International Journal of Informative & Futuristic Research...

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Research Paper

International Journal of Informative & Futuristic Research ISSN (Online): 2347-1697

Volume 2 Issue 10 June 2015

Abstract Developing countries more concentrate on science concepts especially Mathematics concepts. Every civilization changes through getting Mathematics knowledge. Mathematics knowledge provides the major contribution to scientific innovations. Mathematics is one of the important subjects for Ninth standard students. Nowadays, SC/ST people are deprived from socio-economic prospects. Society refuses the development through educational opportunity. The students feel their untouchable position in their classroom and other public place. Such reason has affected their education. They meet learning difficulties in Mathematics continuously. So the study is very important to find that one of the learning difficulties during students meet studying in Mathematics. We analyze the students knowing the basic concepts, rules and laws of four basic operation by using +, - sign rules on numerical and algebraic in Mathematics. The purpose of the study focused on Ninth standard SC/ST students who have learning difficulties in Mathematics is to find the learning difficulties through analysing their achievement test in Mathematics by using research questionnaire. Tool measures students’ achievement as well as learning difficulties about the students knowing the basic concepts, rules and laws of four basic operation by using +, - sign rules on numerical and algebraic in Mathematics. Also we find how to use the +, - sign rules during problem solving in Mathematics. The tool measures the students’ scores out of 60 as allotted timing only. The Pudukkottai educational district is one among backward districts in Tamil Nadu educational districts. In this context, it is worthwhile to find the learning difficulties in Mathematics through diagnostic analysis among SC/ST students’ achievement in Mathematics in Pudukkottai educational district. Such students are studying in Government, Government Aided and Adi-Dravidar schools in Pudukkottai educational district. Thus an attempt is made to explore rules of four basic operations (BODMAS) and rules of +, - sign and rules of combination of both at Ninth standard SC/ST students level.

A Diagnostic Analysis Among The Ninth Standard

SC/ST Students’ Achievement In Mathematics In

Pudukkottai Educational District Paper ID IJIFR/ V2/ E10/ 008 Page No. 3551-3562 Subject Area Education

Key Words Mathematics, Ninth Standard SC/ST Students, Socio-Economic Prospects,

Received On 03-06-2015 Reviewed On 10-06-2015 Published On 12-06-2015

B. Prabakaran

Assistant Professor Department of Education Government College Of Education, Pudukkottai. Tamil Nadu

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ISSN (Online): 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)

Volume - 2, Issue - 10, June 2015 22ndEdition, Page No: 3551-3562

B. Prabakaran: A Diagnostic Analysis Among The Ninth Standard SC/ST Students’ Achievement In Mathematics In Pudukkottai Educational District

1. Introduction

Education initiates the process of discovery of knowledge within the mind and is the medium of

development in social consciousness and national regeneration. The UNESCO‟S World Education

Report (1991) has pointed out that there is a growing international consensus on the importance of

education for the quality of life in society and for national development at large. It combines

intellectual growth with socialization of individual and paves the way for enhanced awareness,

greater openness, ability and courage to question and toughness to search for solution. Education in

other words, must lead a life-long process of development exploration, within its two dimensions,

one being the self and other being the community and the wider society.

Education must seek to permit the individual to the fullest of his capacities for adjustment to

continuous change in order that he may meet the problems of his day and solve them successfully

when they arise. He must be free and unhampered yet steady and reliable, capable of cooperating

for mutual good but capable of clear, independent thinking unswayed by propaganda and

emotionalism. To do this, education needs individualization and liberation. As a result of scientific

and technological inventions and discoveries education has achieved these to a greater extent.

Education plays a predominant role in developing human skills, in improving the conditions of

social environment and in shaping human personality. Education is a fundamental part of a total

society and becomes an indispensable factor for the development of various spheres of society.

