The CXC mathematics examination: A caribbean … ERNEST THE CXC MATHEMATICS EXAMINATION: A CARIBBEAN INNOVATION IN ASSESSMENT A B S T R A C T. In the last decade a new examination

PAUL E R N E S T

T H E C X C M A T H E M A T I C S E X A M I N A T I O N :

A C A R I B B E A N I N N O V A T I O N I N A S S E S S M E N T

A B S T R A C T. In the last decade a new examination system (CXC)has been developed in the Caribbean. This includes mathematics examinations which incorporate three major innovatory features. These are as follows: Increased information on candidates' performance. A high degree of consultation and social concern in the development and implementation of the syllabuses. The syllabus conceived in a broader sense as a curriculum.

1. B A C K G R O U N D : THE CXC E X A M I N A T I O N S

In 1972 the Caribbean Examinations Council (CXC)was established under an

agreement between the governments of fifteen English speaking Caribbean

territories. The Council was given a mandate to develop an exmination system

to replace the overseas examinations in use at the end of five years of

secondary schooling. The most common of these overseas examinations in

use was the Cambridge Board Overseas General Certificate of Education, at

Ordinary Level. In developing the new examination system the council had

four major goals. The new examinations were to:

(1) take the place tradit ionally occupied by GCE 'O' level examinations

and maintain their academic standards;

(2) cater for an increased range of abilities and career intentions;

(3) be based on new syllabuses developed to meet the needs of the region;

and

(4) provide an increased amount of information on the performance of

candidates.

In 1973 the Council established subject panels to develop syllabuses in both

academic and technical or vocational areas. The implementation of the

Council 's programme resulted in the setting of the first CXC examinations in

1979. To a large extent the Council 's four major goals were attained, as the

following indicates:

(1) CXC commissioned a study of the 1979 examination results by the

British consultant Tom Christie. He reported that the performance correlations

o f candidates sitting both the GCE and CXC examination were close in English,

Mathematics and History. However indications were that candidates found

CXC Geography. much easier than GCE. Steps were taken to correct this

discrepancy, and the study repeated for subsequent years (CXC, 1981 a).

(2) In each subject area two syllabuses were developed catering jo int ly

Educational Studies in Mathematics 15 (1984) 397-412. 0013-1954/84/0154-0397501.60 �9 1984 by l). Reidel Publishing Company.

398 PAUL E R N E S T

to the top 40% of the secondary school population. This represents a con- siderable increase in intended range of ability over the GCE examination,

which caters to the top 15% to 20%. The two syllabuses in a given subject area are the General Proficiency syllabus which caters to those students wishing

to pursue the study of the subject, and the Basic Proficiency Syllabus for the remainder of the top 40%.

(3) To ensure that the new examinations reflected local (Caribbean) needs

the subject panels were made up of six or more members drawn from various English speaking Caribbean territories, at least three of whom were normally practising teachers. In addition, the subject panels actively sought and tried to

accommodate the opinions of interested parties in constructing their subject

syllabuses. (4) CXC examination candidates are assessed in two ways by the examin-

ation. First, there is the grading of overall performance on a five point scale.

Second, the cognitive skills and abilities of candidates are assessed, resulting in two, three or four profile grades, according to the subject.

Further general features of the CXC examinations are currently as follows.

Each subject examination is made up of up to three parts:

Paper 1, an objective test of sixty multiple choice items of one and one half hours duration.

Paper 2: an essay and short answer paper of two or two and a quarter hours

duration. Part 3: a school based assessment of a project or of practical skills. In some

subjects, for example mathematics, this third part is not currently used. Many of the general features of the CXC examination are innovatory,

for example "grass roots" involvement in the development of the syllabuses, the syllabus as a more general curriculum and the profiling of student abilities on the examination certificates. These innovatory features are considred in detail for the CXC mathematics examinations.

