Preparation Of Achievement Test In Mathematics Pdf

In the present article multiple choice questions (MCQ) type Mathematics Achievement test is constructing according to blue print. The Construction of test items is an important phase in the development of a test as the reliability, validity of the test depends upon the test items. The discriminative Index find out the difficulty value of each item. The nature of questions for achievement test consisted of matching type and multiple choice questions. This achievement test is constructing for Geometry content of Mathematics for IX th grade student.

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Educational Quest: An Int. J. of Education and Applied Social Science: Vol. 8, No. 2, pp. 651-655, August 2017

DOI: 10.5958/2230-7311.2017.00115.5

Construction and Standardization of Mathematics

Achievement Test for IXth Grade Students

Reena Rani* and Anisha

Institute of Teacher Training and Research, B.P.S. Mahila Vishwavidyalaya, Khanpur Kalan, Sonipat, Haryana, India

*Corresponding author: reena.edu@gmail.com

ABSTRACT

In the present article multiple choice questions (MCQ) type Mathematics Achievement test is constructing

according to blue print. The Construction of test items is an important phase in the development of a test

as the reliability, validity of the test depends upon the test items. The discriminative Index nd out the

diculty value of each item. The nature of questions for achievement test consisted of matching type and

multiple choice questions. This achievement test is constructing for Geometry content of Mathematics

for IXth grade student.

Keywords: Construction, standardization, mathematics achievement

The achievement tests constitute an important tool

in the school evaluation programme. It is necessary

for the teacher to know how for the pupil have

attained in particular subject area. Achievement

test also measure skills and knowledge learned in

a given grade, usually through planned instruction

and training. In Mathematical achievement learning

of mathematical concepts which influences on

students performance in mathematics.

According to N.M. Downie (1961), "Any test that

measures the aainments or accomplishments of

an individual aer a period of training or learning

is called an achievement test."

Conceptual Framework of Achievement Test

This test was constructed on the basis of the

objectives of teaching; knowledge, understanding

and application in mathematics at the secondary

stage. Keeping in view these objectives, the syllabus

of mathematic was analyzed from mathematics text

books of IX class prescribed by NCERT. Identify

the important concepts of Mathematics Geometry

at IX level. Then the items were prepared from the

content of geometry. A mathematics achievement

test is one which is designed to measure knowledge

understanding or skill in specied subject or group

of subjects.

Before constructing the Mathematics achievement

test, investigator analyses the various tests available

for testing in the eld of Mathematics. It was felt

that lack of suitable test to evaluate achievement in

Mathematics Geometry. The achievement tests give

reliable information regarding the decisions taken

in the context of Mathematics education.

Construction of Mathematical achievement

Test

A good test is prepared through a systematic

process. The process of test development was

completed through five basis steps namely:

test conceptualization, test construction, item

scoring and analysis, reliability and validity and

test standardization. For the construction of an

achievement test the investigator was adopted the

following steps which as shown in below:

DEFI

CONST

UCT

SCALE

CONSTRUC

PILOT

TUDY AND

REVISION

INISTRA-

ON AND

ITEM

ALYSIS

VA L I

ATE

Fig. 1: Steps of Test Construction

Rani and Anisha

652

Print ISSN: 0976-7258 Online ISSN: 2230-7311

Preparation Dra for Achievement Test

After the review of literature, Achievement test

was prepared of IXth class for geometry content.

An achievement test on the module of Content

Dierence: Geometry content was prepared by the

investigator. The preliminary dra was given to

expert in education and experienced mathematics

teacher. After receiving their opinions, items in

dicult language were modied to simple language

statement and 20 items were eliminated from the

dra.

Objective of Achievement Test

The review of the literature indicates that

standardized tools for the mathematics achievement

are available for IXth grade, but no such tool is

available for geometry content. In the present work,

investigator has prepared the achievement test in

mathematics of IXth standard students. The most

important steps in planning, a test was to identify

the instructional objective. As researcher has

taken the subject mathematics, so major objective

were categorized as knowledge, comprehension,

application and skill. The instructional objectives

were dened in behavioral term from selected units

of mathematics text book prepared by NCERT for

IXth grade. Achievement test have many purpose:

1. Diagnose strength and weaknesses

2. Assess level of competences

3. Assign Grade

4. Achieve Certication

5. Advanced Placement

6. Content evaluation

7. Informational Purposes

Weightage to instructional objectives and

content

To decide the weightage to be given to dierent

content areas, objective and different form of

questions, and expert opinion of the concerned

Math's teachers was taken in to consideration.

Content of the Test

At this state, the investigator has to determine which

content to be tested in this paper. The test covers

the content of Geometry. All the content was cover

into eight chapters and these chapters as shown in

the table below.

Table 1: Content selected for achievement test

Sl. No. Selected content

1Lines and Angles

2 Triangle

3 Quadrilaterals

4 Circle

5 Cube and Cubiod

6 Cylinder

7 Cone

8 Sphere

SKI

L 35

eightage

bjective

OWLED

10%

LICATI

32.5%

22.

