Topic08 Matematik

INTRODUCTION

After teaching certain topics and related skills, w e need to check our teaching strategies and learning activities. We need to take follow-up action, if strategies and activities are not effective. In other words, t eachers are required to evaluate pupils achievement in the subject taught. This topic is divided into two (2) parts. The first part explains the meaning of evaluation, type of evaluation, the procedure of evaluation, and the aim of evaluation in the process of teaching and learning mathematics. The second part explains how to construct a good test that can be used in measuring pupils achievement. Teachers should be exposed to the procedure of preparing high quality test items.

TEST, MEASUREMENT AND EVALUATION

Test, measurement and evaluation are very important in the process of teaching and learning. All the three concepts are different in meaning but they are always mutually assisting one another. The terms test, measurement and evaluation are

8.1

TToopp iicc

88 Testing and

Evaluation

LEARNING OUTCOMES By the end of this topic, you should be able to:

1. Explain the meaning of test, measurement and evaluation;

2. Implement effective steps in preparing a good test;

3. Construct test items in mathematics; and

4. Analyse and interpret the quality of test items in mathematics.

TOPIC 8 TESTING AND EVALUATION ! 141

easily confused because all of them are related and become parts of a process. If pupils are asked to answer a series of questions, we obtain their score by counting the number of correct answers, and conclude that their achievement is satisfactory . We are therefore concerned with all the three concepts. The test is the set of questions, measurement is the process of obtaining the score, and evaluation determines the score value (satisfactory achievement). The box below gives the specific meaning of each term, as applied to classroom evaluation (Source: Norman E. Gronlund & Robert L. Linn).

Some Basic Terminology: (a) Test

A test is an instrument or a systematic procedure for measuring a sample of behavior. (Answer the question: How well does the individual perform Either in comparison with others or in comparison with a domain of performance tasks? ).

(b) Measurement Measurement is the process of obtaining a numerical description of the degree to which an individual possesses a particular characteristic. (Answer the question How much? ).

(c) Evaluation

Evaluation is the systematic process of collecting, analysing, and interpreting information to determine the extent to which pupils are achieving instructional objectives. (Answer the que stion How good? ).

As a comparison, evaluation is a more comprehensive and inclusive term than measurement, and testing is just one type of measurement. Measurement is limited to quantitative descriptions (measurement) of pupils, and always expressed in numbers (e.g. Hassan solved correctly 30 of the 40 questions). On the other hand, evaluation may include both quantit ative and qualitative (non-measurement) descriptions of pupils. The quantitati ve descriptions include the marks and grades obtained by pupils for various sch ool subjects that they took. The qualitative descriptions may include pupils interest, hobby, personality or disciplinary action(s) taken on them. The diagram i n Figure 8.1 shows the comprehensive nature of evaluation and the role of measurement techniques and the non-measurement techniques in the evaluation process.

TOPIC 8 TESTING AND EVALUATION 142

Figure 8.1: The role of evaluation techniques and value judgment in evaluation

TYPES AND AIMS OF EVALUATION

In the KBSR and KBSM programmes, there are three (3) types of evaluation, namely, evaluation to ascertain the effectiveness in skill mastering, evaluation to ascertain the effectiveness of progress in learning, and evaluation to ascertain the effectiveness of achievement (Mok, 2005). In general, we can categorise the evaluation activities into two (2) main categories: formative evaluation and summative evaluation. (a) Formative Evaluation

Formative evaluation is an activity of testing and measuring pupils strengths and weaknesses in mastering certain skills which they have learned during a certain period of time (e.g. after one week of class). The tests are usually conducted in an informal way such as through observation, quiz, exercise, homework, coursework, oral test, etc. The aim of formative evaluation is more to find out pupils weaknesses in mastering certain skills, so that corrective actions can be taken immediately. Formative evaluation can also be used to determine pupils learning progress through a formal test, such as paper-pencil test, which is normally held after several related skills have been taught in the classroom. The test result will be recorded in Pupil Performance Record, which can be used to make decision on the follow-up actions, such as placing pupils in the suitable group activities, planning remedial and enrichment activi ties.

8.2

Evaluation

Measurement Non-measurement

Value judgment

and/ or

plus plus


(b) Summative Evaluation Summative evaluation is an activity of testing and measuring pupils performance through formal procedures (paper-pencil test, practical, or written examination) after completing a few topics of lesson. Its usually held at the end of school term, after half a year period or one year period. The aim of summative evaluation is to determine pup ils achievement, and the results also can be used to plan the follow-up actions, enrichment and remedial activities. Normally, a summative test is carried out formally as mid-year examination or end-of-year examination. Th e test results will be recorded, with mark and grade, in Progress Report Card. Summative evaluation also covers public examinations, such as UPSR, PKBS, PMR, SPM and STPM.

