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CHAPTER - IV

DESCRIPTION OF TOOLS

In the preceding chapters, the introduction to different variables under study,

the review of related literature, objectives and hypothesis were discussed. The present

chapter deals with the description of tools.

For the present investigation, the following tools were used.

A. Standardized Tests

1. Raven’s Standard Progressive Matrices, J.C. Raven, 1977

2. Socio-Economic Status Scale, Meenakshi, 2004.

3. Self-Concept Inventory, Sagar Sharma, 1968.

B. Self-Developed Tools

4. Achievement Test (developed by investigator)

5. Cooperative learning Lesson Plans (developed by the investigator)

6. Worksheets (developed by the investigator)

7. Formative Tests (developed by the investigator)

A. STANDARDIZED TESTS USED

4.1 Raven’s Standard Progressive Matrices

(i) Description of the Test

It was developed in Great Britain by Raven first in 1960. After that many of

its reprints have been published during the last many years. This test has been

designed as a measure of Spearman’s ‘g’ factor. It consists of 60 matrices or designs,

from each of which a part has been removed and has been mixed up in the

alternatives given below the design. The subject has to choose the missing part from

six or eight given alternatives. The items are grouped into five series termed as A, B,

C, D and E, each containing 12 matrices of increasing difficulty but similar in

principle. The earlier series require accuracy to discriminate the latter, more difficult

series involve analogies, figure permutation and alteration of pattern, and other

logical relations. The test requires education of relations among abstract items. It is a

non-verbal test and has been claimed to be a language-free, education-free and

culture-free test. It was administered in groups’ setting with no time limit.

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Percentile norms are provided for each half-year interval between 6 and 14

years and for each five years interval between 20 and 65 years.

The Standard Progressive Matrices (at appendix A) Sets A, B, C, D and E is a

test of a person’s capacity at the time of the test to apprehend meaningless figures

presented for his observation, see the relations between them, conceive the nature of

the figure completing each system of relations presented, and, by so doing, develop a

systematic method of reasoning.

The scale consists of 60 problems divided into five sets of 12. In each set, the

first problem is, as nearly as possible, self-evident. The problems which follow

become progressively more difficult. The order of the test provides the standard

training in the method of working. The five sets provide five opportunities for

grasping the method and five progressive assessments of a person’s capacity for

intellectual activity. To ensure sustained interest and freedom from fatigue, the

figures in each problem are boldly presented, accurately drawn and, as far as possible,

are pleasing to look at. The scale is intended to cover the whole range of intellectual

development from the time a child is able to grasp the idea of finding a missing piece

to complete a pattern and to be sufficiently long to assess a person’s maximum

capacity to form comparisons and reason by analogy without being unduly exhausting

or unwieldy. The scores obtained by adults tend to cluster in the upper half of the

scale, but there are enough difficult problems to differentiate satisfactorily between

them.

Everyone, whatever his age, is given exactly the same series of problems in

the same order and is asked to work at his own speed, without interruption, from the

beginning to the end of the scale. As the order of the problem provides standard

training in the method of working, the scale can be given either as an individual, a

self-administered or as a group test. A person’s total score provides an index of his

intellectual capacity, whatever his nationality or education. The contribution which

each of the five sets makes to the total provides a means of assessing the consistency

of the estimate and the psychological significance of discrepancies in the test results.

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It is often useful to describe the scale as a test of observation and clear

thinking; by itself it is not a test of “general intelligence” and it is always a mistake to

describe it as such. Each problem in the scale is really the “mother” or “source” of a

system of thought. Hence, the name “Progressive Matrices”. The scale has a re-test

reliability varying, with age, from 0.83 to 0.93. It correlates 0.86 with the Terman-

Merril scale, and has been found to have a “g” saturation of 0.82.

(ii) Administration of the Test

For conducting the test, test booklets and record forms are distributed to the

respective group of students. The students are asked to fill in the information at the

top of the record form. The testing session are held in respective classrooms with

adequate facilities for ventilation and proper setting arrangements. All the necessary

instructions are given to the students. Although there is no time limit to administer the

test, subjects are asked to complete test as early as possible.

