MINISTRY OF EDUCATION AND TRAINING
THE VIET NAM INSTITUTE OF EDUCATIONAL SCIENCES
NGUYEN THE SON
BUILDING INTEGRATED THEMES IN TEACHING
MATHEMATICS IN HIGH SCHOOL
Major : THEORY AND METHOD OF
TEACHING MATHEMATICS
Code: 62 14 01 11
SUMMARY OF DOCTORAL THESIS
Ha Noi, 2017
The Thesis is completed at :
The Vietnam Institute of Educational Sciences;
Scientific supervisors:
1. Assoc. Prof., Dr.Pham Duc Quang, VNIES;
2. Dr. Pham Thanh Tam, VNIES.
Reviewer 1: ...................................................................
...................................................................
Reviewer 2: ...................................................................
...................................................................
Reviewer 3: ....................................................................
.....................................................................
The thesis will be proofed before the thesis review board meeting
at The Vietnam Institute of Educational Sciences, 101 Tran Hung
Dao, Ha Noi.
Time………..Date : ……………………..
The thesis could be found at:
- National Library;
- Library of VNIES.
LIST OF AUTHOR’S RESEARCH PUBLICATIONS
RELATING TO THE CONTENTS OF THESIS
1. Pham Duc Quang and Nguyen The Son (2012). Teaching
Mathematics in high school in the direction of relating to
reality, enhancing practice, application, interdisciplinary.
Journal of Education and Society, No.7, April 2012
2. Nguyen The Son (2012). Approach to integrated teaching in
Mathematics in high school. Journal of Education and
Society, No. 82, July 2012.
3. Nguyen The Son (2015). Orientation of integrated teaching
in Mathematics for secondary students. Journal of
Education, No.363, August 2015.
4. Pham Duc Quang and Nguyen The Son (2016). The integration
tendency in general education in some countries. Journal of
Education and Society, 60 (121), March 2016.
5. Nguyen The Son (2016). Suggest an Integrated Theme
building process in teaching Mathematics in high school.
6. Nguyen The Son (2016). Some measures to help teachers build
and teach Integrated Theme in Mathematics in high school.
Journal of Education and Society, 63 (124), June 2016.
1
PREFACE
1. Reasons to choose the thesis
1.1. The teaching of science in school must be coherently, logically
linked, especially in the context of international integration and the
knowledge economy.
In order to meet the above requirements, teachers need to
know how to integrate sciences in teaching, how to facilitate students
the ways to find, collect and process information sources, how to
flexibly apply knowledge in practice.
1.2. The development of general education curriculum in our country
needs to be changed in line with the international trend
The current general education curriculum has implemented
the integration of multiple disciplines in one subject, integrated many
global issues into many subjects and educational activities. However,
the content is still in favor of the scientific logic of each subject, not
rehearsing for students to find and solve problems in real life ...
Facing with the requirements for fixing the limitations, general
education curriculum will be radically renovated.
1.3. Integrated teaching trend is becoming popular in schools
around the world
Integrating subjects in schools around the world is an
indispensable trend. Therefore, we need to study, research and
advance in using Integrated Teaching in general schools, contribute
to meeting the requirements of developing general education
curriculum, in orientation of developing students‟ competencies.
1.4. The development of the mathematics curriculum in Vietnamese
schools is necessary to meet the needs of human resource
development in the context of international integration in our
country.
2
Deriving from the above reasons PhD candidate selected the
thesis: Building integrated themes in teaching Mathematics in high
school.
2. Purpose of the study
Suggest process and methodology for building Integrated
Themes in Mathematics with some specific Integrated Themes that
illustrate the process and methodology in order to contribute to
renewal and improvement of the quality of mathematics instruction
in high schools.
3. Research tasks
Clarify some theoretical issues about Integrated Teaching
(integration concept, characteristics of Integrated Teaching,
Integrated Teaching types ...);
Select the appropriate building process and structure
Integrated Themes in Mathematics teaching so that teachers can
build Integrated Themes in Mathematics for the future;
Suggest pedagogy to help teachers design Integrated Themes
of Mathematics and deploy teaching them;
Pedagogical experiments examine the thesis‟ feasibility.