Today, it has been conceptualized as a factor that promotes economic growth and therefore, is an

important area for investment. More nations are recognizing their responsibility in the area of

education. Investment in education of youth is considered as most vital by all nations. The world

conference on EFA(1990) states that every person, child, youth and adult should be able to benefit

from educational opportunities, designed to meet their basic learning tools and learning content

required to develop their full capacities.

2. Definitions Of Mathematics

The dictionary meaning of Mathematics is that „it is either the science of number and space or

science of measurement, quantity and magnitude. Mathematics is thus defined as the science of

quantity, measurement and spatial relations. It is systematized, organized and exact branch of

science. It deals with quantitative facts, relationship as well as with problems involving space and

form. It is a logical study of shape, arrangement and quantity.

3. Needs For The Study

Mathematics is one of the important subjects for Ninth standard students. Generally the

Indian culture basically builds on aesthetics and religious irrational thinking. So our country people

believe in many gods rather than Mathematics. So we do not compete with other countries. We will

compete with other countries only by the way of development through Mathematics knowledge

upgrading. But unfortunately we degrade to Mathematics knowledge than world average

knowledge of Mathematics. So many discoveries, research and inventions are not original in India

because there is no proper way of knowledge transfers from teacher to students especially the

teachers insists the concept of Mathematics is a risky subject on all students‟ mind. If Students feel

Mathematics is hard, they will get more difficulties in the subject. So the calculate measurement of

the students achievement in Mathematics through MAM Tool is planned.

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4. Importance Of The Study

Nowadays, SC/ST people are deprived from socio-economic prospects. Society refuses the

development through educational opportunity. Most of the parents are not aware on their children

who do not know how to provide the education opportunity in proper way. Government takes the

steps to provide educational opportunity for all deprived students by the article 45 in the

constitution of India. Socio-economic problems influence with their educational study throughout

their life. The students feel their untouchable position in their classroom and other public place.

Such reason has affected their education. They meet learning difficulties in Mathematics

continuously. So the study is very important to find that one of the learning difficulties during

students meet studying in Mathematics. We analyze the students knowing the basic concepts, rules

and laws of four basic operation by using +, - sign rules on numerical and algebraic in

Mathematics. Till today, improper diagnostic way may make the students‟ drop out and wastage in

high rate. The proper diagnostic research is important in this situation to be increased enrolment in

school level on attract students as much as possible.

5. Scope Of The Study

The purpose of the study focused on Ninth standard SC/ST students who have learning

difficulties in Mathematics is to find the learning difficulties through analysing their achievement

test in Mathematics by using research questionnaire. Tool measures students‟ achievement as well

as learning difficulties about the students knowing the basic concepts, rules and laws of four basic

operation by using +, - sign rules on numerical and algebraic in Mathematics. Also we find how to

use the +, - sign rules during problem solving in Mathematics. The tool measures the students‟

scores out of 60 as allotted timing only. Also the study may help to enhancing students‟ knowledge

about the students knowing the basic concepts, rules and laws of four basic operation by using +, -

sign rules on numerical and algebraic in Mathematics through analysing their strength and

weakness.

6. Objectives Of The Study

The objectives of a research project summarize what is to be achieved by the study. These

objectives should be closely related to the research problem.

6.1 General Objectives

(i) To find out the SC/ST students‟ achievement in learning Mathematics through MAM or

MLDM tool.

(ii) To list out the SC/ST students‟ learning difficulties in Mathematics through MAM or

MLDM tool.

6.2 Specific Objectives

(i) To find out the average of SC/ST students‟ achievement in Mathematics.

(ii) To calculate the percentiles of SC/ST students‟ achievement in Mathematics with

regard to type of schools.

(iii) To list out the reason for the students‟ learning difficulties which are measured through

MAM tool from the percentage analysis?

