Transcript Are we adequately preparing our children to survive in a

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 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.
CXC Grading Scheme 111
• The Caribbean Advanced Proficiency
Examinations (CAPE) is offered for postsecondary 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
1991-1997 CXC Mathematics Pass
Rate Percentage by Country
Year
Anguilla
Antigua
Barbados
Belize
B.V.I.
Cayman
Island
Dominica
Grenada
Guyana
Jamaica
Montserrat
Netherland
Antiles
St kitts &
Nevis
St Lucia
St Vincent
Trinidad &
Tobago
Turks &
Caicos
1991
1992
9.38
35.09
50.62
48.02
58.33
23.26
31.36
48.02
33.17
58.33
1993
1994
1995
1996
1997
Average
23.75
24.49
31.9
51.77
35.19
69.57
25
35.53
49.87
36.53
78.95
25
34.66
48.37
36
70
9.09
28.67
49.03
36.1
46.67
50
30.1
40.03
31.93
47.17
100
31.61
28.31
15.62
23.6
40.09
72.73
31.42
33.99
19.2
27.99
31.94
88.3
36.94
39.12
16.67
24.24
50
90
36.02
20.96
13.49
20.41
19.35
87.76
63.64
75.86
29.31
68.97
32.47
48.24
36.71
61.29
43.24
33.44
19.15
28.41
31.08
32.23
41.69
18.38
27.82
89.8
31.84
40.44
17.23
24.95
57.24
80
88.24
76.76
63.16
44.21
41.85
45.89
41.98
35.87
53.81
57.21
50.39
46.55
40.25
30.81
37.43
41.32
39.39
41.21
35.47
39.1
30.88
28.32
22.81
45.56
32.28
30.67
42.24
31.71
34.59
35.09
29.71
33.76
25.81
27.27
47.5
21.82
25.93
19.12
17.86
26.47
Source: CXC Examination Office
34.76
33.99
17.11
25.35
45.64
41.25
37.17
CXC Mathematics Passes 1991
Country
Anguilla
Antigua
Barbados
Belize
B.V.I.
Dominica
Grenada
Guyana
Students' Statistics
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
% Pass
No. Sat
No. Pass
32
3
9.38%
265
93
35.09%
1448
733
50.62%
454
218
48.02%
36
21
58.33%
296
128
43.24%
314
105
33.44%
3122
598
% Pass
19.15%
Country
Jamaica
Montserrat
S t Kitts &
Nevis
S t Lucia
S t Maarten
S t Vincent
Trinidad &
Tobago
Turks &
Caicos
Students' Statistics
No. S at
12105
No. Pass
3439
% Pass
28.41%
No. S at
74
No. Pass
23
% Pass
31.08%
No. S at
133
No. Pass
84
% Pass
63.16%
No. S at
579
No. Pass
256
% Pass
44.21%
No. S at
15
No. Pass
12
% Pass
80.00%
No. S at
368
No. Pass
154
% Pass
41.85%
No. S at
15036
No. Pass
4854
% Pass
32.28%
No. S at
31
No. Pass
8
% Pass
25.81%
CXC English A Passes 1991
Country
Anguilla
Antigua
Barbados
Belize
B.V.I .
Dominica
Grenada
Guyana
Students' Statistics Country
Students' Statistics
No. S at
42
No. S at
13884
No. Pass
5
No. Pass
3634
% Pass
11.90%
Jamaica
% Pass
26.17%
No. S at
360
No. S at
100
No. Pass
149
No. Pass
41
% Pass
41.39% Montserrat % Pass
41.00%
No. S at
2332
No. S at
316
No. Pass
1001 S t Kitts & No. Pass
87
% Pass
42.92%
Nevis
% Pass
27.53%
No. S at
918
No. S at
797
No. Pass
275
No. Pass
304
% Pass
29.96% S t Lucia
% Pass
38.14%
No. S at
41
No. S at
27
No. Pass
26
No. Pass
16
% Pass
63.41% S t Maarten % Pass
59.26%
No. S at
429
No. S at
498
No. Pass
135
No. Pass
149
% Pass
31.47% S t Vincent % Pass
29.92%
No. S at
830
No. S at
17581
No. Pass
173 Trinidad & No. Pass
4966
% Pass
20.84%
Tobago
% Pass
28.25%
No. S at
3910
No. S at
52
No. Pass
331
Turks &
No. Pass
12
% Pass
8.47%
Caicos
% Pass
23.08%
Comparison between CXC
Mathematics and English A passes
for the Caribbean in 1991
Students’
Statistics
Mathematics
Number who sat 34, 308
English A
(English
Language)
42,117
Number who
passed
10, 729
11, 304
% Pass
31.27
26.84
Performance of Jamaican
Secondary School Students in
CXC Mathematics 1999-2005
Years
2001 2002
Students' Statistics 1999 2000
2003 2004 2005
Number of students
who sat examination 10,467 15,231 12,268 17,124 16,983 15,489 17,232
Number 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
Source CXC Data base 1999 - 2001. Policy Analysis, Research and MIS Unit, Ministry of
Education Jamaica 2002 - 2005
Actual Number Sitting in
Jamaica
Num ber of students w ho sat CXC Maths exam ination in Jam aica
20,000
18,000
Number of students
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
1998
1999
2000
2001
2002
Year
2003
2004
2005
2006
Actual Number Passing in
Jamaica
CXC Maths Passes in Jam aica 1999 - 2005
20,000
18,000
Number of students
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
1998
1999
2000
2001
2002
Year
2003
2004
2005
2006
Percentage Passing in Jamaica
% Pass in CXC Maths 1999-2005
45
40
% of students passing
35
30
25
20
15
10
5
0
1998
1999
2000
2001
2002
Year
2003
2004
2005
2006
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
100
80
81
60
PR C AL G IT
40
20
5
69
0
N=
BSITCXCG
15
85
46
1
2
3
Comparison Between Pre Calculus Score
and CXC Maths Grade for BSc. In Medical
Technology Group
100
90
80
70
PR C ALG M D
60
50
40
30
N =
MEDCXCGR
4
9
8
1
2
3
Comparison between Pre Calculus scores below
50% and CXC Maths grades for all groups
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
Percentage of respondents
Pre Calculus Final
Grade
A
B
C
D
U
Total
Yes
28
42
24
2.6
3.4
100
No
10.4
36.2
31
10.4
12
100
Not Sure
25
35
33
3.5
3.5
100
Cross –Tabulation Of Students’ Liking Of
Mathematics And Their Pre Calculus Grade
Pre Calculus Final Percentage of respondents
Grade
Yes
No
A
33
12
B
42
33
C
20
37
D
3
7
U
2
11
Total
100
100
Students' Liking of Mathematics
Compared With Pre Calculus
Grades
45
40
35
Percentage of
respondents
Yes
% of stud.
30
25
Percentage of
respondents No
20
15
10
5
0
A
B
C
D
Pre Calculus Grades
U
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
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%
3 to less
than 5 More than
hours
5 hours
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
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 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
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
References
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 Forward Retrieved on September 3, 2005 from website
http://www.moec.gov.jm/policies/whitepaper.htm