(c) The A ims of Evaluation

The general aims of evaluation in teaching and learning process are listed below:

(i) To collect information of pupils achievement after teaching and learning activities, interpret and take appropriate action.

(ii) To determine pupils strengths and weaknesses in learning certain skills.

(iii) To determine the achievement of learning objectives.

(iv) To record the evaluation results in individual s performance and profile record.

TEST PREPARATION

The achievement of learning objectives can be evaluated using the three (3) domains: the cognitive domain, affective domain and psychomotor domain. Generally, testing in school focuses mostly on cognitive domain. However, the affective and psychomotor domains are also importan t in the teaching and learning of KBSR and KBSM. As test has become an important measuring instrument in evaluation, it should be prepared acc ording to certain principles and procedure. A high quality test should possess all the five (5) characteristics of a test, i.e., validity, reliability, objectivity, a dministrability and assessability.

8.3

Summarise, in table form, the characteristics of formative and summative tests in terms of concept, aim, activity, format, time, coverage, target, record and follow-up actions.

EXERCISE 8.1


Teacher should plan an appropriate test to ensure the test is reliable and valid. The first step in test preparation is to determine the purpose of the test. If the purpose is to determine pupils strengths and weaknesses in mastering certain skills which they have learned, a formative test is more appropriate. On the other hand, if the purpose of the test is to determine pupils achievement after a few learning units have been covered, then a summative test is more appropriate. The format and type of test must also be determined before constructing the items, whether to use objective or subjective items. Figure 8.2 shows the steps in test preparation.

Figure 8.2: Steps in test preparation

8.3.1 Blooms Taxonomy of Educational Objectives

After determining the purpose and the type of a tes t, a teacher should select the learning contents to be tested. The learning contents; i.e. facts, knowledge and skills; are usually stated as learning outcomes. It is important to keep in mind that there are different levels of outcomes of learning. In 1956, Benjamin Bloom headed a group of educational psychologists to develop an important classification of educational objectives. Blooms Taxonomy of Educational Objectives is the most important description of the levels of cognitive performance. Bloom had identified six (6) levels within the cogn itive domain as listed in Table 8.1. The levels of this taxonomy are hierarchical in nature, from the lowest level of objective to the highest level of objective. It means that the learners must master lower level objectives first before they can reach the higher level

1. Determine purpose of test

2. Determine test contents

3. Formulate Test Specification Table

4. Construct test items

5. Evaluate test items


objectives. The levels of educational objectives for cognitive domain in mathematics are explained below: (a) Knowledge in mathematics can be defined as the ability to recall

information (knowledge, concept, principles) in mat hematics . For example, at this stage, pupils should be able to recall and state the formula for area of rectangle, i.e. area = length x width or A = l x w. It represents the lowest level objective in Bloom s taxonomy. The word low means that it should be mastered first as it provides the basis for higher cognitive activities. This implies that only after a pupil is able to recall information, then he/she can move to the next/higher level.

(b) Understanding in mathematics can be defined as the ability to explain meaning of information (knowledge, concept, princip les) in mathematics . For example, after being able to state the formula of area of rectangle, they should be able to explain the meaning of area , identify the length and width of a given rectangle, and able to compute the area of a rectangle.

(c) Application in mathematics can be defined as the ability to use of

previously learned information (knowledge, concept, principles) and skills in real-life situations . At this level, pupils are expected to be able to solve practical problems by applying the knowledge, princ iples and skills acquired from previous levels.

(d) Analysis in mathematics can be defined as the ability to compare and

contrast, relate or extract the attributes of the knowledge, concept, or skill that have been learned earlier . Pupils should be able to break down complex information into simpler parts. For example , when they want to describe the differences between a cube and a cuboid, they have to recall and understand the knowledge about the characterist ics of each solid.

(e) Ynthesis in mathematics can be defined as the ability to create something

that did not exist before, especially for problem-s olving by integrating information that had been learned at lower levels . For example, given the base and the area of a triangle, pupils should be able to find the height of the triangle.

(f) Evaluation in mathematics can be defined as the ability to make

judgments, to evaluate, to prove, to infer or to conclude a certain statement based on previous levels of learning . For example, pupils should be able to infer what will happen to the area of a square if t he length becomes a half.


