Report written by

Ave Maria McIntosh

and

Loraine Fuller

Mathematics and Statistics Division

University of Technology, Jamaica

Are we adequately preparing our

children to survive in a quantitative

world?

Mathematics Importance For Survival

Gal (2000) speaks of adult numeracy as a growing area in many countries which has resulted in

• Empowerment

• Effective functioning

• Economic status and well being of citizen

Importance of Mathematics

• Interdisciplinary• Helps to make rational decision• Marjoram (1973) states that it gives an

intuitive grasp of economic social and political principles

• Eltom (1978) alludes that there is a shortage of trained people to work systematically in dealing with concrete problems

Instruments to measure survival

• Examination involving Mathematics at the end of primary school. Grade Six Achievement Test (GSAT)

• Examinations involving Mathematics at the end of secondary school. Caribbean Secondary Examination Certificate (CSEC) or Caribbean Examination Council Examination (CXC)

The Caribbean Examination Council(CXC)

Who are they?• Established in 1972 under the agreement by the

participating governments in the area.• Conduct examinations as it may think appropriate.• Award certificate and diplomas on the results of

any such examination.• Empowered to regulate the conduct of any such

examination.• Prescribe the qualification requirements of

candidate.

CXC Council Members• The Vice Chancellor of the University of the

West Indies• The Vice Chancellor of the University of

Guyana• Three representatives from the University of the

West Indies appointed by the Vice Chancellor• Representatives from the participating

government in the region• One representative of the teaching profession

appointed by each National Committee

CXC Grading Scheme 1

• Up to 1997 CSEC results were published on a five – point grading scheme system with grades 1 and 11 being accepted as entry into most tertiary institutions.

• Since 1998 CSEC has instituted a six-point grading system with grades 1, 11 and 111 now being accepted.

CXC Grading Scheme 11

• The CSEC since 1998 hassix overall grades,  I, II, III, IV, V, VI  which indicate the candidates overall performance in the particular subject

while the profile grades, A, B, C, D, E, F are used to indicate strengths and/or weaknesses in the specific skills tested.

 

CXC Grading Scheme 111• The Caribbean Advanced Proficiency Examinations

(CAPE) is offered for post-secondary candidates who require certification and advanced standing.                      

• uses seven overall grades,  I, II, III, IV, V, VI,V11  which indicate the candidates overall performance in the particular subject

• while the profile grades, A, B, C, D, E, F and G are used to indicate strengths and/or weaknesses in the specific skills tested.

 

Participating Territories• Anguilla• Antigua• Barbuda• Barbados • Belize• British Virgin Island• Cayman Islands• Dominica• Grenada

• Guyana• Jamaica• Montserrat• St. Kitts and Nevis• St. Lucia• St. Vincent and the

Grenadines• Trinidad and Tobago• Turks and Caicos

Islands

Map of the Caribbean Region

Year 1991 1992 1993 1994 1995 1996 1997 AverageAnguilla 9.38 23.26 24.49 25 25 9.09 50 23.75

Antigua 35.09 31.36 31.9 35.53 34.66 28.67 30.1 32.47

Barbados 50.62 48.02 51.77 49.87 48.37 49.03 40.03 48.24

Belize 48.02 33.17 35.19 36.53 36 36.1 31.93 36.71

B.V.I. 58.33 58.33 69.57 78.95 70 46.67 47.17 61.29

Cayman Island          100 72.73 88.3 90 87.76

Dominica 43.24 32.23 31.84 31.61 31.42 36.94 36.02 34.76

Grenada 33.44 41.69 40.44 28.31 33.99 39.12 20.96 33.99

Guyana 19.15 18.38 17.23 15.62 19.2 16.67 13.49 17.11

Jamaica 28.41 27.82 24.95 23.6 27.99 24.24 20.41 25.35

Montserrat 31.08 89.8 57.24 40.09 31.94 50 19.35 45.64

Netherland Antiles 80 88.24 76.76    63.64 75.86 29.31 68.97

St kitts & Nevis 63.16 45.89 53.81 46.55 37.43 41.21 30.88 45.56

St Lucia 44.21 41.98 57.21 40.25 41.32 35.47 28.32 41.25

St Vincent 41.85 35.87 50.39 30.81 39.39 39.1 22.81 37.17

Trinidad & Tobago 32.28 30.67 42.24 31.71 34.59 35.09 29.71 33.76

Turks & Caicos 25.81 27.27 47.5 21.82 25.93 19.12 17.86 26.47

Source: CXC Examination Office

1991-1997 CXC Mathematics Pass Rate Percentage by Country

CountryStudents' statisticsCountryStudents' statisticsAnguillaNo. Sat 32Jamaic

aNo. Sat 12105No. Pass3No. Pass3439% Pass 9.38%% Pass 28.41

%AntiguaNo. Sat 265MontserratNo. Sat 74No. Pass93No. Pass23% Pass 35.09%% Pass 31.08