(iii) Scoring of the Test

The scoring of the Raven’s Standard Progressive Matrices is completed with

the help of scoring key given in the manual. Each correct answer is awarded one

score and zero score is given to the wrong answer. A total single score for each

subject is obtained on this test. The necessary percentile scores for the individual and

group tests between the ages of 6 and 65 are shown in Table III, IV and V in manual.

4.2 Socio–Economic Status Scale (SES)

(i) Description to the Test

To determine the socio-economic status of pupils, the Socio-Economic Status

Scale (Appendix B) by Meenakshi was used which is a standardized tool primarily

for use in socio-economic investigation in different parts of India. In this test, socio-

economic status is described as a composite variable consisting of four areas namely

(a) Finance, (b) Property, (c) Education and (d) Social Status. Here is an effort to

gauge and individual’s socio–economic status in a society which a person is

surrounded by and of which he is a member which he affects and is affected by. This

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questionnaire is designed for this purpose on a fixed point-scale; points ranging

between 3 and 10, depending upon the component of the variable under assessment.

The scale is comprehensive in nature and does not discriminate between

rural/urban of male/female subjects. Its reliability is checked by test-retest reliability

method, which was found to be r = .82. Validity of the test described in the manual by

the author, is also quite satisfactory.

(ii) Administration of the Test

Socio-Economic status scale booklet is distributed to all the subjects selected

for the study. The students/subjects are asked to fill his/her name, gender, locality,

age, class, caste category etc. on the space provided. Then the first item of the test is

read and explained by the investigator simultaneously item-wise to help the students

understand them properly. After finishing the SESS, students are asked to check back

and make sure that no item has been missed. Few points are already shared to the

students a day before so that they could fill information properly. It is administered in

groups setting, with no time limit.

(iii) Scoring of the Test

For scoring, the scoring key is used which summarizes the information

recorded on the scale and weightage of each item. The obtained scores of respective

categories are recorded in the scoring table. Before that the total weightage of each

item is counted and recorded against each of the seven categories. The raw scores are

compared with the norms to assign the category to the students accordingly. On the

basis of raw scores, the following status categories were classified.

CATEGORY OF SES STATUS

High 105 or above

Above average Between 90 to 104

Average Between 65 and 89

Below average Between 50 and 64

Poor 49 or below

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4.3 Self-Concept Inventory (SCI)

(i) Test Description

Sagar Sharma (1968) prepared an instrument of Self-Concept on Bills IAV

pattern in Hindi. To free the inventory from ambiguities, to increase the

comprehension of the words and earmark of positive and negative connotation of the

various adjectives, a slightly modified version of the test was used in this study.

This Self-Concept Inventory (Appendix C) is a comprehensive valid measure

of self-concept. It consists of 68 adjectives and a self-rating questionnaire. It can

measure the three aspects of self, i.e., real self-concept, ideal self-concept and ideal-

self discrepancy.

The test-retest reliability, content validity and consistency coefficients of the

test as reported by the author are quite satisfactory. It is a very reliable and valid

measure to study the self-related components of the individuals and has been very

widely used in large number of personality studies and diagnostic investigations

which have shown that this test is a reliable and useful measure to assess the self-

concept of the Indian subjects.

(ii) Administration of the Test

Self-Concept Inventory (Sharma, 1968) was administered on the subjects

belonging to all the three groups under study. Subjects responses in SCI were scored

to get their scores on Real Self-Concept, which is prescribed in column I of SCI.

The testing sessions were held in respective classrooms with adequate

facilities for ventilation and proper sitting arrangements. The test was administered

strictly following the instruction specified in the respective test manuals or as

prescribed by the author. Although there was no time limit to administer the test, the

subjects were asked to complete test as early as possible. The subjects were also told

that they were participating in a research investigation, they should be free and

straight-forward in responding to the question given in the test and should complete

the test without any fear and hesitation.

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They were also instructed to answer carefully and to ensure that all questions

of the tests had been answered.

(iii) Scoring of the Test

The scoring of the Sharma (1968) Self-Concept Inventory was done according

to the procedure given in the manual. Scoring was done keeping in view the positive

and negative connotation of the adjectives given in the inventory. The answers were

rated on a five-point scale and the subjects’ score on any range between 1 and 5.