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7. Statement Of The Problem

Developing countries more concentrate on science concepts especially Mathematics

concepts. Every civilization changes through getting Mathematics knowledge. Mathematics

knowledge provides the major contribution to scientific innovations. Now India concentrates more

on Mathematics enhancing students‟ academic achievement in Mathematics. Mathematics is

developing reasoning ability, logical sequence, rational thinking, problem solving ability and etc.,

therefore, everybody should study compulsory subject namely Mathematics. Nowadays academic

achievements influence the students‟ future carriers and vocational carriers. There is no way to

assess the students‟ potential in education field except academic achievement. No alternate found in

modern world of education field until now. We measure students‟ ability, cognition, skills etc., by

using academic achievement marks analysis. Now most of the students are securing more scores in

their mark statements but their educational outcomes are irrelevant to their mark statements at any

level. We feel that the gap between academic achievements and their competitive examinations that

means they fail the National, International and State competitive examinations. Basic knowledge

foundation ensures successful life in student‟s futures. Every competitive examination gives

importance to test the Mathematics knowledge. If students get basic knowledge in Mathematics,

they will tackle with easy to solve any problem in their life.

Basic knowledge in Mathematics of Ninth standard will be used to secure more marks in

Tenth standard. SC/ST students meet many problems in family as well as society. Their education

is affected by those problems. Also they meet social problems, emotional problems and economic

problems. They are treated as untouchables. The Pudukkottai educational district is one among

backward districts in Tamil Nadu educational districts. In this context, it is worthwhile to find the

learning difficulties in Mathematics through diagnostic analysis among SC/ST students‟

achievement in Mathematics in Pudukkottai educational district. Such students are studying in

Government, Government Aided and Adi-Dravidar schools in Pudukkottai educational district.

Thus an attempt is made to explore rules of four basic operations (BODMAS) and rules of +, - sign

and rules of combination of both at Ninth standard SC/ST students level.

8. Operationalization Of Variable

The meaning of important terms used in study is given below:

Educational Diagnosis

Diagnostic testing is individually administered tests designed to identify weaknesses in the learning

processes. Usually these are administered by trained professionals and are usually prescribed for

elementary, sometimes middle school, secondary, higher secondary and higher studies students.

Educational diagnostic analysis through test identifies the students‟ weakness and errors in the

particular unit or small part in their hard subjects. Now I shall find the study about diagnostic

analysis for the problem of students‟ learning difficulties in numerical and algebraic fundamental

operation by using +, - sign rules in Mathematics, such difficulties affect achievement in

Mathematics as well as lifelong learning process. Suppose we cannot identify the difficulty of

students in proper way, they will not continue their study as long as. Also they never live in their

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successful and peaceful life continuously. This is the important contemporary issue of human

quality learning environment.

Achievement In Mathematics

Achievement test defines an assessment of individual‟s knowledge, skill or accomplishment in one

or more content areas. Achievement test in Mathematics defines level of attainment in any or all

Mathematics skills, usually estimated by performance on a test. Achievement in Mathematics is

less than other discipline achievement based on comparing the public result of Tenth standard in

Tamil Nadu Secondary Board of Examination. Achievement is vital role of influence on future

carrier and getting employment in his life of students. Achievement marks are very important

consideration of our education system in India than any other performance. Mathematics

achievement is the main supporting pillar of the total achievement marks. Everyone uses the

Mathematics through aware or unaware of experience. Mathematics is unavoidable term in every

one life. So Mathematics is one of the main and compulsory subjects from one to Tenth standard.

9. Research Questions In the course of investigating the problem, the following research questions are set forth:

(i) Have Ninth standard SC /ST students experience learning difficulties in

Mathematics?

(ii) Will the Ninth standard SC /ST students learning difficulties in Mathematics

affect next level?

(iii) Will the socio-economic problem affect the achievement in Mathematics?

(iv) Whether inclusive education or separate education is better to SC /ST students

learning in Mathematics?

(v) Do Ninth standard SC /ST students know about (minimum level learning) the

basic rules, laws and methods of four basic numerical operations?

