ANALYSIS OF DATA AND RESULTS. - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/6637/13/13_chapter 5.pdf · ANALYSIS OF DATA AND RESULTS. The present study was intended to test

CHAPTER V

ANALYSIS OF DATA AND RESULTS.

* Surmnar~ af the A d y & Dom.

* m t s of lmkuctional Meihods

* Co-4-

* Inpuence ofSES and Intelligence

* T ~ u t y Q f ~ .

* Discussion of Results.

CHIiPTER v

ANALYSIS OF DATA AND RESULTS.

The present study was intended to test the effectiveness of a model of

instruction on achievement in Mathematics of academically disadvantaged

students in secondary schools of Kerz~la. This chapter presents the analysis of the

data collected and its results.

The Concept Attainment Model was sekded for the experimental

treatment. The non-equivalent pretest posttest control group design was selected

for the study. A sample of 535 students was selected for the study from four

schools, of which 268 formed the e:cperimental group (CAM) and 237 students

formed the control group (CTM). 123 students in the experimental group and

126 students in the control grcup were identified as the academically

disadvantaged (AD).

A pretest was conducted by administering the achievement test in

Mathematics before the experimer~t. Tests were also administered to assess

socio-economic status, intcdligence, achievement motivation, mathematics

attitude, interest in mathematics, hi~rne learning environment, cognitive ability,

self concept and study habits

The treatment variable was instructional method at two levels, namely

Concept Attainment Model of Instuction and Conventional Teaching Method.

.4nalysis of Dara and Results

After the experiment posttests were conducted by administering the same tests

used as pretests. Between pretest and posttest adequate time gap was given to

minimise the 'carry over effect'.

The data obtained from the seleded sample were subjeded to various

descriptive and inferential statistic31 procedures to facilitate testing of the

tenability of the hypothesis foimu1ak.d for the study.

The statistical techniques used are

( 1 ) . The three essential descriptive! statistics, which help to describe a data

distribution, are measures of centrril tendency or position, measures of shape

and measures of dispersion (spread).

(2). Critical Ratio to test the s~gnificance of difference between two means.

(3). Paired 't' test to analyze i he resub of a 'before' and 'after' research design

(4). Analysis of Covariance ,with a view to makes treatment groups, which are

different on pretests, statistically equivalent. Here ANCOVA was used for the

comparison of the effectiveness of Concept Attainment Model of instrudion over

Conventional Teaching Method to .\cademicaUy Disadvantaged students, and

(5). Multiple Regression Analysis was done with a view to predict how the

posttest scores in mathematics achievement test and cognitive ability test were

influenced by the values of other independent variables like socio-economic

status and intelligence levels of academically disadvantaged students.

In the following section, a summary of different statistical analyses of the

data made is presented.

Analysis of Dofa andResulis

Summary of ttce Analysis Done.

5.1. InstructJonal Methods and Student Achieuement in

Mathematics and in Cognitive ilbllity.

5.1.1. Nature of Pretest Scor'?s in Achievement in Mathematics and in

Cognitive Abilihl.

5.1 .I . I . Nature of Pre:est Scores in Achievement in Mathematics

and in Ccbgnitive Ability of the Academically

Disadvantaged Groups (Experimental (CAM) and

Control (CTNL) Groups).

5.1.1.2. Nature of Pretest Scores in Achievement in Mathematics

and in Cognitive Ability of the Academically Advantaged

Groups (Experimental (CAM) and Control (CTM)

Groups).

5.1.2. Nature of Posttest Scores in Achievement in Mathematics and in

Cognitive Ability.

5.1.2.1. Nature of Pc'sttest Scores in Achievement in Mathematics

and in Cognitive Ability of Academically Disadvantaged

Group:; (Exxrimental (CAM) and Control (CTM)

Groups).

5.1.2.2. Nature of Ptxttest Scores in Achievement in Mathematics

and in Cognitive Ability of Academically Advantaged

Groups (Ekperimental (CAM) and Control (CTM)

Groups).

5.1.3.Dependabiliiy of Sample Statistics: Confidence Interval and

Variability of F'opulajion.

5.Z.3.1. Pretest Sorzs of Academically Disadvantaged Groups.

5.1.3.2. Pretest Sccrres of Academically Advantaged Groups.

5.1.3.3. Posttest Scores of Academically Disadvantaged Groups.

.4nalysis of Data and Resulrs

5.1.3.4. Posttest Scoa?s of Academically Advantaged Groups.

5.2. Comparison of Scores in Achievement in Mathematics of

Pupils in the Experimental (CAM) and the Control (CTM)

Groups.

5.2.1. Significance of Difference between Pretest Scores in Achievement

in Mathematics of Atademically Disadvantaged Students in the

Experimental (CAM) 2 nd in the Control (CTM) Groups.

5.2.2. Significance of Differc,nce between Pretest Scores in Achievement

in Mathematics of Academically Advantaged Students in the

Experimental (CAM) and Control (CTM) Groups.

5.2.3. Significance of Differc nce between Posttest Scores in Achievement

in Mathematics of A'ademically Disadvantaged Students in the


5.2.4. Significance of Difference between Posttest Scores of Academically

Advantaged Students in the Experimental (CAM) and Control

(CTM) Groups.

5.3. Comparison of Scores in Cognitive Ability Test of Pupils in

the Ersper?mentol (CAM) and the Control (CTM) Groups.

5.3.1. Significance of Difference between Pretest Scores in Cognitive

Ability of Academically Disadvantaged Students in the

Experimental (CAM) and in the Control (CTM) Groups.

5.3.2. Significance of Difference between Posttest Scores in Cognitive

Ability of Academically Disadvantaged Students in the

Experimental Group (CAM) and in the Control (CTM) Groups.

5.3.3. Significance of Diflerence between Pretest Scores in Cognitive

Ability of Academicz~lly Advantaged Students in the Experimental

(CAM) and in the Gmtrol (CTM) Groups.

Analysis of Data and Results

5.3.4. Significance of Differel~ce between Posttest Scores in Cognitive

Ability of Academically Advantaged Students in the Experimental

(CAM) and in the Conbol (CTM) Groups.

5.4. Comparison of Gain in Performance of Experimental (CAM)

and Control (CTM) Groups - Achievement in Mathematics.

5.4.1. Significance of Dilference between the Gain Scores in

Achievement in Mathematics of Academically Disadvantaged

Students in the Experimental (CAM) and in the Control (CTM)

Groups.

5.4.2. Significance of Difference between the Gain Scores in

Achievement m Mzithematics of Academically Advantaged

Students in the Experimental (CAM) and in the Control (CTM)

Groups.

5.5. CornporEBon of Gain in Jperfonnance ofEkperimenta1 (CAM)

and Control (CTM) Groups - Cognitfoe Ability.

5.5.1.Significance of Difference between the Gain Scores of

Academically Disad~~mntaged Students in the Experimental (CAM)

and in the Control (C:TM) Groups.

5.5.2. Significance of Difference between the Gain Scores in Cognitive

Ability of Acaclemically Advantaged Students in the Experimental

(CAM) and in the Cc'ntrol (CTM) Groups.

5.6. Comparison of Pretest and Posttest Scores of Mgerent

Groups - Achievement in Mmthematfcs.

5.6.1. Significance of Difference between the Pretest and Positest Scores

in Achievement in Mathematics of the Academically

Disadvantaged Students in the Experimental Group.

Analysis of Daia andResuIts

5.6.2. Significance of Difference between the 'Pretest and Posttest Scores

in Achievement in Mathematics of the Academically Advantaged

Students in the Experimental Group.

5.6.3. Significance of Difference between the Pretest and Posttest Scores

in Achievement in Mathematics of the Academically

Disadvantaged Students in the Control Group.


in Achievement in Mathematics of the Academically Advantaged

Students in the Control Group.

5.7. Comparison of Pretest and Posttest Scores of Dffferent

Groups -Cognitive Ability.

5.7.1. Significance of Differtznce between the Pretest and Posttest Scores

in Cognitive ability of the Academically Disadvantaged Students in

the Experimental Group.


in Cognitive ability o f the Academically Advantaged Students in

the Experimental Grctup.


in Cognitive ability 0:: the Academically Disadvantaged Students in

the Control Group.

5.7.4. Significance of Difference between Pretest and Posttest Scores in

Cognitive ability of the Academically Advantaged Students in the

Control Group.

5.8. Genuineness of Diflere~tce in Performance of Groups.

5.9. Compmison of E#ectit~eness of Concept Attainment Model

of Instruction with Conventional Method of Teaching.

Analysis of Uma ana nrsuu3

5.9.1. Comparison of Effecliveness of Concept Attainment Model of

Instruction with Conventional Teaching Method Using ANCOVA

on the Learning of Academically Disadvantaged Students.

5.9.2. Comparison of the Effectiveness of Concept Attainment Model of

instruction with Convc?ntional Teaching Method on Learning of

Academically Advantaged Students Using ANCOVA.

5.10. Ob/ecthe-wise Comparison of E&c#veness of Concept

Attainment Model of Instruction with Conuentional Teaching

Method on Achieoement in Mathematics.

5.10.1. Comparison of Effwtiveness of Concept Attainment Model of

Instruction with Conventional Teaching Method on Achievement

in Mathematics (0bjc.dive-wise) of Academically Disadvantaged

Students.

5.102. Comparison of Effectiveness of Concept Attainment Model of

Instruction (CAM) wifh Conventional Teaching Method (CTM) on

Achievement in Marhematics (Objective-wise) of Academically

Advantaged Students.

5.1 1 . Comparison of the Eflkctiueness of Concept Attainment

Model of lnstnrction and Conventional Teaching Method on

Enhancing Cognftioe Ability of Students.

5.1 1 .I. Comparison of the Effectiveness of Concept Attainment Model of

Instruction and Conventional Teaching Method on Enhancing

Cogn~tive Ability of Academically Disadvantaged Students

5.11.2. Comparison of the Effectiveness of Concept Attainment Model

of Instruction and Conventional Teaching Method on Enhancing

Cognitive Ability o " Academically Advantaged Students.

Analysis of Dafa andResults

5.12. Achievement in Mat,hematics: Comparison of the

E&cHueness of Concept Attxrinment Model of Instruction on

Teaching Mathematics to Academically Advantaged Students and

Academically Msadvantaged Students.


of Instruction on Teaching Mathematics to Academically

Advantaged students and Academically Disadvantaged Students

Using ANCOVA.


of Instruction on Teaching Mathematics (Objective-wise) to

Academically Advan.:aged Students and Academically

Disadvantaged Students.

5.13. Cognitive Ability: comparison of the E&ctiveness of

Concept Attainment Model of Instruction on Cognitive Ability to

Academically Advantaged Students and Academically

Disadvantaged Students.

5.14 Comparison of Progress Made b y the Groups.

5.14.1.Comparison of Progrzss Made by Academically Disadvantaged

Students with that by ,bdemicaUy Advantaged Students in their

Achievement in Mathematics.

5.14.2.Comparison of Progess Made by Academically Disadvantaged

Students with that by Academically Advantaged Students in

Cognitive Ability.

5.15. Injhrence of Socio-economic Status and lntellipnce on

Achievement in Mathematics and Cognitive Ability of

Academically Dieadoantaged Students.

.4nalvsis of Data and Results

5.15.1.Socio-economic Status, Achievement in Mathematics and

Cognitive Ability of the Academically Disadvantaged Students

5.15.1.1. Socio-econornic Status and Achievement in Mathematics

of the Academically Disadvantaged Students

5.15.1.2. Socio-econc~mic Status and Cognitive Ability of the

Academically Ilisadvantaged Students

5.15.2. Intelligence, Achievement in Mathematics and Cognitive Ability

of the Acade~nically Disadvantaged Students

5.15.2.1. Intellzgence and Achievement in Mathematics of the

Academically Disadvantaged Students

5.15.2.2. Intelligence and Cognitive Ability of the Academically

Disadvantage 3 Students

5.15.3. Relationship of Socio-economic Status and Intelligence on

Achievement in Nathernatics of Academically Disadvantaged

Students.