Table 8.1: Blooms Levels of Educational Objectives for Cognitive Domain

Level Description

Kn

owle

dge

Definition

Sample words

Sample behaviors

Student recalls or recognises information, ideas, and principles in the approximate form in which they have learned.

Arrange, define, duplicate, label, list, memorise, name, order, recognise, relate, recall, repeat, reproduce state.

The pupil will d efine the formula of area of a rectangle.

Un

der

stan

din

g

Definition

Sample words

Sample behaviors

Student translates, comprehends, or interprets information based on prior learning.

Classify, describe, discuss, explain, express, identify, indicate, locate, recognise, report, restate, review, select, translate.

The pupil will explain the purpose of the formula o f perimeter of a square.

Ap

pli

cati

on Definition

Sample words

Sample behaviors

Student selects, transfers, and uses data and principles to complete a problem or task with a minimum of direction.

Apply, choose, demonstrate, dramatise, employ, illu strate, interpret, operate, practice, schedule, sketch, solve, use, write.

The student will s olve the problem involving money.

An

alys

is

Definition

Sample words

Sample behaviors

Student distinguishes, classifies, and relates the assumptions, hypotheses, evidence, or structure of a statement or question.

Arrange, assemble, collect, compose, construct, create, design, develop, formulate, manage, organise, plan, prepare, propose, set up, write.

The student will c ompare and contrast the formula of a rectangle and a triangle.

Syn

thes

is

Definition

Sample words

Sample behaviors

Student originates, integrates, and combines ideas into a product, plan or proposal that is new to him or her.

Arrange, assemble, collect, compose, construct, create, design, develop, formulate, manage, organise, plan, prepare, propose, set up, write.

The student will c onstruct a procedure for measuring the volume of a cylinder.

TOPIC 8 TESTING AND EVALUATION ! 147 E

valu

atio

n

Definition

Sample words

Sample behaviors

Student appraises, assesses, or critiques on a basis of specific standards and criteria.

Appraise, argue, assess, attach, choose compare, defend estimate, judge, predict, rate, core, select, support, value, evaluate.

The student will c ritique the effectiveness of using pictograph in presenting data.

8.3.2 Test Specification Table

When the selected contents/topics have been determined, the next step is formulating the Test Specification Table. What is Test Specification Table? A Test Specification Table is a guide for test construction, especially for cognitive-domain test. It is a guide to test developers for them to develop/write test items and to indicate Standards of Learning of a test. Consequently, it becomes an indicator to educators, parents and pupils of the Standards of Learning covered by the test and the number of items in each reporting category and on the total test. The aim of preparing a Test Specification Table is to ensure that the appropriate weight of various topics and levels of skills reflected accurately to the pupils overall ability. Table 8.2 shows an example of a Primary Two Test Specification Table for the first term examination, which contains 20 multiple-choice items.

Why Bloom s Taxonomy of Educational Objectives is important f or teachers in preparing a test?

EXERCISE 8.2


Table 8.2: Sample of Test Specification Table

I II III Topic Sub-topic

L M H L M H L M H

Number

of Items

Percent

Counting 1 1 2 Numbers to 1000

Read and write 1 1 15%

Value of each digit

1 1 2

Compare and arrange

1 1 20%

Addition with highest total 1000

Position of number

1 1

Meaning of addition

1 1 2 Addition with highest total 1000

Addition in daily life

1 1 2 20%

Meaning of subtraction

1 1 1 15%

Subtraction within the range of 1000 Subtraction in

daily life 1 1

Multiplication table

1 1 10%

Multiplication of 2, 3, 4, and 5

Multiplication in daily life

1 1

Meaning of division

1 1

Division facts 1 1 20%

Division by 2, 3, 4, and 5

Division in daily life

1 1 2

Number of question/ Percentage

0 5 5 4 5 1 20

100%

Blooms Taxonomy Levels of difficulty I Knowledge. L - Low II Understanding and Application. M - Moderate III Analysis, Synthesis and Evaluation. H - High


Generally, Test Specification Table contains two (2) important elements, i.e. topic/subtopic is represented along vertical axis, while skill level is represented along the horizontal axis. The skill level can be divided into three levels of difficulties; low, moderate, and high. What is the important of Test Specification Table? A good Test Specification Table can help educators to construct a good and comprehensive test. The importance of Test Specification Table is to ensure that:

(a) Test can be constructed systematically;

(b) Test content covered all the syllabus;

(c) Weight of items for each topic and skill level refl ects accurately the pupils ability; and

(d) Difficulty level of test can be maintained from yea r to a year.