(vi) Do Ninth standard SC /ST students know about (minimum level learning) the

basic rules, laws and methods of four basic algebraic operations?

(vii) Do Ninth standard SC /ST students know thoroughly about sixteen +, - signs

rules when using addition, subtraction, multiplication and division?

(viii) Do ninth standard SC /ST students know thoroughly about BODMAS rules?

10. Research Methodology

10.1 Sampling Of The Study

Simple Random Sampling is a type of probability sampling technique. Lottery method of Simple

Random Sampling Technique is adapted in the study. Each of the 124 schools is assigned a unique

number by the researcher. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-

folded researcher selects 23 schools without replacement. In the present study, 23 Government,

Government Aided Schools and Adi-Dravidar welfare schools are recognized by directorate of

school education under taken by the state government of Tamil Nadu have been chosen, Simple

Random Sampling Technique is followed by the researcher, because, all the SC/ST pupils are

allowed to study in Government, Government Aided Schools and Adi-Dravidar welfare schools.

Some private schools do not give the studying opportunity to SC/ST pupils. The data were collected

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from the 600 Ninth standard SC/ST students in Government Schools, Government Aided Schools

and Adi-Dravidar Welfare Schools by the researcher.

10.2 Tool Used For The Study

The researcher made questionnaire was used as the tool for the study is Measurement of

Achievement in Mathematics, designed by B. PRABAKARAN under the guidance of Dr. R.

KARPAGAKUMARAVEL, Professor, Department Of Education Technology, Bharathidasan

University, Trichy. Entitled “Measurement of Achievement in Mathematics (MAM) tool or

Measurement of Learning Difficulty in Mathematics (MLDM)” Tool through problem solving in

numeric and algebraic Mathematics concepts contain 60 question-answer method questions. Such

questions are answered by the students within 45 minutes which is fixed time. Questions 1 to16

tested about know the rules of using +,-signs in his/her numerical calculation; Questions 17 to 37

describe about the students how to tackle numerical operations at present; Questions 38 to 60

describe about algebraic operations.

10.3 Scoring Procedures

Measurement of Achievement in Mathematics (MAM) tool or Measurement of Learning Difficulty

in Mathematics (MLDM) Tool adopted problem solving method of numeric and algebraic

Mathematics concepts. This part contains 60 one mark questions therefore maximum score is 60

minimum score is 0. The Range is 60. Actual score of student considers his achievement score in

numerical and algebraic by using operations of addition, subtraction, multiplication, division and

exponentiation with rules of +,- signs. Right answer of the each question gets one mark; otherwise

wrong answer of each question gets zero mark.

10.4 Time Fixation Time fixation for the questionnaire is the following method. First I select ten students in Ninth

standard, who are the average and above average students based on class academic achievement in

Mathematics considering as an irrespective of caste. Researcher asks the students to response for all

questions in this questionnaire, when all the questions are completed within 45 minutes by those

students. Thus I fixed 45 minutes as given the reasonable time on the response to all questions.

10.5 Delimitation Of The Study

Delimitation of the study describe as follow:

(i) The study was confined only to the Government, Government Aided and Adi-Dravidar welfare

schools in Pudukkottai educational district. The self-financed schools were not included within the

purview of the study.

(ii) Data were collected only from Ninth standard regular SC students in Pudukkottai educational

district. The open school or mobile school students were left out.

(iii) Even though lot of methods are available, because of suitability, only survey method was

employed and questionnaires were used to collect data from Ninth standard regular SC students in

Pudukkottai educational district.

(iv) Tool is used to Ninth standard and above Ninth standard students following Tamil Nadu state

board syllabus.

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(v) Only 600 samples were taken in 23 Government, Government Aided and Adi-Dravidar welfare

schools in Pudukkottai educational district.

(vi) Statistical techniques like Percentile and percentage calculation were employed.

(vii) Graphical representations like Pie charts only were drawn.

