enfrentar y vencer

retos; reconocimiento del valor de lo

que se aprende para la formación

personal y para la solución de

problemas; honestidad en la

búsqueda de soluciones, convicción

en las respuestas; reconocimiento de

los propios errores y interés por

corregirlos Source: Bosquejo General, Manejo de

Variables, Unidad 4

34

It is regrettable that the standard of illustration is not higher, for example, many of

the drawings of animals in Conjuntos y Numeros look as though they have been

rather carelessly traced. In one instance the illustrations cause confusion and need

additional material or redrawing.39

It was reported by the maths coordinator that some of the longer exercises

consistently fail to engage the students (e.g., the final exercise for the community

water supply and study of house plans). The exercises were developed in Columbia

where the original students were older than the majority of the present ones in

Honduras, perhaps this is the reason why they are less successful in Honduras than

Columbia.

It is desirable that the students are fully conversant with the metric system but

Honduras still mainly uses the Imperial system and more opportunities should be

given for them to become competent in both systems and conversions.

The texts produced in Honduras do not always follow FUNDAEC referencing

conventions (and international good practice). In Aprender Enseñando there is

reference in the introduction to material from the Ruhi Institute being used but it is

not clear where. Substantial passages40 from Para Salvar Las Barreras (FUNDAEC,

1995) have been used without identifying the source.


32. Errors be corrected (the most urgent task), new illustrations commissioned in order

increase the utility of some representations (e.g. Suma y Resta), and the general

attractiveness of the texts improved.

33. The texts are analysed to identify where exercises need to be modified/changed to

make them more engaging to Honduran students and where extra information or

discussion topics could be introduced. This could be put the Teaching and

Evaluation Guides.

34. Activities are developed to enable students to become competent with metric and

imperial systems.

35. Texts follow referencing conventions with regard to acknowledging the origin of

material taken from other sources.

39 The tutors in the Maths Specialist Course reported that students find the diagrams confusing in the first exercises in Suma and Resta, La Union de Conjuntos:1. Tutors said that that these exercises are demoralising since addition is one of the few aspects of maths that students feel confident about, and they get very dispirited when they find they cannot do the first exercises in the book. The Maths Specialists suggested developing a range of activities such as stories the students could act out in order to clarify the concept of combining sets with identical elements. It might be clearer to use intersecting Venn diagrams to represent this concept rather than the current diagrams. 40

e.g. pages 40 -44 in Aprender Enseñando are very similar to pages 28 – 32 in Para Salvar Las Barreras but not referenced

35

Guías de Aprendizaje y Evaluación (Ciclo

Común)41

Informing learners of the content, purpose and

criteria for success of the curriculum is a key

factor in enabling students to become

independent learners (Anthony & Walshaw,

2009); this is emphasised in Varcarcel and Correa

(1995) and they identify the important role of the

Guias de Aprendizaje y Evaluaciόn42 (GAE) in this.

The GAE are booklets of 4 to 10 pages that

accompany each text. They contain an outline of

the curriculum, indicators for assessing student

progress, and two to five short paragraphs of

‘observaciones’ or guidance. This guidance tends

to be fairly general.43

The role of the GAEs in evaluation is discussed in the

Evaluation section below but evaluation is not the key

purpose of the GAE, as is explained in Box 20. The GAEs

are designed to help tutors and students become

active, analytical and collaborative participants in the

learning process by informing them of the curriculum.

Asociación Bayán’s vision (Box 21) has ‘transparency’ as

a key value. One of the ways this is demonstrated in an

educational institution is by making the curriculum and

evaluation criteria clear to the teachers. Therefore for

both philosophical and practical reasons it is important

that tutors are trained to use the GAEs.

Unfortunately this does not appear to be

happening: in 186 hours of observation,

the GAEs were never used or referred to.

The GAE for Book 4 (multiplication and

division) was not usable because it had not

been updated for the revised text. Tutors

cannot use the GAEs without training

because they assume a knowledge and

41

The Bachillerato GEA were not made available until 08/07/10 and so are not included in this report. 42 Learning and Evaluation Guides 43 ag., ‘representar fracciones en la recta numérica implica comprender muy bien los conceptos que se están manejando’ and ‘insistimos en la necesidad de seguir muy cerca el trabajo de cada estudiante para verificar el desarrollo de las capacidades …’

Box 20

En realidad, más que guías de la

evaluación, son guías de estudio para

ser analizadas por el tutor y los

estudiantes antes de iniciar cada

unidad. Se buscar con esto promover

una verdadero participación de

tutores y estudiantes en el proceso de

evaluación, mayor conciencia sobre

los propósitos que se pretenden y

hacer realidad la evaluación

permanente y participativa

Source: Aprender Enseñando:41

Box 21

Ser una organización comprometida con el bienestar

individual y colectivo, la excelencia, la innovación y la transparencia; con una sólida base ética, moral y espiritual, coherente en su accionar; con

una actitud y práctica de aprendizaje.

Source: Bayán website

Source: Asociación Asociación Bayán website

Box 22

The secret of what anything means to us

depends on how we've connected it to all the

other things we know. That's why it's almost

always wrong to seek the "real meaning" of

anything. A thing with just one meaning has

scarcely any meaning at all

Source: Minsky, 1987 p. 64

36

methodology which the tutors do not necessarily

have.

Another important role that the GAEs could play

is in enabling tutors and students to create links

between concepts and topics. The formation of

links is believed to be important in the process of

building up rich conceptualisations (Box 22). The

GAEs, with their brief, clear descriptions of

concepts, skills and attitudes could help tutors

and students do this.

When the tutors are in the communities they

often have very limited access to support. The

field assessors may visit a SAT centre once every

two weeks but they, and other tutor colleagues,

often do not have the knowledge to help (it is

anyway unrealistic to expect field assessors to

know the specifics of 70 texts). Almost every

coordinator and tutor interviewed spontaneously

requested additional materials so that (often

isolated) tutors could have something to refer to

for guidance and extra information.

Ma (1999) in an internationally acclaimed study

found that having guidance such as that in Box 23

played an important role in developing teacher

capacity. The GAEs, Aprender Enseñando and

texts44 comprise the tutors’ written orientation/instructions on mathematics and pedagogy.

These contain a wealth of guidance on different topics but it is often difficult to locate it

because there are no indexes and tables of contents (if present) tend to be very general.

There is a need to identify what support the tutors need and, if present in the texts, make it

easier to locate and, where necessary, develop new materials. This would assist with micro

centro45 trainings as well as individual study.


36. The Guias de Aprendizaje y Evaluación are studied in the training and tutors are

mentored in their use in the communities.

37. There is increased reflection and use of the introductions to the texts.

44 The introductions to the texts are an under-utilised resource. They are read through at the beginning of a training and were not observed to be referred to subsequently. 45

Short training organised locally for a small group of tutors to address a specific training need.

Box 23

Teachers’ manuals provide the

background for the maths in the

corresponding textbook and

suggestions of how to teach it. The

introduction of a typical teacher’s

manual gives an overview of the

textbook, its main topics, the rationale

for the text book’s organisation, the

relationship between the topics in the

textbook and the topics of the

preceding and succeeding volumes.

The main body is a section by section

discussion of each topic and subtopic

of the textbook. The discussion of

each topic focuses on these questions:

What is the concept connected with

the topic

What are the difficult points of

teaching the topic

What are the important points of

teaching the topic

What are the errors and confusions

that students tend to have when

learning this topic.

Source: Ma (1999)

37

38. Appropriate additional materials, are developed in collaboration with tutors, to

support the tutors in their mathematical development and teaching practice (Irish

Aid funding has been requested for this). The Guias de Aprendizaje y Evaluación

are adapted if necessary, studied in the trainings and tutors are mentored in their

use in the communities.

39. Appropriate additional materials, are developed in collaboration with tutors, to

support the tutors in their mathematical development and teaching practice (Irish

Aid funding has been requested for this).

Practical application of maths

Linking the maths being learnt in the classroom to real life applications is widely

acknowledged to be motivating and conceptually enriching. The tutors expressed great

enthusiasm for the practical nature of SAT maths in interviews and questionnaire responses.

Interestingly, assisting with their own university studies was the most common example

given of how studying maths had benefitted them46 (Box 23). 78%47 said that they usually

related the maths they taught in class to maths in daily life, and 96%48 said that maths was

useful in community development projects.

When asked for examples of how students used

their maths in the community, the most

frequently mentioned activities were ‘shopping’,

‘measuring out land’ and ‘planting’. Surprisingly

there was no mention of statistics.

Statistics

Coordinators report that statistical projects (for

example, on chicken production, community

health, etc.) are sometimes done in a perfunctory

way because these projects are not as

important as the end of module tests in

determining if a student passes the

module.

The data in the texts is often out of

date (e.g., in El Estado de Salud de La

Comunidad the data is for 1997), and

46

There were many references to ‘daily life’ but ‘university studies’ was the only specific example. 47

98% of respondents answered this question 48

95% of respondents answered this question

Box 24

Quien trabaja por el mejoramiento de

las condiciones de vida en el campo

debe ser capaz de analizar indicadores

sociales, entender como se

construyen, aplicarlos para

poblaciones especificas, determinar su

utilidad y también sus limitaciones e

incluso hacer propuestas para mejorar

los indicadores existentes.

Source: Bosquejo General: Destrezas

Algebraicas en la Vida Rural

38

sometimes statistical concepts are introduced but not elaborated sufficiently in the text

(e.g., the concept of the mean in the text Aritmética en la Investigación Científica). In the

training for Destrezas Algebraicas en la Vida Real very little discussion or analysis of social

indicators was observed which was surprising as it is a fundamental tool in community

development (Box 24)

Linking SAT and community maths

53% of tutors reported that ‘mis alumnus comparten en la clase los métodos matematicas

que sus padres utilizan en su vida cotidiana’. When asked for examples, after some head

scratching, tutors gave examples of simple agricultural situations, e.g., spacing between

plants. The educative process should generate ‘una armoniosa fusión de saberes, del saber

tradicional con el conocimiento moderno (Valcarcel & Correa, 1995). It appears that this

process and potential is under-developed in Honduras-SAT as yet.


40. More up to date data is used in the trainings.

41. Tutors are given copies of this data to use in the communities.

42. Statistical concepts

inadequately explained in the

texts should be identified, and

extra exercises developed.

43. Trainings are carefully planned

so that key statistical concepts

are adequately developed

44. Ways of increasing the value

that students place on

statistical projects are

investigated (and the copying

of previous years’ assignments

stopped).

45. Ways of integrating traditional

representations and methods

(estimation, measurement, etc.) are investigated.

Evaluation

In SAT, evaluation is more concerned with continuous reflection on the process rather than

making judgements on a final result (Box 25). Effective evaluation requires acting and

observing simultaneously; this is a power of the mind which has to be developed (Box 26).