4. Scientific hypothesis
If an appropriate integration model is identified and
implemented in an appropriate procedure to the proposed measures
in the thesis, it is possible to design Integrated Themes of
Mathematics in high schools and the teaching of those themes will
improve the teaching results of mathematics in high school.
5. Subjects and scope of the study
Research subjects: Integrated Themes in Mathematics in
Vietnamese schools.
Research subjects: Integrated Teaching in Mathematics in
Vietnamese high schools.
3
Scope of the study: The thesis focuses on the process of constructing
Integrated Themes in teaching mathematics in high school; illustrates
through some mathematics themes s in high school under the current
curriculum in Vietnam.
6. Research Methodology
Theoretical research; observation and investigation method;
pedagogical experiment research; experience summation method;
expert method.
7. New contributions of the thesis:
In theory: Clarify some issues related to integrated Teaching
such as concepts of: integration in teaching, teaching themes,
teaching integrated themes, ...; propose some models of integration
which is appropriate to Mathematics in Vietnamese schools; Propose
the process of building of Integrated teaching in Mathematics in
Vietnamese schools; initially clarify the method and form of
Integrated Teaching in Mathematics in Vietnam.
In practice: Propose pedagogical measures to help teachers
design and teach integration in mathematics in high school; design
some Integrated Themes in Mathematics in high school; give some
guidelines to help teachers design and develop mathematics in high
school.
8. Proposed points for Defense
- The proposed form of integration in mathematics in high
schools has scientific rationale and feasible in teaching mathematics
in our country.
- The designing process of Integrated Themes as proposed in the
thesis has scientific rationale and feasible in teaching mathematics in
our country;
4
- It is possible to design Integrated Theme in teaching
Mathematics in our country basing on the proposed process and the
standards of knowledge, skills in our current curriculum;
- Teachers can base on the guidelines to design and implement
Teaching Integrated Themes in Mathematics in our country,
following the current standards of knowledge and skills in our
current curriculum.
9. Thesis structure
In addition to the introduction, conclusion, the list of tables,
and the lists of references, the thesis consists of 3 chapters.
CHAPTER 1
SOME GENERAL ISSUES ON INTEGRATION
IN EDUCATION
In this chapter, we focus on the following main contents.
1.1. Concepts of integration
1.1.1. Some concepts of integration from foreign research
By studying some domestic and foreign studies, the majority
view that Integration derived from Latin with the meaning of
reconstructing the general, the whole, the system on the basis of
individual parts. In education, integration can be understood as the
consolidation of the various types of knowledge and the
corresponding disciplines.
1.1.2. Concept of integration in some domestic researches
Through the understanding that, up to now, although there
are many different approaches, there are also different notions of
integration, but there are some common points, such as: Integration
is a process of combining different objects into a unified whole.
The result of this combination process is the formation of a
new system or may include parts that are more or less relating to
5
previous systems, which are more closely interrelated and there is a
change in quality of each part‟s attributes.
1.1.3. Integration is an indispensable trend in educational
curriculum development
By studying some of the research on the integration of
authors in and outside the country such as Susan M. Drake, Robin
Fogarty or Xavier Roegiers, Tran Duc Tuan, Nguyen Anh Dung ... it
is shown that integration as indispensable trend in constructing
general education curriculum in 21st century.
1.2. Research on integration
1.2.1. Some models of educational curriculum of
integration
According to Susan M. Drake, Robin Fogarty or Xavier
Roegiers, or Nguyen Anh Dung ... shows that there are some models
of educational curriculum of integration
as followings:
Type 1. Multidisciplinary integration, subject teachers select
and organize the requirements, towards the common objectives,
across a common theme.
Type 2. Interdisciplinary integration, lecturers teach or
lecture around common themes with all related subjects and can
contribute more or less to common goals and accomplishments.
Type 3. Transdisciplinary Integration instructional practice is
organized around and based on the issues that students care about,
attached to the real context.