B. SELF-DEVELOPED TOOLS

4.4 Achievement Test

Achievement test is designed to measure, knowledge, understanding or skills

in a specified subject or a group of students. Achievement testing refers to the

assessment of the outcomes of formal instruction in cognitive domain (Dwyer, 1982).

It can also be thought of as a sample of indicator of a student’s knowledge taken at a

particular point of time (Ebel, 1972). In other words, an Achievement test is designed

to measure students’ grasp of knowledge or his proficiency in certain skills. Or, an

achievement test may mean a sample of behaviour that provides opportunity for

comparison with performance standard, as in criterion-referenced testing (Gronlund,

1973; Hambleton et. al. 1976; Popham, 1978). It aids both the teacher and the

students in assessing learning readiness, monitoring learning process, diagnosing

learning difficulties and evaluating learning outcomes (Gronlund, 1977).

The investigator made a thorough survey of Achievement Tests in the current

available literature for seventh grade but could not locate an appropriate Standardized

Achievement Test in Mathematics to evaluate the pupils’ knowledge, comprehension,

application and skills on the topics selected for treatment.

The following steps were followed for developing the tests

(a) Planning the Test

Planning is essential not only in teaching but in all spheres of life. Planning

stage of the test tries to answer what content area is to be covered by the test, what

type of items are to be included in the test and what are the objectives that are going

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to be tested. These questions are important to answer, but too often, they are not

answered prior to the item-writing phase. No doubt, a good test rarely serves multiple

purposes equally well.

Stanley and Hoppins (1978) observed that the planning stage of a test should

include the nature of test items and the statement of conditions under which it will be

administered. The Achievement Test was planned with the objective of measuring

achievement in Mathematics of VII Grade students on selected topics. According to

Gronlund (1988), the planning of Achievement Test takes into account:

(i) Determining the purpose of test;

(ii) Identification and defining the intended learning outcomes;

(iii) Preparing the test specifications; and

(iv) Constructing relevant test items;

Achievement tests do serve multi-facet educational functions. The process of

building them should cause instructors to think carefully about the objectives of

instruction in a course prescribed. It should cause them to define their objectives

operationally, that is, in terms of the kinds of tasks a students must be able to handle

to demonstrate achievement of those objectives and from the students’ perspective,

the process of taking a test and discussing the outcome afterward can be a richly

rewarding learning experience. As Stroud (1946) put it long ago, “It is probably not

extravagant to say that the contribution made to a student’s store of knowledge by

taking of an examination is as great, minute for minute, as any other enterprise he

engages in”.

(b) Objectives of the Test

For the purpose of constructing an Achievement Test, objectives defined in

behavioural terms from selected units of Mathematics text-book of class VII

prescribed by CBSE. Since the major concern here was to test the academic

achievement, accordingly it was decided to test the major areas of cognitive domain,

i.e., knowledge, understanding, application and skills from psychomotor domain.

After determining objectives, the learning outcomes were stated as observable

terminal performance. In order to make sure that the Achievement Test measures a

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desired behaviour, test specifications were developed covering the objectives and

subject-matter selected to be taught during the experiment.

(c) Content of the Test

The test covered the content of the following five units:

1. Rational Numbers

2. Practical Geometry

3. Perimeter and Area

4. Algebraic Expressions

5. Exponents and Powers

To decide the weightage to be given to different content areas, objectives and

different forms of questions, expert opinions of the concerned Mathematics teachers

were taken into consideration.

(d) Preparation of the Test Items/Item Writing

112 objective type test items belonging to recall and recognition type, with

wide range of difficulty were constructed from 5 units of Mathematics syllabus

prescribed by Central Board of Secondary Education for Class VII. Further, these test

items involved multiple choice type, fill in the blanks, true/false and short answer

type items. The most commonly used kinds of objective items are multiple choice,

true-false, matching, classification and short answer (Wesman, 1971).