(viii) Tool measures only Ninth standard students knowing basic rules, regulation and knowledge

about four basic operations by using +,- signs rules on numerical and algebraic concepts in

Mathematics.

10.6 Statistical Techniques

Statistical techniques like Percentile and percentage calculation were employed.

11. Descriptive Analysis

This section deals with the descriptive analysis of data for descriptive analysis, percentage,

percentile, median, quartile deviation and range are calculated and the data are interpreted by using

these statistics.

11.1: Availability Of MAM Tool

Frequencies and percentages are calculated to find out the availability of MAM tool in 600

schools in Pudukkottai educational district. The calculated values are presented below in a tabular

form.

Table: Calculation Of Frequency And Percentage Of Students’ Different Responses Is Obtained From

MAM Tool.

S. NO. QUESTION 1 2 3 4

1. 12+24= 573 27 95.5 4.5

2. -15+27= 336 264 56 44

3. 26-34= 167 433 27.83 72.17

4. -43+(-25)= 202 398 33.67 66.33

5. 12-24= 208 392 34.67 65.33

6. -15-27= 131 469 21.83 78.17

7. 26-(-34)= 198 402 33 67

8. -43-(-25)= 96 504 16 84

9. 12×24= 366 234 61 39

10. -15×7= 289 311 48.17 51.83

11. 26×-34= 233 367 38.83 61.17

12. -15×-12= 272 328 45.33 54.67

13. 48÷4= 376 224 62.67 37.33

14. 72÷(-6)= 226 374 37.67 62.33

15. -90÷6= 243 357 40.5 59.5

16. -110÷(-10)= 260 340 43.33 56.67

17. (-1)(-12)+(-38)= 46 554 7.67 92.33

18. (-1)(-1)(-80)+70= 57 543 9.5 90.5

19. (-96)+(-1)(-16)= 48 552 8 92

20. -77-(-1)(-10)= 31 569 5.17 94.83

21. -15×-15= 228 372 38 62

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22. -5×-5×-5= 178 422 29.67 70.33