5.15.4. Relationship of Socio-economic Status and Intelligence on

Cognitive Ability o. Academically Disadvantaged Students.

5.15.5. Multiple Regressior Analysis for the relationship of SES and IQ

with Gain Scoras in Achievement in Matfrematics of

Academically Disadvantaged Students in the Experimental

Group.

5.15.6. Multiple Regessior~ Analysis for the relationship of SES and IQ

with Gain Scores in Cognitive Ability of Academically


5.16. Tenability of Hypotheses.

5.1 7. Discussion of Results.

Andvsis of Data and Results

Analysis in Detail

The analysis in detail is presented in the following sections

.P 5.1. Instructional Methods and Student Achievement in

Mathematics and in Cognittoe Ability

5.1.1. Nature of Pretest Scores ,in Achievement in Mathematics and in

Cognitive AMllty

Average is a short hand dzscription of a mass of quantitative data

obtained from a sample. Measures 3f Central Tendency also describe indirectly

but with some accuracy the population from which the sample was drawn.

Sample averages are close estimatrzs of larger population averages and he$ to

make predictions beyond the limits of a sample. The measures of central values

and dispersion are simple values, descriptive of the distributions and are of much

useful when we compare differeni samples. The statistical measures like mean,

median, standard deviation, quz~rtile deviation, skewness and kurtosis were

computed for the pretest scores in achievement in Mathematics and in Cognitive

Ability of the experimental group (academically disadvantaged and academically

advantaged groups) and control group (academically disadvantaged and

academically advantaged groups) to determine the nature and dependability of

the sample statistics and to compare the scores of all the groups in the analysis.

The maximum score in the acnievement test was 110 and for the cognitive

ability test it was 30.

Anatpsis of Data and Resuks

5.1.1 .l. Nature of Pretest Score* in Achievement in Mathematics and

in C~ognitiue Ability of the Acalemjcally Disaduantaged Groups

(Experimental (CAM) and Contrcd (Cm) Groups).

The mean, median, range, standard deviation, quartile deviation, skewness

and kurtosis of pretest scores of Act ievement in Mathematics and in Cognitive

Ability of the academically disadvantaged group (experimental and control

groups) are given in Table 5.1

Table 5.1

Measures of Central Tendenc~xrs ion.Skewness and Kurtosis of the Pretest

Scores of Achievement in Mathematics and Cosnitive Abilitv of Academically

Diadvantaqed - Exaerirnental (CAlW and Control (CTM) Groups.

Group Number Mean Mediitn Range SD QD Skewness Kurtosis

Achievement in Mathematics

AD-CAM 123 21.39 21 13 - 30 3.61 2.5 -0.03 -0.26

AD-CTM 126 20.35 20 14 - 27 2.98 2.13 -0.16 -0.46

Cognitive ability

AD-CAM 123 9.16 9 1-14 2.35 1.5 -1.025 1.83

AD-CTM 126 9.51 9.5 6-14 2.02 1.5 0.04 0.43

The mean and median of the experimental (CAM) and control (CTM)

groups are not having much difference in both cases. The skewness is negative

for both groups. This indicates thzt the scores are massed at the upper end of the

distribution. The mean scores of jub-groups are very low. This implies that they

had a poor performance in the pretest. The highest and least values are also

below 30% in achievement test. It indicates that most of the students got low

Analysis of Dato andResults

scores in the pretest. The median is around 20 in achievement test scores. It

shows that 50% of the students scored below 20. While analysing the value of

kurtosis we can arrive at a concll~sion that there is a relatively smaller

concentration of scores near the mzan than in the normal distribution. By

analysing the values of measures of central tendency and dispersion, it can be

inferred that the performance of the group in the pretest is very low in

achievement test in Mathematics and n Cognitive Ability test.

5.1.1.2. Nature of Pretest Scorer in Achfeuement in Mathematics and

in Cognitfue Ability of the Academically Advantaged Groups

(Experimental (CAM) and Control (CTM) Groups).

The mean, median, range, standard deviation, quartile deviation,

skewness and kurtosis of pretest scol.es of the academically advantaged group

m (experimental and control groups) were calculated and given in Table 5.2

Table 5.2

Measures of Central Tendencv. Diwrsion. Skewness and Kurtosis of the Pretest

Scores of Achiewment in Mathematics and in Cmitive Abilitv of Academically

Advantaqed (Experimental (CAM) and Control (CTM)) Groups.

Group Number Mean Median Range SD QD Skewness Kurtosis


AA-CAM 145 26.28 26 18-38 3.37 2 0.24 0.37

AA-CTM 111 26.16 26 14-35 3.72 2 -0.08 0.75

Cc gnitive ability

AA-CAM 145 13.12 13 7-19 1.91 1s 0.08 0.48

AA-CTM 111 13.44 13 9-21 2.31 1.50 0.51 0.40

/trralysis of Data andResults

The mean, median and slandard deviation of pretest scores in

Achievement in Mathematics and in Cognitive Ability of the academically

advantaged group in the experimenkl (CAM) and the control (CTM) groups are

not having much difference. The mean and median of achievement scores are

around 26 for both the groups. The inference is that both the groups performed

poorly in the pretest. Since the median of the pretest scores in achievement for

both the groups is 26, it can be conc:luded that 50% of the students from these

groups scored below 26. The skewne:~ of the first group is positive which implies

that the scores are massed at the lc~wer end of the distribution. For the other

group it is negative which implies th,3t the scores are massed at the upper end.

By analysing the range of pretest scores in achievement, the students in the

experimental group scored slightly higher than thek counterparts. The standard

deviation of the pretest scores in Achievement in Mathematics and in Cognitive

Ability indicates that the scores are not much dispersed from the central value.

There are no deviant scores in both the cases. The skewness of the Cognitive

Ability scores is positive for both the groups which implies the scores are massed

at the lower end of the distribution For cognitive ability and achievement test

scores the kurtosis is less than 0.263, which is the value of normal distribution.

Hence it is clear that the scores are rot concentrated near mean in both cases.

Analysis of Da!a and Results

5.1 -2. Nature of Posttest Scores in Achievement in Mathematics and

in Cognitiue Ability.

The measures of central tendency and measures of dispersion of posttest

scores in Achievement in Mathemaiics and Cognitive Ability of Academically

Disadvantaged Group and Academically Advantaged Group were determined to

throw light on the nature of posttest scores

5.1.2.1. Nature of Posttest Scornes in Achieuement in Mathematics and

in Cognitive AbiHty of Academically D L s A t o g e d Groups

(Experimental (CAM) and Contt-01 (CTM) Groups.

The mean, median, rang?, standard deviation, quartile deviation,

skewness and kurtosis of posttest scores in Achievement in Mathematics and in

Cognitive Ability of academically disadvantaged students in experimental group

and control group are given in Table 5.3

Table 5.3

Measures of Central Tendencv, D i m i o n , Skewness and Kurtosis of the

Posttest Scores in Achievement in Mathematics and Cocrnitive Abilitv of

Academicallv Disadvantaqe~er imental (CAM) and Control (CTM) Grouw.

Group Number Mean Median Range SD QJJ Skewness Kurtosis

Achie~etnent in Mathematics

AD-CAM 123 70.15 70 57 - 79 4.47 3 -0.37 -0.08

AD-CTM 126 42.37 43 27 - 55 4.67 2.5 -0.48 0.43

Cognitive ability

AD-CAM 123 15.75 16 5-25 4.01 2 -0.15 0.4

AD-CTM 126 11.42 12 7-16 2.11 1.5 -0.02 -0.50


The mean and median of the posttest scores of the experimental group

are much higher than that of the control group for both the sets of scores. The

median of achievement test scores of the experimental group is 70. This

indicates that 50% of the students sccred above 70. The median of achievement

test scores of the control group is 43, that is 50% of control group scored below

43. The highest and least of the achievement test scores of the experimental

group are 79 and 57 respectively me.~nwhile, the highest and least scores of the

control group are 55 and 27 respectively. This shows that the experimental

group had a better performance in achievement test than the control group.

There is not much difference in staridard deviation and quartile deviation; thii

means that the individual differences in the groups are approximately the same.

Both the distributions are negatively skewed. This implies that the scores are

massed at the higher side of the distributions. For cognitive ability, the

distribution of scores of the experimental and control groups are negatively

skewed. This implies that the scoles are massed at the higher side of the

distribution of experimental group and the control group. The value of kurtosis is

less than 0.263 in all the four distriblltions. This implies that they are platykurtic.

By analysing the values of measure3 of central tendency and dispersion, we can

infer that performance of the exper mental group is better compared to control

group in both cases.

Anabsis of Data and Results

5.1 2.2. Nature of Posttest Scores in Achiwement in Mathematics and

in Cognitive AMHty of Academically Advantaged G r o u p (Experimental

(CAM) and Control (CTM) Groups.

The measures of central tendency, dispersion, skewness and kurtosis of

the posttest scores in achievement i n Mathematics and in Cognitive Ability of

academically advantaged students in the experimental and in the control groups

were calculated and presented in Table 5.4.

Table 5.4

Measures of Central T e n d e n a s p e r s i o n , Skewness and Kurtosis of the Posttest Scores in Achievement in Mathematics and in Cosnitive Abilitv of Academicallv Advantaued - Experimental (CAM) and Control (CTM) Grouvs.

Group Number Mean Median Range SD QD Skewness Kurtosis

Achievemeilt in Mathematics

AA-CAM 145 82.33 83 75-90 3.59 2.5 0.00 -0.54

AA-CTM 111 70.48 70 61-80 4.31 2.5 -0.06 -0.17

Cognitive ability

AA-CAM 145 19.87 20 10.28 4.06 2.5 -0.51 -0.31

AA-CTM 111 16.54 17 6-25 2.57 1.5 -0.33 2.28

The measures of central tendency of the academically advantaged group

in the experimental (CAM) anti in thz control (CTM) groups are having much

difference. The mean of the experim2ntal group is higher than that of control

group. The median of achievement test scores of the experimental group is 83,

which indicates that half of the studer,ts from the group got scores above 83. In

the case of the control group, the mc,dian is 70. This indicates that half of the

Analysis of Data and Results --

students from the experimental group scored above 83 while the control group

scored above 70 only. Hence the expzrimental group stood in a higher position

-? than the control group. By analyzing the measures of central tendency and

dispersion, we can arrive at a conclusion that the performance of the

experimental group is far higher compared to that of the control group.

In cognitive ability test scores, the mean and median of the experimental

group is much higher than that of the control group. The value of kurtosis of

cognitive ability scores in AA-CTM is near to 0.263, which is the value of a

normal distribution. In all the other cases it is less than 0.263, which implies the

distributions are platy kurtic This means that there is relatively smaller

concentration of scores near the mean than does the normal distribution. This

c shows that the performance of the experimental group is better than that of the

control group.

5.1.3. Dependabjrtry of Sample Statistics: Confidence lnt-l ond

Variability of Population.