Both essay and problem tests are less time consuming to prepare than

objective test. But the objective test generally can be scored more rapidly and more

reliably than either of the other types, particularly the essay test. A good objective test

can be constructed so that it will rank a group of students in nearly the same order as

that resulting from a good problem test. But this is not to say that the various types

can be used interchangeably with equal ease and effectiveness (Birenbaum and

Tatsuoka, 1987)

Test items were prepared in conformity with the blue-print designed for that

purpose. While constructing items, it was ensured that no objective remained untested

and language of the test items was understandable and unambiguous and the

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instructions were clear. The test items were arranged properly and assembled into the

test. Easy items were given a place in the beginning and difficult items towards the

end. The preliminary draft in Achievement Test was given to experts in education,

which included experts in measurement and evaluation, experienced Mathematics

teachers. They were requested to give their opinion about the language and

appropriateness of the items. Only those items were selected which had 80%

unanimity. Items having difficult language were modified in simple language.

(e) Preparation of Directions to Test Items

Appropriate directions to test items were prepared. The directions were clear

and concise so that the students understood them easily. Clear instructions were given

at the beginning of the test.

The Achievement test was divided into five sections, viz, Multiple choice,

Fill in the blanks, True-False and Short answer type questions. The first section of the

Achievement test involved multiple choice type items which is more popular and

used extensively because they reduce the chance of guessing and focus on clarity of

subject matter. In this section 3 or 4 possible answers were provided for each item

and students were asked to select/underline/encircle the correct alternative. This

particular section emphasized upon selection of correct alternating rather than the

production of the answer. Producing an answer is not necessarily a more complex or

difficult task, or one more indicative of achievement than choosing the best of the

available alternatives (Quellmalz, Capell and Chou, 1982). In most instances, free-

response and choice type measures are found to be equivalent or nearly equivalent, as

defined by their inter-correlation, within the limits of their respective reliabilities.

Further, the choice-type measure is nearly always more reliable than the free-response

measure and is considerably easier to score (Hogan, 1981 and Paterson, 1926).

The next section in the Achievement test was ‘fill in the blanks’. In this

section, some important words or phrases were deliberately omitted from the

statement of the given problem. Students were asked to write the correct response in

the answer-sheet against the blank.

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The third section of the Achievement test included the true-false type items.

From one point of view, true-false tests seem like a breeze-easier than they ought to

be (Ebel, 1975, Frisbie, 1973). The basic reason for using true-false test items was

that they provided a simple and direct means of measuring the essential outcomes of

formal education. Research evidence has shown that students can attempt three true-

false items in the time required to attempt a pair of multiple choice items (Frisbie,

1973, 1974). The students were asked to write True (T) or False (F) as the appropriate

response against the prescribed statement in the answer sheet.

The fourth and last section of the achievement test involved short answer type

questions. A short answer test item aims to test knowledge by asking them to examine

and supply a word, phrase or number that answers the question or completes the

sentence. Short-answer items deal mainly with factual information reported in single

value, short phrases, numbers or quantities. Generally, short-answer items are much

less affected by guessing than are true-false or multiple-choice items. These things

were taken into consideration while framing this section. Students were directed to

write or solve the problem at their appropriate place and to give the answer as soon as

possible.

(f) Preparation of Directions for Scoring

Cashen and Ramseyer (1969, 1985) found that the test scores of elementary

students were lowered substantially when they were required to record their answers

on a separate answer sheet. To facilitate objectivity in scoring, answer key was

prepared. In scoring the answer recorded in the test booklets, the investigator used a

coloured pen. The marking was done using scoring key already prepared by the

investigator; one mark for a correct answer and zero for an incorrect answer.

(g) Administration of the Test

After making the required improvements, the test was printed and

administered on a sample of 40 students of VII class, who had already studied the

contents covered in the test. Detailed instructions were provided to the students. No

time limit was fixed for the try-out test. It was found that students took, on an average

70 minutes to answer all the questions.

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The try-out test and scoring key are given in Appendix D.

(h) Item Analysis

After scoring the try-out test, the investigator took the 40 sample answer-

sheets by deleting the rest at random. The following steps were followed for item

analysis;

1. Firstly, all 40 answer-sheets were arranged in the descending order

from highest score at the top to lowest score at the bottom.

2. Then, divided these 40 answer sheets into three groups the upper 27%

answer-sheets with highest scores formed the upper group; the 27%

answer sheets with lowest scores formed the lower group; and the rest

of the answer-sheets formed the middle group.