Box 25

En SAT pretendemos evaluar procesos, más

que resultados. No se trata de registrar si el

estudiante adquiero tal concepto o

desarrollo tal capacidad o actitud, sino de

analizar sus progresos en caso de que sean

mínimos, tratar de detectar las causas y

encontrar la manera de superar esa

situación; lo mismo en casa de buenos

avances, promover el ir más allá en la

búsqueda de aplicaciones o de ampliaciones.

Source: Aprender Enseñando:40

39

The main purpose of evaluation in SAT, as stated

in Aprender Enseñando, is ‘assessment for

learning’. Aprender Enseñando states that the

GEA should be used to capture the learning

process; and make adjustments based on the

information. It is difficult to see how tutors can

use the GEAs to do this because the GEAs are

mainly lists of the concepts, capacities and

information that students should develop or

acquire, (and their related indicators), but there is

no mention of how the process should be

captured. It is assumed that the tutor will be able

to interpret the GEAs, but as they have not

studied them in the trainings this is not possible.

At the moment they are more a guide for

‘summative’ or end of course assessment than for

‘assessment for learning’.


46. Tutors are systematically supported in

the use of GEAs for assessment for learning and, if necessary the GEAs are adapted

or additional material provided.

Community Evaluation

All of the parent groups are expected to be active in the evaluation of learning and

identification of goals. Some groups are very active (Box 27).

Box 27

En algunas comunidades de X además de la sociedad de Padres y Madres de familia existe un

asociación a la que se le llama la Junta del Colegio. Esta junta está conformada por 5 a

7 miembros, electos en una reunión donde todos los habitantes de la comunidad participan

(tengan o no hijos estudiando en el centro educativo). Esta junta vela por el desarrollo de

actividad para todo el centro ... Su labor es apoyar al máximo el bienestar de la comunidad

educativa y se encargan de las actividades macro, es decir actividades en las cuales toda la

comunidad debe estar involucrada. Es importante mencionar que muchos de los miembros de

la junta son jóvenes, que tiene niños pequeños que no van ni al Kínder o están en la escuela y

algunos no tienen hijo.

Source: coordinator email junio 2010

Box 26

The image of two birds, one eating

and the other watching pervades

Eastern and Western art. There are

multiple interpretations ... an

educational interpretation is that the

two birds are forms of attention ... the

eater is the part of us that gets caught

up in doing while the watcher is the

internal monitor-witness that

observes without judging. The

watcher has been likened to

conscience which needs to be

awakened and developed...When

applied to teaching it means it means

having a part of you separately

witnessing the lesson, able to observe

and suggest alternative actions

Mason & Johnston-Wilder (2004)

40

Evaluation – testing and retesting

Maths: a problematic part of the

program

Of the five SAT curriculum areas,

students generally have least success

with the maths’ tests. Data on test

performances are available from 2008,

and shows that maths has almost

invariably been the area with the

highest number of test retakes (Figure

1). It was reported orally that maths has been

problematic since the beginning of the program. This can be

largely explained by the fact that tutors come from a low

quality educational system (Box 28) and that the tutors’

literacy levels affects maths understanding (Box 29). It is

widely believed by tutors that the maths in the SAT

curriculum is at a higher level than

other Honduran Bachilleratos; one reason for this could be that it demands more

conceptual understanding and for this to be articulated. It is therefore unsurprising that

there are significant problems.

Percentages of retakes for 2008

Students take a test at the end of each module and if they score less that 60% they are

required to retake it. Data on retake rates for different regions was available for 2008

(Block 2 & 3). 2008. 2008, Block2, Impulsor 2 was selected as an example because it was the

most complete. The wide range is remarkable and sometimes difficult to explain. The two

regions with the highest retake rates border on the region with the lowest rate (I, M & K).

The tutors would have attended the same training and the student population was similar.

01020304050

Percentage of students retaking test by area

2008

2009

2010

0

20

40

60

80

100

A B C D E F G H I J K K L M Npe

rce

nta

ge

of

stu

de

nts

re

tak

ing

te

st

Region

2008 Block 2: Impulsor II

Photograph:Ruth Moulton

Figure 1

41

Some centres had lower retake rates at each level. It has been suggested that one reason

for this could be that different criteria are used to define a retake. In 2008 a student could

retake the test various times, and some centres might have counted each attempt as a

retake while others only counted the student once. Also, it was reported to the consultant,

some centres allow students to redo a couple of answers in a test if they only are a few

marks short of 60, and do not count this as a retake, while other centres do not allow this.

It is also possible that good practice is affecting retake rates. If so, this should be identified

and widely shared. A standardised system of data collection and analysis is necessary to be

able to make any judgement.

Data on summative assessment (if valid and reliable) can be valuable in the evaluation

process. Currently the test data are of limited value as the retake rate is a blunt instrument

for measuring performance. All students gaining 0-59 marks have to retake. There is no

way of knowing if a student scored 59 or 0, and whether those passing scored 60 or 100.

Data on maths performance is held in the Institutes to which each SAT centre is affiliated,

but is difficult to obtain. It would greatly assist Asociación Bayán in identifying trends and

assessing the effectiveness of educational interventions, as well as to monitor the progress

of individual students, if data on test scores were collected.


47. Criteria for defining a ‘retake’ are standardised (Asociación Bayán is developing a

data entry system to improve accuracy of entry and calculations, and there are

plans to produce a data collection manual for staff) and reports are archived.

48. Data on student and tutor test scores are collated and analysed.

Comparing SAT performance with the government system

The Universidad Pedagogica Nacional Francisco Morazan is in the process of carrying out a

study for the Secretaria de Educación Pública (SEP) comparing the ‘rendimiento academico y

factores asociados’49 of SAT over 2008-2010 with a control. The control is the Secondary

School or Centro de Referencia (CER) that the SAT group is associated with for administrative

purposes. There are 53 SAT Centres (853 students) and 25 CERs (1,234 students) in the

study.

There was not a statistically significant difference between the two groups but as the

questions are based on the CER and not the SAT curriculum, the validity of the comparison is

questionable50. It was interesting to note that the SAT students who had not been taught

49

Academic achievement and associated factors. 50

However, due to frequent teacher strikes/absences, the CER students may not have been taught the material that the test was based on either!

42

statistics, probability and geometry did about as well as the CER students, who supposedly

had been taught these subjects! The Hewlett study, which has a more rigorously defined

comparison group, plans to apply questions which have been designed for an international

comparison study.

Tutors and mathematics: knowledge, attitudes and beliefs about teaching and learning51

It is widely recognised that obtaining information on attitudes and beliefs is problematic,

and the results should therefore be treated with caution. However, as SAT is concerned

with the development of attitudes and beliefs and the impact they have on action, it is

something that must be attempted. Based on empirical evidence, it is essential to ‘start

where the learner is’ and this requires knowing something of the underpinning premises

that the learner is using to construct his/her understanding of mathematics.

Tutor attitudes to maths: the positive results of training

The tutors reported generally

positive attitudes towards maths

in the questionnaire survey

(Appendix 3). Almost all the

tutors said that being good at

maths was something that was

accessible to all, not just the

‘brainy’. They appeared to enjoy

learning maths, and feel ‘un gran

satisfación con exíto con un

problema matematico’52. All53 SAT tutors thought ‘las matematicas son utiles y necessarias

en todos los ambitos de la vida’54. But, interestingly, only 76% thought that maths was

necessary for understanding the sciences. There is a tendency in attitudinal questionnaires

to report what is considered to be the ‘correct’ attitude, and so the answers may be

aspirational or compliant, but, even taking this into account, there is a pleasing positivity

about maths.

A remarkable 98% of tutors55 reported feeling more positive about maths after studying the

SAT texts, and 66%56 of tutors felt they were ‘capáz y hábil’ at maths. 83% reported that

51

A rigorous selection process, interviews and two week initial training, assist Asociación Bayán in selecting tutors who appear to have an attitude of learning and are orientated towards service to the community. Co coordinators expressed the expectation that as the number of SAT graduates working as tutors increases, the training process will become easier because they will already be familiar with the texts and core values/assumptions. 52

‘Very satisfied with when a maths’ problem is solved’. 53

Over 99% of respondents replied to this question/statement 54

‘Maths is useful and necessary for all aspects of life’. 55

All tutors who had studied with SAT for more than a year reported improved attitude to maths 56

95% of respondents replied to this question/statement

43

after training they felt they understood all the material and could do all the exercises. This is

supported by interviews and casual conversations in which tutors often spontaneously said

how much they had learnt with SAT. It is an outstanding achievement to have enabled the

vast majority of tutors to feel more positive about maths (Box 28).

Tutors particularly mentioned the

practical application of maths, the

emphasis on ‘porque?’57, and how

easy it was to ask questions in SAT

trainings. However there appears

to be a minority who struggle in

each training and, are either left

behind or slow the progress of the

whole group. If the standard of

maths in SAT is to be raised it is

vital that these tutors are

identified and systematically

supported.


49. Tutors who find maths difficult are identified at the beginning of their training so

that they can be given extra support

57

‘why?’

Box 28

A mí me encanta las matemáticas y yo siento que lo que

he aprendido en SAT me ha ayudado mucho en mis

estudios universitarios y en mi vida diaria.

Siempre me he sentido que me gusta las matemáticas

pero desde que estoy en la sistema he descubierto que

se resuelven muchos problemas de la vida con mejor

facilitad.

Estudiar los textos de SAT y es muy importante ya que

ayudan en gran manera en nuestra vida como

profesional también para tener alguna destreza

conocimiento al momento de usar el estudio superior

en la universidad.

Source: comments on tutor questionnaires

44

Building on an apprenticeship of observation

Almost all tutors have had a long apprenticeship of

observation in the transmission approach during their

twelve or so years of schooling and the questionnaire

survey indicated that many hold beliefs consistent with

this approach (Appendix 3). Research shows that this

deep identification with often respected teachers58 and

their mode of delivery means that ‘superficial attempts’

to change teachers to a more active style will either be

‘neglected’ or ‘ignored’ (Schwille & Dembélé, 2007:30).

The skills that tutors have acquired in the transmission

method (e.g., clear explanations, see photograph)

should be recognised and developed and their beliefs

about teaching and learning explored (Box 29). One

coordinator said that he noticed that tutors who were

less good at maths tended to have more participatory

lessons, and that the most knowledgeable ones tended to take over and teach in a more

formal way. This implies that tutors may have a tendency to adopt more transmission style

if their knowledge increases and trainers should be aware of this.

Changes in beliefs59 and practice are complex but it is possible that changes in practice

precede changes in belief (Swan, 2008). It is

therefore important to use participatory and active

methods when training to demonstrate alternative

methods and tutors should be given specific and

supported opportunities to develop their practice

towards active methods which have been shown to

be effective. It is very probable that most tutors are

disposed towards doing this as they reported

developing student capacity for independent

learning as a priority (Appendix 3). Research with

teachers indicates that sustainable changes in

practice are achieved by making a few, small

changes in consultation and collaboration with other

teachers (Hodgen & Wiliam, 2006). Field assessors

could play a very important role in facilitating this.