2. I N N O V A T I O N S IN THE CXC M A T H E M A T I C S E X A M I N A T I O N

Some of the general innovatory features of the CXC examinations are particularly of interest in the realm of mathematics assessment. Three such innovations will be considered in detail. These are: (2.1) Innovations in the provision

of information about mathematics candidates' examination performance. (2.2) The innovatory breadth of consultation and concern with social needs in the development of the syllabus. (2.3) The innovatory conception and implementation of the mathematics syllabus as a curiculum. Before turning to the examination of these features in greater depth it is worth considering

CARIBBEAN INNOVATION IN ASSESSMENT 399

the sense in which they are innovatory. Features of the CXC examination

system are innovatory in the local context wherever they represent new practices in the Caribbean. Innovation in this restricted sense is largely determined with reference to the previously established practices of the Overseas GCE

examinations. Some of the features of the CXC examination system are innovatory in a broader international context, if not always in conception at least in implementation. An example is provided by the increased information

on candidate performance in the graded profiles of cognitive abilities. A similar proposal is contained in the British N and F examination proposals.

Irrespective of the fact that the CXC proposals antedate the N and F proposals, the CXC profiling of abilities is innovatory on the international scene in its

implementation.

We turn now to a more detailed consideration of the three innovatory features of the CXC examination in mathematics.

2.1. Innovations in the Provision of Information on Mathematics Candidates' Performance.

The medium for the communication of information on a candidate's per-

formance in mathematics (and in other subjects) in the CXC Examination

is the CXC Secondary Education Certificate. This bears the entry results in

mathematics in the following three dimensions and order: Proficiency: Grade: Profile.

The proficiency specified is either Basic (meaning the candidate sat the

Basic Proficiency examination in mathemtics) or General (denoting the General

Proficiency examination). The grade indicates the overall grade attained by

the candidate at whatever proficiency level examination he or she sat in mathematics. The grades awarded are from the five point scale: I, II, III, IV, V.

The profile assesses performance in each of the three abilities entitled: Computation, Comprehension and Reasoning. The profile grades are drawn

from a four point scale: A, B, C and N/A. An example of the headings and mathematics results as they might appear

on a CXC Secondary Education Certificate is shown in Table I.

This example is taken from CXC (1977a) which also gives the following official interpretation of terms:

Basic Proficiency connotes subject activity designed to complete a secondary school course in the specific subject.

General Proficiency connotes subject activity designed to provide a foundation for further studies in the specific subject area beyond the fifth year of secondary schooling.


TABLE I Example of entry on a CXC Secondary Education Certificate

Subject Proficiency Grade Profile

Mathematics General V Computation: (C), Comprehension: (N/A), Reasoning: (N/A).

Overall Grades: Grade I - Candidate has a comprehensive working knowledge of the

syllabus.

Grade II - candidate has a working knowledge of most aspects of the

syllabus.

Grade III - candidates has a working knowledge of some aspects of the

syllabus.

Grade IV - candidate has a limited knowledge of a few aspects of the

syllabus.

Grade V - candidate has not provided sufficient evidence on which to

base a judgement.

Profile Grades: A - Above Average; B - Average;

C - Below Average; N/A - No Assessment Possible

The three abilities graded in the profile of Abilities publicly announced

as Computat ion, Comprehension and Reasoning can be roughly equated

(CXC, 1977b) with three cognitive levels of thinking as follows:

Computation is Recall by which is meant: The recall of rules, procedures,

definitions and facts, that is i tems characterized by rote memory.

Comprehension is Algorithmic thinking which means: The ability to trans-

late from one mathematical mode to another, as well as the application of

learned algorithms.

Reasoning is Problem Solving which means: The ability to:

1. translate a non-routine problem into mathematical symbols and then

choose suitable algorithms to solve the problems;

2. Combine two or more algorithms in a novel way to solve a problem.

3. Use an algorithm in reverse order or part of an algorithm to solve a

problem. In order to arrive at the three profile grades for a candidate, the marks

for the paper are apport ioned to the three cognitive levels Recall :Algorthmic

Thinking:Problem Solving in the ratio 3:5:2, respectively. This is the current

ratio. Previously, for example in CXC ( t977b) the ratio was 1: 3:1. Appendix


I contains an example of a CXC question and a scheme apportioning marks

to the three levels.

One of the major innovations of CXC is the setting of examination papers which give these weightings to the three cognitive abilities in mathematics.