Type 4. Internal integration, when subjects are discrete; The
connected; The Shared model/ The Nested.
Type 5. Integration through learners (includes 2 models: The
immersed / meditated model, the networked model).
6
Through exploring theories and practices, we find that
Mathematics in our high school has potential opportunities to deploy
integration in the models of: Integration within the subject;
Interdisciplinary integration, Transdisciplinary Integration;
Integrated by and through learning (immersed / meditated).
Moreover, according to the author's point of view, Teaching
Integration in mathematics should be carried out slowly, gradually
over time, so that teachers can absorb and implement effectively.
1.2.2. Research on integrated process of building
Integrated Themes
Researching some researches in Vietnam and overseas
shows that:
+ Susan M. Drake offers an 8-step process of integration.
+ Xavier Roegiers also identifies some processes in different
approaches: content based Integration process (conducted in 6
phases); Integrated approach based on integration objectives
(conducted in 5 phases); ...
+ According to Gary and Jerri-Ann Jacobs, the design 4-step
process of designing Integrated Themes.
+ According to The California Center for College and
Career, there are 11 main steps when building process of integrated
themes.
+ After researching this matter, Do Huong Tra and Nguyen
Van Bien proposed the 7 step process of sciences integration themes.
...
Comments: Due to the many different approaches to
integration, there are also many processes for building
INTEGRATED THEMES. Through research and study, the author
finds that Gary's and Jerri-Ann Jacobs's approach and process of
building the community is closest to mathematics curriculum.
7
1.2.3. Study and organize integrated teaching in some
countries around the world
1.3. The process of constructing integrated themes in
mathematics
1.3.1. Integrative concepts, integrated lessons, integrated
curriculum, and integrated instruction
a) An integrated theme is a situation related to learning that
teachers and students can exploit to discover and gain knowledge,
apply knowledge, form and develop competencies
b) An integrative learning lesson is the smallest unit of
learning in which it is capable of forming knowledge, skills and
attitudes needed for learners to solve a particular part task or a whole
task, contributing to the establishment of profession competence for
learners.
c) Integrated lesson plan is a design of activities and
situations intended to be organized for learners during class time to
address learning tasks.
d) Integrated teaching aims to create students „competencies
to effectively solve practical situations based on the mobilization of
contents, knowledge and skills in many different fields.
1.3.2. The process of constructing and integrating thematic
structures in Vietnam and abroad
Researching some national and international researches
shows that there are different processes, such as:
+ Gary and Jerri-Ann Jacobs of the Group “High Tech High
Charter School” thinks there are 4 steps: Identify integration goals;
Identify Integrated Themes; Plan the implementation, clarify the task
map; Project evaluation.
+ The Matt Perry team proposed 11 steps as constructing
Integrated Themes.
8
+ In the teacher training materials, MoET proposed the 6-
step process of constructing Integrated Themes, Boets apply and
design in details.
+ Nguyen Van Bien [24] suggested 7 step process of
constructing Integrated Themes for Natural sciences.
....
Based on the results of the study and practices of Education
in the country, the author proposes the process of constructing and
structuring an Integrated Theme of Mathematics in the following
steps: (1) Define learning objectives (2) Suggest Integrated Themes
for subjects. (3) Expect activities - Mapping, plan implementation.
(4) Assessment of integrated units.
1.4. Preliminary status of research and development on
integrated teaching in Vietnam
By researching documents, the author found that: with some
little integrated appearing subjects, like Math, there is still potential
idea of integration. Although not explicitly stated about integration,
the requirements for integration are quite evident in educational goal
of mathematics. At present, with Mathematics, there are also some
integrated exams, Interdisciplinary integration, but mainly internal
integration, some articles incorporate some contents directedly
involve to Interdisciplinary in suitable conditions. Themes discussed
by teachers include: Math equations; Exponent and exponent;
Statistics in life;
In general, integration has not become unified point of
views, across all levels. The use of integrated perspective is mainly
in subjects in elementary school, documents are limited. The
acquisition of foreign experience on the implementation of integrated
perspective is still not complete and authentic in defining aims,
contents, methods and assessment of students‟ learning outcomes ...