58

Surprisingly (considering reports of the standard of maths teaching in Honduras) 79% of tutors thought that they had had good teachers at school (questionnaire). This is at variance to a discussion on previous maths’ experiences in the maths specialist training when several tutors said how ‘traumatised’ they had been. 59

For example, a change from seeing the student as ‘a mine rich in gems’ rather than ‘an empty pot’.

Box 29

Any attempt to encourage teachers

to modify their beliefs about

teaching and learning must

therefore entail the explicit

recognition of existing beliefs and

their situated nature, attend to the

constraints and difficulties under

which teachers work and allow

teachers time to reflect on the

contradictions between ‘good

practice’ and ‘existing practice’. Source: Swan, 2006:173

45

Theory- based practice

Research indicates that the ability to relate practice to theory is an important tool in the

process of reflecting on experience. Most tutors are studying at the university and it would

be enriching for them to form links between the educational theory that they are learning

there and SAT theory and practice. It is possible that the failure to fully implement the SAT

methodology is due to a lack of understanding of the reasons for some of the practices. The

importance in SAT of relating conceptual understanding to the practical application of

knowledge was mentioned during trainings, but few other instances of linking practice to

other aspects of the SAT theoretical framework or wider educational theory were observed.

Also developing tutors’ theoretical knowledge would assist tutors to modify their practice in

a systematic way as they could research and modify their practice using a theory of change

model. 60


50. The tutors’ pedagogic/theoretical learning in SAT is linked to the educational

theory and pedagogy studied in the university.

51. Tutors are systematically informed about SAT methodology and theory.

52. Tutors form groups to conduct simple collaborative action research on SMALL

changes in practice based on a theory of change model.

53. Assessors are trained to support tutors in developing more participatory practices

and to promote and support action research.

Maintaining positivity: getting unstuck

‘Being stuck is an honourable state’ (Mason

& Johnston Wilder, 2004:287). Being stuck

helps learners develop powers of

reflection, perseverance and courage. It is

often a necessary stage when studying and

applying maths and learners should realise

this. The most stressful thing for tutors

(25% of responses61) was ‘cuando me

atasco o bloqueo en la resolución de un

problema’. When asked how they

overcame ‘maths blockages’, tutors did not

have any defined strategies apart from ‘not

giving up’.

60

a cost effective and perhaps most efficient way of conducting educational research. 61 The second most stressful thing was being unexpectedly asked to do a presentation at the whiteboard (19%).

46

Box 31

El sistema educativo de Honduras presenta un retraso de 100 años respecto a las

naciones vecinas de Costa Rica y Panamá, según un informe divulgado este lunes por la Organización de Naciones Unidas para la Ciencia, la Cultura y la Educación (UNESCO) y el Banco Centroamericano de Integración

Económica (BCIE). En materias como matemáticas o lenguaje el porcentaje de

aprobados es inferior al 47 por ciento, una tasa muy lejana al 70 por ciento exigido en

los Objetivos de Desarrollo del Milenio (ODM) establecidos en 2000 por Naciones

Unidas. A pesar de que la tasa de alfabetización de Honduras ascendió del 68

al 80 por ciento en la década de los noventa, el documento de UNESCO señala la necesidad urgente de mejorar el sistema

educativo hondureño.

'Estamos 100 años atrás de lo que están Panamá y Costa Rica, sin compararnos con

países como Canadá, Estados Unidos o Japón, sino a nuestros vecinos más

cercanos', señaló el coordinador de la Red de Educación de Honduras, Elmer Villeda,

durante la publicación del informe.

En los últimos tres años apenas se han impartido un cincuenta por ciento de las

clases establecidas en el calendario escolar hondureño, según otro informe publicado

por la Federación Iberoamericana del Ombudsman (FIO), una red que sirve de

apoyo a todas las defensorías del pueblo de América Latina, informó el diario 'El

Heraldo'.

Source: 20 de abril http://noticias.terra.es

Box 30

The knowledge gap between the US and

Chinese teachers parallels the learning gap

between Chinese and US students ......the

quality of teacher subject matter knowledge

directly affects student learning – and it can

be immediately addressed

Source: Ma (1999)


54. Tutors are taught techniques for

overcoming ‘bloqueos’, and that this

is normal and even useful for the

learning process.

Tutor knowledge

Tutors are not expected to be ‘teachers’.

They guide their students through each of

the five components of the program and it

would be unrealistic to expect all tutors to

have the knowledge of a specialist maths

teacher but a sound basic knowledge is

necessary (Box 30). All coordinators

interviewed expressed concern about the

level of tutors’ mathematical knowledge

although 66% of the tutors reported

themselves as ‘capáz y hábil’. It should be

remembered that judgements about one’s

own performance are made via comparisons

within a reference group.62 Many of the

tutors may feel that they are relatively good

at maths63, but this does not necessarily

mean their maths is good enough to fully

62

Students at the university report knowing more maths in their peers and on at least one occasion being asked to assist the lecturer in teaching the other students (email correspondence with coordinator) 63

Tutors often reported how studying maths with SAT had meant they were one of the better students on their university maths courses.

47

access the SAT curriculum (Box 31 and Box

32). 64

The students entering SAT come from rural

primary schools. Frequent teacher absence

and small schools, in which five grades are

sometimes taught together, means that

the students have usually received a

woefully inadequate primary education.

Teaching quality is important for all

students, but it has most impact on the

weakest (Hodgen & Wiliam, 2006). This

increases the pressure on SAT tutors to be

good at their job.

Basic mathematical operations

Tutors sometimes had difficulties with the vocabulary (Box 33), underlying concepts and

procedures for basic mathematical operations.

For example, long division. In Book 5, Aritmetica

en la Investigación Científica, it was observed that

many tutors had problems with the long division

algorithm, and none used the recommended

vocabulary at the beginning of the session. One

tutor who came to the board could not even begin

to do the calculation, and two admitted not

knowing what to do with the decimal point. The

Trainer however was excellent at probing and

checking tutor understanding, and by the end of

the session all the tutors appeared to be

proficient. It often seemed that the tutors did not

64

Tutors take the end of module test at the same time as their students and this information is used by

coordinators to identify where more training is needed. This information does not appear to be collected

centrally.

Box 32

Hay un ejercicio que hacemos con ellos por ejemplo. ¿4 x 6 es lo mismo de 6 x 4? y la mejoría, el

99% dice que sí, es el mismo. Pero si se presentan situaciones de la vida cuando no es la misma

… claro tiene razón, porque ellos han aprendido las tablas aritmética y allá no más. No han

aprendido a relacionarlo con algo cuando les viene a SAT les cuesta.

Source: coordinator interview, May, 2010

Box 33

Una cosa curiosa también es que nos hemos

encontrado que los tutores tienen muchos

dificultades en la parte de comunicación, de

leer, de escribir, comprehension de lectura.

Tienen muchísima dificultad en

matemáticas. ... el lenguaje que se utiliza en

los textos supone que la persona, en la parte

de comunicación, comprende lo que está

pidiendo. Por ejemplo dice agrégale el doble

del producto de tal cosa por tal cosa…y allí

nos detenemos. Source: coordinator interview March 2010

Box 34

When doing an exercise requiring the

calculation of the average of food

consumed and weight of 25 chickens

six tutors came to the board to

demonstrate how they did this. Each

one painstakingly used the standard

long division algorithm even when

the number to be divided was 75000.

No one questioned this or suggested

an alternative.

Source: Observation February, 2010

48

have a sense of the numbers that they were dealing with; increasing the use of estimation

would help develop this. It was very rare to see different methods of working out a problem

discussed (Box 34) although it is a part of the SAT methodology.


55. Estimation techniques are taught and

practised.

56. Different procedures for working out a

calculation are compared (when appropriate)

particularly in respect to their efficiency.

The transition to Bachillerato

Just as students have difficulties adapting to

the SAT system when they enter Ciclo Comun

so to the transition to Bachillerato is

problematic and these difficulties often stem

from inadequately understood concepts in

Ciclo Comun.

There is rightly a strong emphasis on developing algebraic competency in SAT (Box 35).

Tutors and coordinators identified algebra

generally, and in particular the expression of

everyday problems algebraically, as the most

problematic and disliked topic. Difficulties are

apparent from the beginning. For example, at a

course for maths specialists sustained help was

needed to define the elements in the set ‘people

attending this course’. Other basic ideas from the

first maths module, such as ‘an element can

belong to both a set and a subset’ had to be

clarified. If the most competent tutors were

unsure, it is to be expected that the average tutor

will struggle, and the average assessor will be

unable to offer much support in the classroom.

In Bachillerato, weaknesses present in Ciclo

Comun become more apparent, e.g., in all six

classes observed of Polynomios II, tutors taught a

mechanical method for expanding quadratic equations. Understanding of this method was

not probed, and a substantial number of student errors went uncorrected. Twenty

Box 35

Nobody has ever been able to reach the

concrete. The concrete is so abstract

that nobody can reach it. We can only

function because of abstraction.

Abstraction makes life easy, makes it

possible ...The essential point is this

algebra is an attribute, a fundamental

power of the mind. Not of mathematics

only.

Source: Gattegno, 1970, cited in Mason &

Johnston-Wilder, 2004

Box 36

Micro centro de polinomios con

tutores de II Bach, A & B. El micro

centro se realizo con el objetivo de

reforzar tutores ya que durante la

visita pedagógica realizada al grupo

se observo debilidades en el manejo

de contenido, se reforzaron conceptos

como los siguientes, propiedades de la

multiplicación, terminos semejantes,

productos notables, propiedades de la

potenciación, grado de un polinomio.

Source: assessor monthly report, March

2010

49

Bachillerato tutors were asked if they could suggest an alternative way of representing a

quadratic equation in order to make it more meaningful to students (e.g., a diagram, graph

or real life example). Only one tutor was able to do this, relating it to an area of land. In

three SAT classes, students were asked if they could make a diagram of what they were

doing. None could at the beginning of the lesson, but following an example, most students

were able to do this and expressed relief at having gained a new level of understanding (as

did the tutors). It appears from monthly reports that

some assessors are very effective at identifying when

support is required and providing it (Box 36)

Finally it was noted that opportunities for developing

algebraic skills in the Ciclo Comun are sometimes not

used. For example, in a lively and practical lesson on

triangles and parallelograms, insufficient time was

allowed for students to explore and develop their

own formulae.

With the help of a skilled trainer many tutors make

substantial progress but limited time in training

means that additional support is needed by some

tutors (Box 37 and photograph).


57. Activities in the texts that are particularly suitable for developing algebraic skills

in the Ciclo Comun texts should be identified before training and carefully planned.

58. Work with algebra should include multiple representations.

Box 37

Destrezas Algebraicas:327: A

water supply problem

26 tutors in the group working in

friendship groups of two to four.

The text book gives 9 variables (no

of inhabitants, average number of

animals per family etc) to make

into a formula for calculating the

daily water requirement.