This is a worthwhile innovation in that a single testing instrument, the

examination, is producing an increased amount of information about candidates. This increased information can be put to several uses. For example, a

candidate whose overall grade is disappointing but whose profile grades are weighted in favour of higher cognitive abilities may be recognised as having

greater mathematical ability than a single overall graded examination result

would reveal. A possible criticism of the system of profile grading is that the number

of cognitive abilities assessed is small. There are six abilities corresponding

to the different general objectives in cognition classified by Bloom (1956). More specifically for mathematics Avitat and Shettleworth (1968) specify

five taxonomic levels of objectives, but only list three corresponding think-

ing processes. These three processes clearly resemble those employed in the CXC and in fact served as a model for the three cognitive abilities chosen for

testing by the CXC. This influence notwithstanding it could be argued that the number of abilities graded in the profile should have been greater to reflect the six fold classification in Bloom (1956), say. A possible response to this criticism is in terms of the practicability and reliability of the assessment. Setting questions which test three different cognitive abilities as is the current practice, is difficult enough. A proliferation of the number of cognitive

abilities would increase the difficulty. Furthermore, in specifying which ability in a given part of a question tests decisions have to be made. With an increased number of cognitive abilities to be tested, the distinctions between

them must be less pronounced, and the decision making process will inevitably become less clear cut and more arbitrary. This will result in a diminished

reliability in the assessment. Overall a balance has to be struck between the

amount of information to be provided by the examination and the reliability and practicability of collecting the information. Precisely which number from two to six is the best number of profile grades is difficult to determine. In the view of the present writer the balance struck by the CXC is probably optimal.

A further innovatory feature of the information the CXC provides is the novel system by which the overall grades are defined. These are far more

realistically operational than many other systems of grading. Thus grade I does not denote that a candidate has achieved a distinction, whatever that means, but that he has demonstrated a comprehensive working knowledge of the

syllabus. The meanings of the other grades are similarly realistic and

402 PAUL ERNEST

operational. Whilst there still remains the problem of assigning ranges of marks to these grades for each examination the definitions given provide more guidance in selecting these ranges than many traditional grade definitions.

2.2. The Innovatory Breadth of Consultation and Concern with Social Needs in the Development of the Syllabus

One of the major aims of the Caribbean Examinations Council in developing the CXC Examinations system was to reflect and satisfy the needs of the region. In order to fulfil this aim, widespread consultation was built into the process of syllabus construction in all subjects, including mathematics. A further move to aid the fulfillment of this aim was the adoption of a social framework within which the functioning of the examination system was viewed. This is reflected in the interpretations of the two examinations or proficiencies offered in the mathematics (and in other subjects). The general proficiency, connoting subject activity designed to provide a foundation for further studies in the subject area. The basic proficiency, connoting subject activity designed to complete a secondary school course. The CXC mathematics panel have thought further on the anticipated social uses of the mathematics examinations, even to the extent of considering the preparation and needs of occupations (from CXC, 198 lb).

LIST OF OCCUPATIONS The following is the list suggested by the Panel . . . . . . . (The list is not intended to be exhaustive):

Basic Level Bankers, Book-Keepers, Business Persons, Caterers, Civil Servants and Employees of Statutory Boards, Clerical staff, Extension Officers (Agriculture), File Officers, Journalists, Lawyers, Ministers of Religion, Nurses, Police Officers, Politicians, Primary School Teachers, Sales Persons, Stenographers. Tertiary students in: (a) Liberal Arts (e.g. Languages, History, etc.); (b) Fine Arts (e.g. Music, Drama); (c) Social Sciences (except Economics); (d) Polytechnics at the craft level; (e) Teachers' colleges (except for Mathematics and Physical Sciences).

General Level

Agronomists, Doctors and Professionals in related medical fields (e.g. veterinary surgeons, dentists, etc.). Economics, Engineers, Pilots, Geo- graphers, Scientists, Secondary teachers of Mathematics and Science,

C A R I B B E A N I N N O V A T I O N IN A S S E S S M E N T 403

Research workers in the Social Sciences, Technocrats, Tertiary students in:

(a) The Physical Sciences;

(b) Economics or Geography:

(c) Mathematics.

In addition to revealing the careful thought given to the social uses of the

Mathematics examinations, as an extract from an official letter to the President

of a regional mathematics association it also demonstrates the responsiveness

of CXC to interested professional bodies. Throughout, the development of the

Mathematics syllabus has been characterized by the breadth of consultation

and responsiveness of the CXC.