%BarbadosNo. Sat 1448St Kitts &

NevisNo. Sat 133No. Pass733No. Pass84% Pass 50.62%% Pass 63.16

%BelizeNo. Sat 454St LuciaNo. Sat 579No. Pass218No. Pass256% Pass 48.02%% Pass 44.21

%B.V.I.No. Sat 36St MaartenNo. Sat 15No. Pass21No. Pass12% Pass 58.33%% Pass 80.00

%DominicaNo. Sat 296St VincentNo. Sat 368No. Pass128No. Pass154% Pass 43.24%% Pass 41.85

%GrenadaNo. Sat 314Trinidad &

TobagoNo. Sat 15036No. Pass105No. Pass4854% Pass 33.44%% Pass 32.28

%GuyanaNo. Sat 3122Turks & CaicosNo. Sat 31No. Pass598No. Pass8% Pass 19.15%% Pass

25.81%CountryStudents' statisticsCountryStudents' statisticsAnguillaNo. Sat 32

JamaicaNo. Sat 12105No. Pass3No. Pass3439% Pass 9.38%% Pass 28.41

%AntiguaNo. Sat 265MontserratNo. Sat 74No. Pass93No. Pass23% Pass 35.09%% Pass 31.08

%BarbadosNo. Sat 1448St Kitts &

NevisNo. Sat 133No. Pass733No. Pass84% Pass 50.62%% Pass 63.16

%BelizeNo. Sat 454St LuciaNo. Sat 579No. Pass218No. Pass256% Pass 48.02%% Pass 44.21

%B.V.I.No. Sat 36St MaartenNo. Sat 15No. Pass21No. Pass12% Pass 58.33%% Pass 80.00

%DominicaNo. Sat 296St VincentNo. Sat 368No. Pass128No. Pass154% Pass 43.24%% Pass 41.85

%GrenadaNo. Sat 314Trinidad &

TobagoNo. Sat 15036No. Pass105No. Pass4854% Pass 33.44%% Pass 32.28

%GuyanaNo. Sat 3122Turks & CaicosNo. Sat 31No. Pass598No. Pass8% Pass 19.15%% Pass

25.81%

CXC Mathematics Passes 1991No. Sat 32 No. Sat 12105No. Pass 3 No. Pass 3439% Pass 9.38% % Pass 28.41%No. Sat 265 No. Sat 74No. Pass 93 No. Pass 23% Pass 35.09% % Pass 31.08%No. Sat 1448 No. Sat 133No. Pass 733 No. Pass 84% Pass 50.62% % Pass 63.16%No. Sat 454 No. Sat 579No. Pass 218 No. Pass 256% Pass 48.02% % Pass 44.21%No. Sat 36 No. Sat 15No. Pass 21 No. Pass 12% Pass 58.33% % Pass 80.00%No. Sat 296 No. Sat 368No. Pass 128 No. Pass 154% Pass 43.24% % Pass 41.85%No. Sat 314 No. Sat 15036No. Pass 105 No. Pass 4854% Pass 33.44% % Pass 32.28%No. Sat 3122 No. Sat 31No. Pass 598 No. Pass 8% Pass 19.15% % Pass 25.81%

Anguilla

Country

St Maarten

St Vincent

Trinidad & Tobago

Turks & Caicos

Jamaica

Montserrat

St Kitts & Nevis

St Lucia

B.V.I.

Dominica

Grenada

Guyana

Antigua

Barbados

Belize

Students' StatisticsCountry Students' Statistics

No. Sat 42 No. Sat 13884No. Pass 5 No. Pass 3634% Pass 11.90% % Pass 26.17%No. Sat 360 No. Sat 100No. Pass 149 No. Pass 41% Pass 41.39% % Pass 41.00%No. Sat 2332 No. Sat 316No. Pass 1001 No. Pass 87% Pass 42.92% % Pass 27.53%No. Sat 918 No. Sat 797No. Pass 275 No. Pass 304% Pass 29.96% % Pass 38.14%No. Sat 41 No. Sat 27No. Pass 26 No. Pass 16% Pass 63.41% % Pass 59.26%No. Sat 429 No. Sat 498No. Pass 135 No. Pass 149% Pass 31.47% % Pass 29.92%No. Sat 830 No. Sat 17581No. Pass 173 No. Pass 4966% Pass 20.84% % Pass 28.25%No. Sat 3910 No. Sat 52No. Pass 331 No. Pass 12% Pass 8.47% % Pass 23.08%

Country Students' Statistics Country Students' Statistics

Anguilla Jamaica

Antigua Montserrat

BarbadosSt Kitts &

Nevis

Belize St Lucia

B.V.I. St Maarten

Dominica St Vincent

GrenadaTrinidad &

Tobago

GuyanaTurks & Caicos

CXC English A Passes 1991

Comparison between CXC Mathematics and English A passes

for the Caribbean in 1991Students’