All groups were flummoxed and

unable to start task. Many

requested trainer’s assistance.

Two groups, with trainer help,

developed formulas which they

explained coherently at the board,

correcting errors after trainer

input. Most groups began to make

inroads into the task after

significant assistance from trainer

and other tutors, but one group of

three was unable to make any

independent progress on the task.

After lunch, in the next session a

new topic was started.

Source: Observation May 2010

50

Preparing for training

To study or not to study texts

Tutors do not usually work through the texts before trainings although they are requested

to do this65. When interviewed a tutor who had done the exercises reported finding the

training boring as it mainly consisted in redoing the exercises. If all tutors were expected to

read the texts, but not actually do the exercises, before the training and note where they

had questions or comments it would assist trainers in allocating training time efficiently.


59. Tutors read the texts before training and note where they have difficulties. At the

end of the training review, this list of difficulties can be reviewed, progress

assessed and further support needs identified.

60. Tutors read texts before training and note down ideas for additional teaching

materials, activities etc. so that these can be shared at the training.

Maintaining the quality of maths training

The Training

Some coordinators are seriously concerned that the rapid expansion of SAT and loss of some

key personnel has diminished the quality of training, not only from a technical point of view

but, more vitally, there has been a loss of ‘la mística del trabajo’ or ethos.

In the great majority of maths trainings there was a purposeful and collaborative

atmosphere and the most tutors appeared to make good progress. It was noticeable that

the trainer’s style had a large impact on the learning environment; in some observed

sessions there was a rather subdued atmosphere, questions were rarely asked by tutors,

and a mainly ‘transmission’ teaching style was used. It also appeared that some sessions

were not carefully planned. This resulted in key concepts/skills/attitudes not being clearly

identified and developed. This probably significantly affected tutor progress and their

capacity to adequately accompany their students.

Although most tutors engaged wholeheartedly with the training process, there was a

(sometimes sizeable) minority in some sessions that did not. Concern was also expressed

that the incidence of unprofessional conduct during trainings was increasing. Some tutors

also complained about feeling pressured by other members of the group not to ask

questions or discuss issues so that the text could be completed quickly. It was reported by

coordinators that, worryingly, it tended to be tutors who have been longer in SAT who were

less motivated during the trainings.

65

There is evidence that a few tutors (perhaps ones with the weakest maths) copy out other tutor’s answers if asked to fill in the texts before the trainings

51


61. The training of trainers is made a priority.

62. All training sessions are planned.

63. Maths trainers have relevant teaching

experience.

64. The most capable and enthusiastic tutors

who are studying, or have studied, maths

and pedagogy at the university are trained

as trainers (this is already happening)

Supporting tutors’ development of practice in

the field

The importance of providing teaching manuals,

additional teaching tools and videos are mentioned

in other sections of this report.

In some areas the provision of micro centros is well

developed and plays an important role in

supporting tutors. In other areas micro centros

cannot be as responsive to the tutor needs because

of a lack of trained staff. The maths specialists

could play an important role in the provision of

micro-centros but it is necessary to train them. This

is happening, in the past seven months 24

tutors/assessors received a five day maths

specialist training.

The role of the field assessor

The field assessors are another set of SAT heroes;

on motorbikes, buses or foot they travel on bad

roads or paths to visit remote communities. It was

not unusual to meet an assessor (or coordinator) in

bandages from a recent motorbike accident (Box

38) or, as happened recently, shocked by an assault

in which his motorbike was stolen and he was tied

up and thrown down a hillside.

According to the coordinators, because of lack of

training, some assessors have a limited

understanding of the SAT methodology, and this

affects the quality of the acompanimiento they

provide the tutors. Field assessors, although they sometimes attend general trainings,

Box 38

Two hours from home and an hour

away from Comayagua an assessor

collided with a motorbike that was

going the wrong way up a one way

street, both motorbikes lost balance

and fell and both riders were taken to

see the community nurse; the

assessor was bandaged up and given

something for the pain. He carried on

his journey to the Institute in order to

hand in paperwork so his tutors would

be paid. When he arrived at the

Institute the director was shocked by

his injuries and took him to the

hospital. He was bandaged up again

and given an injection for the pain. A

mechanic mended and adapted his

motor bike so he could ride it with

injured leg. He arrived in Comayagua

about an hour later, soon after

7.00pm. He went to the SAT centre to

collect text books. It was a wet, cold

and windy night. The coordinator,

who had just got home after a 12 hour

day travelling to the communities,

returned to the centre to hand over

the texts, check that he could get to

his sister’s house in Comayagua and

that he would attend properly to his

injuries. When he arrived at his

sister’s house he had to be helped off

the bike and carried in. Three months

later he is ’90%’ recovered.

Observation and tutor interview

March and August 2010

52

appear to receive very little specialist training; the one assessor training organised (to the

consultant’s knowledge) during the first half of 2010 was cancelled. Field assessors who

have not been SAT tutors often do not know the texts well.

It would of course be difficult for any field assessor to become an expert in all 70 texts, but

they could specialise in one area (as with the maths specialists) as well as general pedagogy.


65. Field assessors’ training needs are reviewed and met.

Institutional links

In the Final Report to the donor 1045-0688 (1 July 2004 – 30 June 2006) it says that one of

the lessons learned was: ‘La participación de los actores como las universidades en el

desarrollo del programa incrementa la credibilidad del programa, facilita la consecución de

becas de estudio para los estudiantes, y reduce

los costos relacionados a consultorías y

asesoramientos’.66 This was surprising to read

given that, while Asociación Bayán has excellent

links with various government departments,

there was no contact related to pedagogy or

educational theory with a Honduran university

or other educational establishment in the first

half of 2010 as far as the consultant was aware.

Bayan has had an agreement with the

Universidad Autonomia de Honduras (UNAH)

since 2001 which states that they will work

together to ‘mejorar la calidad professional de

los docentes y superar la calidad de vida de los

pobladores de la Mosquitia67 (this was later

extended to all regions in which SAT was

working). However despite many attempts and

considerable effort on Bayan’s part (Box 40) this

relationship has not developed.

66 The participation of universities in the program’s development has raised the status of the program, helped obtain scholarships for students and reduced consultancy and evaluation costs. 67 Improve teaching quality and the quality of life for the inhabitants of the Mosquitia.

Box 40

Tenemos un Convenio Marco con

UNAH,

Don X los contactó a Curla de la Ceiba

tambien, para otro convenio, no

prosperó

La universidad pedagogica ha dado algo de cursos, como "Preparación de Instrumentos de Evaluación" para Bayan, donde participaron varios coordinadores La universidad pedagogica fue abordado en multiples ocaciones para un reconocimiento oficial a las capacitaciones de Bayan, no aceptaron, etc.

Source: email from Executive Director,

August 2010

53

This is a loss for UNAH because Asociación Bayán, with 14 years of experience implementing

SAT, has much to contribute to Honduran educational discourse.

This relative isolation, national and international,

means that Asociación Bayán is not, in the view of

the consultant, doing enough to draw on recent

research findings around international best

practice in maths teaching, and to see if it

contains elements that are appropriate for

adoption and adaption.

Although the quote in Box 39 is referring to

community development it could be argued that it

is these activities which maintain the vigour and

development of any process. Some coordinators

have expressed the concern that the SAT-

Honduras risks stagnating if it does not become

part of a wider dialogue, more closely linked with

the Honduran educational system68, and to

rigorous national and international educational

debate. Therefore, even though there are huge

time pressures on key staff, time should be found for this.

The comparative evaluations being undertaken by the Universidad Pedagógica Nacional Francisco Morazan, and the Hewlett study have not, as yet, contributed to any developments in practice or theoretical understanding. To date there has been no substantive progress report of the research being undertaken under the Hewlett study but it is expected that it will make a substantial contribution to understanding the taught and learned69 SAT curriculum and its impact on students.

Finally, it is surprising to the consultant that there are not closer links with FUNDAEC. Networking or developing a forum with other SAT Programs for informal discussion of methodological/pedagogic/ philosophical questions would be invaluable for Asociación Bayán, and FUNDAEC might also benefit from such a link (for example, when the Ciclo Comun texts were revised, it could have been useful to have sought Asociación Bayán’s reflections on its considerable experience with SAT).

68 Recent changes in the Honduran curriculum may require adjustments in the SAT curriculum e.g., the teaching of the division algorithm, 69

The ‘official’ curriculum is what tutors are expected to teach, as set out in the GEA and texts but what is ‘taught’ curriculum (what actually happens) will depend on tutor knowledge, interests, and skills. Students also affect the curriculum by their previous knowledge, attitudes towards learning etc.

Box 39

It could be claimed that a people

were in charge of their own

development only if they were

learning systematically about the

changes that occurred in their society,

and were consciously incorporating in

their continuous learning process

appropriate elements from the

universe of knowledge: their own, the

modern knowledge system, as well as

the experiences of other people and

groups in the world who are facing

similar challenges.

Source: Arbab et al, 1988

54


66. Asociación Bayán’s teaching staff form links, both formal and informal with other

educational institutions, and engage more actively with national and international

discourses on education.

67. An inter SAT Program learning network be created.

55

Conclusion

The maths component of the tutor training program has achieved many notable successes:

The training and supporting in the communities of about 700 tutors over the last

decade.

The vast majority of tutors questioned reported that: SAT had made them feel

more positively about maths; after the trainings they could do the exercises in

the text book; they felt confident explaining the exercises and enjoyed teaching

maths; those studying maths at the university said that SAT had significantly

helped them with their studies, that they understood more and were able to use

maths more in practical applications.

It was observed that the inclusive and relaxed, but purposeful, atmosphere of

the trainings is usually replicated in the SAT classrooms.

There is therefore a sound foundation to build on. The rapid expansion of SAT has

however put the training process under considerable strain; all interviewed coordinators

expressed concerns about maintaining the quality of SAT. It was also found that some

key elements of the SAT methodology were not being fully implemented, and that there

were other factors which, if addressed, could significantly improve the program.

The most important recommendations of this report are therefore that:

Asociación Bayán continues to build on these good foundations by continuing to

reflect and experiment with ways of further developing ‘an atmosphere of

consultation’. Activities which are a part of the SAT methodology, but which have

only partially been adopted, or not been adopted by Asociación Bayán, are fully

implemented, unless consultation with FUNDAEC identifies them as being no

longer appropriate.

Priority is given to building the capacity of:

o trainers to use the SAT methodology fully rather than partially

o the field assessors to ‘accompany’ the tutors in the development of their

general pedagogic skills;

o carefully selected maths field support staff to effectively support the

tutors develop their (more specific) maths pedagogy/knowledge.

Relevant insights, techniques and tools originating outside SAT, particularly those

associated with increased classroom participation, conceptual development and

‘formative assessment’, are identified and considered for adoption and

adaptation, since (according to the consultant’s experience and relevant research

literature) these have the potential to significantly enhance some key aspect of

the SAT pedagogy/curriculum.

56

Effective fora for the consultation of pedagogic and other educational issues are

established.