The Mathematics Panel has from the onset given practising teachers a major

role in the syllabus development through the inclusion of at least three on the

panel. As one of its members reports (Isaacs, 1982), the panel

first consulted the syllabuses submitted by the national curriculum committees of some of the territories and drew up a draft syllabus which it deliberately left incomplete. This incomplete draft was then distributed to the secondary schools in the participating territories for comment, amendment and expansion.

(page 2)

From the feedback the mathematics panel drew up the second (complete) draft of the two syllabuses to be examined by the Council.

(page 2)

The second drafts of the mathematics syllabuses were circulated to teachers,

the general community and specialists in mathematics and mathematics edu-

cation. The panel took note of these interested parties ' reactions, and were

particularly concerned with the response to the Basic syllabus. This was

at tempting to meet local needs, as perceived by the panel by including math-

ematical topics which are relate to the everyday life of the general Caribbean

citizen under the heading "Consumer Ari thmet ic" (the section of the syllabus

dealing with this topic is reprinted as Appendix II). A tangible piece of evi-

dence of the response of the panel to outside demands is the following:

One innovative feature suggested by the panel was dropped after discussion with the teachers; that of including project work as a school based component of the overall assess-

ment of the candidates. (Isaacs, 1982, page 3)

At tempts to ascertain and to accommodate the views of interested parties

continue to be made and the mathematics syllabus is repeatedly subjected

to revision. One important indicator of the extent to which the CXC exam-

ination in mathematics has succeeded in meeting the needs of the region is given by candidates ' rate of success.

During the period 1977 to 1980 the percentage of candidates passing the

404 PAUL ERNEST

TABLE II Performance in GCE mathematics

Percentage passes at Caribbean centres

Year Barbados Jamaica Trinidad & Other Tobago centres

1977 34 34 21 24 1978 40 35 15 23 1979 47 38 16 30 1980 30 28 15 22

the GCE examination varied between 15% and 47% at the major Caribbean

centres, as is indicated in Table II. This is a low pass rate, especially when it is

noted that 47% is an untypically high pass rate. In the period 1979 to 1982,

the pass rate at CXC (calculated as the percentage attining grades I to III)

varied between 86% to 53% (Table III). This is a far more satisfactory pass

rate. Direct comparisons can be made for the years 1979 and 1980. In 1979

the overall percentage pass rate at GCE may be estimated to be about 40%,

whilst at CXC it is 61%. In 1980 the overall pass rate at GCE is under 30%,

whilst at CXC it is 66%.

These results suggest that the CXC mathematics examination is meeting

the needs of Caribbean students and teachers much more closely than the

GCE mathematics examination. The findings are all the more remarkable

in the light of the earlier reported comparability study by Tom Christie (CXC,

1981a), who found that the standards of the two examinations in math-

ematics were comparable in 1979.

2.3. The lnnovatory Conception and Implementation o f the Syllabus as a Curriculum

A traditional examination syllabus, for example a GCE syllabus, consists

of the list of topics that may be examined. Understandably, such a syllabus

will determine what is taught to students, at least to those who are aiming

at the appropriate examination. What is less often realized is that an exam-

ination syllabus exerts an influence on how subjects are taught. This point

is made by Isaacs (1982):

Public examinations in the English speaking Caribbean have been the major determinant of what is taught in our schools. They also, to a lesser extent, determine how the subjects are taught. Most teachers would feel abandoned if they did not have the public examinations to use as a goal and a threat with their students.

(page I)

CARIBBEAN INNOVATION IN ASSESSMENT

TABLE III Performance in CXC mathematics at General Proficiency level

405

Year 1979 1980 1981 1982

Percentage i~i Grades I to Ill 61 66 76 53

Faced with this unintended use of examinations syllabuses, the CXC Council could have chosen one of two alternatives. Either develop and publish a traditional syllabus in each subject, together with an admonition to teachers not to use it as anything more than a list of contents. Or develop a new type of syllabus consciously intended to influence the teaching of the subjects con-

cerned beyond the mere determination of content. The CXC chose this second more innovatory alternative. The syllabuses developed and implemented by the subject panels on behalf of the CXC are closer to the specification of a subject curriculum than a traditional syllabus. These features are shared by all the subject areas, but for present purposes attention will be devoted to the mathematics syllabuses.