The standard errors of the sample mean and standard deviation of the

pretest and posttest scores of the cor~trol group (CTM) and experimental group

(CAM) were calculated. The depend~~bility of the sample statistics for the pretest

and posttest scores in achievement in Mathematics and in cognitive ability of

experimental and control groups were determined by computing the standard

errors of the mean and the standard deviation and by establishing the

confidence intervals. The results arc! given separately for pretest and posttest

Analysis of D m and Results

scores (the maximum score for achie~~emenf test is 110 and for cognitive ability

test, it is 30)

5.1.3.1. Pretest Sores ofAcaden~ically Disadvantaged Groups.

The mean, standard deviation, their standard errors, and ranges of Mpop

and SDpop of the pretest scores in achievement in Mathematics and in cognitive

ability of academically disadvantaged students of experimental (CAM) and

Contiol (CTM) groups are given in Table 5.5

Table 5.5

Mean. Standard Deviation, Standard Errors and Ranses of b o p and S h o p of

the Pretest Scores in Achievement -thematics and in m ~ t i v e Abiitv of

Academicalhr Disadvantased Students in Exwrimental (CAM) and Control

(CTM) Groups. -

Range of Group N Mean SD SE, SE, Range of SDpop

--- r\chievement in Mathematics

AD-CAM 123 21.39 3.61 0.33 0.23 20.55 - 22.25 3.01- 4.21

AD- CTM 126 20.35 2.98 0.27 0.19 19.35-21.05 2.51- 3.47

Cognitive ability

AD-CAM 123 9.16 2.35 0.21 0.09 8.62- 9.70 2.12- 2.58

AD- CTM 126 9.51 2.02 0.18 0.13 9.05- 9.97 1.68- 2.36

The ranges of Mpop and SDpop are narrow at 0.99 confidence level in

both the cases, as it is obvious from Table 5.5.This indicates that sample means

and standard deviations of the pretest scores in achievement and in cognitive

ability test of academically disadvantaged students in the experimental and the

Analysis of Data and Raulfs

control groups are comparable i~i th ths3se of the population of the study. Hence

they are dependable for further analysis.

5.1.3.2. Pretest Scores of Acadentically Advantaged Groups.


and SDpop of the pretest scores in achievement in Mathematics and in cognitive

ability of academically advantaged students of the experimental (CAM) and the

Control (CTM) groups are given in Table 5.6.

Table 5.6

Mean, Standard Deviation, Standard Errors and Ranaes of MPOP and Shop of

the Pretest Scores in Achievement i i ~ Mathematics and in -1tive Abilitv of

Academicalhr Advantaued Students in Experimental (CAM and Control (CTM)

Groups.

Range of Range of Group N Mean SD SE, SZ,

-- MPP SDpop

Achievenlent in Mathematics

AA-CAM 145 26.28 3.:37 0.28 0.2 25.56-27.00 3.89-2.85

AA- CTM 111 26.16 3.72 C.35 0.25 25.26 -27.06 3.08 - 4.37

G~gnitivc. ability

AA-CAM 145 13.12 1.91 0.16 0.11 12.73-13.55 1.63- 2.19

AA- CTM 111 13.44 2.31 0.22 0.16 12.87- 14 1.9- 2.72

The ranges of Mpop and SDpop of the pretest scores in achievement and

in cognitive ability of the academi~llly advantaged students of the experimental

(CAM) and the control (CTM) groc ps at 0.99 confidence level are narrow. This

indicates that the pretest scores in achievement and in cognitive ability from the

AnuIysis of Data and Results

sample of the advantaged students in the experimental and the control groups

are comparable with those of the population of the study. So they are

dependable for further statistical anal!,sis

5.1.3. 3. Posttest Scores of Academicdfy Disadvantaged Groups.

The mean, standard deviatior~, their standard errors, and ranges of Mpop

and SDpop of the posttest score:, in achievement in Mathematics and in

cognitive ability of academically disadvantaged students in the experimental

(CAM) and in the Control (CTM) grc~ups are given in Table 5.7

Table 5.7

Mean. Standard Deviation, S t @ (1 Errors, and Ranws of MWP and S b p of

the Posttest Scores in Achiev-I in Mathematics and in Cocmitive Abilitv of

Academicah D i d v a n t a q e c m e n t s in Experimental (CAM) and Control

(CTM) Grouvs. --

Group N Mean SD 3% SEb Range of Range of


AD-CAM 123 70.15 4.47 0.4 0.29 69.12- 71.18 3.72- 5.22

AD-CTM 126 42.37 4.67 0.42 0.3 41.29- 43.08 3.9- 5.44

C ognitiie ability

AD-CAM 123 15.75 4.01 0.36 0.26 14.82- 16.68 3.34- 4.68

AD-CTM 126 11.42 2.11 0.19 0.13 10.93-11.91 1.77-2.45

It can be seen from Table 5.7 that the ranges of Mpop and SDpop of the

posttest scores of academically disadvantaged students of the experimental

(CAM) and control (CTM) groups at 0.99 confidence level are very narrow. It is

obvious from these narrow range: that sample means and the sample deviations


of posttest scores in achievement and in cognitive ability of the academically

disadvantaged students in the experimental (CAM) and the control (CTM)

groups are very much dependable fcr further analysis

5.1.3.4. Posttest Scores of Acarlemically Aduontoged Groups.


and SDpop of the posttest scores in achievement in Mathematics and in

cognitive ability of academically adcantaged students in the experimental (CAM)

and in the Control (CTM) groups an: given in Table 5.8.

Table 5.8

Mean, Standard Deviation. Standard Errors and Ranses of Mtm~ and SDDOD of

the Posttest Scores in Achievement: in Mathematics and in Cosnitive Abilitv of

A&demicalb Advantaaed Students in the Exwrirnental (CAM) Group and in the

Control ICTM) Group. --

Range of Range of Group N Mean SD SEm SEo

-- M P ~ P S W P Achiew merit in Mathematics

AA-CAM 145 82.33 3.59 0.3 0.21 81.57- 83.11 3.05- 4.13

AA- CTM 111 70.48 4.31 0.41 0.29 69.42- 71.54 3.56- 5.06

(bgnitive ability

AA-CAM 145 19.87 4.06 0.34 0.24 18.98- 20.74 3.44- 4.68

AA- CTM 111 16.54 2.5? 0.24 0.17 15.92-17.16 2.13- 3 ---

The figures given in Table !j.8 show that the ranges of Mpop and SDpop

of sub-samples of the control (CTE4) and the experimental (CAM) groups at 0.99

confidence level are narrow. It is obvious from these narrow ranges that sample

means and sample deviations of the posttest scores in achievement and in

Analysis of Data andResults

cognitive ability of the academically advantaged students in the control (CTM)

and in the experimental (CAM) grou D are very much dependable

All the findings of the analysis done for the nature and dependability of

the achievement scores in Mathematics and in cognitive ability scores obtained

for the sample of the study are stable and dependable. This indicates the

trustworthiness of the data collected from the sample. The results of the analysis

of the test scores for the sample in Mathematics achievement and in cognitive

ability are applicable to the population of the study also

5.2. Comparison of Scores tin Achievement in Mathematics of

Pupils in the Experimental (CAM) and the Control (CTM)

Groups.

The pretest scores and postte!;t scores of the experimental (CAM) and the

control (CTM) groups were analyzed and compared by calculating the critical

ratio and testing for its significance

5.2.1. SigniJlcance of Di$er.ence between Pretest Scores in

Achievement in Mathematics of Academicoliy Disadvantaged Students

in the Experimental (CAM) and in the Control (CTM) Groups.

The mean and standard deviation of the pretest scores in Achievement in

Mathematics of academically disadvantaged students in the experimental (CAM)

and the control (CTM) groups were calculated. The critical ratio was computed

and tested for significance. The data and result of the test of significance is given

in Table 5.9.

Analvsis of Dma and Results

Table 5.9

Data and Result of Test of S-ance of the Difference between the Mean

Pretest Scores in Achievement in Nathematics of Academicah Disadvantased

Students in the Experimental (CAM) -ntrol (CTM) Grouos.

Group N Mean SD CR

AD-CAM 123 21.39 3.61 2.5*

AD-CTM 126 20.35 2.98

*p < 0.05

The critical ratio is 2.5, which is less than the table values at 0.01, 0.001

levels of significance (2.576, 3.291) and greater than the table value at 0.05 level

of significance (1.96). Hence it is zkar that the difference between the mean

pretest scores is significant at 0.05 level of significance (CR= 2.5; p < 0.05).

This indicates that two groups of a~:ademically disadvantaged students (CAM &

CTM) differed significantly in their i~itial academic abilities. The means of pretest

scores for experimental and contrcl groups (CAM & CTM) are 21.4 and 20.35

respectively. This shows that the zxperimental group performed better in the

pretest than the control group. This might be the result of non equated classroom

groups selected for the treatment

5.2.2. Significance of Digerence between Pretest Scores in

Achievement in Mathematics trf Acalemiccdly Aduontaged Students in

the Experimental (CAM) and Control (CTMJ Groups.

The mean and standard deviation of the pretest scores of academically

advantaged students in the experimental (CAM) and the control (CTM) groups

Analysis of Data and Resubs

were found. The critical ratio was calculated and tested for significance. The data

and result of the test of significance are given in Table 5.10

C Table 5.10

Data and Result of Test of Simificznce of the Difference between the Mean

Pretest Scores in Achievement in b4athematics of Academicallv Advantaqed

Students in the Experimental (CAM) 2nd Control (CTM) Groups.

Group N Me sn SD CR

AA-CAM 145 26.28 3.37

AA-CTM 111

The calculated critical ratio is 0.27. The table values at 0.05, 0.01, 0.001

levels of significance are 1.96, 2.576 and 3.291 respectively. Here the critical

ratio is not significant at both levels 'CR= 0.27; p > 0.05). It reveals that the

difference between the means of pretest scores is not significant at both levels.

Hence it is obvious that academically advantaged students in the two groups

(CAM & CTM) did not differ significartly in the initial academic ability.

5.2.3. Significance of Di@kmnce between Posttest Scores in

Achievement in Mathematics of Academically Disadvantaged Students

in the Experimental (CAM) and Control (CTM) Groups.

The mean and standard deviation of the posttest scores of academically

disadvantaged studen.ts in the experimental (CAM) and control (CTM) groups

were calculated. The critical ratio was computed and tested for significance. The

data and result of the test of significant% are given in Table 5.1 1.

Analysis of Dafa and Results --

Table 5.11

Data and Result of Test of Simifiwnce of the Dierence between the Mean

Posttest Scores of Academicalkr Disadvantased Students in the Experimental

(CAM) and Control (CTMI G r o s p---

Group N Mean SD CR --

AD-CAM 123 70.15 4.47 47.%'**

AD-CTM 126 42.37 4.67

*** p .c: 0.001

The value for significance at 0.001, 0.01 and 0.05 levels are 3.291,2.576

and 1.96 respectively. It is clear that the critical ratio 47.96 is significant at 0.001

level (CR= 47.96; p < 0.001). This indicates that the mean posttest scores of the

academically disadvantaged students in the two groups (CAM & CTM) differ

significantly. It is evident from analysis of the means that mean scores of the

experimental group are higher than that of control group. Hence a tentative

conclusion can be taken that Concept Attainment Model of Instruction is more

effective than the Conventional Teaching Method for Mathematics instruction to

academically disadvantaged students.

5.2.4. Signiflance of w e r e n c e betwen Posttest Scores of

Academicaffy Advantaged Students in the Experimental (CAM) and

Control (CTM) Groups.

The mean and standard tieviation of the posttest scores of academically

advantaged students in the experimental (CAM) and control (CTM) groups were

Anaijwis of Data and Results

calculated. The critical ratio was calc~~lated and tested for significance. The data

and results of the test of significance are given in Table 5.12.

4 Table 5.12

Data and ResuH of Test of S~qnificance of D~fference between the Mean Posttest

Scores in Achievement in mat he ma ti,^ of Academicak Advantaqed Students in

the Experimental (CAM) and C& (CTM) Groups.

Group N Mean SD CR

AA-CAM 145

AA-CTM 111 '70.48 4.31

"** p < 0.001

The values for significance at 0.05,O.Ol,and 0.001 levels are 1.96,2.576,

and 3.921 respectively. The value of critical ratio calculated is 23.43, which is

"I highly significant at 0.001 level (CR=23.43; p i 0.001). This indicates that the

mean posttest scores of academi~~lly advantaged students in the two groups

(CAM & CTM) differ significantly. It can be observed that the mean of the

experimental group is higher than that of the control group. It can therefore, be

tentatively arrived that the Concept Attainment Model of instruction is more

effective than the Canventional Teaching Method for academically advantaged

students in their Mathematics teaching.