The collection and analysis of field data and feedback is systematised and

standardised (where appropriate) and archiving systems are improved.

Other recommendations are that:

Aprender Enseñando is used to develop consultation skills, and its delivery is

collaboratively planned so that all tutors have a comparable experience.

Tutors are explicitly taught the characteristics of ‘exploratory talk’, provided

opportunities to develop these skills, and mentored in facilitating appropriate

kinds of ‘exploratory talk’ in the classroom.

Training sessions are planned for developing a wide range of pedagogic skills,

particularly those associated with assessment for learning, conceptual

development, and increased participation.

Recommended activities/methods, if not explicit in the text, are clearly explained

to the tutors.

Topics in which tutors regularly experience difficulties are identified before

training so that sufficient time can be allocated to them, and related questions,

reflection, activities and discussion adequately planned.

Sufficient time is allocated for ‘independent working’ in the trainings.

Tutors have a written record (e.g., training handouts) to support classroom

practice and/or training in the taking of pedagogic notes, since inspection of

many tutor texts revealed that tutors rarely take pedagogical notes.

Trainers allow time between questions and responses, and discuss the reasons

for doing this with the tutors.

Activities in which question formation is explicitly requested, or which lend

themselves to this, are clearly identified in the trainings in order to help tutors

more effectively utilise the texts.

Trainers experiment with small group work as a way of encouraging the

formation of more reflective student questions, and encourage the tutors to do

the same.

Tutors are supported and mentored in the didactic use of questions and ‘error

analysis’ as a ‘formative assessment’ tool; this includes being informed of the

utility of this approach; experiencing it in their training; highlighting appropriate

SAT text examples; being made aware of the key relationship between errors and

‘misconceptions’; and being mentored in developing their own questions in field

assessor accompaniment.

Trainers/tutors are taught a range of techniques for increasing tutor/student

participation when answering questions.

57

Trainings are planned so that key statistical concepts are developed and

understood.

More up to date data is used in the trainings, and tutors are given copies of these

data to use in the communities.

The reasons why independent working is important are presented and discussed

in the trainings.

Maths trainers have relevant experience.

The most capable and enthusiastic tutors who are studying, or have studied,

maths and pedagogy at the university are trained as trainers (this is already

happening to some extent).

Field assessors’ training needs, as regards supporting tutors’ pedagogic

development, are reviewed and met.

Statistical concepts inadequately explained in the texts are identified, and

additional exercises developed.

Ways of increasing the value that students place on statistical projects are

investigated (and the copying of previous annual assignments is stopped).

Ways of integrating traditional representations and methods (estimation,

measurement, etc.) are investigated.

Tutors are systematically supported in the use of the Learning and Assessment

Guides for assessment for learning and, if necessary, additional materials are

provided.

More efficient methods to check answers and correct procedures (e.g., use of

small individual white boards, peer checking, etc.) are used in the trainings and

classes instead of whole class presentations by individual students/tutors.

Student/tutor presentations of work are used as the basis for discussions.

Tutors/students experience and reflect on a range of techniques for improving

group work

A range of formative assessment techniques is used; those in the texts are

identified and, where necessary, additional ones are introduced; and

trainers/tutors/students are supported in developing their capacity to use them.

The use of the Guias de Apprendizaje y Evaluación as a formative assessment tool

is investigated, or students are given other means to help them monitor their

own progress.

Tutors/students are given clear criteria of how to assess their own and others’

work, and guidelines are written on how to peer teach/accompany a

tutor/student without creating dependency (perhaps using the Guias de

Aprendizaje y Evaluaciόn).

The texts are analysed to identify which exercises need to be modified/changed

to make them more engaging to Honduran students, and where additional

58

information or discussion topics need to be introduced (these could be put into

the Teaching and Evaluation Guides).

Errors in the texts are amended and new illustrations are commissioned where

the current ones are unclear (e.g. Suma y Resta) or unattractive (e.g., Conjuntos y

Numeros)

When the representations are physical, they are made, as far as possible, with

locally available and sustainable/recycled materials.

Texts produced in Honduras follow FUNDAEC (and normal practice) referencing

conventions with regard to identification of the origin of material taken from

other sources.

Activities are developed to enable students to become competent in both metric

and imperial systems.

Tutors are taught techniques for overcoming ‘bloqueos’, and that the process of

meeting and overcoming maths learning blockages is perceived as normal and

often key to the learning process.

Estimation techniques are taught and practised.

Work with algebra includes multiple representations.

Tutors read the texts before training and note where they have difficulties. At

the end of the training review, this list of difficulties can be reviewed, progress

assessed, and further support needs identified.

Tutors who find maths difficult are identified at the beginning of their training so

that they can be given extra support.

Sufficient time is allowed at coordinator meetings for consultation on pedagogy,

particularly with respect to the development of an enriched and common

understanding of the SAT methodology.

Asociación Bayán’s teaching staff form links, both formal and informal, with

other educational institutions, and engage more actively with national and

international discourses on education.

An inter SAT/PSA Program learning network is created.

The tutors’ pedagogic/theoretical learning in SAT is linked more closely to the

educational theory and pedagogy studied in the university.

Tutors are given opportunities to share good practice e.g., via intranet, trainings,

micro-centres, tutor meetings, the SAT Bulletin, etc.

Tutors read texts before training and note down ideas for additional teaching

materials, activities, etc., so that these can be shared at the training.

Tutors/students are given opportunities to work in different groups during

training.

Tutor/student capacity to work in groups is developed by using different types of

group work, and by providing opportunities for analysis of the effectiveness and

inclusivity of the group work.

59

Tutors form groups to conduct simple collaborative action research on small

changes in practice based on a ‘theory of change’ model, and field assessors are

trained to promote and support this action research.

Criteria for defining ‘retake’, ‘opinar’ and other terms on the feedback forms that

are subject to very different interpretations are standardised (it can be noted

that Asociación Bayán is developing a data entry system to improve accuracy of

entry and calculations, and there are plans to produce a data collection manual

for staff).

The indicators and procedures used in the Hewlett study for classroom

observations are investigated for adoption/adaptation.

Data on student and tutor test scores are collated and analysed.

Reports are archived so that reflection on, and documentation of, processes are

facilitated.

60

References

Abdu’l Baha. Cited in a letter dated 5 March 1922 written by Shoghi Effendi to the Bahá'ís of

the United States and Canada, published in "Bahá'í Administration: Selected Messages 1922-

1932", pp. 21-22

Anthony, G. & Walshaw, M. (2007) Effective Pedagogy in Mathematics. Educational

Practices Series – 19. Geneva. International Bureau of Education. FUNDAEC: its principles

and its activities

Arbab, F. Correa, G. & de Valcarcel, F. (1988). FUNDAEC: its principles and its activities. Cali:

CELATER

Atherton, J S (2010) Learning and Teaching; What works and what doesn't [On-line] UK:

Available: http://www.learningandteaching.info/teaching/what_works.htm

Chingos, M. & Peterson, P. (2010) May:draft. Predicting Teacher Effectiveness by college

selectivity, experience etc. Paper prepared for conference on: Merit Pay: Will it work? Is it

Politically Viable? Sponsored by the Harvard Program on Educational Policy and

Governance.

Hattie, J. (1999) Influences on Student Learning: Inaugural Lecture, Professor of Education,

University of Auckland.

Hattie, J., Timperley, H. (2007) The Power of Feedback. Review of Educational Research. Vol

77 (1): 81-112

Hodgen, J. & Wiliam, D. (2006) Mathematics inside the Black Box: Assessment for learning in

the mathematics classroom. London: inferNelson

Ignacio, G. I., Barona, E. G., & Nieto, L. B. (2006) El Dominio Afectivo en el Aprendizaje de las

matemáticas. Revista Electronica de Investigacion Psicoeducativa 8, Vol 4 (1): 44-72

www.investigacion-psicopedagogica.org/revista/

Informe de Progreso Educativo de Honduras. (2005). Programa de Promoción de la Reforma

Educativa en America Latina y Caribe (PREAL). Washington, DC/Chile: Inter-American

Dialogue/Corporación de Investigación y Desarollo

Ma, L. (1999, 2010ed). Knowing and Teaching Elementary Mathematics. New York:

Routledge.

Mason, J. & Johnston-Wilder, S. (Eds) (2004) Fundamental Constructs in Mathematics

Education. Abingdon:Routledge

http://www.learningandteaching.info/teaching/what_works.htm

http://www.investigacion-psicopedagogica.org/revista/

61

República de Honduras. (2010). Visión de País 2010-2038 y Plan de Nación 2010-2022.

Tegucigalpa. www.visiondepais2010-2038.com

Rivkin, S. G., Hanushek, E. & Kain, J.F. (2005) Teachers, Schools and Achievement,

Econometrica 73(2): 417-458

Schwille, J. & Dembele, M. (2007). Global perspectives on teacher learning: improving policy

and practice. Paris:UNESCO

Swan. M. (2006). Collaborative Learning in Mathematics: a challenge to our beliefs and

practices. London/Leicester. NRDC/NIACE

Wilensky, U. (1991). Abstract Meditations on the Concrete and Concrete Implications for

Mathematics Education in in I. Harel & S. Papert (Eds.) Constructionism. Norwood N.J.:

Ablex Publishing Corp.

UNDP. (2009ª). Informe Sobre Desarrollo Desarrollo Humano. Honduras 2008/2008. De la

exclusión social a la ciudadania juvenil. Programa de las Naciones Unidas para el Desarrollo

(PNUD). Tegucigalpa, Honduras

UNDP. (2009b). Encuesta Nacional de Percepción sobre Desarrollo Humano 2008: Juventud,

Desarrollo Humano y Ciudadanía. Programa de las Naciones Unidas para el Desarrollo

(PNUD). Tegucigalpa, Honduras

Wiliam, D. (2006). Assessment: learning communities can use it to engineer a bridge

connecting teaching and learning. Journal of Staff Development Vol 27(1), 16-20

William, D. (2007). Assessment for Learning: why, what and how? Professorial lecture,

Institute of Education, University of London, 24th April.

