Report written by Ave Maria McIntosh and Loraine Fuller Mathematics and Statistics Division

1. Report written by Ave Maria McIntosh and Loraine Fuller Mathematics and Statistics Division University of Technology, Jamaica

2. Are we adequately preparing our children to survive in a quantitative world?

3. 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

4. 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

5. 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)

6. 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.

7. 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

8. 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.

9. CXC Grading Scheme 11 • The CSEC since 1998 has six 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.

10. CXC Grading Scheme 111 • The CaribbeanAdvanced Proficiency Examinations (CAPE) is offered for post-secondary candidates who require certification and advanced standing. • uses sevenoverall grades,  I, II, III, IV, V, VI, V11which indicate the candidates overall performance in the particular subject • while the profile grades, A, B, C, D, E, Fand Gare used to indicate strengths and/or weaknesses in the specific skills tested.

11. 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 Participating Territories

12. Map of the Caribbean Region

13. 1991-1997 CXC Mathematics Pass Rate Percentage by Country Source: CXC Examination Office

14. Trinidad & Tobago Trinidad & Tobago St Kitts & Nevis St Kitts & Nevis Turks & Caicos Turks & Caicos Students' statistics Students' statistics Students' statistics Students' statistics Montserrat Montserrat St Maarten St Maarten St Vincent St Vincent Country Country Country Country No. Pass No. Pass No. Pass % Pass No. Sat No. Sat No. Sat % Pass No. Pass % Pass No. Sat No. Pass No. Sat % Pass No. Sat No. Sat No. Sat % Pass % Pass No. Sat No. Pass % Pass % Pass No. Pass No. Pass No. Pass No. Pass % Pass No. Sat No. Sat % Pass % Pass No. Pass No. Sat No. Pass No. Sat % Pass No. Sat No. Sat No. Pass No. Sat % Pass % Pass No. Pass % Pass % Pass No. Pass No. Pass Jamaica Jamaica St Lucia St Lucia 25.81% 80.00% 80.00% 32.28% 41.85% 32.28% 28.41% 63.16% 44.21% 25.81% 63.16% 44.21% 28.41% 41.85% 31.08% 31.08% 12105 15036 12105 15036 4854 3439 3439 4854 154 256 368 579 133 256 579 133 154 368 15 12 12 31 84 74 23 23 84 74 31 15 8 8 Barbados Barbados % Pass No. Pass No. Sat % Pass No. Sat No. Pass No. Sat No. Sat No. Pass % Pass No. Sat No. Pass No. Pass No. Sat No. Pass No. Sat % Pass No. Sat % Pass No. Pass % Pass No. Pass % Pass % Pass No. Sat No. Pass % Pass No. Pass No. Sat % Pass % Pass % Pass No. Pass No. Pass No. Pass No. Sat % Pass No. Sat No. Sat No. Pass No. Pass No. Sat No. Sat % Pass No. Sat % Pass No. Pass % Pass Dominica Dominica Grenada Grenada Anguilla Anguilla Antigua Antigua Guyana Guyana Belize Belize B.V.I. B.V.I. 48.02% 50.62% 43.24% 33.44% 35.09% 19.15% 58.33% 33.44% 43.24% 19.15% 58.33% 48.02% 35.09% 50.62% 9.38% 9.38% 3122 3122 1448 1448 128 296 128 314 314 218 218 105 105 598 733 265 265 598 733 296 454 454 36 36 32 32 93 93 21 21 3 3 CXC Mathematics Passes 1991

15. CXC English A Passes 1991

16. Comparison between CXC Mathematics and English A passes for the Caribbean in 1991

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

18. Actual Number Sitting in Jamaica

19. Actual Number Passing in Jamaica

20. Percentage Passing in Jamaica

21. The University of Technology, Jamaica

22. Business Administration Pre Calculus Lecture

23. 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.

24. 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.

25. 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 PreCalculus Examination than those students with CXC Mathematics grades 2 or 1.

26. 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.

27. Comparison between Pre Calculus score and CXC Maths grade for BSc. in Computing and Information Technology group

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

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

30. 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.

31. 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

32. 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.

33. Cross –Tabulation Of Students’ Perception Of The Relevance of Pre Calculus To Their Studies And Pre Calculus Grade

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

35. Students' Liking of Mathematics Compared With Pre Calculus Grades

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

37. Results Of The Study Into Attitudes And Perceptions Of UTECHS’ Students Towards Pre Calculus The 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

38. 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

39. 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 poorestattempts • Implementing Mathematics diagnostic tests for students entering the university

40. UTECHS’ Strategies To Address Poor Performances In Mathematics 111 • Long Term • Implementinga mobile seminar series with high school mathematics teachers in rural areas. • Implementing Mathematics computer diagnostic tests for all students entering the universitywith 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

41. UTECHS’ Strategies To Address Poor Performances In Mathematics 1V • Long Term • Launching 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

42. 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)

43. 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

44. 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

45. Eltom, 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 ForwardRetrieved on September 3, 2005 from website http://www.moec.gov.jm/policies/whitepaper.htm References