5.3. C o m p d s o n of Scores in Cognitive Ability Test of Pupils in


The pretest scores and posttest scores in cognitive ability of students

belonging to the experimental (CAM] and control (CTM) groups were analyzed

and compared by calculating the critical ratio and then by testing for significance

5.3.1. Significance of Diflerence betmen Pretest Scores in CogniHue

Ability of Academically Disadvantaged Students in the Experimental

(CAM) and in the Control (CTM) Groups.

The mean and standard deviation of the pretest scores in cognitive ability

of academically diidvantaged students in the experimental (CAM) and the

control (CTM) groups were calculat~d. The critical ratios were computed and

tested for significance. The data and result of the test of significance are given in

Table 5.13

Table 5.13

Data and Result of Test of Sicmificmof the Difference between the Mean

Pretest Scores in Coqnitive A m ) f Academicallv Disadvantaaed Students in

the Exwimental (CAM) and C-ol (CTM) Grou~s.

Group N Mean SD CR

AD-CAM

AD-CTM 126 9.51 2.02

The values for significance at 0.05, O.Ol,and 0.001 levels are 1.96,2.576,

and 3.921 respectively. The critical ratio calculated is1.05, which is less than the

table value at both levels. Hence the critical ratio is not significant at all levels

Analysis of Data and Resulfs

(C R = 1.05; p> 0.05). This sh~~ws that the two groups did not differ

significantly in their pretest scores, and that they were equal in their cognitive

ability.

5.3.2. Signiflconce of Mflerence between Posttest Swres in Cognitive

Ability of Academically Disaducmtaged Students in the Experimental

Group (CAM) and in the Contro,l ( C m ) Groups.

The mean and standard deviation of the posttest scores in cognitive

ability of academically disadvantagc:d students in the experimental (CAM) and

control (CTM) groups were calcul;tted. The critical ratio was computed and

tested for significance. The data ancl result of the test of significance are given in

Table 5.14.

Table 5.14

Data and Result of Test of Siqnificance of the Difference between the Mean

Posttest Scores in Comitive of Academicah Disadvantaqed Students in

the hwrimental (CAM) and the Gmbol [CTM) Grouw. --

Group N Mean SD CR

AD-CAM 123

AD-CTM 126 11.42 2.11 --

*** p< 0.001

The critical ratio obtained is 10.63.The table values at 0.05, 0.01 and

0.001 level are1.96, 2.576 and 3.291 respectively. The obtained CR of 10.63 is

far greater than 3.291 and hence can be marked 'very significant' (C R= 10.63;

p< 0.001). By referring Table 5.14, it is seen that the mean of experimental

Attalysis of Data and Results

(CAM) group is greater than that of the control group. Hence a conclusion can

be made tentatively that the experimental group gained mote than the control

$ group in cognitive ability.

5.3.3. S i g n i h c e of Difference -en Pretest Scores in Cognitive


(CAM) and inthe Control (CTM) Groups.

The mean and standard deviation of the pretest scores in cognitive ability

of academically advantaged studerits in the experimental (CAM) and control

(CTM) groups were found. The critical ratio was calculated and tested for

significance. The data and result c~f the test of significance are given in Table

Tabk 5.15

-and Simioficance of the Difference between the Mean

Pretest Scores in Cocmitive of Academicalkr Advantaqed Students in the

-CAM) and the Control (CTM) Groups.

Group N Mean SD CR

AA-CAM

AA-CTM 111 13.44 2.31 ----

The calculated critical raticl is 1.09. The values for significance are 1.96 at

the 0.05 level, 2.576 at the 0.0:. level and 3.291 at the 0.001 level. Since the

C R does not reach the 0.05 Iev~zl, the obtained mean difference of 0.54 can be

marked 'not significant' (C R= 1.09; p> 0.05). Thus it can be concluded that

the two groups did not differ significantly at any levels.


5.3.4. Signiflcmce ofmflerence between Posttest Scores in Cognitiue


(CAM) and in the Control (CTM) Groups.

The mean and standard deviation of the posttest scores in cognitive

ability of academically advantaged students in the experimental (CAM) and in

the control (CTM) groups were calc~lated. The critical ratio was calculated and

tested for significance. The data and result of the test of significance are given in

Table 5.16.

Table 5.16

Data and Result of Test of mmce of the Difference between the Mean

Posttest Scores in Coclnitive abilitv sf Acadernicak Advantased Students in the

Experimental (CAM) and t h e m o l (CTM) Groups. -- -

Group N Mean SD CR

Af-CAM 145 19.87 4.06 7.98***

Af-CTM 111 16.54 2.57

"** p < 0.001

The values for significance at 0.05, 0.01, and 0.001 levels are 1.96,

2.576, and 3.921 respectively. The critical ratio calculated is 7.98, which is

significant at 0.001 level (CR=7.5,8; p c 0.001). This indicates that the mean

posttest scores of academically ad-~antaged students in the two groups (CAM &

CTM) differ significantly. This implies that the two groups differ significantly at

0.001 level. Since the mean score of the experimental group is higher than that

Anulysis of Duiu and Results

of the control group, the performance of the first group is considerably higher

than the other group.

5.4. Comparison of Gain in Petformance of Experimental (CAM)

and Control (CTM) Groups -Achievement in Mathematics.

The mean and standard deviation of the gain scores in achievement in

Mathematics of the students in the two groups were computed. The difference

between the mean gain scores was ailculated and tested for significance.

5.4.1. Significance of Diflererce between the Gain Scores in

Achievement in Mathematics of Academically Disaduantqed Students

in the Experimental (CAM) and in the Control (C'IM) Groups.

The effectiveness of Conc(?pt Attainment Model of instruction to

academically disadvantaged students was found out by computing the critical

ratio in respect of the difference between means of the gain scores and then

testing it for significance. The data and result of the test of significance is given in

Table 5.17.

Table 5.17

Data and Result of the Test of Sicm~ficance of Difference between Mean of the

Gain Scores in Achievement in Mathematics of Academicallv Disadvantaqed

Students in the Experimental (CAM) and Control (CTM) Groups.

Group N Mean SD CR

AD-CAM 123 43.76 6.05 36.75***

AD-CTM 126 22.02 5.4

The result presented in Table 5.17 indicates that the critical ratio

calculated is significant at 0.001 level of significance. The critical ratio obtained is

Analysis o f Data and Results

36.75. The values for significance at 0.001, 0.01 and 0.05 levels are 3.291,

2.576 and 1.96 respectively. Hencc: it can be inferred that there is significant

difference between the means of the gain scores of academically disadvantaged

students in the experimental (CAM) rind control (CTM) groups.

The values of mean gain scores for academically disadvantaged students

in the experimental (CAM) and ccntrol (CTM) groups are 48.76 and 22.02

respectively. It may be noted that the academically disadvantaged students in the

experimental group have a glittering performance as compared to their

counterparts.

5.4.2. Significance of Di-sce between the Gain Scores in

Achievement in Mathematics of Academically Aduantaged Students in

the Experimental (CAM) and in f he Control (C'IM) Groups.

The effectiveness of Concept Attainment Model of Instruction to

academically advantaged students was found out by computing the critical ratio

and then testing it for significance. T1e data and result of the test of significance

are given in Table 5.18

Table 5.18 Data and Result of the Test of Siqnificance of the Difference between Mean of

the Gain Scores in Achievement in Mathematics of Academicah Advantaped

Students in the EkwrimeniaI (CAM) and the Control (CTM) Grouvs.

Group N Ms?an SD CR

AA-CAM 145 56.06 4.63 17.9***

AA-CTM 111 44.32 5.60

*::* p < 0.001


The values for significance iit 0.001, 0.01 and 0.05 levels are 3.291,

2.576 and 1.96 respectively. The critical ratio calculated is 17.9 which is

significant at 0.001 level (C R= 17 9; p< 0.001). This indicates that there is a

significant difference between the means of the gain scores of the experimental

group (CAM) and the control group :CTM). By analysing the means given in the

Table 5.18, the value obtained for the academically advantaged students in the

experimental group is higher than that of the control group.

5.5. Comparison of Gain in Performance of Experimental (CAM)

and Control (0 Groups - Cognitive Ability.

The mean and standard deviation of the gain scores in cognitive ability of

the students in the two groups were computed. The difference between the

mean gain scores in cognitive ability was tested for significance by calculating the

critical ratio.

5.5.1. Significance of Differrnce between the Gain Scores of

Academically Disaduantclged Strrdents in the Ewperimental (CAM) and

in the Control (CTNI) Groups.

The effectiveness of Concept Attainment Model of instruction to

academically disadvantaged students was found out by computing the critical

ratio for the difference between the means of the gain scores in cognitive ability

and testing it for significance. The data and result of the test of significance are

given in Table 5.19.

Analysis of Data and Results --

Table 5.19

Data and Resuit of the Test of SiQnifitance of the Difference between Means of

the Gain Scores in Cocnritive Abilitv o-demicallv Disadvanta~ed Students in

the Ekverimental (CAM) and the Coni&TM) Groups. -

Group N Mean SD CR --

AD-CAM 123 6.59 3.83 12.85***

AD-CTM 126 1.91 1.30

The values for significance itt 0.001, 0.01 and 0.05 levels are 3.291,

2.576 and 1.96 respectively. The CR calculated is significant at 0.001 level

(C R= 12.85, p< 0.001). Table 5.19 makes it clear that experimental group is

in a better position than the control group. This implies that the experimental

group gained more when cornpared to the control group

5.5.2. Significance of DiB'eence between the Gain Scores in Cognitive

Ability of Academically Advantaged Studeirts in the Experimental

(CAM) and in the Control (ClBl) Groups.

The effectiveness of Cortcept Attainment Model of instruction to

academically advantaged students was found out by calculating the difference

between means of the gain scores in cognitive ability and testing it for

significance. The data and result of the test of significance are given in Table

5.20.


Table 5.20

Data and Result of the Test of Siqnificance of the Difference between Means of

the Gain Scores in Comitive Ability of Academically Advantased Students in the

Exwrimental (CAM) and the C m ( C T M ) Grou~s.

Group N Mean SD CR

AA-CAM 145 6.72 4.26 8.95***

AA-CTM 111 3.1 --

2.07

*"* p < 0.001

The result presented in Table 5.20 indicates that the critical ratio

calculated is significant at 0.001 levc:l of significance (CR = 8.95; p< 0.001).

The critical ratio obtained is 8.95. The table values for at 0.001. 0.01 and 0.05

levels are 3.291, 2.576 and 1.96 res~'ectively. Hence we can ascertain that there

is significant difference between the means of the gain scores of academically

advantaged students in the experime~ltal (CAM) and the control (CTM) groups.

The values of mean gain scores for academically advantaged students in

the experimental (CAM) ancl the :ontrol (CTM) groups are 6.72 and 3.1

respectively. It may be noted that the academically advantaged students in the

experimental group have a bri&,mnt performance as compared to their

counterparts.

5.6. Comparison of Pretest and Posttest Scores of Dierent

Groups - AcMevement in Matl~ematics.

The difference between posttt:st scores and pretest scores in achievement

in mathematics of academically di~advantaged and academically advantaged

Analysis of Duta and Results

students in the Experimental and in the Control Group was found. The t-values

using paired 't' test were calculated ar~d tested it for significance.

? 5.6.1. Significance of Digerence between the Pretest and Posttest

Scores in Achieventent in ,Mathematics of the Academically

Disaduantaged Students in the Experimental Group.

The effectiveness of Concept Attainment Model of instruction to

academically disadvantaged students in achievement in Mathematics was found

out by computing the t-values using :>aired 't' test and tested it for significance.

The data and result of the test of significance are given in Table 5.21.

Table 5.21

Data and Result of the Test of Sisnific,ance of the Difference between the Pretest

and Posttest Scores in Achievement in Mathematics of Academically

Diadvantaqed Students (Experimentrl Group).

Group Posttest Pretest Mean X1 Mean X2 XI - X 2 SD t value

AD-CAM 70.15 21.39 48.76 6.05 89.31***

*** p < o.ooi

The calculated value of 't' is 83.31. The table value of 't' for df = 122 at

0.05, 0.01 and 0.001 levels are 1.9798, 2.6166 and 3.3722 respectively. This

indicates that the 't' value is significant at 0.001 level (t = 89.31; p< 0.001).