3. After forming the three groups, the next step was to find out and

tabulate the number of correct responses of an item in each group. The

difficulty of an item is indicated by the total number of pupils who

answered it correctly; the larger this number the easier the item. Item

difficulty was estimated by determining the percentage of pupils who

answered the item correctly. The percentages were converted into

proportions. The average of the proportion of correct responses on

each item in the three groups was taken to be an estimate of the

difficulty value of that particular item.

The formula for computing difficulty value ‘dv’ of each item is

( )

3

PlPmPudv

++=

Where,

dv = difficulty value of the item;

Pu = Proportion of correct responses to the item form the upper

group;

Pm = Proportion of correct responses to the item from the middle

group.

Pl = Proportion of correct responses to the item from the lower

group.

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4. Internal Consistency Discrimination Index (rb)

The relationship between the total scores derived from a test and item scores

are referred to as internal consistency discrimination index of an item. It was found

by using the following formula

rb = Pu – Pl

Where,

rb = internal consistency discrimination index;

Pu = proportion of correct responses to the item from the upper group;

Pl = proportion of correct responses to the item from the lower group.

(i) Final Selection of the Items

Final selection of the items was made on the basis of difficulty value and

discrimination index of each item.

a. Difficulty Value

Most of the items selected were having medium difficulty value and

few items with high and low difficulty values were also taken

Lindeman (1971) emphasized that easy items should be included in a

test in order encourage the pupils of low ability. Some difficult items

should also be included to challenge the able pupils. However, in the

interest of constructing a measuring instrument of maximum quality

and utility, most items included should be in the middle range of

difficulty.

b. Internal Consistency Discrimination Index.

According to Garrett (1967), items with validity indices 0.20 or more

are regarded as satisfactory. Thorndike (1955) considered an item with

a validity coefficient as high as 0.25 as an outstanding ‘valid’ item.

Hence, the researcher retained those items for the final draft which

were having internal consistency of 0.25 and higher. The items with

zero discrimination power and negative discriminating power were

discarded while selecting items for the final draft.

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Gronlund (1988) states, “Zero discrimination power (0.00) is obtained when

an equal number of pupils in each group answer correctly. Negative discrimination

power is obtained when more pupils in lower group answer correctly than pupils in

the upper group. Both types of items should be removed from norm-referenced test

and then discarded or improved”.

Thus, 70 items were retained in the final form of the test. The blueprints of the

first and the final draft of Achievement test were as shown in Tables 4.1 and 4.2

Table 4.1

Blue-print of First Draft of the Achievement Test

Chapter Cognitive Levels of Objectives

Q1 Q2 Q3 Q4 Total Items

Rational Numbers 3 5 10 4 22

Practical Geometry 4 2 2 1 9

Perimeter and Area 11 8 6 3 28

Algebraic Expressions 2 10 10 3 25

Exponents and Powers 3 11 11 3 28

Total 23 36 39 14 112

Table 4.2

Blue-print of Final Draft of the Achievement Test

Chapter Cognitive Levels of Objectives

Q1 Q2 Q3 Q4 Total Items

Rational Numbers 3 3 7 4 17

Practical Geometry 4 1 2 - 7

Perimeter and Area 9 4 3 1 17

Algebraic Expressions 1 5 7 1 14

Exponents and Powers 2 7 5 1 15

Total 19 20 24 7 70

Q1 = Knowledge; Q2 = Comprehension; Q3 =Application; Q4 = Skill

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In the final draft of the Achievement Test, chapter-wise description of the

number of items retained at different levels of objectives are as given in the Table 4.3

Table 4.3

Number of items retained in the final draft of Achievement Test at different

cognitive levels of objectives

Cognitive

level of

objectives

Chapter-wise serial number of items retained Total

Rational

Numbers

Practical

Geometry

Perimeter

and Area

Algebraic

Expressions

Exponents

and

Powers

Knowledge

Level

1,25,41 6,7,8,45 9,10,11,29,

30,32,47,48,

49

15 40,57 19

Understanding

Level

2,26,62 46 31,52,53,54 13,14,16,58,

68

18,20,24,

38,39,51,

70

20

Application

Level

3,4,5,27,

28,60,61

59,44 36,65,66 17,33,35,37,

50,55,69

19,21,22,

56,67

24

Skill Level 42,43,63,

64

-

12 34 23 7

Total 17 7 17 14 15 70

(j) Standardization of Achievement Test

Seventy items were selected for the final form of the achievement test. This

selection sets the state for the standardization or experimental validation of the test,

including establishing reliability and validity.