8.3.3 Construction of Test Items

Formal test refers to the cognitive test such as quiz, monthly test, mid-term examination, end-term examination, IQ test, perform ance test, and other summative test such as UPSR, PMR, SPM, etc. As the purpose of the test has been determined earlier, teacher can develop test items based on Test Specification Table. The selection of objective and/or subjective questions depends on the purpose of the test. Generally, for summative purpo se, the objective questions are more appropriate, because it can cover more topics in a short period of time. If the purpose is to examine pupils problem-solving ability, subjective questions are more appropriate, because we can see their strengths and weaknesses in every step of the answer. (a) Objective Test

Normally in mathematics, there are two main categor ies of objective test, i.e. structural- objective test and multiple-choice -objective test. The tests are call objective since there is only one correct answer to each item. The multiple-choice-objective test consists of at least three (3) types of items, namely, true/false items, matching items, and multi ple-choice items.

(i) Structural-objective test items Items are constructed in such a way that the candidates are required to give a short answer in the space given. The following are some examples of items which are commonly used.


Examples of Structural-objective Test Items ! What is the formula of the volume of a cylinder?

__________________________________________________________ ! 30% of 60 = _________________ ! 1.5 kg 200 g = ____________ g ! An equilateral triangle has ____________ equal sides while a

scalene triangle has _________ equal sides. ! If the length of a cube increases 2 times, the volume will increase

________ times.

(ii) Multiple choice objectives test items This type of item will give the opportunities for c andidates to choose one correct answer set in the item according to the instruction given. Examples of True/ False Items Tick ( ) the correct answers.

No Statement True False

1. A triangle has four (4) equal sides

2. 0.01 kg = 10 g

3. The average of 5, 7, and 9 is 7

Examples of Matching Items ! Match these measurements with their appropriate uni ts.

The distance from Telok Intan to Ipoh m

The length of a pencil box km

The area of a badminton court m2

The height of a coconut tree mm

The thickness of five (5) sheets of paper cm


! Match the following figures:

(iii) Multiple-choice items A multiple-choice item consists of a problem and a list of suggested answers. The problem can be stated as a direct question or incomplete statement and it is called stem of the item. The suggested answers (usually four answers, i.e. A, B, C, D) may include words, numbers, symbols, or phrase and are called alternatives (or choices/options). Multiple-choice items are most often used as compared to other types of objective test since it has high validity, more objective and easier to manage in a short period of time. However, it is not easy to construct good multiple- choice items. A good multiple-choice item should have the following characteristics:

! The instruction is clear and easy to understand.

! Its difficulty level should be the same as given i n Test Specification Table.

! No negative form, and if any, the words such as NO or NOT should be capitalised and bold.

Circle

Square

Triangle

Rectangle

What will happen to a test, if it was not construct ed based on a Test Specification Table?

EXERCISE 8.3


! Options of answers are appropriate to the question. For example, if the item requires an answer in numerical form, t hen all the options are in numerical form.

! The choices are arranged in ascending or descending order.

! The correct answers are well spread among the options A to D.

! There is only one correct answer for each item.

! The distracters (wrong answers) are in similar for m to the correct answer to avoid guessing.

! The options are arranged in vertical order.

Examples of Multiple-choice Items ! Given that the area of the right-angle triangle is 30 cm2, find the

length of BC.

A. 3 cm B. 6 cm C. 9 cm D. 15 cm

! kg = ? I 250 g II 2500 g III 0.25 kg IV 25 kg A. I and II B. II and III C. III and IV D. I, II, and III

(b) Subjective Test

Subjective test requires candidates to provide the answers to questions using their own thinking skills and knowledge in a particular topic. It can be used to assess the lowest level as well as the higher levels of objectives, such as analysis, synthesis and evaluation. There are two (2) types of subjective items that are appropriate in mathematics: the mechanical-problem items and problem-solving items.

(i) Mechanical-problem items Usually, this is a short item which requires candid ates to react to the question in short- answer form. Candidates should answer the question using their own strategy.

A

10 cm

C


Examples of Mechanical-problem Items ! Calculate the average of 5, 6, 9, 5, 8, 10 and 11. ! Find the area of a square which is 5 cm in length.