Hence it is seen that there is significant difference between the means of pretest

and posttest scores of academtcally c isadvantaged students in the experimental

Analysis of Daia andResults

group. This proves that the Concept Attainment Model of instruction is effective

in teaching Mathematics to academic:ally disadvantaged students.

5.6.2. Signiflcunce of Diflerence between the Pretest and Posttest

Scores in Achievement in Mathematics of the Academically

Advantaged Students in the Experimental Group.

The effectiveness of Conczpt Attainment Model of instruction on

achievement in Mathematics of academically advantaged students was found out

by computing the t-values using paired 't' test and tested it for significance. The

data and result of the test of significance is given in Table 5.22.

Table 5.22

Data and Result of the Test o w h c a n c e of the Difference between the Pretest

and Posttest Scores in A c h i e v m in Mathematics of Academically Advantmed

Students (Euwrimental Group).

Posttest Pretctst Group Mean X1 Mean X2

XI-X2 SD t value

AA-CAM 82.33 26.:!8 56.05 4.63 145.68***

*** p < 0.001

The 't' ratio obtained is 145.68. From Table of t-ratio, the value of 't' for

df =I44 at 0.05, 0.01 and 0.0'31 levels are 1.9776, 2.6122 and 3.3631

respectively. The obtained t of 145.68 is Far greater than 3.3631and hence can

be marked 'very significant.' This indicates that the 't' value is significant at

0.001 level (t = 145.68; p c 0.001). Hence it is seen that there is significant

difference between the means of pretest and posttest scores of academically


advantaged students in the experimental group. This proves that the Concept

Attainment Model of instruction is effective in teaching Mathematics to

2 academically advantaged students.

5.6.3. SigniJfcance of mflerenct? between the Pretest and Posttest

Scores in Achievement in Mathematics of the Academically

Disadvantaged Students in tbe Ct~ntrol Group.

The Pretest and Posttest Scores of the academically disadvantaged

students in the control group was anitlyzed and significance of the difference in

means was found out by computing the t-values using paired 't' test. The data

and result of the test of significance is given in Table 5.23.

Table 5.23

Data and Result of the Test of Sianificance of the Difference between the Pretest

5 and Posttest Scores of Achievemelt in Mathematics of the Academically

Disadvantawd Students (Control G r o a d --

Posttest Pretest Group XI-X2 SD t value Mean X 1 Mean X2

AD-CTM 42.37 20.35 22.02 5.4 45.76***

*** p < 0.001

The obtained value of 't' is 45.76. The value of 't' for df = 125 at 0.05,

0.01 and 0.001 levels from table clf t-ratio, are 1.9795, 2.616 and 3.3709

respectively. This indicates that the 't' value is significant at 0.001 level (t =

45.76; p< 0.001). The result reveals that there is significant difference between

the means of pretest and posttest sco..es of academically disadvantaged students

Analvsis of Dota and Results

in the control group also. The result presented in Table 5.23 indicates that the

conventional method was also effectivz in increasing the achievement of pupils

5.6.4. Significance of fhflerencc? between the Pretest and Posttest

Scores in Achieuement in iWuthematics of the Academically

Advantaged Students in the Control Group.

The pretest and posttest score:$ of the academically advantaged students

in the control group was analyzed and significance of the difference in means

was found out by computing the t-~mlues using paired 't' test. The data and

result of the test of significance is given in Table 5.24.

Table 5.24

Data and Result of the Test of S&n&ance of the Difference between the Pretest

and Posttest Scores in Achievemc:nt in Mathematics of the AcademicaUv

Advantased Students lControl Groujk

Posttest Prete~t Group XI-X2 SD t value Mean X I Mean X2

AA-CTM 70.48 26.16 44.32 5.60 83.37***

*** p < 0.001

The calculated value of 't' is 133.37. The table value of 't' for df = 110 at

0.05 0.01 and 0.001 levels are 1.082, 2.6215 and 3.3765 respectively. This

indicates that the obtained 't' value is significant at 0.001 level (t = 89.31; p<

0.001). This result shows an improl~ement in the achievement of pupils on the

posttest.


5.7. Comparison of Pretest crnd Posttest Scores of Different

Groups - Cognitive AMlity.

The means of the Pretest and Posttest Scores in cognitive ability of

academically disadvantaged and academically advantapd students in the

experimental and control groups were found. The differences between the

means were tested for significance by c:alculating the t ratio using 'paired t test'

5.7.1. Significance of Dlflerence between the Pretest and Posttest

Scores in Cognitive ability of the Academically Msadtnmtaged

Students in the Experimental Group.

The effectiveness of Concept Attainment Model of instruction in cognitive

ability of academically disadvantaged students was found out by computing the

t-values using paired 't' test. The data and result of the test of significance are


Table 5.25

Data and Result of the Test of Siqnificmof the Difference between the Pretest

and Posttest Scores in Coqnitive Al~ilitu of the Academicallv Diadvantased

Students (Exwrimental Group),

Posttest Pretest Group XI-Xi! SD t value Mean X I Mean X!

AD-CAM 15.75 9.16 6.59 3.83 19.07***

*** p < 0.001

The calculated value of 't' is 1'3.07. The table value of 't' for df = 122 at

0.05, 0.01 and 0.001 levels are 1.97'38, 2.6166 and 3.37217 respectively. This

Analvsis of Data and Resulfs

indicates that the 't' value is significant at 0.001 level (t = 19.07; p< 0.001).

Hence it is seen that there is significant difference between the means of pretest

and posttest scores of academically disadvantaged students in the experimental

group. This proves that the Concept Attaii~ment Model of instruction is effective

in enhancing cognitive ability of academically disadvantaged students.

5.7.2. Signijlcance of DiBrence between the Pretest and Posttest

Scores in Cognitiw ability of the Acudemidy Advantaged Students

in the Experimental Group.

The effectiveness of Concept Attainment Model of instruction in

enhancing cognitive ability of acad~?mically advantaged students was found out

by computing the t-values using parred 't' test and tested it for significance. The

data and result of the test of significance is given in Table 5.26.

Table 5.26

Data and Result of the Test of Siqnficance of the Difference between the Pretest

and Posttest Scores in Coanitivc! Ability of the Academicallv Advantased

Students (Ex~erimental Group).

Posttest Pretest Group Mean X I Mean X2 XI-X2 SD t value

AA-CAM 19.87 13.12 6.75 4.26 18.99***

**" p < 0.001

The 't' ratio is 18.99. Entering table of t-ratio for df = 144, we find the t's

at 0.05, 0.01 and 0.001 levels to be 1.9776, 2.6122 and 3.3631 respectively.

This indicates that the 't' value is significant at 0.001 level (t =18.99; p< 0.001).

Analysis of Data andResults --

That is the difference of 6.72 is signifcant at 0.001 level. Hence it is seen that

there is significant difference between the means of pretest and posttest scores of

i? Academically Advantaged students in the experimental group. This proves that

the Concept Attainment Model of Instruction is effective in enhancing cognitive

ability of Academically Advantaged students

5.7.3. Signifcatace of Df&rence betroeen the Pretest and Posttest

Scores in Cognitiue AbIIity of the Academically Disadvantaged

Students in the Control Group.

The means of the pretest anti posttest scores in cognitive ability of the

academically disadvantaged students in the control group were calculated.

Significance of the difference in means was found out by computing the t-values

using paired 't' test. The data and result of the test of significance is given in P *

Table 5.27.

Table 5.27

Data and Result of the Test o f m l i c a n c e of the Difference between the Pretest

and Posttest Scores in Coanitive Ability of the AcademicaUv Didvantaced

Students (Control Group).

Posttest Pretest Group XI-X2 SD t value Mean X I Mean X2

AD-CTM 11.42 9.51 1.91 1.30 16.49*** --

*** p < 0.001

The obtained value of 't' is 16.49. The value of 't' for df = 125 at 0.05,

0.01 and 0.001 levels, obtained irom table of t-ratio, are 1.9795, 2.616 and


3.3709 respectively. This indicates thet the 't' value is significant at 0.001 level (t

= 16.49; p< 0.001). The result ir,dicates that there is significant difference

1 between the means of pretest and posttest scores of academically disadvantaged

students in the control group also. The result presented in Table 5.27 indicates

that the conventional method is alsct effective in increasing the cognitive ability

of academically disadvantaged students.

5.7.4. Significance oj Diflepencc? between Pretest and Posttest Scores

in Cognitive AblBty of the Academicdiy Adbentaged Studmts in the

Control Group.

The pretest and posttest scores in cognittve Eebility of the academically

advantaged students in the control group was analyzed and significance of the

difference in means was found o ~ t by computing the t-values using paired 't'

test. The data and result of the test of significance is given in Table 5.28.

Table 5.28

Data and Result of the Test of Siaiificance of the Difference between the Pretest

and Posttest Scores in Cosniti~re abilitv of the Academicallv Advantaqed

Students (Control Group).

Posttest Pretest Group Mean X1 Mean X2 X1-X2 SD t value

The 't' ratio is 15.79. Entering table of t-ratio for df = 110, we find t at

0.05, 0.01 and 0.001 levels arc, to be 1.982, 2.6215 and 3.3765respectively.


The obtained t is considerably larger than 3.3771. Hence, the obtained

difference is significant beyond the 0 001 level. This indicates that the 't' value is

significant at 0.001 level (t = 15.79; p< 0 001). This indicates that the students

in the control group also performed well in the posttest.

5.8. Genuineness of DiRerence in Pedonnance of Groups.

The analysis of the pretest scores of the academically disadvantaged

students in the experimental (CAM) and control (CTM) groups did not show any

difference at 0.001 level of significance. The analysis of the pretest scores of the

academically advantaged students i 2 the experimental (CAM) and control (CTM)

groups also did not show any sigrrificant difference. It means that there is not

much difference between the inital abilities of the experimental and control

groups.

The analysis of the gain scores showed that the experimental group has a

marginal advantage over the control group. Also the analysis of the posttest

scores and their comparison with the pretest scores of the experimental and the

control groups indicate that then: is an increase in the posttest scores of the

experimental group than the other. Even though the difference between means

of pretest and posttest is significant, the comparison of gain scores reveals that

the experimental group has an advantage over the control group.

But by mere comparison 'of posttest scores, it can not be concluded that

the experimental group differed :;ignificantly from the control group. It is highly

inconvenient to sort students from different classes to form equated groups in a

normal classroom condition. So the, investigator selected different batches of

intact classroom groups from different institutions to form the two groups i.e.

experimental (CAM) group and control (CTM) group. It is very difficult to

ascertain whether or not the differences between the pretest and posttest scores

have caused exclusively due to expei.imental factor.

In experimental research in schools, most attributes of students (such as

achievement level, self-esteem, attitudes, and so on) are relatively stable before

experiment. If we randomly assign students to different treatments and give them

measures of achievement or attitude etc, it is likely that, no matter how powerful

the treatment, the main determinant of student scores will be their abilities or

attitudes before the project began. This problem can be overcome by the use of

Analysis of Covariance (ANCOVA), in which prior abilities are controlled.

Furthermore, ANCOVA can make treatment groups, that are different in pretests,

statistically equivalent, if the pretest differences are not too large (Slavin, 1992).

According to Glass and Hopkins 11984) ANCOVA is a method of statistical

analysis used to increase statistical power and reduce bias, that is, to equate

groups on one or more variables. Although ANCOVA can reduce bias, it can

never remove all possible sources of confounding. The use of ANCOVA method

is thus justified for the analysis of the scores of the present study.

Analysis of Dota and Results

5.9. Comparison of Efictiveness of Concept Attainment Model

of Instruction with Convention~ol Method of Teaching.