(i) Reliability of the Test

Reliability is one of the most important pre-requisites of a measuring

tool. Reliability refers to the consistency of test score or it is the degree

of consistency between two measures of the same test. The reliability

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of a test refers to the extent to which a test measures consistently from

one administration of the test to another. The reliability of the test is

measured by split-half method (odd-even method). The coefficient of

reliability was found to be 0.86.

(ii) Validity of the Test

Validity is the extent to which a test measures what it purports to

measure (Cronbach, 1970). Validly is a concern for the relationship

between the purposes set to achieve, on the one hand, and the efforts

made, the means employed and what these efforts and means actually

achieve, on the other. The validity of the Achievement Test

constructed for the study was taken for granted in accordance with

Guilford’s (1971) statement: “There are some measures whose validity

is taken for granted, for example, achievement test scores”.

Regarding the method of establishing the validity of the test, Mouley (1970)

stated: ‘At the most elementary level, it is necessary for all the tests to have content

validity, i.e., each question must be related to the topic under investigation; there

must be an adequate coverage of the overall topic; the question must be clear and

unambiguous etc. The most adequate approach to validation consists of checking the

agreement between the responses elicited by the question against the criterion.

The test was validated against the criterion of content validity. Content

validity is the most important criterion for the usefulness of the test, especially of an

achievement test. It is a measure of the match between the content of the test and the

content of ‘teaching’ that precedes it. The measure is represented subjectively after a

careful process of inspection comparing the content of the test with the objective of

the course of instruction Thorndike (1975) maintained that problem of content

validity is parallel to the problem of preparing a blue-print for a test and then building

a test to match the blue-print. The Achievement test was found to possess content

validity as there was correspondence between the table of specifications and test

items.

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(k) Final Form of the Test

The final form of the Mathematics Achievement Test contained 70 items.

(The final test along with the scoring key is given in Appendix E)

4.5 Cooperative Learning Lesson Plans (Instructional Material for Teacher-

Directed Instruction in Cooperate Learning Setting)

The steps followed in the development of teacher-directed instructional

material in co-operative learning setting were as follows:

(i) Selection of the content

The content was selected from the Class VII syllabus of Mathematics,

prescribed by Central Board of School Education, New Delhi published by NCERT,

October 2007 as outlined in Table 4.4.

Table 4.4

Chapter-wise Content Specification

Chapter

Number Contents

1

Rational Numbers (Need, Meaning/Definition, Positive and

Negative Rational numbers, Number Line, Standard form,

Comparison of Rational numbers, operations on Rational numbers

2 Practical Geometry (Construction of parallel line, construction of

Triangles under SSS, SAS, ASA and RHS Criterion)

3

Perimeter and Area (Area of Squares and Rectangles, Triangles as

parts of Rectangles, Congruent Parts of Rectangles, Area of

Parallelogram, Area of Triangles, Area of Circles, circumference

and its Applications

4

Algebraic Expressions (Expression Formation, Terms, Coefficients,

Factors of a term, Like and Unlike Terms, Monomials, Binomials

and Polynomials, Addition and Subtraction of Algebraic

Expressions, Finding the value of an expression and geometrical

patterns)

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5

Exponents and powers (Exponents, Laws of Exponents

Multiplication, Decision , Power of a power, Number with

exponent zero, Decimal Number System and Expression in the

Standard Form)

(ii) Content Analysis

Content was divided into 25 sub-topics/subject units limit so that each unit

may be taught in 40 minutes’ duration. Care was taken to place each sub topic/sub-

unit in a logical and psychological sequence.

For each type of learning matrix, analysis and sequence analysis were

conducted, because students were likely to learn more if the material is presented in a

correct sequence. Planning for learning sequence was done in a logical order. One

learning event precedes another event because it is a component or because it

provides a meaningful context for what is to follow.