(ii) Problem-solv ing items Usually, this is an essay or structural items which require candidates to obtain the solutions through systematic steps, using high level of thinking. They can use any problem-solving model, s uch as the Polya Model. Examples Problem-solv ing Items ! A total of 20% of the pupils in a primary school ar e Chinese, 10 %

are Indian and the rest are Malay. Given the number of Chinese pupils is 120, find

(a) The number of Indian pupils.

(b) The total number of pupils in the school.

! Construct a pictograph based on the information giv en in the table

below.

Year Number of Cars Sold

January 120

February 90

March 60

April 30

(c) Construction of informal Test

Informal tests cover activities such as observation, oral question and answer, quiz, classroom reading, coursework/project , homework and so on. The aim is to identify and assess pupils strengths and weaknesses in

Subjective test in mathematics is usually more diff icult than the objective test. Give your comment.

EXERCISE 8.4


mastering certain skills which they have learned. I ts usually carried out as a formative test. The test results will be written in the Student Performance Record.

ITEM EVALUATION

The teacher must evaluate all the items carefully based on the format, content and language to avoid mistakes or ambiguities before the test is administered. In addition, teachers have to ensure that the items are appropriate and accurate according to the Test Specification Table. The instruction must be clear and simple and the time management should be reasonable. To ensure that all items have characteristics of a good test (such as validity, reliability, objectivity, administrability, and assessibility), we need to co nduct a pre-test for the items. Items can be tested to pupils in the same class level. The information from the pre-test will assist the teacher to correct the weaknesses in the test items.

8.4.1 Item Analyses

The test item which had been constructed by the teacher has to be pre-tested to ensure that the item has the characteristics of a good item. In this respect, the appropriate indices that can be used indicators are difficulty index and discrimination index. (a) Difficulty Index

Difficulty index is an index that determines the de gree of difficulty of each item, that is, whether is too easy, average or too difficult. The value of index can be calculated using the following formula:

Number of candidates with correct answer

Total number of candidates attempted the item

For a large number of candidates, the following method can be used to calculate the difficulty inde x:

RU = Number of candidates in the upper group who answ ered correctly RL = Number of candidates in the lower group who answ ered correctly TU +L = Total number of candidates in the upper and lowe r groups

Difficulty Index (p) = LU

LU

TRR

8.4

Difficulty Index =


The number of candidates in the upper group (high-a bility group) and the number of candidates in the lower group (low-abilit y group) are 27% of the total number of candidates taking the test. The remaining 46% of the candidates are considered to be in the middle group (average-ability group) and are not used in computing of the difficulty and discrimination indices. The value of difficulty index for each item will he lp teachers to interpret the suitability and the quality of each item. The follo wing Table 8.3 gives us the guideline on how to make an interpretation and deci sion on test items:

Table 8.3: Interpretation of Items According to Ddifficulty Index

Difficulty Index Interpretation Decision

0.00 0.20 Too difficult Remove/modify

0.21 0.40 Difficult Modify

0.41 0.60 Average Accept

0.61 0.80 Easy Modify

0.81 1.00 Too easy Remove/modify

(b) Discrimination Index It is necessary for us to look at another index before we make any decision about the suitability of test items, that is, the d iscrimination index. Discrimination index is an index that determines th e power to differentiate between high-score and low-score candidates. The value of index can be calculated using the following formula:

The value of discrimination index for each item wil l help us to interpret the suitability of each item, whether it can be used for a test. The following table gives a guideline as to how to make interpretation and decision for certain each test item:

Discrimination Index (d) = LU

Lu

TRR

!

21


Table 8.4: Interpretation of Items According to Discriminati on Index

Discrimination Index Interpretation Decision

0.00 0.10 Very poor Remove

0.11 0.20 Poor Remove/modify

0.21 0.30 Average Accept

0.31 0.40 Good Accept

0.41 1.00 Very good Accept

(c) Procedure to Compute the Difficulty and Discrimination Indices Assume that there are N candidates set for a test. First, arrange the candidates who scored highest to the lowest marks in the test. The number of candidates in the upper group is 27% of the total number of candidates set for the test, i.e. 27% of N candidates. Similarly, the number of candidates in the lower group is also 27% of N candidates. The next step is to identify the number of candidates in the upper group and in the lower group who answered each item correctly. The final step is to compute the difficulty and discrimination indices using the formulae given ear lier.