Reports to donors:

Scaling up the System of Tutorial Learning (SAT) as an alternative education program tackling rural poverty and gender inequity in Honduras: 01:07:04 to 30:06:06 (No:1045-0688)

Building Sustainable Livelihoods through Agriculture 01.01.07 to31.07.07 (CIDA)

Fortaleciendo la Consolidación del Programa Educativa Rural SAT en Intibucá, La Paz y Comayagua. 06.07 to 12.07 (IBIS)

Internal Reports:

2010 January Informe de Actividades;

Perfil Nacional for 2010 (Block 1)

Perfil Nacional 2009 (incomplete due to the coup)

Perfil Nacional 2008 (Blocks 2 & 3)

http://www.visiondepais2010-2038.com/

62

Appendix 1: Observations: maths trainings70

Date Area Text Hours 25.01-29.01 1 Impulsor texts – maths specialists 45 8.02-9.02 2 Matematics 5 8 18.03 3 Micro capacitación – Polinomios II 4 26.03 3 Micro capacitación – Medidas del Espacio 4 26.04 1 Matematicas 1 & 6 7 27.04 4 Matematicas 1 & 6 4 28.04 1 Matematicas 3 & 1 7 29.04 1 Matematicas 3 4 30.04 1 Matematicas 3 2 6.05 4 Matematicas 6 2 13.05 1 Polinomios 1 7 14.05 1 Polinomios 1 7 17.05 1 Destrezas Algebraicas 4 18.05 1 Destrezas Algebraicas 7 19.05 1 Destrezas Algebraicas 4 25.05 5 Matematicas 3 3 26.05 5 Matematicas 3 & Matematicas 6 4 27.05 5 Matematicas 3 2

Observaciones: maths lessons

fecha Región Textos horas 22.02 6 Matematicas 5, Matematicas 5, Matematicas 4 3 1.03 6 Matematicas 5 1 2.03 6 Manejo de Variables, Polinomios II, Matematicas 5 4 17.03 7 Manejo de Variables, Polinomios II, El Espacio y Sus

Elementos 4

22.03 8 Matematicas 5, Polinomios II, Polinomios II, 3

Observaciones: reuniones

fecha Lugar grupo horas 2.03 6 Asesores 2 8.03-9.03 3 Coordinaros 12 31.05 9 Asesores 2

Summary of Interviews (semi-structured)

grupo no duración (approx)

Notes

coordinaros 9 0.5 – 3.0 horas

5 coordinators were interviewed on more than one occasion.

Assessors del campo

7 0.3 – 0.5

Tutores 25 0.3 – 0.5 During visits to centres and during breaks in training sessions a

70 31 hours of general training were observed: Aspirantes: Filosofía de SAT, Aprender Enseñando,

Tecnología 1, Second Year: 1 Descripciones,Third Year: Alfabetización, Lecturas 5

63

hours large number of conversations were held with tutors; these gave valuable insights and informed the framing of interview questions.

Appendix 2 – Summary of the field assessors’ session observations71

Si No na ¿El tutor utiliza metodología del enfoque analítico y participativo (no magistral)?

30 86% 0 0% 5 14%

¿Los estudiantes se sientan en circulo? 26 74% 4 11% 5 14% ¿El tutor formula preguntas adicionales a las que hay en el texto?

27 77% 3 9% 5 14%

¿Las preguntas del tutor son simples, precisas, entendibles y necesarias?

26 74% 3 9% 6 17%

¿Antes de avanzar en otro tema existe una conclusión del punto anterior?

25 74% 5 14% 5 14%

¿Se estimula la participación de todos? 25 74% 2 6% 8 23% ¿Durante su estadía en el aula cuantos participantes vio opinar

© 8/11, 10/16,18/21,14/15 12/12,6/9,20/23, 22/24, 13/17, 8/12,10/15,11/11, 13/17 (Y) 4/23, 8/16, 6/18, 7/17,3/19, 6/24, 4/12, 9/20 27/27 20/20 23/23

10

¿Usa tanto la lectura comentada como trabajo en grupo y lectura individual?

28

80%

1 3% 6 17%

¿Asegura que los participantes utilicen las puntuaciones de lectura correctamente?

26

74%

2 6% 8 23%

¿Da la oportunidad de lectura a todos los participantes?

30 86% 0 0% 5 14%

¿Hay investigación del conocimiento local (tradicional) suficientemente?

24 69% 1 3% 10 29%

¿Se asegura la comprensión del grupo antes de pasar a otros temas?

25 71% 3 9% 7 20%

¿Verifica los textos para asegurar la precisión de las respuestas escritas allí?

20 57% 7 20% 8 23%

¿Verifica la ortografía y gramática de los participantes en sus textos

19 54% 7 20% 9 26%

¿Avance del contenido está de acuerdo al tiempo transcurrido y previsto?

24 69% 4 11% 7 20%

¿Estima que el grupo podrá finalizar los textos hasta la fecha de evaluaciones?

25 71% 3 9% 7 20%

71 3 assesores (Area 5) (18 tutors) C1- 8, C2- 8, C3 – 2, 2- 6 hours, Oct 09, June 09, April 09, 3 assessors (Area 10) (11 tutors) C1 -4, C2 -4, C3-1, B2-2, 2 – 5 hours, (abril 2010) 1 assessor (Area 11) (3 tutors) C1, B1, B1 + 3 tutors

64

¿La asistencia diaria esta al día? 29 83% 1 3% 5 14% ¿Comienza puntualmente las sesiones (incluyendo luego de los recreos)?

27 77% 2 6% 6 17%

¿Se observa un ambiente limpio y organizado?

30

86%

1

3%

4

11%

¿Se observa un ambiente ordenado y disciplinado en general?

28 80% 3 9% 4 11%

¿Los participantes cumplen con las responsabilidades asignadas y son obedientes?

30 86% 1 3% 4 11%

¿Se observa respeto hacia las opiniones de los compañeros?

29 83% 2 6% 5 14%

¿Se observa respeto hacia el tutor/a? 30 86% 0 0% 5 14%

¿La practicas agropecuarias y de Servicio cuentan con un plan de fechas

8 23% 2 6% 25 71%

¿Todos los estudiantes participan en las actividades

8 23% 0 0% 27 77%

¿Los recursos para las practicas están disponibles

10 29% 0 0% 25 71%

¿La comunidad participa en la ejecución de las practicas y proyectos

8 23% 1 3% 26 74%

¿Se busca la participación de organizaciones para los proyectos

5 14% 0 0% 30 86%

¿El/la tutor/a monitorea el avance de las practicas con la frecuencia requerido

9 26% 0 0% 26 74%

¿El registro de las experiencias y practicas se lleva con el rigor debido

8 23% 3 9% 24 69%

¿Se lleva asistencia en cuanto a las practicas

8 23% 1 3% 26 74%

¿Las practicas se llevan en forma paralelas al avance de contenidos

8 23% 0 0% 27 77%

¿Se observa proyecto de servicio a la comunidad (si es positivo descríbalo)

4 11% 5 14% 26 74%

¿Se implementan los experimentos en el aula durante la lección?

2 6% 0 0% 33 94%

¿Tienen disponible los instrumentos e insumos oportunamente

2 6% 0 0% 33 94%

¿Demuestra seguridad en la realización de las experiencias?

2 6% 0 0% 33 94%

¿Hubo algún experimento durante la visita? (si si explique cuál)

2 6% 3 9% 30 94%

¿Hubo algún experimento se concluyo con éxito? (si no explicar las causas)

2 6% 0 0% 33 94%

¿Elabora su plan de clase y lo utiliza para el mejor desarrollo de su clase?

22 63% 6 17% 7 20%

¿Están al día sus informes administrativos para la Dirección Departamental

27 77% 3 9% 5 14%

¿Es muy puntual y es un ejemplo positivo en cuanto a su conducta

31 89% 0 0% 4 11%

65

¿Planea actividades académicas pertinentes para mejor comprehension del grupo?

27 77% 1 3% 8 23%

¿Promueve actividades de recaudación de fondos con sus estudiantes

28 80% 2 6% 5 14%

¿Decora apropiadamente su aula para apoyar la educación del grupo

24 69% 3 86% 8 23%

¿Se observa un ambiente alegre y de motivación en el grupo

30 86% 0 0% 5 14%

66

Appendix 3: Summary of field assessors comments on classroom observations72

(not monthly reports)

M E T O L O G I A

Se sientan en grupos ya que el mobiliario ahorita no da para que estén en circulo también la cantidad de alumnos Recomendación: elaborar preguntas para repaso de la lección y verificar los textos de los estudiantes Durante esta visita los estudiantes hicieron exposición No están en circulo por que el espacio es reducido están sentado en forma de U Que pregunta a los estudiantes que expliquen lo que entienden de la que ¿ Explore a los estudiantes ¿ qué va a estudiar antes de entrar al contenido de texto Cuando use ‘b’ no dijo ‘b’ grande o ‘v’ pequeña dijo a los estudiantes ‘b’ labial o ‘v’ dental. Fue una jornada muy interesante Se recomienda que pregunta a cada estudiante que lee lo que entiende do lo que leyó x Se debe realizar preguntas …cada párrafo Se debe enfocar a las temas Bien participativos (2) Esta cumpliendo con la metodología (3) Constructivista y participativa (2) Expositiva, analítica, Constructivista, dinámica y participativa Material didáctico (3) Material didáctico bonito

E V A L U A C I O N P R O C E S S O

siempre ratifique la ortografía de las palabras que utilizan los estudiantes al escribir las respuestas a las preguntas del texto No estaban dentro del aula de clases Hacer un repaso del tema anterior antes de seguir otro Se dieron algunas sugerencias a la tutora para prepares(¿) Cada vez que termine una lección revise las respuestas escritos por los estudiantes y rectifique la ortografía x (y no solamente verbal) (2) Revisar los textos para verificar se esten trabajando Avanzar con las (¿) para poder (¿) con el plan de evaluación En el texto de la matamatica no hay revisión de las respuestas Algunas estudiantes presentaron debilidad al escribir algunas palabres El en texto de conjuntos y números en el lección ……no lo hay …… respuestas Hasta cierta tematico si hay pero en mayoría no le hay. No en todos los textos esta revisado toda la temática (2)

D I S

Debe d ser puntual en la hora de entrada Ensenar a los estudiantes a respetar las ideas de los demás En conjuntos de 5 estudiantes una exposición

72 Number of comments per tutor 1 – 15.

67

C I P L I N A

Les (¿) fuera del aula porque la maestra de primeria tenían reunión a pesar de esto estaban bien organizados bajo la sombra de un árbol Algunos alumnos no trabajan en los textos inspectados por lo menos dos. Plan for ‘un archivo del la conducta de cada estudiante’ Cumplen con sus obligaciones asignadas (5) Trabajan bien en sus textos Bien aplicados Cumplen con sus normas Todas se integran al trabajo Bien disciplinados Son educados Portan uniformes completos Plan for ‘un archivo del la conducta de cada estudiante’ Buena cooperación entre alumnos Respeto entre compañeros Trabajan mutualmente Estudiantes respetosos al tutor Buena relación (5) Excelente relación Muy respetosas Muy buena entrega y compromiso ante el grupo Excelente relaciones con las personas de la comunidad (4)

P R A C T I C A S

En este bloque no llevan prácticas agrícolas x Hacer un cronograma de actividades antes de empezar el proyectos entre todos los padres de familia ¿ en terreno. En las practicas apoyan los padres de familia El día de hoy no estuvo en el aula, estaban trabajando en el campo con las prácticas de tecnología. Se sugiere elaborar un plan para las practicas agropecuarias

- proyectos de la comunidad (2) Estimule a los estudiantes a realizar proyectos de servicio a la comunidad Hay un proyecto planificado pero aun no ha sido ejecutado Cría de pollos campaña de alfabetización no lo hubo x campaña de limpieza en la comunidad (2) Agua caliente, – Parcela bien cultivada

E X P E R I

No presencia ningún experimento (11) Insectario se concluye con éxito muy presentable Experimento sobre la temperatura Agua caliente, tibia y fría

68

M E N T O S T U T O R

Tiene que hacer su horario de clase y pegarlo en un lugar visible dentro de aula. (3) No presento el plan de clase por olvido No andaba su plan de clases y que estaban trabajando en el campo Se sugirió laborar puntualmente el plan de clase y ¿ del mismo ¿ evitar (¿) y (¿) mejor su clase Cada día que se imparta las clases debe tener sus planes de clase para cada capacidad Tratar de mantener el entusiasmo en los estudiantes No decora el aula porque es aula prestada y los (¿) de la escuela no les gusta que peguen cosas en las paredes No tienen paredes están recibiendo clases en el galpón (porque no hay nada puesto en los paredes) No existe material (¿) en el aula de clase. So se observo algunos aspectos .. que la visita fue en la parcela … mayor tiempo Planificación esta al día

69

Appendix 4: Questionnaire Survey

The percentages on the left hand side are the percentage of students responding to each

question.73 The numbers on the left are the percentage of responses in each category.