23. -5×5×-4= 208 392 34.67 65.33

24. 75÷(-1)(-75)= 107 493 17.83 82.17

25. -82÷82= 151 449 25.17 74.83

26. -45÷(3+2)= 143 457 23.83 76.17

27. 75×0= 236 364 39.33 60.67

28. 0×0×80= 213 387 35.5 64.5

29. 0÷75= 198 402 33 67

30. 75÷1= 256 344 42.67 57.33

31. 82÷(10×-10)= 30 570 5 95

32. 60+30-70-10+25= 168 432 28 72

33. 1100×12+15÷3= 49 551 8.17 91.83

34. 178-1078+80-(24×5÷12)= 26 574 4.33 95.67

35. 175×175÷(-25×-25)= 31 569 5.17 94.83

36. (45+15-70)÷(75×15÷25+10-35)= 20 580 3.33 96.67

37. 1÷75×75= 12 588 2 98

38. X+X= 94 506 15.67 84.33

39. X+Y= 50 550 8.33 91.67

40. 2X+7X= 229 371 38.17 61.83

41. 2X+7Y= 20 580 3.33 96.67

42. X-X= 111 489 18.5 81.5

43. X-Y= 40 560 6.67 93.33

44. 3X-11X= 79 521 13.17 86.83

45. -8X-2Y= 11 589 1.83 98.17

46. -6X-(-5X)= 41 559 6.83 93.17

47. 8X×5X×2X= 77 523 12.83 87.17

48. 5X-7Y+8X-3Y= 32 568 5.33 94.67

49. (8X2+12X-5)+(15X

2-20X+15)= 14 586 2.33 97.67

50. (12X2-115X-5)-(15X

2-20X+15)= 10 590 1.67 98.33

51. (3X2+15X-5)×(2 X

2-4X+15)= 4 596 0.67 99.33

52. (3X2-5X+2)÷(X-1)= 6 594 1 99

53. 5X2Y

3×21X

3Y

2= 29 571 4.83 95.17

54. 75X4Y

5÷15XY

7= 6 594 1 99

55. (3X2+4Y+2)+(32X+9Y)= 8 592 1.33 98.67

56. (8X2-4Y

2)-7 (X

2+7X+13)= 3 597 0.5 99.5

57. (22X2+11X+11)×10Y

2= 4 596 0.67 99.33

58. (75X2+15Y+20)÷5X= 6 594 1 99

59. 7X3+5X

2+3X+1+(6X

2+5X+3)+(10X+20)+30= 6 594 1 99

60. 7X3+5X

2+3X+1- (6X

2+5X+3)- (10X+20)- 30= 6 594 1 99

1 indicates correct response;

2 indicates wrong response;

3 indicates percentage of correct response;

4 indicates percentage of wrong response.

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11.2 : Graphical Representation :Question -1: Percentage Of Students’ Responses

Figure 1: Respondents Responses

11.3 Frequency Table

This frequency table is calculated by researcher whose classification from MAM tool.

Table 2: Frequency Distribution From Students’ Scores

S.No. Interval Frequency Cumulative Frequency

1 0-12 311 311

2. 13-24 215 526

3. 25-36 52 578

4. 37-48 22 600

5. 49-60 0 600

The above table reveals that 0 SC/ST students got very high achievement in Mathematics which

means no one knows well all basic operations rules and regulation by using +,- sign rules; 22

students got high achievement in Mathematics which means they know well some basic operations

rules and regulation by using +,- sign rules; 52 students got average achievement in Mathematics

which means they know half amount of knowledge about the basic operations rules and regulation

by using +,- sign rules; 215 students got low achievement in Mathematics which means

achievement in Mathematics small amount of knowledge about the basic operations rules and

regulation by using +,- sign rules on numeric and algebraic concept in Mathematics; 311 students

got very low achievement in Mathematics which means blind knowledge about the basic operations

rules and regulation by using +, - sign rules on numeric and algebraic concept in Mathematics. The

final conclusion reveals that all the SC/ST students meet difficulty to knowledge about the basic

operations rules and regulation by using +, - sign rules on numeric and algebraic concept in

Mathematics.

95%

5%

0% 0%

RESPONSES

CORRECT WRONG

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11.4: Diciles (Percentiles)

Percentile frequencies (Deciles) are calculated to find out the availability of MAM tool in

600 schools in Pudukkottai educational district. The calculated values are presented below in a

tabular form.

Table 3: Calculation Of Diciles From Students’ Scores

S.No. Percentile Value

1. P10 =D1 2

2. P20=D2 4

3. P30=D3 6

4. P40=D4 9

5. P50=D5 11

6. P60=D6 13

7. P70=D7 15

8. P80=D8 18

9. P90=D9 25

10. P100=D10 46

The above table reveals that 10% students got achievement in Mathematics is less than or equal to 2

marks out of 60; 20% students got achievement in Mathematics is less than or equal to 4 marks out

of 60; 30% students got achievement in Mathematics is less than or equal to 6 marks out of 60;

40% students got achievement in Mathematics is less than or equal to 9; 50% students got

achievement in Mathematics is less than or equal to 11 marks out of 60; 60% students got





achievement in Mathematics is less than or equal to 46 marks out of 60. The median value (P50 =D5)

is 11 marks out of 60; Quartile deviation is (17-5)/2=6 marks out of 60; Mode is 2 marks out of 60.