The mathematics syllabus goes well beyond the listing of contents in a traditional mathematics syllabus. The CXC mathematics syllabus CXC (1977b) includes the following:

(1) Rationale for the Mathematics Syllabuses (reprinted in Appendix II). (2)Objectives of the syllabuses (reprinted in Appendix II), with a

summary of the considerations which led to their adoption. (3) Organisation of the syllabuses, including a discussion of the social

purposes of the two syllabuses. (4) Form of the examination, including definitions of the cognitive abilities

tested for the profile grades (listed in section 2.1 above) (5) Details of the topics in the Basic proficiency syllabus. There are nine

topics: Sets, Relations, Functions and Graphs, Computation, Number Theory, Measurement, Consumer arithmetic, Statistics, Algebra, Geometry.

For each of these topics there is a short listing of content, a list of general objectives, and a list of specific (or behavioural) objectives. These are repro- duced in full for the sample topic Consumer arithmetic (Appendix III).

(6) Details of the topics in the General Proficiency syllabus. There are twelve topics, those included in the Basic Proficiency syllabus and Trigonometry, Vectors & Matrices, Reasoning & Logic. As in the Basic syllabus for each topic is listed: contents, general objectives and specific

(behaviourat) objectives for the topic.

406 PAUL ERNEST

(7) The syllabus also includes 67 sample problems classified by topic and

specific objective illustrating the Basic and General Proficiency Sylla-

buses (four of these sample problems are shown in Appendix IV). Solu-

tions and comments to the teacher are provided for these problems.

(8) An indication of the weighting to be attached to different topics in

examination. This is in effect an indication of the relative importance

assigned to different topics in the different syllabuses. From this list it can be seen that the CXC syllabus includes substantially

more than a traditional public examination syllabus. The math.ematics syllabus

approximates more closely to a curriculum guide than to a mere examination

syllabus, and in this respect represents a major innovation.

The CXC feel that their curriculum responsibilities extend beyond the published syllabus; CXC (1977b). The CXC Mathematics Panel have recognised that there is a lack of suitable teaching materials to cover some of the

topics in the CXC syllabus. Consequently the panel commissioned teacher's units for certain topics. Currently the teacher's units on Probability and

Statistics, and on Reasoning and Logic are nearing completion. These and the previous reasons justify refering to the mathematics syllabuses and related materials are constituting a mathematics curriculum.

3. CONCLUDING REMARKS

In the preceding three sections innovatory aspects of the CXC mathematics

examination have been considered. The innovatory features have been

examined from the viewpoint of mathematics although frequently the innova-

tions are not specific to mathematics but a function of the overall CXC exam-

inations system. Nevertheless by focusing on the innovations in mathematics evaluation a more detailed appraisal has been possible.

The three major innovatory areas considered are not the sole innovations introduced by the CXC system. They have been isolated as of particular

interest from the viewpoint of mathematics education. It is interesting to note that there are two common threads running through the three areas

of innovation. These threads or themes are first, the operational philosophy underlying the examinations, and second, an awareness of the social and Caribbean context of the examinations. The operational philosophy manifests itself in the specification of the meanings of the overall examination and profile grades, in the social role the examinations are intended to play through the specification of the professions the proficiencies are directed at, and lastly, in the behaviouristic specific objectives in the syllabuses. The

concern with the social and Caribbean contexts manifests itself in the subject


panels concerns with consultation, again in the examinations' relationship with possible professions, and in the inclusion of socially useful topics in the syllabus. A further indication of the social concern is the assumption of broader curricular responsibilities than the mere provision of a traditional syllabus.

Overall, justification has been offered for the claim that the development and implementation of the CXC examinations systems represents an innovation in mathematics assessment.

APPENDIX I

Examples o f a Question with a Marking Scheme Apportioning Marks to the Three Profile Dimensions

Question 3(ii) from the June 1981 CXC General Proficiency Mathematics paper:

If 5 is added both to the numerator and denominator of a fraction, the result is equivalent to 3/4. If 3 is subtracted from both the numerator and denominator of the original fraction the new result is equivalent to 1/4. Find the original fraction.

(9 marks)

A senior mathematics examiner of the CXC presented the example of a marking scheme for this question shown in Table IV. The notations R I , A1, and P2 indicate that the corresponding solution steps are awarded 1, 1 and 2 marks each respectively, and that the skills employed are deemed to be recall (computation), algorithmic thinking (comprehension) and problem solving (reasoning), respectively.