The effectiveness of C:oncept Attainment Model of Instruction over

Conventional Method of Teaching is found by comparing the pretest and

posttest scores in achievement in Mathematics of academically disadvantaged

students from experimental ((:AM) and control (CTM) groups. In the same

manner the academically advantagecl students from the both the groups were

also compared.

5.9.1. Comparison of Eflectivent*ss of Concept Attainment Model of

Instruction with Conventional 'leaching Method Using ANCOVA on

the Learning of Academically Disadvantaged Students.

The scores of the 505 studenk; were consolidated. One group containing

268 students formed the experimental group and other group with 237 students

formed the control group. In the exxrimental group 123 students and in the

control group 126 students were iderltified as Academically Disadvantaged. The

pretest and posttest scores of the Academically Disadvantaged students in the

experimental (CAM) and the control (CTM) groups were analysed statistically

using the technique ANCOVA. Before proceeding to ANCOVA, the scores were

subjected to ANOVA. The data and result are given in Table 5.29.


Table 5.29

Results of the Summan, of Analvsis of Variance of the Pretest and Posttest

Scores in Mathematics of Academicallv Didvantased Students in Exverimental *

and Control Groups. --

Source of df SSx SSy MSx MSy Fx variation FY

---

Among 1 68.51 48065.6 68.51 48065.6 Means 6.27* 2299.36***

Within 247 2698.11 Ei163.2i 10.93 20.9 Groups

*p <0.05 ***p <0.001

The F ratios were tested for siwificance. The table values of F for df = l /

247 are 3.8853, 6.749 and 11.1686 at 0.05, 0.01 and 0.001 levels of

significance respectively. The calcuklted value of Fx is 6.27. The value of Fx is

significant only at 0.05 level. (Fx == 6.27; p c 0.05). This indicates that the !z

difference between the means of pretest scores of the two groups differ

significantly only at 0.05 level. The Fy value is significant at 0.001 level (Fy =

2299.36; p <0.001). This indicates that the two groups differ significantly in the

posttest.

The total sum of squares, adjusted mean square variance for posttest

scores and F ratio were computed They are presented in Table 5.30 together

with the result of Analysis of Covariance

Anatjsis of Data and Results

Table 5.30

Results of Summarv of Analvsismvariance of the Pretest and Posttest Scores

in Achievement in MathematidAcademicalb Disadvantased Students in r) .

Exuerimental (CAM) and Contr- M) Groups. --

Source of df SSxy SSy.x MSy.x S&.x Fy .x variation -- Atnong

1 1814.68 48065.6 47044.22 216.9 Means

2244.05** * Within 246 128.63 5157.14 20.96 4.58 Groups

-- ' ** p c: 0.001

Here Fy.x is 2244.05. From the Table F for df = 11 246, interpolated

value of F at 0.05 level is 3.8854, at 0.01 level is 6.7493 and at 0.001 level is

11.1693. Since the calculated Fy.x ratio is greater than the value obtained from

Table F (Fy.x = 2244.05; p .c O.OOl), it is significant at all levels. This significant 2

ratio for the adjusted posttest scorc:s shotvs that the final mean scores of students

in the experimental and the control groups differ significantly after they were

adjusted for the differences in the -3retest scores.

This significant F ratio necctssitates us to proceed to test for significance of

the difference between the adjusted posttest means of the experimental and

control group


Table 5.31

Results of the Test of S i w i f i m e 3 f f e r e n c e between the Adjusted Means for

Posttest Scores in Mathematics of Memica lh , Diadvantased Students in

Experimental (CAM) and C o n t G l ' M ) Groum.

Group N Mx MY My.x ED,., t

AD-CAM 123 21.30 70.15 70.18 0.58 47.97* **

AD-CTM 126 20.3.5 42.37 42.34 ---

*** p <0.001

From table of t-ratio, to,,,= 3.3322, b,,=2.5968 and b,,=1.9702 for df

= 246. The difference in the adjusted means for posttest scores of the

academically disadvantaged students in the experimental group (AD-CAM) and

the control group (AD-CTM) was tested for significance. The value of t is

significant at 0.001 level.

This indicates that the perfc~rmances in achievement test in Mathematics

of experimental group, whose adju:jted posttest scores are higher, are better than

that of the control group. It may be noted here that the Concept Attainment

Model of instruction is more effective in teaching mathematics to academically

disadvantaged students than thz Conventional Teaching Method. This is

illustrated in Rg.5.1

5.9.2. Compmison of the Eflmtiueness of Concept Attainment Model

of instruction wfth Conuentional Teaching Method on Learning of

Academically Advantaged Students Using ANCOVA.

Out of sample strength of 505 students, 268 students were in the

experimental group and 237 :;tudents were in the conbol group. In the


experimental (CAM) group, 145 students were identified as academically

advantaged and in the control group, 111 students were identified as

academically advantaged. The prete:jt and posttest scores in the achievement test

in mathematics were analyzed statisiically using the technique ANCOVA. Before

proceeding to ANCOVA, the scores were subjected to ANOVA. The data and

results of ANOVA are given in Table 5.32

Table 5.32

The Results of Summaw o f m U A of the Pretest and Posttest Scores in

Mathematics of A c a d e m i c a l l v ~ ~ t a s e d Students in the Exuerimental (CAM]

and the Control (CTM) Grouv~,

Source of Variation d f SSx SSy MSx MSy Fx FY

Among Means I 0.81 8344.1 0.81 8844.1

0.07 575.98***

Within Groups 254 3158.05 3500.14 12.43 15.36

*:k* p <0.001

The table values of F for df := 11 254 at 0.05. 0.01 and 0.001 levels of

significance are 3.8846, 6.7474 and 11.164 respectively. The calculated value of

Fx and Fy are 0.07 and 575.98 respectively. The value of Fx is not significant at

all levels. This reveals that the two groups do not differ in their scores in the

pretests. Fy is significant at all levels (Fy = 575.98; p <0.001). This implies that

the two groups differ significantly in i heir posttest achievement. The total sum of

squares, adjusted mean square variances for the posttest scores and F ratio were

computed. They are presented in Table 5.33 together with the ANCOVA.

Fbure 5.1. Pretest and adjusted posttest means in achievement of academically disadvantaged students in the experimental and the control groups.

Analpis of Data and Results --

Table 5.33

Results of Summaru of ANCOVA of the Pretest and Posttest Scores of

Achievement in M a t h e m a t i c A Academicallv Advantawd Students in

Experimental (CAW and Control (C7.M) Grouvs. ~ ~

Source of d f S'xy Sy.x MSy.x Sl3y.x Fy.x Variation

Among 1 84.78 8827.99 8827.99 means

3.92 575.78*** Within 253 257.89 3879.08 15.33 Groups ---

*** p <0.001

The table values of F for df = I/ 253 are 3.8847, 6.7476 and 11.16467

respedively for 0.05, 0.01 and 0.031 levels of significance. The Fy.x obtained

575.78 is significant (Fy.x = 575.7:3; p< 0.001). As revealed by the F value of

ANCOVA given in Table 5.33, the final mean scores of students in the e

experimental and control groups differ significantly after they are adjusted for the

difference in the posttest scores,

The significant F ratio for the adjusted posttest mean scores shows that

the final mean scores of students in both the groups Tier significantly after they

have been adjusted for the differences in the pretest scores. The significance of

difference in adjusted posttest means is tested by 't' test. The data and results are

given in Table 5.34

Analysis of Dora and Results

Table 5.34

The Results of the Test of S i c m i w e of Difference between the Adjusted Means

for Posttest Scores in M a t h e m a w Academicdv Advanlased Students. * - Group N Mx MY My.x shy., t

-

AA-CAM 145 26.28 82.33 82.32 0.5 23.85***

AA-CTM 111 26.16 70.48 70.48

*** p < 0.001

From Table of t-ratio, the value of t a t 0.01 level is 2.5%, at 0.05 level is

1.9698 and at 0.001 level is 3.3399 for df = 253. The t value is 23.85 vide

Table 5.34 and it is significant at C.OO1 level (t = 23.85; p< 0.001). Ps per the

results obtained in Table 5.34, the performance of the students in the

experimental group is better than that of the control group. Hence it is evident

that the Concept Attainment Mcdel of instruction is an effective method of

teaching mathematics to academically advantaged students (vide Fig 5.2).

5.10. Objective-wise Comparison of Effectiveness of Concept

Attafnment Model of Inslmction roith Conventional Teaching

Method on Achieuement In Mathematics.

Scores are categorized okjective- wise and ANCOVA was done in order

to have objective wise cornparisc~n of effectiveness of Concept Attainment Model

of instruction with Conventional Teaching Method in achievement in

mathematics.


5.10.1. Comparison of Ejlfectiueness of Concept Attainment Model of

Instruction with Conuentiond l ' d i n g Method on Achieuement in

Mathematics (Objectfoe-wise) of Academically Disadvantaged

Students.

The scores obtained by the academically disadvantaged studenis in the

experimental (CAM) and the control (CTM) groups (123 students in CAM group

and 126 students in CTM group) in the achiewment test in mathematics were

consolidated objective wise and analyzed statistically. The resub of ANOVA are

presented in Table 5.35.

Table 5.35

The Consolidated Results of Sumrrarv of ANOVA of the Pretest and Posttest

Scores in Achievement inJ&&matics (Obiective-wise) of Academically

Didvantaued Students in th&perimental [CAM) and the Control (CTM)

Source of Variation df S S x S ~ S I MSx MSy Fx FY ---

Among Knowledge Means 1 20.57 2982.71 20.57 2982.71

5.48* 728.47** * 247 927.56 1011.35 3.76 4.1

Groups

Among , Application Means 155.22 32ti6.39 155.22 3266.39 71.9SC** 867.86***

247 532.87 929.64 2.16 3.76 Gmups

Analysis Among 1 104.35 288.18 104.35 288.18 Means

35.16*** 51.86*** 247 703.08 1372.58 2.97 - 5.56

Analysis of Dda and Results

From the Table F, for df = 11 247, F at 0.05 level is 3.885, and F at 0.01

level is 6.749 and F at 0.001 level is 11.16867. The calculated values of Fx and

x Fy indicate that there is significant difference between the experimental and

control groups in their pretest and posltest scores at 0.001 level for the objectives

comprehension, application and analysis. The pretest scores for the objective

knowledge, experimental and control group differ significantly at 0.05 level but

their posttest scores differ significantb~ at 0.001 level. The data and results of

analysis of covariance are given in Table 5.36.

Table 5.36

The Consolidated Results of t h h m m a ~ of Analvsis of Covariance of the

Pretest and Posttest Scores in Achiecement in Mathematics (Obiective-wise) of

Academicallv Disadvantased S t u d e r l u the Exverimental (CAM) and the

s Control (CTM) G~OUPG.

Source of Variation df SSxy SSy.x MSy.x S 5 . x Fy.x

Among I Knowledge Means -24".71 2906.10 2906.1

2.03 702.27*** Within 246 -22.78 1010.79 4.11 Gmups

Among , Understanding Means -610.83 3493.7 3493.7 2.72 473.93***

Within 246 95.::2 1813.44 7.37 Groups

Among , Application Means 712.04 2550.79 2550.79

1.94 675.13*** Within 246 -10 23 929.45 3.78 Gmups

Analysis Among 1 171.41 277.89 277.89 Means 2.36 49.99***

Within 246 -60.36 1367.61 5.56 G m u ~ s

Analusis of Duta and Results

From the Table F, for df = 11 :!46 value of, F at 0.05 level is 3.885, F at

0.01 level is 6.7493 and Fat 0.001 level is 11.1693. The Fy.x is significant for all

the four objectives. These significant ,atios for the adjusted posttest scores show

that the final mean scores of students in the experimental goup and the control

group differ significantly after they were adjusted for the difference in the pretest

scores.

These significant F ratios necessitated testing for significance of difference

between the adjusted posttest means of the experimental and control group.

Table 5.37

The Consolidated Results of the Test of Sicmificance of Dierence between the

Adiusted Means for Posttest Scores in Achievement in Mathematics (Obiective-

wise) of the Academicah Disadvan- Students in the Experimental (CAM1

and Control Grouw.