9
CONCLUSIONS OF CHAPTER I
Based on theory and practice of teaching in our country, it is
possible to design Integrated Themes in Mathematics in direction of:
Internal mathematics integration; Interdisciplinary integration;
Transdisciplinary Integration.
Through studying some materials of domestic and foreign
experiences as the rationale of theory and practice, the author has
proposed the process of building and structuring Integrated Themes
in Mathematics in our country, the process includes 04 steps: Define
learning objectives; Suggest Integrated themes for subjects.
Expected activities - Mapping, plan implementation; Assessment of
integrated units.
CHAPTER 2
SOME MEASURES TO HELP TEACHER BUILD
INTEGRATED THEMES IN TEACHING MATHEMATICS
In this chapter, we focus on the following main contents.
2.1. Orientations to set out measures
We need to rely on the following guidelines
Orientation 1: As design some themes for integrating
mathematics, it is necessary to consult some other related disciplines
and teaching methodology of theirs, to ensure the feasibility.
Orientation 2: Appropriately pay attention to both types of
teacher‟s activities including: design integrated themes and teaching
methodology.
Orientation 3: designing process and teaching methodology
of Integrated Themes should be feasible and effective; possibly
tested through pedagogical experiments.
Orientation 4: Measures should be consistent with theory
and practice, ensuring the goals of teaching mathematics in high
10
school: consistent with the theory of mathematics teaching in high
school; In line with the teacher training and fostering process;
2.2. Some measures helping teachers build and teach
integrated themes
Based on theoretical and practical research, we propose
pedagogical measures to help teachers effectively implement the
design and teaching of integrated mathematics instruction as follows:
2.2.1. Measure 1: Prepare teacher training materials for
integration and integrated teaching.
2.2.1.1. The rationale of the measure
a) Philosophy rationale: To do well, it is essential to master
theories and basic knowledge of the subject.
b) Psychology rationale: Encouraging learning and
recognizing learners' endeavors, creating the confidence of the
learner is the basis for effective teaching.
2.2.1.2. The purpose of the measure: To help teachers deeply
understand integration, Integrated Themes and Integrated Teaching.
2.2.1.3. How to implement measures
a) Compile training teacher materials on Integrated Teaching
On the rationale of the content presented in Chapter 1 of the
thesis, we proceed to compile training materials in order to
disseminate and equip the general staff with theoretical and practical
bases for peace of mind, firmly believe in design and teach
integration.
b) Train teachers on designing the process of integrated
themes: Organizing form: Combine the form of teaching in classes,
discussions and the appropriate amount of time for the participants to
11
engage in the training (can refer to some topics that we have
designed and presented in hhis thesis).
2.2.2. Measure 2: Organize for teachers to experience in
designing and teaching integrated themes
2.2.2.1. The measure rationale
+ Base on the education principle of "Learning with
Practicing": To master a skill requiring a focused practice with a
certain amount of time.
+ Psychological rationale: The meaning of practical
experience, the meaning of Integrated Teaching.
+ Reality of fostering teachers: The situation of training and
fostering for teachers, especially at the provincial and district levels
are still limited.
2.2.2.2. The purpose of the measure
Through experiencing and designing the teaching of
Integrated Themes help teachers actively design and implement of
teaching a school.
2.2.2.3. How to implement measures
+) Renovate contents, training methods, professional training
for core staff of BOETs.
+) Instruct teachers to know how to design integrated themes
The building of Integrated Themes is carried out following
the process described in the previous chapter. In this section, the
author gives out more clearly the activities in the steps of the process
including: Identify problematic situations; Identify the standards of
knowledge, skills, attitudes, capacities, ... anticipate learning
activities; Develop integrated theme content; Identify teaching
12
facilities and equipment; Design process of the teaching of integrated
themes.
+) Instruct teachers to organize learning activities basing on
integrated theme. Teachers should pay attention to some contents:
active teaching techniques; How to transfer tasks to students; How to
organize students to report; How to evaluate results.