The apportionment of the marks to the three profiles is: Recall; 5.21 marks (~ of 9), Algorithmic thinking; 2.84 marks, and Problem solving; 0.95 marks.

The examination paper is marked out a total of 132, 99 marks for Section I from which question 3(ii) is taken, and 33 marks for Section II. The questions in Section II are more heavily weighted in favour of the Problem solving profile.

The marking scheme actually used is more elaborate. This is because the question is tested in one or two pilot schools and the different approaches used by students or suggested by the mathematics panel are incorporated into the final marking scheme. At the marking session the examiners are briefed on the marking scheme and mark around a table under the direction of a table leader.

408 P A U L E R N E S T

TABLE IV

Marking scheme

Solution Marks Comments

Let the fraction be x/y R 1

x + 5 3 Then - (1) A 1

y + 5 4-'

x - - 3 1 and - - - (2) A1

y - - 3 4'

From (1): 4(x + 5) = 3(y + 5) R a ~ 4 x + 2 0 = 3 y + 15 R 2 = 4 x - - 3 y = - - 5 . (3) R 1

From (2): 4 (x - - 3) = y - - 3 R 1 = 4 x - - 1 2 = y - - 3 RI ~ 4 x - - y = 9 (4) R~

Subtract (3) from (4). A

Then 2y = 14 A 1 ~ y = 7 R 1

S u b s t i t ~ o r y in (4). A

4 x - - 7 = 9 = 4 x = 16 AI

x = 4 R~ 4

The fraction is ff R

4 + 5 9 3 CHECK: - P2

7 + 5 12 4

4 - - 3 1

7 - - 3 4

Cross multiply

Correct transposition of his expression

Correct transposition of his expression

Or any correct algorithm to eliminate 1 unknown

Correct answer only Any correct application of algorithm to his equations

Correct answer only

Correct answer only

Check for his answer

A P P E N D I X II

Rationale for the Mathematics Syllabuses

The guiding pr inciples for the m a t h e m a t i c s syl labuses are t ha t m a t h e m a t i c s

as t a u g h t in Ca r ibbean Schoo l s should be:

( i ) re levant to the exis t ing and an t i c ipa t ed needs o f Ca r ibbean socie ty;

(ii) re la ted to the abi l i ty and in te res t o f Ca r ibbean s tuden t s ;

(iii) al igned to the p h i l o s o p h y o f the educa t i o n a l sys tem.

These pr inc ip les focus a t t e n t i o n on the pract ica l uses o f m a t h e m a t i c s as


well as some of the fundamental concepts which help to unify mathematics

as a body of knowledge. Any traditional content which does not contribute to either of these ends has been omitted and more general and unifying concepts included. Mathematics is to be studied as a single subject rather than as a set of unrelated topics.

Objectives of the Syllabuses

1. To help the student acquire a range of mathematical techniques and skills

and to foster and maintain the awareness of the importance of accuracy.

2. To make mathematics relevant to the interests and experience of the stu-

dent, helping him to recognise mathematics in his environment. 3. To cultivate the ability to apply mathematical knowledge to the solution of

problems which are meaningful to the student as a citizen.

4. To cultivate the ability to think logically and critically.

5. To develop positive attitudes such as open-mindedness, self-reliance, persistence and a spirit of enquiry.

6. To prepare students for the use of mathematics in further studies. 7. To develop appreciation of the wide application of mathematics and its

influence in the advancement of civilization.

8. To cultivate a growing awareness of the unifying structures of mathematics.

(CXC, 1977b, pages 1 & 2)

A P P E N D I X III

Syllabus for the Topic: Consumer Arithmetic

Content

Percentages; profit & loss; discount, dividends; simple interest & compound

interest, mortgages; hire purchase; rates & taxes; insurance; currency conver- sion; invoices.

Objectives

1. To help students appreciate that business arithmetic is indispensable in everyday life;

2. To make the students competent in performing the calculations required in normal business transactions and computing one's own budget;

3. To help students appreciate the advantages and disadvantages of different ways of investing money;


4. To help students appreciate the need for both accuracy and speed in

calculations.