12. Discussion Of The Results

The present study reveals most of SC/ST students have more learning difficulties in Mathematics,

which affects their achievement in Mathematics in Ninth standard. Also, these Ninth standard

SC/ST students learning difficulties in Mathematics continue in tenth standard and affects Tenth

Public Examinations results in Pudukkottai Educational District. Most of SC/ST students have not

known the rules, regulation and basic concepts about four basic operations by using +, - sign rules

on numerical and algebraic in Mathematics. The following concepts have created confusion among

Ninth standard SC/ST students. Infact, many of them are ignorant of the following concepts in

numeric

(i) Any number is multiplied by unity is equal to same number

(ii) Any number is divided by unity is equal to same number.

(iii) Multiplication of any number and their multiplicative inverse is equal to unity.

(iv) Any number is multiplied by zero is equal to zero.

(v) Zero is divided by any number is equal to zero.

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(vi) The sixteen +, -sign rules.

(vii) The BODMAS rule.

(viii) The combination of BODMAS and+, - sign rules.

In fact, many of them are ignorant of the following concepts in algebraic

(ix) Same variable of two terms can be added

(x) Same variable of two equal terms can be subtracted, the result is zero.

(xi) Two distinct variables two terms cannot be added and subtracted, the result is no

change.

(xii) All the SC/ST students meet learning difficulties in algebraic four basic operations

than numerical four basic operations by using +, - sign rules.

The research reveals that 0 SC/ST students get very high achievement in Mathematics

which means no SC/ST student knows well basic operations rules and regulations by using sign

rules of +, - .

13. Suggestions Of The Study

The present study reveals that the SC/ST students have more learning difficulties in

Mathematics especially basic numerical and algebraic operations rules and regulation by using +, -

sign rules. The students‟ social backwardness, their economical and emotional problems are more

affected by students‟ achievement in Mathematics. The study identified only students weakness but

not suggested any suitable remedies in basic numerical and algebraic operations rules and

regulation by using +, - sign rules. Therefore further researches may be conducted to find the

suitable remedies to eradicate this weakness.

14. Conclusion

It has been found that the SC/ST students of ninth standard remain ignorant of the basic

concepts of mathematics, the teaching-learning of mathematics upto Eighth standard has no bearing

on the mathematical knowledge of ninth standard students, as the result, teachers of mathematics

have to give more stress on tenth standard students. To avoid wastage and stagnation among SC/ST

students, teachers have to work hard. Still, this result makes only in improper outcomes and

attending competitive examinations in our inefficient manner. Hence, SC/ST students have to

enhance drill and practice gradually in mathematical basic concept from first standard to ninth

standard. Also, it is recommended that Government may appoint the guides and counselors district

wise; they may solve many psychological and socio-emotional problems of SC/ST students. This

may result in better learning.

References

[1] Alkhateeb Haitham, M., (2001): Gender Differences in Mathematics Achievement among High

School Students in the United Arab Emirates, 1991-2000, School Science and Mathematics,

Vol.101.

[2] Ashlock, R. B., (1994): Error Patterns in Computation, 6thEdition. Englewood Cliffs, NJ: Prentice

Hall.

[3] Bloom, Benjamin S., et al (1971): Handbook on Formative and Summative Evaluation in Student

Learning, McGraw hill, U.S.A.

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[4] Ketterlin-Geller, et al (2009): Diagnostic Assessments in Mathematics to Support Instructional

Decision Making, Practical Assessment, Research & Evaluation, 14(16). Available online:

http://pareonline.net/getvn.asp?v=14&n=16.

[5] Madhivanan, M., et al (2012): Mathematics 9 Standard, Department of School Education, Tamil

Nadu Textbook Corporation, Government of Tamil Nadu.

[6] Najib Abd. Ghagar, M et al (2011): Multilevel Analysis of Achievement in Mathematics of

Malaysian and Singaporean Students, Journal of Educational Psychology and Counseling, Volume

2, Jun 2011, Pages 285-304/ ISSN: 2231-735X.

[7] Russell, M and Masters. J., (2009): Formative Diagnostic Assessment in Algebra and Geometry,

Paper presented at the Annual Meeting of the American Education Research Association, San Diego,

CA.

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