Section Group N Mn My Myx S&,,.., t-value

Knowledge bpt l

Control

Comprehension Exptl

Control

Application Exptl

Control

Analysis Exptl

Control

Analysis of Dma and Results

From table of t-ratio, t at 0.001, 0.01 and 0.05 levels are 3.332, 2.5968

and 1.97016 respectively for df = 2'16. The values of t are significant at 0.001

level. This reveals that the experim6:nial group, whose mean posttest scores is

higher, is better than the control goup for the objective-wise achievement in

mathematics. It can be concluded that the Concept Attainment Model is effective

in improving achievement in mathematics at different levels of objectives in the

cognitive domain of academically di:jadvantaged students

5.10.2. Comparison of E@ctfivtmess of Concept Attainment Model of

Instructlion (CAM) with Conuentional Teaching Method (CTM) on

Achieuement in Mathematics (Objectiuecwise) of Academically

Aduantaged Students.

In the experimental group c~f 268 students, 145 students were identified

as academically advantaged and in the control group of 237 students, 111

students were identified as academically advantaged. The scores obtained by

these students in the achievement test were consolidated objective wise under

different objectives like knowledgz, comprehension, application and analysis.

They were analyzed statisticall!r using the technique ANCOVA. Before

proceeding to ANCOVA, the staktical technique ANOVA was used. The results

of ANOVA are presented in Table 5.38.

Anatpis of Data and Results

Table 5.38

Consolidated Results of Summaw of ANOVA of the Pretest and Posttest Scores

in the Achievement in Matheratics (Obiedive-wise) of Academicalh -?

Advantaced Students in t h e m r i m e n f a 1 (CAM) and the Control (CTM)

Groups.

Source of Variation df SSx SSY MSx MSy Fx FY --

Knowledge Among Means 1 2.2% 57.8? 2.28 57.87

0.48 23.54*** Within Groups 254 1212.08 624.36 4.77 2.46

Compre- Among hension M~~ 1 13.12 240.33 33.12 240.33

6.80** 54.1 I*** Within 254 1236.76 1128.11 4.87 4.44 Groups

Applicat~on Among Means 13.31 893.22 13.31 893.22 291.94***

Within 3.44

Groups 254 981.41 777.14 3.86 3.06

Analysis Among Means 1 11.22 1684.79 11.22 1684.79

3.01 324.36*** Within omups 254 947.78 1319.32 3.73 5.19

From Table F, the values o f F after interpolation for df =1/ 254 at 0.05

level is 3.8846, 0.01 level is 6.7474 and at 0.001 level is 11.164. The F ratios

calculated for the groups were tested for significance. Fy ratios were significant

for all the objectives {Fy (knowledge)=23.54, Fy (comprehension) = 54.11, Fy

(application) = 291.94, Fy (analysis) = 324.36); p .c 0.001). This indicates that

the differences in posttest mean!; are significant. That is, the two groups differ

significantly in the posttest for ihe objectives like knowledge, comprehension,

application and analysis. As revealed by the F values of ANOVA for pretest (Fx)

given in Table 5.38, the F ratio for the objective comprehension only is

significant (Fx = 6.80; p < 0.01). This implies that the groups differ in the

pretest means only for the objective comprehension. The total sum of squares,

adjusted mean square variance for posttest scores and F ratio were found out.

They are presented in Table 5.39 along with the results of analysis covariance.

Table 5.39

The Consolidated Results of the S~~mmarv of Analvsis of Covariance of the

Pretest and Posttest Scores in Achievement in Mathematics (Objective-wise) of

Academicallv Advantaaed Students1 the Exwrimental (CAM) and the Control

ICTM) Groups.

Source of Variation df SSxy SSy.x MSy.x SDy.x Fy.x ----

w Knowledge Among Means I 11.49 51.99 57.99

1.57 23.50*** Within Groups 253 -12.07 624.24 2.47

Comprehension Among Means 1 -89.21 244.88 244.88

Within 2.11 55.15***

Groups 253 76.13 1123.42 4.44

Application Among Means I -109.0.1 900.5 900.5

Within 1.74 296.11***

Groups 253 87.22 769.39 3.04

Analysis Among Means I -137.5 1662.18 1662.18

Within 2.28 318.78***

Groups 253 -10.12 1319.21 5.21

Analysis of Data andRes~~Itts

From the Table F, the value$, of F after interpolation for df = 11 253 at

0.05 level is 3.885, at 0.01 level is 6.748 and at 0.001 level is 11.165. The F

ratios calculated for the groups were tested for significance. The Fy.x ratios were

significant for all the objectivfzs. 1Fy.x (knowledge) = 23.5, Fy.x

(comprehension) = 55.15, Fy.x (application) = 296.11, Fy.x (analysis) =

318.78; p < 0.001). This shows tnat the F ratios for adjusted posttest scores

were significant which indicates he final mean scores of students in the

experimental group and in the control group differ significantly after they were

adjusted for the differences in the pletest scores.

If F is not significant, there ij no reason for further testing as none of the

mean differences will be significan:. The significance of differences is tested by

the 't' test.

The adjusted means for the posttest scores of students in the experimental

and the control group in achievement test in mathematics were calculated using

regression coefficient. The data ant1 results are given in Table 5.40

From the table of t-ratio, the values of 't' at 0.05 level is I.%%, at 0.01

level is 2.5962 and at 0.001 level is 3.3309 for df = 253. As represented in

Table 5.40 the results of the 't' test show that all the values are significant at all

levels. The results indicate that tl-e experimental group scored better than the

control group in all the four levels of objectives. It is very clear that the Concept

Analysis of Dafa and Results

Attainment Model of instruction is ,Jery effective in teaching mathematics than

the Conventional Teaching Method.

Table 5.40

The Consolidated Results of the Test of Siqnificance of Difference between the

Adjusted Means for Posttest Scores in Achievement in Mathematics (Obiective-

wise) of Academicallv Advanm!Students in the b r i m e n t a l (CAM) and the

Control [CTM) Grouw.

Section Group N M. My MYX SEm. t --

Knowledge Exptl CAM 145 8.71 23.21 23.209

0.199 4.77*** Control CTM 111 8.54 22.26 22.260

Comprehension Exptl CAM 1 4 7.76 25.66 25.682

0.267 7.42*** Control cm 1 1 1 8.48 23.72 23.699

Application Exptl CAM 1 4 5 4 4 0 16.29 16.306

0.221 17.25*** Control cm 11 i 4.87 12.51 12.493

Analysis Exptl CAM 145 5.375 17.17 17.171

0.289 17.92*** control Cm 11 I j.rro 11.98 11.984

Table 5.41 The Consolidated Results o f Analvsis o f Covariance of t h e Pretest and Posttest Scores of Academicallw Advantaqed Students and Academicallv Diadvantawd Students.

S1 Source o f df SSx SSy SSxy SSy.x M S y . x SDy.x Fy.x Level o f Objectives Category Group N o Variation Significance

1 Total Academically CAM 8 Among Means 1 68.51 48085.60 1814.68 48065.60 47044.22 Disadvantaged CTM Within Groups 7 2698.11 5163.27 128.63 5157.14 20.96 4.58 2244.05 p< 0.001

Academically CAM & Among Means Advantaged CTM Within Groups

2 Knowledge Academically CAM & Among Means Disadvantaged CTM within G~~~~~

Academically CAM & Among Means A CTL! .;;,ii ,,,,

3 Compre- Academically CAM & Among Means hension Disadvantaged CTM Within Groups


4 Application Academically CAM & Among Means Disadvantaged CTM within G~~~~~


5 Analysis Academically CAM & Among Means Disadvantaged CTM within G~~~~~


Table 5.42

The Consolidated Results of Adiusted Means of Posttest Scores of Academicah Advantmed and Academically

Students in the Ewerirnenta D w d v a n ~ I and Control Groum-Total & Obiective-wise ~1 Objectives C a t e ~ ~ y Group N MX MY ~ y . x SE@, t Level of no Signifknee 1 Total AD CAM 123 21.39 70.15 70.18 0.58 47.97 P<0.001

CTM 126 20.35 42.37 42.34 AA CAM 145 26.28 82.33 82.32 0.5 23.85 P<O.001

CTM 111 26.16 70.48 70.48

2 Knowledge AD CAM 123 6.52 19.75 19.74 0.257 26.89 P<O.001 CTM 126 7.1 12.83 12.83

AA CAM 14s 8.14 L>.LI 22.2 n 199 4.77 ~co.001 -- -. CTM 111 8.54 22.26 22.26

3 Comprehension AD CAM 123 5.50 21.11 21.24 0.344 23.35 RO.001 CTM 126 6.75 13.25 14.94

A A CAM 145 7.76 25.66 25.68 0.267 7.42 P<0.001 CTM 111 8.48 23.72 23.70

4 Application AD CAM 123 4.33 14.93 14.94 0.026 29.52 P<0.001 CTM 126 2.75 7.68 7.67

AA CAM 145 4.40 16.29 16.31 0.221 17.25 P<O.001 CTM 111 4.87 12.51 12.49

5 Analysis AD CAM 123 5.05 14.37 14.34 0.299 7.56 WO.001 CTM 126 3.75 12.22 12.77

AA CAM 145 5.38 17.17 17.17 0.289 17.92 PCO.001 CTM 111 5.80 11.98 12.01

Fieure 5.2. Pretest and adjusted posttest means in achievement in mathematics of academically advantaged students in the experimental and control groups

Analvsis of Data and Results

5.11. Comparison of the EAfectiveness of Concept Attainment

Model of Instruction and Conventional Teaching Method on

Enhandng Cognitive Ability o f Students.

The cognitive ability test scclres were consolidated group wise and the

statistical technique ANCOVA was applied in order to compare the effectiveness

of Concept Attainment Model of instrudion.

5.1 1 .I. Compmimn of the Effectiveness of Concept Attainment Model

of Instruction and Conuentioinal Teaching Method on Enhancing

Cognitive AbUity of Academically Disadvantaged Students.

The scores obtained in the Cognitive ability test of 123 students in the

Experimental (CAM) group and 126 students in the control (CTM) group, who

were identified as academically disadvantaged were consolidated and anaiyzed

statistically using the technique fINCOVA. Before proceeding to the test

ANCOVA, ANOVA was done. The results of the kst ANOVA are given in Table

Table 5.43

Summaw of Analvsis of Variance of the Pretest and Posttest Scores in Cosnitive

Abilitv of Academicallv Didvantawd Students in the Ex~erimental (CAM) and

the Control (CTM) Groups.

Source of Variation df SSx SY MSx MSY Fx Fy

Among Means 1 7.42 116!51 7.42 1165.51

1.55 114.15***

Within 247 1184.24 252:..89 4.79 Groups 10.21


The F ratios were calculated and tested for significance. The table values

of F after interpolation for df = l/ 247 are 3.8853 at 0.05 level, 6.749 at 0.01

P level and 11.1686 at 0.001 level. The calculated value of Fy is significant at

0.001 level (Fy = 114.15; p < O.CO1). This evidently shows that the groups

differ significantly in their posttest. Since Fx ratio is not significant, it can be

noted that the groups did not differ significantly in their pretest scores.


scores and F ratio were calculated. 'They are presented in Table 5.44 along with

the result of analysis of covariance.

Table 5.44

Summary of Analvsis of Covariance of the Pretest and Posttest Scores in

Coqnitive Abilitv of Academicah IYidvantaqed Students in the Experimental I

(CAM) and Control (CTM) Grou~s.

Source of df SSxy S y . x MSy.x SDy.x Fy.x Variation

Among 1 -93.01 Means 1295.09 834.02

2.79 166.91***

Here, Fy.x = 166.91. From Table F, for df = 1/ 246, the interpolated

values of F at 0.05 level is 3.8854, F at 0.01 level is 6.7493and F at 0.001 level

is 11.169. Hence the Fy.x is significant at 0.001 level. The significant ratio for the

posttest scores shows that the final mean score of students in the experimental


and control groups differ significant19 after they were adjusted for the difference

in the pretest scores.