Statistics

Mathematics English A

(English Language)

Number who sat 34, 308 42,117

Number who passed

10, 729 11, 304

% Pass 31.27 26.84

1999 2000 2001 2002 2003 2004 2005Number of students who sat examination 10,467 15,231 12,268 17,124 16,983 15,489 17,232Number of students Grade 1+11+111 4,305 6,022 5,014 6,165 6,114 3,640 6,036% Pass 41.13 39.54 40.97 36 36 23.5 35.03

YearsStudents' Statistics

Source CXC Data base 1999 - 2001. Policy Analysis, Research and MIS Unit, Ministry of Education Jamaica 2002 - 2005

Performance of Jamaican Secondary School Students in CXC Mathematics 1999-2005

Number of students who sat CXC Maths examination in Jamaica

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

Nu

mb

er

of

stu

de

nts

Actual Number Sitting in Jamaica

CXC Maths Passes in Jamaica 1999 - 2005

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

Nu

mb

er

of

stu

de

nts

Actual Number Passing in Jamaica

% Pass in CXC Maths 1999-2005

0

5

10

15

20

25

30

35

40

45

1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

% o

f s

tud

en

ts p

as

sin

g

Percentage Passing in Jamaica

The University of Technology, Jamaica

Business Administration Pre Calculus Lecture

About Pre Calculus • A first year course of four credit hours (60 hours)

designed for most first year students enrolled in a degree programme at the university.

• The pre-requisite for this course is a passing grade in CXC, GCE O Mathematics or their equivalence.

• The final score for Pre-Calculus comprises a course work component weighted 50% and a 2hr final examination weighted 50%.

• A student is deemed to have passed if he or she attained a final minimum score of 50 % in the combined coursework and final examination grade.

Pre Calculus Contents• The syllabus revisits some of the topics

taught in CXC Mathematics and introduces some new areas at post CXC level.

• Some of these topics included on the syllabus are Set Theory, Relations and Functions, Indices and Logarithms, Series and Sequences, Remainder and Factor Theorems, Graphs and Matrices.

Purpose of study on Pre Calculus Performance 2001

• To determine whether there is a link between the Pre-Calculus grade and the CXC Mathematics grade the student entered the University with.

• To establish whether or not those students who entered with a CXC Mathematics Grade 3 pass are more prone to fail the Pre Calculus Examination than those students with CXC Mathematics grades 2 or 1.

Results of study on Pre Calculus Performance 2001

• Distinct patterns of relationships were observed for some science and engineering groups.

• Correlation coefficient obtained for the overall university picture was 0.369 and was significant at 0.05 level.

Comparison between Pre Calculus score and CXC Maths grade for BSc. in Computing

and Information Technology group

468515N =

BSITCXCG

321

PR

CA

LG

IT

100

80

60

40

20

0

81

5

69

Comparison Between Pre Calculus Score and CXC Maths Grade for BSc. In Medical

Technology Group

894N =

MEDCXCGR

321

PR

CA

LG

MD

100

90

80

70

60

50

40

30

Comparison between Pre Calculus scores below 50% and CXC Maths grades for all groups

ALLCXCGR

321Missing

60

50

40

30

20

10

Objectives For The Study Into Attitudes And Perceptions Of UTECHS’ Students towards

Pre Calculus 1• To determine the attitudes toward Pre Calculus of first

year degree students.• To determine if there is a relationship between

students’ attitude towards Pre Calculus and their performance in the subject.

• To establish if there is a difference in performance between students who see the relevance to their specialization and those who do not.

• To determine if parents’ or siblings’ attitude towards Mathematics impact on students’ attitude towards Pre Calculus and Mathematics in general.

Objectives For The Study Into Attitudes And Perceptions Of UTECHS’ Students Towards

Pre Calculus 11• To determine if the attitude of mature students (those

out of the school system for more than 10 years prior to doing the degree) differs from that of non-mature students (those who left the school system less than 10 years before)

• To determine if the performance of mature students differs from that of non-mature students

Instruments Used In The Study On Attitudes And Perceptions Of UTECHS’ Students

Towards Pre Calculus

Questionnaire consisting of 23 items covering

• 9 different aspects of attitude and perception to Pre Calculus measured on a five point Leikert scale.

• 4 aspects of influence factors which are age, gender, faculty and CXC Mathematics grade.