Specific: The student will be able to:

1. Calculate profit and loss as a percentage;

discount and sales tax when these are given as percentage;

marked price when cost price and percentage profit or loss are

2. Calculate

3. Calculate

given;

4. Calculate

give n;

5. Calculate

in simple

cost price when selling price and percentage profit or loss are

payments by instahnents as in the case of H.P. mortgages, etc.,

cases;

6. Calculate tax from instructions;

7. Apply given rules to calculate fuel bills, electricity bills, etc.;

8. Calculate simple interest and compound interest (not more than 3 periods):

9. Use tables to determine compound interest for more than 3 periods;

10. Convert currency using exchange rates;

I 1. Calculate returns on different types of investments;

12. Use ready reckoners.

(CXC, 1977b, page 13)

A P P E N D I X IV

Sample Items Illustrating Some of the Specific Objectives of the CXC Basic Mathematics Syllabus

TOPIC:Measurement

S.O.4.: "Measure the areas of irregularly shaped figures".

EXAMPLE 14: The area o f figure ABCDE drawn on centimetre graph paper

(A) is greater than 30 cm 2 .

(B) is less than 20 cm 2 .

(C) lies between 20 cm 2 and 25 cm 2 .

(D) lies between 25 cm ~ and 30 cm z .

]Figure 4 omitted]

S.O.8: "Estimate the margin of error for a given measurement".

EXAMPLE 15: A sportsmaster t imed one of his athletes over the 100 metres

dash. The athlete took 11.5 seconds by his watch to cover the distance. It is

believed that the actual t ime taken is in the range (11.5 + 0 .1)s and that the

length of the track is in the range ( I00 -+ 1)m.

C A R I B B E A N I N N O V A T I O N IN A S S E S S M E N T 411

Use tables, or slide rule, to calculate the average speed correct to 3 signifi-

cant figures, of the runner, if

(i) the track was actually 99 m long and he took 11.6 s, and

(ii) the track was 101 m long and the athlete took 11.4 s.

(iii) Express the range within which the average speed of the runner lies in

the form (a + b) m s -1 .

S.O.9: "Give to an appropriate degree o f accuracy, results o f calculations

involving numbers derived from a set o f measurements".

EXAMPLE 16: Construct parallelogram ABCD such that AB = 6.5 cm, BC =

4.0 l cm and angle DAB = 36 ~ .

By making the appropriate measurements calculate the area of the parallelo-

gram giving your answer to the appropriate degree o f accuracy.

TOPIC:Consumer Arithmetic

S.O.12: "Use ready reckoners"

EXAMPLE 17: [table omit ted] .

The table shows an extract from a "decimal reckoner" giving the price of

N articles at 27 c each.

I f the unit price of the following items is 27 c, use this table to find the

price of:

(i) (a) 23 articles;

(b) 573 articles;

(ii) 6�88 yd. of material;

(iii) 5.29 kg o f foodstuff.

(CXC, 1977b, pages 26 and 27)

B I B L I O G R A P H Y

Avital, S. M. and Shettleworth, S. J.: 1968, Objectives for Mathematics Learning, Some ldeas for the Teacher, Bulletin No. 3, The Ontario Institute for Studies in Education, Toronto.

Bloom, B. S. et al.: 1956, Taxonomy o f Educational Objectives: Handbook 1; Cognitive Domain, McKay, New York.

CXC: 1977a, CXC Secondary Education Certificate Fact Sheet, Caribbean Examinations Council, Barbados.

CXC: 1977b, CXC Secondary Education Certificate Mathematics Syllabus June 1979 (Including Amendments and additions in September 1980 and August 1981), Caribbean Examinations Council, Barbados.

CXC: 1981a, CXCNews Volume 1 No. 2, Caribbean Examinations Council, Barbados. CXC: 1981b, Letter to President o f Mathematical Association o f Jamaica, dated 19 May

1981 on behalf of Registrar, CXC, The Garrison, St. Michael 20, Barbados.

412 P A U L E R N E S T

Isaacs, I.: 1982, The Development and Implementation of the Caribbean Examinations Council's Mathematics Syllabus, paper read at Carimaths: Caribbean Conference on Mathematics for the Benefit of Caribbean Communities and its Reflection in the Curriculum, October 18-21, 1982, Paramaribo, Suriname.

School o f Education, Mona,

University o f the West Indies, Kingston 7, Jamaica

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