(iii) Writing of Instructional Objectives

Instructional objectives were developed in terms of the behavoural outcomes

expected from the learners. These concepts and skills that needed to be learned by the

students in a particular unit were identified and decisions regarding their sequence

were taken. Instructional objectives were written for each sub-unit, as placed in Table

4.5.

Table 4.5

Chapter-wise Instructional Objectives

At the end of instructions, learners will be able to:

(1) Rational Numbers

1.01 define rational numbers.

1.02 recognize the need of rational numbers.

1.03 distinguish numerator and denominator.

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1.04 identify positive and negative rational numbers.

1.05 generate another rational number equivalent to the given rational number.

1.06 construct the equivalent rational numbers.

1.07 represent a rational numbers on a numbers line.

1.08 transform the rational number in standard form.

1.09 compare two integer, fractions and rational numbers.

1.10 find unlimited number of rational numbers between any two rational

numbers.

1.11 use different operations like addition, subtraction, multiplication, division

etc. on rational numbers.

1.12 develop the ability to calculate rapidly and accurately.

(2) Practical Geometry

2.01 construct a line parallel to given line.

2.02 recall important properties concerning triangles.

2.03 modify the construction of parallel lines by using the idea of equal

corresponding angles instead of equal alternate angles.

2.04 construct a triangle when the lengths of its three sides are known i.e., SSS

criterion.

2.05 construct a triangle when the lengths of two sides and the measure of the

angle between them are known i.e., SAS criterion.

2.06 construct a triangle using ASA criterion.

2.07 construct a right – angled triangle when the length of one leg and its

hypotenuse are given i.e., RHS criterion.

2.08 develop the ability to draw rough sketch of triangles using different

criterions.

2.09 discriminate the different shapes of triangles and different criterions.

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(3) Perimeter and Area

3.01 recognize the plane figures viz., squares and rectangle.

3.02 recall formulae for the perimeter of a regular polygon, square and rectangle.

3.03 recall formulae for the area of square and rectangle.

3.04 find the area and perimeter of square band rectangles.

3.05 analyze the arise problem as which is given and what is to find out.

3.06 develop the ability to think correctly, to draw inferences and to generalize.

3.07 develop the ability to estimate and check results.

3.08 relate triangles as parts of rectangles.

3.09 use the concept of congruency to get the area for each congruent part of

rectangles.

3.10 draw a parallelogram on a graph paper.

3.11 find the perimeter and area of parallelogram.

3.12 recall and recognize the area of triangles.

3.13 compute height or base if area of triangle or parallelogram is given.

3.14 identify circle in a group of other circular shapes.

3.15 state circumference, radius and diameter.

3.16 evaluate the value of п (Pi).

3.17 infer about the area of a circle with a given radius.

3.18 recall the formula for the calculation of the area of a circle.

3.19 solve the new problems related to circle parallelogram, square and rectangle

(plane figures).

3.20 convert the units for lengths.

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(4) Algebraic Expressions

4.01 labels variables and constants.

4.02 classify the expressions, terms factors and coefficients.

4.03 identify like and unlike terms.

4.04 classify the expression as a monomial, a binomial, a trinomial or

polynomial.

4.05 collect and simplify combining like terms.

4.06 compute different operations like addition and subtraction on algebraic

expressions.

4.07 find the value of an expression whether particulars values of variables are

given.

4.08 generate the number pattern which in turn shows an expression.

(5) Exponents and Powers

5.01 justify the need of exponents and powers recognize the base and exponent if

a number expressed in exponential form.

5.02 express a number in exponential form.

5.03 write a number as a product of powers of prime factors.

5.04 compare two numbers stated in exponential form.

5.05 recall different laws of exponents.

5.06 use the laws of exponents.

5.07 simplify and write the answer in exponential form.

5.08 write/convert large numbers in the standard form.

5.09 find the number from the expanded number form.

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(iv) Developing the Lesson Plans

25 lesson plans were developed to be administered as instruction treatment to

class VII students. During planning, besides keeping in the mind the abilities,

interests and needs of students, logical order of the content was also taken care of.

Appropriate learning conditions were utilized while designing lessons and provisions

for desired instructional events were made. Appropriate instructional aids were

planned, wherever required in the lesson. The lessons were arranged properly in

sequence relating to their pre-requisites.