+) Instruct teachers integrated teaching.
Basically, the method and form of integrated teaching are not out of
orientation for renewing teaching method in high schools.
About the organizing process, integrated teaching includes
the following steps:
Step 1: Identify integrated lesson.
Step 2: Compile the integrated lesson plan, including the
main tasks: Identify the objectives of the lesson; Identify the contents
of the lessons; Identify teaching and learning activities of teachers
and students; Identify the teaching aids used in the lesson; Determine
the time for each part. About determining the time, it is essential to
pay attention to the teaching-learning time for each skill mentioned;
Experiences are drawn after implementing the lesson plan:
Preparation, implementation, testing, assessment of knowledge, skills
and attitudes that students need to comprehend.
Step 3: Carry out the integrated lesson
Step 4: Check, evaluate.
+) In the thesis we illustrate in detail the above through the
example of the Subject: surface area and volume of the object
Step 1. Determine learning objectives. The main product of
step 1 is the following section A:
13
A. Objectives. After finishing this subject, the learners: get
understood about the surface area and volume of the object; be able
to calculates (or estimates) the surface area and volume of an object;
from that they are able to calculates the ratio between the volume
and surface area of the object; Know how to create objects with the
smallest surface area, but have the largest volume; get understood
the benefits or disadvantages through the relationship between the
ratio of surface area and volume of an object in daily life; Get to
know that mathematics has practical applications, inter-discipline.
Step 2. Propose integrated theme and assign responsibilities
Determine the focus of integrated theme: Area and volume in
reality. The product of this section is Section B below:
B. The main content of the topic.
(a) Structure frame of contents; (b) Core questions for the
topic; (c) What students want to do; (d) The order of implementing
sections of the topic: Give out problematic situation; Knowledge
(formula) of calculating area; Calculate the area of the object without
knowing the formula; Knowledge (formula) of calculating volume;
Calculate the volume of the object without knowing the formula;
Calculate the S / V ratio (where S is the surface area, V is the volume
of the object); Apply ratio between surface area and volume in
practice, inter-discipline; comprehensive training.
Step 3. Expect activities, diagram, plan implementation.
Based on the objectives, the main product of this section could be:
(1) Rationale. (2) The knowledge (formula) of calculating area. (3)
Knowledge (formula) of calculating volume of objects. (4) Ratio
between surface area and volume. (5) Application f ratio between
surface area and volume in real life, inter-discipline, including
14
contents: packaging manufacture, Surface area and volume in
biology; Surface area and volume in physiology; Surface area and
volume in life; Surface area, volume in aviation; Surface area and
volume in chemistry – physics; Balloon.
Step 4: Evaluate integrated units.
2.2.3. Measure 3: Organize teacher to evaluate and self-
evaluate on design results and teach integrated themes.
2.2.3.1. The basis of the measure
- General reasoning on evaluation of student performance;
Method, assessment tools which contribute to promote the self-
reliant spirit, activeness and creativeness of learners.
- Psychological rationale: According to cognitive theories,
the purpose of teaching is to create opportunities for learners to
understand the real world. Therefore, to achieve learning objectives,
not only learning outcomes, but also learning process and thinking
process are important.
2.2.3.2. The purpose of the measure
By evaluating and self-evaluating design results, teaching
integrated theme in Mathematics helps teachers to check the
feasibility of the design process and the results of integrated theme
constructed, from which adjust and supplement the finishing
integrated theme that was built.
2.2.3.3. Method of implementing measure
- Help teachers, students comprehend the evaluation of
learning outcomes through integrated teaching.
In addition to evaluating learning outcomes as tradition,
(assess by score, test), it should be combined with process
assessment, mental assessment, participating attitude,
15
communication and collaboration skills, product evaluation, ...
follow the direction of evaluating performance ability of students.
Thus, in addition to the traditional assessment teachers also need to
combine different methods, such as: Observation, checklist, record,
...