ERS

ING

Fig. 2: Weigthage given to every objective in percentage

form

Blue Print

Blue Print is a detail plan of any action or outline.

It provides the users with basis instruction on

the rationale for the process in creating test blue

print. In education area, blue print provides

students an interactive approach for education

planning, curriculum expectation and the learning

objective. A test Blue Print ensures appropriate

items representation of content. The details of test

aer second try out is given in the form of blue

print. The graphical presentation is given below:

Key of the test

The marking scheme helped to prevent inconsistency

in judgment . In the item scoring for multiple type

Construction and Standardization of Mathematics Achievement Test for IXth Grade Students

653

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question were scored 1 for correct response and zero

for wrong response.

Table 3: Scoring paern of multiple choice question

items

Item Type Correct Responces Wrong

Responces

Multiple Choice 1 0

First try out

The pilot testing was done on a sample of forty

IXth students, selected on the basis of purposive

sampling. The number of the students in the rst

dra was kept small because it was used to check

the ambiguity of items and appropriateness of

language. Aer administration of preliminary dra,

suggestions and observations were taken from these

students in relation to understanding of statements,

appropriate of language, repetitition if any. Some of

the statements were modied as per the observation

given by the IXth class students. The edited scale

constituted sixty items. The pilot test helped the

investigator to give the nal test.

Item Analysis

Item analysis helps to detect the strength and

weakness of test items. The two extreme groups, the

high and low 27% formed the criterion group for the

calculation of diculty and discrimination indices

of the test items. The following formulae were used.

P = Diculty level

Ru = Higher group given corrected response

R1 = lower group given corrected response

Nu = Total number of person of higher group

N1 = Total number of person of higher group

On the basic of these formulas level and question

find difficulty level. Sometimes students given

answer on guessing. To remove these guessing

researcher use these formulas given under:

=−

S = Correct score

R = Number of correct response

W = Number of incorrect responses

K = Number of response options or choice used

in the item

The process of Item Analysis is carried out by using

two contracting test groups composed from the

upper and lower 27% of the testees on which the

items are administered or trial tested. The upper

and lower 27% when used are beer estimate of the

actual discrimination value. They are signicantly

dierent and the middle values do not discriminate

suciently. In other to get the groups, the graded

test papers are arranged from the highest score to

the lowest score in a descending order. The best

27% are picked from the top and the poorest 27%

from the boom while the middle test papers are

discarded.

Ebel and Frisbie (1986) gave the following rule of

thumb for determining the quality of the items, in

terms of the discrimination index. Table 4 shows the

values DI and their corresponding interpretation.

Table 4: Discrimination index

Range Grade Recommendations

> 0.39 Excellent Preserve

0.30-0.39 Good Possibilities for enhancement

0.20-0.29 Average Need to verify/review

0.00-0.20 Poor Reject or review in depth

< -0.01 Worst Remove

Table 2: Number of items

CONTENT/UNIT

Sl. No. Instructional

objective

Angles Triangles Quadriletral Cube and

Cubiod

Circle Cylinder Cone Sphere Total Per.(%)

1 Knowledge 3 1 4 10

2 Understanding 2 2 1 3 1 9 22.5

3 Application 3 2 2 1 2 2 1 13 32.5

4 Skill 4 1 2 3 2 1 1 14 35

Total 9 7 5 5 3 3 5 3 40 100

Rani and Anisha

654

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Table 5: Distribution of discriminating index of items

of rst dra of achievement test

Range ITEMS Total

> 0.39 1,2,4,6,9,10,11,14,15,16,17,20,24,29,35,37,

38,40,44,46,49,50,51,52, 53,57,58,59,

0.30-0.39 3,19,25,28,30,31,32,33,36,41,48,55 12

0.20-0.29 7,26,42,43, 4

0.00-0.20 5,8,21,22,23,34,39,45,47,54,60, 11

< 0.01 12,13,18,27,56, 5

Total 60

Final Try -out

Aer rst try out of the mathematics achievement

test was given and administered on another group

of 40 students of IXth class. Same process of rst try

out was followed for nding diculty value and

discriminating index.

Table 6: Item analysis Final Try out dra

Level of

Diculty

Medium (.034-0.66) Remark Total

> 0.39 1,2,4,6,9,10,11,14,15,16,17,20,2

4,29,35,37,

38,40,44,46,49,50,51,52,53,57,

58,59,

Excellent

items

0.30-0.39 3,19,25,28,30,31,32,33,36,41,

48,55

Good

Items

Total 40

Tryout is an essential step in the construction

and standardization of a test. It helps to detect

the difficulty and discriminating power of the

test whereby the test items may be arranged in a

sequential manner. The investigator established a

rapport with the respondents and apprised them

about the purpose of the test. Then the instruction

and statement of test was explained in the class. The

marking scheme were used in two form: Correct

answer was given one marks, wrong answer was

given zero mark. The dra of the Achievement test

is given in Table 6.