(Questionnaire on following page)

73 If a question does not have a percentage it is because there appeared to be confusion amongst the first year students as to whether or not they should answer the question. Taking this into account the response rate was about 95% for all questions.

70

El objetivo de este cuestionario es recolectar información que nos ayude a mejorar la

capacitación y el apoyo que le damos. Esperamos que los resultados de estos puedan ser

compartidos y utilizados por capacitadores de otras partes del mundo.

No estamos colectando información que revele su identidad, por lo que sus respuestas

permanecerán como anónimas. Utilizaremos esta información para conocer su opinión sobre las

matemáticas y el proceso de enseñanza de las mismas.

Por favor, responda a las preguntas en cuanto las lea – nos gustaría conocer su primera opción,

y siendo éste un cuestionario anónimo, siéntase libre de responder de la manera más honesta

posible.

Este cuestionario ha sido elaborado para conocer su valiosa opinión COMO TUTOR/A de

matemáticas.

Para contestar el cuestionario, marque con una X la respuesta que considere más oportuna. Las

escalas de valores son las siguientes:

Casi siempre, Generalmente, 50% del tiempo, Rara vez, Muy rara vez.

Casi siempre

General-mente

50% el tiempo

Rara vez

Muy rara vez

1 93%

Mis estudiantes realizan todos los ejercicios del texto de matemáticas.

45 51 3 1 0

2 97%

Mis estudiantes resuelven los ejercicios por sí mismos y consultan a sus compañeros de vez en cuando.

33 36 21 7 2

3 98%

En la resolución de ejercicios matemáticos, mis estudiantes solo utilizan los métodos que yo les enseño.

35 36 21 6 2

4 96%

Al resolver los ejercicios matemáticos, mis estudiantes comienzan con los más “fáciles” y dejan para el final los “difíciles”.

40 29 7 16 7

5 97%

Yo motivo a mis estudiantes para que terminen los ejercicios lo más rápido posible.

32 29 11 14 14

6 95%

Mis estudiantes comparan diferentes métodos de resolución de problemas matemáticos.

25 35 17 18 6

7 98%

Cuando doy una explicación, lo hago a toda la clase de una vez.

30 35 9 14 13

8 96%

Relaciono las matemáticas que mis estudiantes han aprendido en textos anteriores con lo que enseño en el texto actual.

46 46 2 5 1

9 94%

Mis estudiantes me sorprenden con respuestas, comentarios o preguntas que encuentro originales.

20 31 22 23 3

71

10 96%

Evito que mis estudiantes cometan errores razón por lo cual explico las cosas con cuidado desde el principio.

36 46 10 5 3

Casi siempre

General-mente

50% el tiempo

Rara vez

Muy rara vez

11 95%

Todos los ejercicios que mis estudiantes trabajan en clases pueden ser resueltos con explicaciones que se encuentran en el texto.

37 42 12 6 3

12 97%

Mis estudiantes aprenden discutiendo sus ideas.

40 46 7 6 1

13 98%

Mis estudiantes aprenden trabajando en pares o en grupos pequeños.

46 35 12 6 2

14 95%

Mis estudiantes inventan sus propios métodos para resolver ejercicios matemáticos.

9 10 17 48 17

15 94%

Yo les indico a mis estudiantes cuales ejercicios deben resolver.

18 36 8 18 21

16 96%

Yo disfruto enseñando matemáticas.

50 43 6 1 0

17 95%

Mis estudiantes aplican en su vida cotidiana lo aprendido en mis clases.

36 42 14 6 2

18 95%

Yo relaciono lo avanzado en mis clases de matemáticas con lo que mis estudiantes aprenden en los otros textos.

41 44 12 2 2

19 95%

Mis estudiantes justifican sus respuestas en los ejercicios de Verdadero/Falso.

40 34 10 11 4

20 96%

Yo motivo a mis estudiantes a que razonen la resolución de los ejercicios matemáticos, aunque les tome más tiempo.

49 45 3 1 2

21 97%

Yo relaciono lo avanzado en matemáticas con la afirmación de valores espirituales.

33 45 12 6 4

22 95%

Las matemáticas son útiles en los proyectos de servicio a la comunidad.

50 46 3 1 0

23 95%

Me siento segura/o cuando explico a mis estudiantes cómo realizar los ejercicios matemáticos.

46 53 1 0 0

24 98%

Me siento segura/o cuando ayudo a mis estudiantes a entender cómo funcionan las operaciones y formulas matemáticas.

41 49 1 0 0

25 96%

Mis alumnos comparten en la clase los métodos matemáticos que sus padres utilizan en su vida cotidiana.

24 29 11 29 7

26 95%

Tomo tiempo de mis clases para contextualizar lo aprendido en la realidad de la comunidad en la que trabajo.

36 39 14 9 2

72

Los temas de matemáticas que encuentro más fáciles de enseñar son:

Los temas de matemáticas que encuentro más complicados de enseñar son:

Cada sección presentada a continuación, excepto la última, cuenta con 4

afirmaciones. Lea cada una y valórelas de modo que el total sume 100%. Estas

valoraciones deben reflejar su opinión con respecto a ellas.

Si lo desea, puede escribir comentarios personales.

Las Matemáticas son:

Un conjunto de verdades universales, reglas y procedimientos estandarizados que deben ser enseñados a los estudiantes

32

Una materia creativa en la que cada individuo crea sus propios conceptos y métodos.

20

Una de las herramientas fundamentales para el avance del desarrollo autosustentable de la comunidad.

28

Un conjunto interactivo de ideas creado en forma colectiva a través del intercambio de perspectivas e interpretaciones.

19

Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%

Aprender es:

Un proceso individual basado en observar, escuchar y hacer ejercicios similares hasta que la nueva conducta se afiance.

20

Un proceso individual basado en la exploración y la reflexión. 21

Un proceso interactivo en el que los estudiantes son desafiados a desarrollar su entendimiento a través de actividades desarrolladas y analizadas en grupos.

31

Un proceso motivado por el deseo de contribuir a la sociedad y en el que cada persona desarrolla sus potenciales.

28

Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%.

73

Enseñar es:

Introducir el aprendizaje con conceptos sencillos, yendo paso a paso hacia conceptos más difíciles. Dar instrucciones verbales y verificar, a través de ejercicios, que éstas hayan sido comprendidas, para corregir vacios de comprensión a través de los errores.

34

Facilitar discusiones en las que el estudiante conjuntamente con su tutor profundice el conocimiento de las matemáticas y exploren la interconexión e interdependencia de lo aprendido para el desarrollo personal y social.

28

Saber reconocer cuándo un estudiante está listo para aprender; proveer un ambiente estimulante que facilite la exploración y que, a través de experiencias cuidadosamente estructuradas, evite aprendizajes errados.

19

Establecer una serie de diálogos no estructurados y estimulantes entre el tutor y los estudiantes, en los que los conceptos y su interrelación son explorados verbalmente. Si se generan conceptos errados, estos son expuestos para su análisis y corrección.

19


Cuando enseño, mis prioridades son dirigidas a que mis estudiantes logren:

Motivarse y tomar responsabilidad sobre su propio aprendizaje.

24

Utilizar la matemática para explorar y describir el mundo y resolver problemas de su vida cotidiana.

32

Completar los textos y estar preparados para los exámenes.

9

Explicar los conceptos y formulas matemáticos.

11

Comportarse correctamente, participar en actividades y ser solidarios con sus pares.

12

Reconocer la calidad de su trabajo y la de otros y saber qué hacer para mejorar. 11


74

Este cuestionario ha sido elaborado para conocer su valiosa opinión COMO ESTUDIANTE de las

matemáticas.

Para contestar el cuestionario, marque con una X la respuesta que considere más oportuna. Las escalas de valores son las siguientes:

Muy de acuerdo, De acuerdo, No he decido, En desacuerdo, Muy en desacuerdo

Muy de acuerdo

De acuerdo

No he decido

En des acuerdo

Muy en des acuerdo

1 98%

Las matemáticas son útiles y necesarias en todos los ámbitos de la vida.

83 17 0 0 0

2 96%

Las matemáticas son difíciles, aburridas y alejadas de la realidad.

1 1 5 38 56

3 93%

En matemáticas es fundamental aprenderse de memoria los conceptos, formulas y reglas.

9 30 8 43 11

4 97%

Las únicas matemáticas que me interesan son las que tengo que enseñar, porque las tengo que conocer.

2 4 2 47 45

6 98%

Las destrezas o habilidades que utilizo en clase para resolver problemas no tienen nada que ver con las que utilizo para resolver problemas en la vida cotidiana.

2 2 2 56 37

7 98%

Busco distintas maneras y métodos para resolver un problema.

57 40 1 2 0

8 99%

Aprendo mucho inventando nuevos problemas.

56 36 4 3 2

9 98%

Si no comprendo las matemáticas difícilmente podré asimilar y dominar otras asignaturas relacionadas con ella (como física, química etc.)

43 33 9 9 6

10 98%

Mi rendimiento en matemáticas depende en gran medida de la actitud del/a capacitador/a hacia mí.

20 34 9 28 9

11 99%

Cuando dedico más tiempo de estudio a las matemáticas, obtengo mejores resultados en la resolución de problemas

78 22 0 0 0

12 95%

Cuando resuelvo un problema, suelo dudar de si el resultado es correcto.

4 20 14 50 13

13 94%

Me considero muy capaz y hábil en las matemáticas.

15 51 24 10 1

14 95%

Estoy calmado/a y tranquilo cuando resuelvo problemas de matemáticas.

30 62 2 6 1

15 99%

Los/as buenos/as profesores/as que explican con bastante claridad y entusiasmo

30 1 2 0

75

y son agradables hacen que gusten las matemáticas.