It is possible to make a common table (or rubric), so that it
would easy to visualize the overall task, requirements that need to be
met. It is also possible to make a separate table (rubric), to clarify
each task, each aspect that require assessment: Knowledge
requirements; capacity requirement ... For example, as shown in the
following table:
Table 2.3: Rubric table showing the tasks, requirements to reach
Level
to reach Knowledge
Communicate
capacity ICT capacity ....
Level 1 Know .... Know how.... Innitially know
how to use .....
Level 2 Understand .... ......... .........
...... ......... .........
Level t Creative apply ... ......... .........
By the description above, we can quantify by the score for
each task performance, according to the specified learning content.
- Organize teachers to design evaluation forms
To assess the scientific, integrative, feasibility, and
effectiveness of the integrated themes proposed by groups, the design
of evaluation and self- evaluation forms must be designed. It is also
necessary to design evaluation forms on the interest of the learner, on
the teaching organization methodology; Combine teacher evaluation
and student learning outcomes.
16
- In the thesis, we illustrate in detail the above details
through: Teacher Feedback notes on integrated theme; Student
feedback notes on integrated theme lesson; Individual and group
evaluation forms.
CONCLUSIONS OF CHAPTER 2
In chapter 2, the author has proposed orientations and
measures to help teachers understand, build and be able to teach
integrated theme in mathematics in high school.
Measures proposed include: (1) Prepare training materials
for teacher on integration and integrated teaching; (2) organize
teacher to experience designing and carry out integrated teaching; (3)
Organize teachers to evaluate and self-evaluate the design results and
teach integrated themes.
These measures help teachers enhance their awareness of
integration, inter-discipline, have an appropriate understanding about
it in order not to diverge when approaching and conducting
construction of integrated theme as well as organization of integrated
theme.
Through experiential learning on design and teaching
integrated theme helps teachers understand and be active to design
and deploy to teach an integrated theme. This can be considered as
the central, core of the thesis. Moreover, this is the decisive stage of
quality of integrated theme.
Through evaluation and self-evaluation of the results of the
design and teaching, integrated themes help teacher test the
feasibility of the design process, integrated theme built, from which
to adjust and complete the integrated theme built.
17
CHAPTER 3
PEDAGOGICAL EXPERIMENT
In this chapter, we focus on the following main contents.
3.1. Purposes, requirements, tasks, organizational
principles and pedagogical experiment content
- The pedagogical experiment objectives: To initially test the
feasibility and effectiveness of proposed pedagogical measures.
- Pedagogical experiment content:
Session 1 (2 teacher training sessions). Session 2 (2 courses
teaching pedagogical experiment). The second experiment evaluation
is conducted in two forms: (1) Qualitative assessment: Teacher teach
and the group of teachers who observe give comments on the
feasibility and effectiveness of teaching integrated theme (using
questionnaire); Exploring the interest of students when studying
integrated theme, evaluation and self-evaluation of students, groups
of students ... (questionnaire). (2) Quantitative assessment: Based on
the results of the test and comparison between the experimental and
the control class.
3.2. Time, object, process, methods of evaluation of
pedagogical experiment results
- Time, pedagogical experiment subject:
Session 1. Training teachers is divided into 2 courses: the first (15-16
June 2015), 23 teachers; the second (22-23 / 6/2015), 83 teachers.
Session 2. Organize to teach experimental teaching: The first
(08-11 / 5/2016); the second: Experimental and control classes (May
15-18, 2016).
- Method to evaluate pedagogical experiment results: writing
examination; Q&A using teacher‟s questionnaire ; Survey
18
questionnaire for students; Class observation; Mathematical Statistics
method.
3.3. Pedagogical experiment content
3.3.1. Contents, results of pedagogical experiment – phase 1
- Pedagogical experiment content:
Session 1 (1/2 day): Gathering teachers; Training the
compiled contents; guide on further references materials of
integration.
Session 2 (1/2 day): Divide groups to discuss, study sample
lesson plan. On that basis, the training class unifies to synthesize and
complete the integrated theme.