Cross –Tabulation Of Students’ Perception Of The Relevance of Pre Calculus To Their

Studies And Pre Calculus Grade

Yes No Not SureA 28 10.4 25B 42 36.2 35C 24 31 33D 2.6 10.4 3.5U 3.4 12 3.5

Total 100 100 100

Percentage of respondentsPre Calculus Final

Grade

Cross –Tabulation Of Students’ Liking Of Mathematics And Their Pre Calculus Grade

Yes NoA 33 12B 42 33C 20 37D 3 7U 2 11

Total 100 100

Pre Calculus Final Grade

Percentage of respondents

Students' Liking of Mathematics Compared With Pre Calculus

Grades

0

5

10

15

20

25

30

35

40

45

A B C D U

Pre Calculus Grades

% o

f stu

d.

Percentage ofrespondentsYes

Percentage ofrespondents No

Cross –Tabulation Of The Time Spent Preparing For Pre Calculus And CXC/O Level

Mathematics Grade

CXC/GCE 'O' Level Grades

Less than 1 hour

1 to less than 3 hours

3 to less than 5 hours

More than 5 hours

1(A) 25.70% 64.10% 5.10% 5.10%

2(B) 24.50% 57.70% 12.80% 5%

3(C) 19.30% 58% 13.40% 9.30%

4(D) 0% 50% 33.30% 16.70%

Results Of The Study Into Attitudes And Perceptions Of UTECHS’ Students

Towards Pre CalculusThe findings revealed a positive relation between students’ attitude as measured:• Extent of liking Pre Calculus; and the performance in

Pre Calculus• Self rating of competence and performance in Pre

Calculus• Perception of relevance of the subject and

performance in Pre calculus• The willingness to attempt tutorial questions before

tutorial sessions and performance in Pre Calculus

UTECHS’ Strategies To Address Poor Performances In Mathematics 1

Short Term•Extend the number of tutorial hours per week from one to two for all Pre Calculus groups

•Lecturers are required to provide two hours per week for students’ consultation.

•Developing student- friendly worksheets on each topic to provide practice opportunities

UTECHS’ Strategies To Address Poor Performances In Mathematics 11

Short Term•Implementing a seminar series at UTECH with high school mathematics teachers concentrating on topics

identified by CXC and teachers as those topics with poorest attempts

•Implementing Mathematics diagnostic tests for students entering the university

UTECHS’ Strategies To Address Poor Performances In Mathematics 111

Long Term•Implementing a mobile seminar series with high school mathematics teachers in rural areas.

•Implementing Mathematics computer diagnostic tests for all students entering the university with CXC grades 11 and 111 as well as for mature students.

•Establishing a developmental mathematics course for students with low scores on the diagnostic test

UTECHS’ Strategies To Address Poor Performances In Mathematics 1V

Long TermLaunching a Mathematics and Statistics learning resource centre which will have•Dedicated rooms for individual consultations and small group teaching•A range of complementary resource material to to be developed in house or purchased. e.g.. videos, computer software packages, workbooks•Web based support which includes exercises to enable students to become competent in areas of weakness•Adequate lecturer support for structured consultations•Carefully selected student proctors to provide peer assistance •Technical support staff

Government’s Strategies Through The Ministry Of Education, Youth And Culture To Address

Problems 1•Increased budgetary allocation since 1996 to Early Childhood and Primary education institutes in order to foster sound education for all students

•Ensuring that computers and computer software as well as internet connections are available to all schools

•Decreasing student-teacher ratios in all schools on a gradual basis. For primary schools this was targeted to be 1:35 by the year 2003 and 1:30 for grades 1 and 2 by the year 2005. (Ministry of Education, 2001)

Government’s Strategies Through The Ministry Of Education, Youth And Culture To Address

Problems 11•Implementing an integrated curriculum in the primary schools

•Assisting with the payment of fees for the core subjects of Mathematics, English Language and Information Technology for CXC examinations at the high school levels.

•Improving infrastructure in all schools

•Improving on the training of teachers in the basic schools

Summary

• Based on the CXC passes over the years we are not adequately preparing our children to survive in a quantitative world.

• There is a weak positive correlation between CXC Mathematics grades and Pre Calculus grades of students at UTECH

• There is a weak positive correlation between students’ attitude and performance in Pre Calculus

• Measures are being put in place both at the University and national levels to attempt to solve the problem

• Some of the problems are deep-seated and require consistent interventions

ReferencesEltom, M. E. A. (1979). Proceedings of the international Conference held in Khartoum March 6-9, 1978 Developing Mathematics in Third World Countries. New York: North –Holland Publishing Company Amsterdam

Gal, I. (2000). Adult Numeracy Development , Theory Research, Practice. (1 st ed.). Cresskill, NJ: Hampton Press, Inc.

Holt, M., & Marjoram, D. E. T. (1973). Mathematics in a changing world. London: Heinemann Educational Books.

Examinations. Retrieved on July 21, 2005 from Caribbean Examinations Council website http://www.cxc.org/

Ministry of Education,Youth and Culture-Jamaica 2001 White Paper The Way Forward Retrieved on September 3, 2005 from website http://www.moec.gov.jm/policies/whitepaper.htm