67

Muy de acuerdo

De acuerdo

No he decido

En des acuerdo

Muy en des acuerdo

16 96%

Cuando estaba en la escuela y en el colegio tuve bueno/as maestro/as de matemáticas.

36 42 6 13 2

17 96%

La gente a la que le gustan las matemáticas suele ser un poco rara.

4 10 7 46 32

18 96%

Las matemáticas son para cabezas inteligentes y creativas.

6 10 3 41 39

19 95%

La gente que es buena en matemáticas no tiene que gastar tiempo pensando cómo resolver un problema.

9 16 7 49 19

20 95%

Las clases de matemáticas se me hacen eternas, son muy pesadas, no estoy a gusto y siento deseos de salir corriendo.

2 5 6 44 44

21 96%

Ante un problema complicado suelo darme por vencido/a fácilmente.

3 2 2 58 36

22 93%

Cuando me enfrento a un problema, experimento mucha curiosidad por conocer la solución.

49 49 2 0 0

23 95%

Me provoca gran satisfacción resolver con éxito un problema matemático.

72 27 1 0 0

24 94%

Si no encuentro la solución de un problema, tengo la sensación de haber fracasado y de haber perdido el tiempo.

5 6 7 63 20

25 95%

En mis estudios matemáticos muestro perseverancia y paciencia.

46 52 0 1 1

Si tiene más de un año trabajando con SAT, por favor conteste el siguiente grupo de preguntas:

26 Mi percepción de las matemáticas es más positiva desde que recibo las capitaciones de SAT.

85 13 2 0 0

27 Otros tutores me buscan para ayudarles con las matemáticas.

17 61 5 17 1

28 Después de una capacitación siento que no entiendo toda la materia y que no puedo resolver todos los ejercicios.

3 6 8 51 32

Si está estudiando o ha estudiado matemáticas en la universidad o en la Pedagógica, por favor conteste la siguiente pregunta:

29 Mis estudios de matemáticas con SAT me han ayudado con mis estudios de matemáticas en otras instituciones.

70 28 0 0 2

76

Lea las afirmaciones sugeridas a continuación y marque con una X el número que mejor

represente cómo se siente usted cuando realiza cada una.

La escala es de 1 a 5, siendo 1 – calmado y totalmente sin estrés, y 5- muy nervioso y/o muy estresado.

Si tiene algún comentario sobre su experiencia estudiando matemáticas con SAT, o si desea hacer

alguna sugerencia, por favor compártala con nosotros en este espacio.

1 Muy

calmado/a

2 3 4 5 Muy

Estresado/a

1 Revisando el texto de matemáticas. 66

21 7 2 2

2 Planeando la clase que voy a enseñar al día siguiente.

62 23 9 4 2

3 Viendo el capacitador explicar álgebra en el pizarrón.

52 26 12 3 7

4 Empezando a estudiar el texto antes de ir a la capacitación.

51 24 9 12 3

5 Interpretando gráficos matemáticos.

40 33 20 5 3

6 Llegando a la capacitación y pensando en la capacitación de matimáticas.

61 19 10 6 4

7 Cuando voy a trabajar en el pizarrón durante la capacitación.

39 22 20 9 10

8 Cuando el/la capacitador/a me propone ‘por sorpresa’ que resuelva un problema.

33 29 13 13 12

9 Cuando me atasco o bloqueo en la resolución de un problema.

31 15 19 17 17

10

Si hay otra acitividad matemática que le de estrés anótela aquí:

77

Appendix 5: Additional comments of the tutors on the questionnaire

1. 2. Pues, bueno yo he aprendido mucho de las matemáticas en SAT estoy bien agradecido

por las capacitaciones. Y le ayuda a la preparación tanto persona como ensenar al

alumnos unos no la ha ¿a la clase y preparándolo. Se siente con confianza y eso le ¿ a

alumno.

2. 7. Las matemáticas vista en SAT han despertados interés en mi persona yo ya no tengo

miedo a matemáticas porque he aprendido como poder a desarrollo a cómo enfrentarle.

También he aprendido comprender situaciones de la vida porque (¿) miedo de la

matemáticas.

3. 10. A mí me encanta las matemáticas y yo siento que lo que he aprendido en SAT me ha

ayudado mucho en mis estudios universitarios y en mi vida diaria.

4. 12. Hay textos de mi matemática que se hacen fácil desarrollarlo de igual manera que

hay textos que se debe dar más tiempo para desarrollarlos ya que tiene un nivel de

complejidad y se vuelven un poco más difícil su realización en los textos de Bachillerato

se le debe dar mas ¿??? en estos textos en las capacitaciones. Ya que se necesita ir con

los conceptos darlos a impartirlos a los estudiantes.

5. 15. SAT nos ayuda mucho en las clases de matemáticas porque debemos contenidos muy

amplios y bien definidos

6. 18. En mi comentario lo que les puedo decir es que en SAT es donde yo he aprendido

mucho de matemática muy bonito la moralidad. Se aprende mucho en capacitaciones ya

que los capacitadores son personas muy preparados.

7. 19. Mi experiencia como tutora de SAT ha sido muy importante porque aprendemos la

clave las operaciones de matemática de diferentes maneras y las comprábamos con

situaciones de la vida diaria.

8. 20. Las matemáticas estudiados con SAT me ha servido mucho en mis estudios

universitario también a encontrado el porqué de los ejercicios.

9. 24 Los textos de matemáticas son muy interesantes pero se le debe dar más tiempo ya

que esto texto de matemática necesita más practica que los de lectura (Matemática 3)

10. 27 Siempre me he sentido que me gusta las matemáticas pero desde que estoy en la

sistema he descubierto que se resuelven muchos problemas de la vida con mejor

facilitad.

11. 31. todo lo que he aprendido hasta hoy en las matemáticas de SAT me parece muy

interesante porque el alumno y yo comprendemos lo que hacemos.

12. 34. Por los momentos pues tengo un mes de trabajo y me siento bien al saber que tengo

la capacidad de ayuda a la comunidad y a su persona y se obtiene diferentes expresiones

a vivir en otro parte y compartir unos conocimientos diferentes.

13. 37. Soy ingresada de SAT 100% y para mí las matemáticas aprendidas en SAT ya que el

tutor se detiene y se explica detalladamente tratando dar la explicación más clara y dar

un mejor resultado en la evaluaciones

14. 39. En SAT los experiencias en matemáticas es fascínate porque aprende a desarrollar su

propia concepto y te pone a utilizar tu lógica que ha a veces esta muy dormida y puedes

aplicar esta lógica matemáticas en problemas de la vida diaria y te lleva resolver estos

problemas de la vida diaria.

78

15. 43. Todavía no tengo un ano pero siento que ya me ha ayudado bastante las

capacitaciones de matemática

16. 44. Desde del momento que comencé a trabajar siento que he aprendido muchas

conceptos que en el colegio no aprende.

17. Sugerencias que el capacitador nos trate con paciencia y confianza

18. 45. Es un proceso muy bonito y importante porque son ejercicios mucho mas

explicativos que un educación de nuestro mismo nivel y estos ejercicios los podemos

utilizar para resolver ejercicios de la vida cotidiana

19. 52. Las matemáticas de SAT me ha ayudado a ser mas analítico y a ponerlo en práctica

en la vida real

20. 59 Es la primero vez que recibo una capacitación de SAT de matemáticas y fue muy

productivo. Me fue muy bien y creo con dedicación estaré preparado a dar esto texto

con el ayuda de Dios

21. 65. Mi experiencia es que encuentro mucho más fáciles los textos. Creo que es una forma

muy efectiva de enseñanza

22. 75. Pienso que para las matemáticas es necesario usar diferentes materiales el tutor o

capacitador tiene que tener paciencia para que los estudiantes le comprended y captan

mejor

23. 76. Soy egresado de SAT y me siento totalmente satisfecho porque educación que he

recibido soy tutor del mismo programa y me siento feliz de poder compartir mis

conocimientos a mis alumnos y a otras personas, Gracias. He tenido la fortuna de ser

una persona humilde y agradable ante la sociedad en SAT aprende muchas cosas que me

ha gustado en la vida. Agradezco a la Asociación Bayan y a SAT por el gran apoyo que

me ha brindado. Espero seguir adelante, seguir adelante y siempre resaltado al nombre

de SAT donde quiero que yo vaya

24. 77. Hasta el momento los textos estudiados con SAT me ha gustado mucho los mejores

capacitadores de matemáticas que he tenido son X y Z

25. 78. Estudiar los textos de SAT y es muy importante ya que ayudan en gran manera en

nuestra vida como profesional también para tener alguna destreza conocimiento al

momento de usar el estudio superior en la universidad. Sugerencia que los textos de

SAT tenga suficiente espacio como para desarrollar ejercicios con mejor orden también

que haya una secuencia en algunos temas que están muy similares.

26. 83. La experiencia de trabajo con SAT es muy bueno ya que he mejorado en el área de

matemáticas porque durante estuve en la escuela y en el colegio no había aprendida

mucho sobre la materia. En SAT encontramos con una matemática bien desarrollada

donde retomarnos la matemática estudiado anteriormente y cosas de nuestra vida

diaria

27. 92 Estudiando matemáticas en SAT me ha mejorando miro la matemática en manera

diferente, y me gusta más y me siento más confianza y miro que la matemática no es

como de niño pensé que era. Que SAT ha desarrollado en me el interés para seguir

aprendiendo mucho más sobre matemáticas.

28. 99. Hay algunos temas que son más complicados que otros por eso sugiera que para

algunos textos siempre haya micro centros aun que hayamos terminado el texto erg

expresiones y ¿ Algebraicas

29. 101. Mas que un comentario tengo un profunda agradecimiento ya que todos las

capacitaciones de matemáticas que he recibido me ha ayudado mucho porque antes me

forma parte de SAT les tenía miedo a las matemáticas y ahora es una de las clases que

79

más me gusta y lo más importante que a mis estudiantes les gusta y disfrutan las clases

de matemáticas.

30. 105. Experiencia la manera de ver las matemáticas con la metodología me ha ayudado

sobre la manera y he aprendido a razonar mejor los problemas presentados. Sugerencia

la capacitación de matemáticas debería ser al principio de la primera semana

31. 106. Respeto al texto que sea siempre de ver en los primeros días porque uno tiene más

relajado en cambio cuando los dan al final de la semana uno se desespera o se estresa

mas por el cansancio o porque nos desesperamos por unos que no ponen atención.

32. 121. En SAT se obtiene la herramienta necesaria para poder entrar diferentes ejercicios

y poder resolverlos

33. 123. En SAT la matemática se explique de una manera muy intangible porque se aplica a

la realidad y se explica con modelos sencillos pero muy importantes.

34. 128. Hacer preguntas, contestar respuestas breves que el alumno afirmaciones se

presentan para analizarlos en sentido positivo y negativo

35. 132 Las matemáticas así como el trabajo de SAT no ha sido solo una fuente de empleo

sino que ha cambiado positivamente mi vida. Gracias a Dios por el SAT.

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