Session 3 (1/2 day): Group discussion, new integrated theme
proposal. The groups proceed to discuss, each group continues to
divide into smaller ones (2-3 teachers/ 1 group) to study and discuss
with other subject teachers about new integrated theme.
Session 4 (1/2 day): Groups present; exchange sample lesson
plan, gained knowledge and complete new integrated theme.
- Pedagogical experiment results of the first stage
+) Qualitative
The training class atmosphere is exciting and active.
Trainees shows positive, active in exchanging and receiving training
knowledge. To evaluate the quality of the training (effectiveness of
measure 1), we conducted the survey on learners via the feedback
form (Appendix 7) and synthesized the results and found that the
majority of teachers attending the training have ticked good mark on
training contents (high ratio).
+) Quantitative
19
After 2 training sessions, the author and the group of
teachers in the city cluster have focused on discussing and
completing products: completing 01 sample integrated theme;
Proposing 01 new integrated theme: "The application of powers and
exponents in reality" (Appendix 2); Proposed integrated lesson plan:
"The sphere in spatial coordinates" (Appendix 3).
3.3.2. Content and results of experimental phase 2, the first
time
- Content of pedagogical experiment – phase 2, 1st time
Phase 1. Assigning, planning (1 period)
Forms: Teachers and students work together in class.
Activities: (1) Planning the implementation of the group; (2) Present
the group's work plan.
Phase 2: Groups on their own complete assigned tasks (2
periods, 1-2 cases: 1 lesson, 3 lessons: 1 lesson).
Stage 3: Report results (time: 1 period)
Activity (1) Groups report working result; (2) result evaluation.
- Result of the second phase, 1st time.
+) Qualitative
Collect the teacher‟s feedback form on the topic taught and
use the 8c form to conduct product reviews, individual and group co-
operation. Through synthesizing, analyzing, finding that: observing
teachers always have positive feedback on the feasibility of the topic;
pedagogical experiment class atmosphere is exciting and active.
Pedagogical experiment students are more active, more confident,
does not see subjects academically, and most students think that the
subject is important for some contents of other subjects, as well as
practical.
20
+) Quantitative
Comments: Through the examination, synthesis of results,
the author found that the class has a good, good score (7-10 points)
reached 50%. Some students are still confused when encountering
new mathematical form with LM factor, practical. Demonstration of
the implementation of statistical probability for students, has had a
certain impact on students when applying to solving problems with
practical factors.
3.3.3. Contents, results of pedagogical experiment phase 2,
second time
- Content of pedagogical experiment, phase 2 , 2nd
time.
Learned from the experimental results of the phase 2, the 1st time, the
author adjusts limitations of measures to ensure the feasibility of the
measures proposed.
- Pedagogical experiment results 2, 2nd
time
+) Qualitative
The teaching process compiled is appropriate to the teaching
reality; integrated theme has shown high feasibility, innovation in
teaching method, reasonable construction of integrated theme. The
majority of observing teachers have evaluated it brings back
creativity and effectiveness.
Classroom atmosphere of the experimental group was more exciting
and active than the control class.
Students in the experimental group are more visible in the ability to
mobilize knowledge to solve problems in reality, inter-discipline
faster, more appropriate. Activeness, group co-ordination of the
experimental class are clearly demonstrated through learning
activities.
21
+) Quantitative
Test 1. Evaluate the effectiveness of knowledge acquisition
in subject theory
Figure 3.2: Chart of Frequency of Score Test1 (phase 2, second time)
Evaluate of the average scores of the two groups:
Set assumption0H : The average scores for the acquisition of
subject theory of the two experimental and control groups after
experiment were similar;
1H is the average score of the acquisition of subject theory of
the experimental class is higher than that of the control group after
the experiment. We have:
The assumption is accepted. The average scores of the two groups
are similar.
Test 2. Evaluate the application of the acquired knowledge
of students to practice, inter-discipline, as a basis for assessing
capacity formed in the experimental classroom.