The following events of instruction need to be initiated at various points of the

lesson plan, that is:

(a) Direction attention;

(b) Information learner of the objective;

(c) Stimulating recall of pre-requisites;

(d) Presenting stimulus material;

(e) Evolving student responses;

(f) Providing feedback;

(g) Guiding thinking;

(h) Enhancing retention and transfer; and

(i) Evaluating student performance (Gagne, 1977)

After accomplishment of the process of lesson designing, the lesson plans

were developed under the following headings:

� Topic;

� Instructional objectives;

� Entry behaviour;

� Instructional aids; and

� Instructional programme.

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The lesson plans were developed as per guidelines from the book and

discussion with the experts in this field. (Appendix –F)

4.6 Development of Worksheets

(i) Preparation

Equal number of worksheets, i.e., 25 worksheets were developed to be utilized

for practice in cooperative learning setting (by forming small groups) immediately

after the lesson is delivered by the teacher (researcher). Though the time limit was not

strictly followed, students in groups were allowed to complete them at their own

pace. The worksheets were constructed in such a way that all the groups were able to

complete them within 40 minutes.

The items in the worksheets were so framed that they covered each and every

aspect of the lesson delivered by the teacher. Different types of items were framed

viz. fill in the blanks type, true/false type, multiple choice type, short answer type,

etc.

(ii) Try-out of the Worksheets

Worksheets were tried out on a small group of students to obtain their

response regarding effectiveness of worksheets and were modified according to the

need raised.

(iii) Validation of Worksheets

Responses of students to the worksheets and their scores on the post-test

indicated that they were instructionally sound. Changes were made, when needed,

with respect to sequence; content; presentation; and clarity in language. The

suggestions of experts were incorporated. Lessons and worksheets were again

reviewed (A copy of a worksheet out of twentyfive worksheets is given in

Appendix G).

4.7 Formative Tests

Overall 13 formative tests were developed to measure the performance of

students after teaching each of the five chapters. The number of formative tests was

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decided after taking care of length and difficulty of the content prescribed in the

chapter, their number was varying from two to four each chapter. The tests were

developed through the following steps.

i) Planning

Planning is a must for the successful execution of a task. It not only caters to

the proper realization of the aims or purposes of doing that task but also helps in

proper utilization of the time and energy on the part of human and material resources.

Planning of formative tests covers selection of topic, development of instructional

objectives and preparation of items. The investigator selected five units from syllabus

of Mathematics of class VII and 13 formative tests were prepared, keeping in the

view the length and difficulty of the chapter.

ii) Preparation

The first draft of the test was developed keeping in mind the instructional

objectives (as given earlier in Table 4.5). After consulting the experts in the field of

Mathematics, formative tests were developed. These tests were combination of both

subjective and objective type questions. Objective type questions were allotted one

mark each and short answer type questions (subjective type) were allotted 2-5 marks,

depending upon length of the question.

iii) Try-out

All the formative tests were tried out on a small group of students of class

VIII who had already studies the content. There was no time limit. After the test,

students were asked to point out items which were not meaningful or comprehensible

or were not in the syllabus. The difficulty values and discriminating power of items

were also calculated.

iv) Final Draft of Formative Tests

The items were arranged from easy to difficult on the basis of difficulty values

index. The items were improved, keeping in mind the difficulty value and

discrimination power of the items. Very poor items were rejected. Comments and

suggestion of students were also incorporated in the final draft thus developed.

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v) Validity

Content validity was determined by comparing the items in a test with content

and objectives of a particular domain to see that they match, as it is essential for a

valid test to reflect content of a particular domain. The entire formative test

represented a fairly well-defined universe of content, so they were considered valid

(A copy of two out of thirteen formative tests is given in Appendix H).

Overview :

It was envisaged that the use of seven crease tools would provide enough data

to inspect the problem in its minutest particulars and lend a hand to put forward the

measures of impact on the predetermined variables outlined for the study, namely, the

effectiveness of cooperative learning strategies (STAD and Jigsaw) in relation to

learning outcomes and self-concept. The data collected was subjected to mean score

analysis and interpretations along selected variables in an experimental situation to

arrive at significant findings of the study.