Reliability of the Tool

The reliability of the tool was estimated by Split

– half method. The tool was administered and d

the odd on the group of 40 students. In split half

method 80 questions were divided in two halves.

The rst set of scores represents performance on the

odd–numbered items 1,3,5,7, etc. and the second

set of scores on even numbered items 2,4,6,8, etc.

Coecient of correlation was computed between

the rst and second set of scores. Spearman –Brown

Prophecy was used to find out the reliability

formula give under:

rtt

r = Reliability coecient of whole test

r = Reliability coecient of half -test

The reliability coefficient between two ratings

was found to be 0.86. The reliability of the tool

was estimated by test-retest method. The tool was

administered and repeated on the same group of 40

students aer a time interval of 4 weeks. Coecient

of correlation was computed between the first

and second set of scores. The reliability coecient

between two ratings was found to be 0.84.

Validity of the tool

The validity coecient reported here show that the

achievement test used in the study is reasonably

Table 7: Number of items in the nal dra of achievement test at dierent cognitive levels of objectives i.e.

Knowledge, Understanding, Application and Skill

CONTENT/UNIT

Sl.

No.

Instructional

objective

Angles Triangles Quadriletral Cube and

Cubiod

Circle Cylinder Cone Sphere Total

No.

1 Knowledge 1, 3,4,(3) 10(1) 18 4

2 Understanding 2 ,6(2) 12,13(2) 20,21 33,34,35(3) 38(1) 9

3 Application 14,15,16(3) 17,19(2) 25,26(2) 29(1) 31,32(2) 36,37(2) 40(1) 13

4 Skill 5,7,8,9,(4) 11(1) 22,23,24(3) 27,28 30(1) 39(1) 14

Total 9 7 5 5 3 3 5 3 40

Note: Figures in parenthesis shows Number of questions.

Construction and Standardization of Mathematics Achievement Test for IXth Grade Students

655

Print ISSN: 0976-7258 Online ISSN: 2230-7311

valid. Content validity of the test, which requires

the determination of the adequacy of each item

was ensured through careful planning of the test,

satisfying the adequacy of sampling of test items

models of the construct to be measured and the

meticulous analysis of the test items of experts. The

statistical validity of the test items included in the

test was compared with the objectives of the topics

taught. It was found that there was correlation

between the items and objectives. So it can be clam

that test has got content validity. The coecient

of correlation was 0.87. The validity coefficient

reported here show that the achievement test used

in the study is reasonably valid.

Norms

A standardized test must have norms which should

be the average performance of a group or groups

that the examiner has taken for the administration of

the nal form. Norms are measure of achievement

which represents the typical performance of a group

or groups. Norms are used for interpreting the

scores of the individual or a class. This achievement

test follow the age norms.

CONCLUSION

Achievement tests have been used for the

certication and selection to assess student progress

at the end of secondary school and for admission

to higher education. It has been widely used in

occupation and professional licensing situation as

well. An achievement test is also used for purposes

of guidance and counseling. It has found useful

in remedial teaching programmes as well as in

determining the class to which a student should

be admied into. Administration of these tests at

regular intervals is helpful to teacher in knowing

the kinds of difficulties faced by the pupils in

learning. So nally we can say that the achievement

test may use as aid in the evaluation of teaching

the importance of instructional techniques and the

revision of curriculum content.

REFERENCES

Best, J.W. 1982. Research in Education, 4th Edition, Prentice

Hall of India Pvt. Ltd., New Delhi.

Bloom, Benjamin S. 1956 Ed., Taxonomy of Educational

Objectives, David McKay Company, Inc., New York.

Downie, N.M. 1961. Fundamentals of measurement. Oxford

University Press, New York.

Ebel, R.L. 1972. Essentials of Educational Measurement,

Prentice Hall, Englewood Clis, New Jersey.

Ebel, R.L. and Frisbie, D.A. 1986. Essentials of educational

measurement. Englewood Clis, NJ: Prentice-Hall.

Singh, R.D., Ahluwalia, S.P. and Verma, S.K. 1991. Teaching

of mathematics: Eectiveness of CAI and conventional

methods of instructions.

ResearchGate has not been able to resolve any citations for this publication.

Robert L. Ebel

1965 ed. published under title: "Measuring educational achievement". Incl. bibl., index.

Fundamentals of measurement

N M Downie

Downie, N.M. 1961. Fundamentals of measurement. Oxford University Press, New York.

Teaching of mathematics: Effectiveness of CAI and conventional methods of instructions

R D Singh
S P Ahluwalia
S K Verma

Singh, R.D., Ahluwalia, S.P. and Verma, S.K. 1991. Teaching of mathematics: Effectiveness of CAI and conventional methods of instructions.