Table 3.5: Experimental-control group frequency distribution
ix 3 4 5 6 7 8 9 10 Total of students x 2S
Experimental (1n) 1 2 8 11 10 6 2 0 40 6,33 1,87
0,052 2
1 2
6,32 5,921,143 1,671
2,48 2,29
40 38
TN DC
TN DC
X XT t
S S
n n
22
Control (2n) 4 5 10 10 6 3 0 0 38 5,47 1,93
Table 3.6. Frequency distribution of experimental-control group
scores
ix 3 4 5 6 7 8 9 10 Total of students x
Experimental 2,5 5 20 27,5 25 15 5 0 40 6,33
Control 10 12,5 25 25 15 7,5 0 0 38 5,47
Assumption 0H : The average scores for the two groups were
similar; The argument1H is the average score of the experimental
class is higher than the control (level 0,05 ). We have:
Assumption0H is rejected. So the average score of the
experimental group was higher than that of the control group.
We test the variance of the experimental and control groups with the
assumption 0H : the difference between the variance of the
experimental and control groups was not significant.
Because of this, we have chosen accreditation standards:
Value to term in the distribution table corresponds to level
and with degrees of freedom 39; 37 is 1.75. We see 1,032 <1.75 or <:
Accept the hypothesis ie there is no difference between the variance
of the experimental class and the control class.
CONCLUSIONS OF CHAPTER 3
Through the pedagogical experiment, it initially showed that:
teachers get understood integration, integrated teaching; Initially
understand the process and be able to design integrated theme. Some
0,052 2
1 2
6,33 5,472,75 1,671
1,87 1,93
40 38
TN DC
TN DC
X XT t
S S
n n
2
2
1,931,032.
1,87
DC
TN
SF
S
23
topics that we assign to teacher of pedagogical experiment
(described in detail in the Appendix) are considered as the illustration
of the feasibility of the process and the proposed measures.
Through the lesson of teaching integrated theme, it is shown
that: Teachers can teach integrated theme in Mathematics.
Moreover, the training contents we have mentioned above
shows that it is useful, teachers can understand and initially build
integrated theme, inter-discipline in math.
However, to teach integrated theme, it is necessary to train
teachers about the understanding as well as the process of
constructing lessons, especially how to implement project-based
teaching. Training content on lesson organization, project-based
teaching we mentioned above is practical, teachers can understand
and step by step teach integrated theme, inter-discipline in Math.
The good thing is that students can understand and initially
study with integrated theme, inter-discipline in Math. Most are
interested in being involved, many see the practicality, or the
meaning of the knowledge they have learned.
CONCLUSIONS OF THESIS
The thesis author has focused on researching to propose
integrated form, the design process of integrated theme in
mathematics, mainly based on current curriculum. Through studying
the thesis topic, the author has achieved the following main
outcomes:
1) Study domestic and international experiences on integration
through some studies by Susan, Forgaty ... to clarify the integrated
forms in high school.
24
2) Base on the theoretical basis and reality of teaching in
Vietnam to suggest integrating forms in math: Integration within
Math subjects; Interdisciplinary integration cross-disciplinary
integration (create new topics, cross-disciplinary subjects as in
traditional way).
3) Propose a four-step process for designing an integrated
theme in Math. Provides the framing of the integrated theme in Math
with five major contents (not required but flexible).
4) Have implemented the above to build some illustrative
integrated themes in integrated teaching of Math in high school,
namely the examples and appendix in the full-text thesis.
5) Have compiled training content (material)for the teacher
who participate in pedagogical experiment. Through pedagogical
experiment, it is visible that this content is useful, teacher
understands and are able to deploy the idea of the thesis author.
6) Have organized two training courses for 106 teachers of
high schools in Bac Ninh. Have carried out pedagogical experiment
with 01 integrated theme in Han Thuyen high school, Bac Ninh and
initially achieved good results, it is recognized through pedagogical
experiment that: school teachers are approached the new teaching
method and trust, are pleased to apply this method into the
appropriate lesson; students are very interested, creative and
passionate exploring.
Pedagogical experiment results have initially demonstrated the
feasibility of the proposed measures.
This leads to a conclusion: Acceptable scientific hypothesis;
Research missions and research purposes have been completed.