Example 1 Number of pupils = 40 Number of pupils in upper group or lower group = 27 % x 40 = 10.8 ! 11 Let RU = 8, RL = 3 for a particular item (from the test results). (i) Item difficulty index (p) = = (8 + 3)/22 = 11/22 = 0.50 (ii) Item discrimination index (d) = = (8 3)/11 = 5/11 = 0.45 Interpretation The difficulty index (0.50) and discrimination inde x (0.45) indicate that the item has average difficulty and very good discrimination , and therefore, the item is suitable and acceptable to be included in a test.


Example 2 Number of pupils = 40 Number of candidates in upper/lower group = 27% x 4 0 = 10.8 ! 11 Let RU = 10, RL = 7. (i) Item difficulty index (p) = = (10 + 7)/22 = 17 /22 = 0.77 (ii) Item discrimination index (d) = = (10 7)/11 = 3/11 = 0.27 Interpretation The difficulty index (0.77) and discrimination inde x (0.27) indicate that the item is easy and average discrimination, and therefore, the item is not suitable and should be modified. Another pre-test should be cond ucted on this item. According to research, a good item for a test usually has difficulty index between 0.40 and 0.60; and discrimination index of more than 0.4 (Mok, 2004). However, these indices are directly related to the performance of the group of pupils who sat the test. It means that both indices may change if the pre-test is conducted to the different groups of pupils with different perfo rmance. We also cannot make a comment about the difficulty or suitability of cert ain item just by reading the item (face validity). You should conduct a pre-test on the item and then analyse the result. The value of both indices can be calculated using Microsoft Excel or any suitable software such as Quest 2.

PROCEDURE OF EVALUATION

Generally, the evaluation procedure consists of five (5) stages as shown in Figure 8.3. You will find that, by following this procedur e stage by stage, it will be easier to understand the process of evaluation, specifically for primary school mathematics. The five (5) stages are:

8.5

Find the difficulty and discrimination indices of a n item, given that the total number of pupils taken the test was 60, RU = 12 and RL = 4. Was it a good item?

EXERCISE 8.5


(a) Test preparation;

(b) Test administration;

(c) Marking answer script;

(d) Evaluation of test result; and

(e) Interpretation and decision making. These stages are briefly explained below.

Figure 8.3: Procedure of evaluation

(a) Test Preparation The first stage is the test preparation stage, which is the most important stage in evaluation. As it was explained earlier, test preparation includes determination of the purpose of test and test content, preparing test specification table, developing and evaluating the items, pre-testing and analysing the items, and finally, improving the ite ms.

(b) Test Administration

The second stage is the test administration stage, in which the actual test is given to the pupils. A test timetable should be pre pared before a series of tests can be implemented. Pupils should be given enough time to read and answer the questions in a particular test. Question papers should be made available on the test day and test invigilators should be appointed to run the test.

(c) Marking Answer Script

The third stage is the script-marking stage, in whi ch the answer scripts will be marked by teachers who had been appointed to mark the answer scripts. Marking scheme should be prepared earlier and a meeting should be held to moderate the answers. The moderation process is important to ensure a fare marking when the questions are ambiguous.

Evaluation of Result

Interpretation and Decision Making

Test Preparation Test Administration

Marking Answer Script


(d) Evaluation of Test Result The fourth stage is the evaluation stage, in which the test results/marks are evaluated for the purpose of giving grades. The grading scale (the range of marks for each grade) should be prepared earlier and should be revised based on the overall distribution of the marks obta ined. In the case of formative evaluation, the focus of evaluation shoul d be on the strengths and weaknesses of pupils, rather than grades.

(e) Interpretation and Decision Making The fifth and the final stage is the interpretation and decision making stage, in which the grades are interpreted in the light of the purpose of the test. Based on these grades, the class teacher may want to regroup his/her pupils to enhance, for example, cooperative learning, or may be some of them need remedial activities before they can begin the next topic.

! Testing is the most important part of evaluation in the teaching of any subject, including mathematics.

! This topic has briefly explained the procedure for preparing a good test.

! There are several types of items can be used to gather information on a pupils development in mathematical understanding.

! By analysing a pre-test result, we can calculate both the difficulty and discrimination indices in order to determine whethe r the item has the appropriate indices.

Difficulty Index

Discrimination Index

Evaluation

Measurement

Testing


1. Describe why we should conduct a pre-test.

2. Describe the meaning of Test Specification Table.

3. Explain the meaning of evaluation in the context of testing.

1. Construct a Test Specification Table for Primary School Mathematics Year 4 which is suitable for mid-year examination.

Topic08 Matematik

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