If F is not significant, then there is no need for further testing. The

significance of the difference is test2d by 't' test. The adjusted means for the

posttest scores of academimlly disacvantaged students in the experimental and

control groups in cognitive ability were calculated using regression coefficient.

The data and results are given in Table 5.45.

Table 5.45

The Results of the Test of Siqnificance of Difference between the Adiusted Means

for Posttest Scores in Cosnitive At~ilitv Test of Academicallv Didvantaaed

Students in the b r i m e n t a l (CAM) and the Control (CTM) G~OUDS.

G K O U ~ N MX MY MY .X Shy., t

Experimental AD- CAM 123 9.16 15.75 15.87

0.35 12.96*** Control AD- CTM 126 9.51 11.42 11.3

From table of t-ratio, the values oft at 0.05 level is 1.9701, at 0.01 level is

2.5968 and at 0.001 level is 3.33218 for df = 246.The t value as per Table 5.45

is 12.96, which is significant at all levels. This indicates that there is significant

difference between the experimental group and the control group. The results

presented in Table 5.45 show that the experimental group bagged markedly high

scores than the control group. This is ,Jety clear in fig 5.3. Hence it is evident that

the Concept Pittainment Model of nstruction is very effective in enhancing

cognitive ability of academically disadvantaged students.

IAU-CAMPL. AD-CTM

F h r e 5.3. Pretest aod adjusted posttest means In cq uve ability ui academically disadvantaged students in the experimental and ~untrol groups

Analysis of Doto and Results

5.1 1.2. Comparison of the E$ectiueness of Concept Attainment Model

of Instruction and Conventional Teaching Method on Enhancing

Cognitive Abilfty ojAcademica,lly Advantaged Students.

The scores obtained by 14!5 students in the experimental (CAM) group

and 111 students in control (CTMI group who were identified as academically

advantaged, in cognitive ability test were consolidated and analyzed statistically

using the technique ANCOVA.

Before proceeding to the tes; ANCOVA, ANOVA was done. The results of

the test ANOVA are given in Table 5.46.

Table 5.46

Summan, of Analvsis of Variance of the Pretest and Posttest Scores in Cocmitive

Ability Test of Academicallv Adva~ltased Students in the k r i m e n t a l (CAM1

and the Control (CTM) Groups. --

Source of Variation df SSx SSy MSx MSY Fx FY

Among Means 1 5.79 693.63 5.79 693.63

1.32 56.78***

Within 254 1114.61 3102.81 4.39 Groups 12.22

*** p < 0.001

As per the results in Table .5.46, Fx= 1.32 and Fy = 56.78. From the

Table F, the values of F after interpolation for df = l / 254 are 3.8846, 6.747

4and 11.164 at 0.05, 0.01, 0.001 k~vels respectively. Hence it is clear that Fx is

not significant. (Fx = 1.32; p > 0.05) and Fy is significant at 0.001 level (Fy =


56.78; p <0.001). This implies that the groups were equivalent in their pretest

abilities and diier significantly in thcir posttest scores.


scores and F ratio were calculated. They are presented in Table 5.47 along with

the results of analysis of covariance

Table 5.47

Summarv of Analusis of Covariance of the Pretest Scores and Posttest Scores in

Coqnitive Abilitv Test of Academic& Advantaqed Students in the Experimental

(CAM) and the Control (CTM) Gram

Source of df SXY SSy.x MSy .x SDy.x Fy .x Variation -- Among Means 1 -63.38 755.48 755.48

3.34 67.87***

From the Table F, for df =: 11 253, the interpolated values of F at 0.05

level is 3.8847, at 0.01 level is 6.:'476 and at 0.001 level is 11.1646. Here Fy.x

value is 67.87 (vide Table 5.47). I-Ience it is seen that Fy.x is significant at 0.001

level. This significant ratio for t h ~ adjusted posttest scores shows that the final

mean scores of students in the texperimental group and in the control group

differ significantly after they were adjusted for the differences in the pretest

means.

The significance of difference between the adjusted posttest means of

experimental and control groups is tested by t test.

Anulvsis of Data and Results

Table 5.48

The Data and Results of the Test of Sicmificance of Difference between the

Adiusted Means for Posttest Scores in Cocmitive Abilitv Test of Academicak h Advanlased Students in the ExDerirnental (CAM) and Control (CTM) Grouos.

Group N Mx MY My.x SED,, t --

Experi~nental AA- CAM 145 13.12 19.87 19.95

0.42 8.26*** Control AA- CTM 111 13.44 16.54 16.46

*** p<o.001

From table of t-ratio, the vrilues at 0.05 level is 1.9698, at 0.01 level is

2.5962and at 0.001 level is 3.3099 for df = 253. The results of the test

contained in Table 5.48 show that the difference is significant at all levels. Hence

it is evident that the Concept Attainment Model of instruction is very effective in

promoting cognitive ability also (vide fig 5.4.)

F i m 5.4. Pretest and adjusted pusitest means in mgmuve ability academically advantaged students in the experimental and control groups

I

Analysis ofDato ond Results

5.12. Achievement in 1Wathematics: Comparison of the

mcttiveness of Concept Attainment Model of Instruction on

Teaching MutkemaUcs to Academically Advantaged Students and

Acad- Disadaantage43 Students.

The experimental group, ~ h i c h was taught using Concept Attainment

Model of instruction, consists of 268 students. Out of 268 students 145 was

identified as academically advantaged and 123 were academically

disadvantaged. The pretest and posttest scores of both the subgroups of

experimental group were analyzecl systematically and subjected to ANCOVA.

5.12.1. ContpmIson of the Efirkctioeness of Concept Attainment Model

of Instmction on Teaching Mathematics to Acadedcalfy Aduantaged

Students and Aademicdfy Disadwntqed Students Using ANCOVA.

The achievement test scorzs of 145 academically advantaged students in

experimental group (AA-CAM) and 123 academically disadvantaged students in

the experimental group (AD-CAM) were found out. Before proceeding to

ANCOVA the statistical procedure ANOVA was applied. The data and results are


Analysis of Daia and Results

Table 5.51

Results of Summaw of Analvsis of Variance of the Pretest and Posttest Scores in

Mathematics of Academicallv Admntased and AcademicaUv Disadvantased a Students in the Experimental Group(CAM).

Source of Variation

df MSx

Among Means

130.52*** 612.14***

Within 266 3226.45 4292.51 12.13 Means

16.14

The F ratios were tested for significance. The table values of F for df = l /

266 are 11.156 at 0.001 level, 6.7446 at 0.01 level and 3.8824 at 0.05 level.

The values of F x and Fy are significa~t at 0.001 level. (Fx = 130.52; p< 0.001&

Fy = 612.14; p< 0.001). This indicates that both the groups differ significantly

in their pretest scores as well as posttest scores

The total sum of squares, ac'justed mean square variance for posttest

scores and F ratio were computed. They are given in Table 5.52

Table 5.52

Results of Summaw of Analvsis of Covariance of the Pretest and Pattest Scores in Mathematics of AcademiaUv Admntawd and Academicallv Disadvantawd Students in the Experimental Group (<:AM)

Source of Variation df SSxy SSy.x MSy.x SDy.x Fy.x

- ------ Among 1 Means

3954.62 6664.65 6664.65

4.02 411.46*** Within 265 -23.09 Groups 4292.51 16.19


The Fy.x is obtained as 411.46. The value of F for df = 11 265 from the

Table F is 11.1567 at 0.001 level, 6.7498 at 0.01 level and 3.884 at 0.05 level.

4 By analyzing the values it is clear that Fy.x significant at 0.001 level. The

significant ratio of Fy.x indicates that both the groups differ significantly at 0.001

level.

The significance of the difference between the adjusted posttest means of

both the groups is found out usinsi t-test. The data and result are presented in

Table 5.53

Table 5.53

Results of the Test of Simificance of Difference between the Adjusted Means for

Posttest Means in Mathematics of kkademicalhr Advantaqed and Disadvantaced

Students in the Exwrimental Grou1> (CAM).

Group N Mx MY My.x s%,, t

AA-CAM 145 26.28 82.33 82.34 0.51 23.93***

AD-CAM 123 21.39 7'0.15 70.18 --- *** p < 0.001.

From table of t-ratio, the value of b,,, =3.3289, at t,,,, = 2.595 and at

b,, =1.9694 for df = 265. It is clear that obtained difference is significant at

0.001 level (fig 5.5). Hence we car1 ascertain that the Concept Attainment Model

of instruction is more effective for academically advantaged students than the

disadvantaged students.

Analysis of Daia and Results

5.12.2. Comparison of the Efiectiveness of Concept Attainment Model

of Instruction on Teeching Mothematics (objective-dse) to

Academically Advanteged Strrdents and Academically Disadurmtoged

Students.

The scores in Mathematics Achievement test of academically advantaged

students and academically diiad~mntaged students in the experimental group

(CAM) were consolidated objecthe wise. The statistical procedure ANOVA was

applied before proceeding to ANCOVA.

Table 5.54.

Consolidated Results of Summary of ANOVA of the Pretest and Posttest Scores

in the Achievement in Mathematics (Obiedive-wise) of Academically

Advantaqed Students and Academicallv Disadvantased Students in the

herirnental G r o u ~ (CAM).

Source of Variation df S x SY MSx Msy Fx FY

Knowledge Among Means 1 325.25 802.56 325.25 802.56

Within 72.51"- 237.18"' Groups 266 1193.21 !300.13 4.49 3.38

Comprehension Among Means 1 336.20 1389.96 336.20 1389.%

Within 86.17"' 198.42"' Groups 266 1037.81 1863.39 3.90 7.01

Application Among Means 1 0.52 122.35 0.52 122.35

Within 0.15 39.41"-

Groups 266 900.1'5 825.75 3.38 3.10

Analysis Among Means 1 7.27 516.03 7.27 516.03

Within 2.02 119.11*" ~ r o ~ p s 266 959.8i 1152.15 3.61 4.33

55 . Pretest aad adjusted p d t s t m e m ia ew:hicvcfll& in mwbmdcs'of d & l y disadvantaged sludernts and aadcmidy advantaged shdents in the e x ~ ~ n t a l group


The value of F for df = 11 266 at 0.05 level is 3.8824, at 0.01 level is

6.7446and at 0.001 level is 11.1.36. The obtained values of Fx indicates that

there is significant difference between the pretest scores of the experimental and

control groups in the objectives Knowledge and Conlprehension (for Knowledge,

Fx=72.51; p < 0.001, for Compr(zhension, Fx= 86.17; p <0.001). There is no

significant diirence between the pretest scores of the experimental and control

groups in the objectives Application and Analysis (for Application, Fx= 0.15;

p > 0.05, for Analysis Fx = 2.02; p > 0.05). The calculated values of Fy shows

that the two groups differ significar~tly in their posttest at all levels of objectives.


Table 5.55

Consolidated Results of Summan, of ANCOVA of the Pretest and Posttest Scores

in the Achievement in Matheinatics (Objective-wise) of Academicallv

Advantaqed Students and Academicalb Disadvantaqed Students in the

Exwrimental Grow (CAM).

Source of Variation df Sx.y S y . x MSy.x SI3y.x Fy.x

Knowledge Among Means I 510.91 673.95 673.95 . -. '99.16*** 1.84 Within 1

-. . -- - - - 265 -.- - ~

Groups

Comprehension Among Means 1 68.3.50 925.63 925.63

Within 2.64 132.78***

Groups 265 12:<.78 1847.41 6.97

Application Among Means I 7.5'93 121.33 121.33

Within 1.76 39.09***

Groups 265 53 96 822.53 3.10

Analysis Among Means 1 61 25 511.65 511.65

Within 2.09 117.68***

Groups 265 4.('3 1152.13 4.35

From Table F for df = 11 265 the values of F are 3.883 at 0.05 level

6.7448 at 0.01 level and at 0.001 level 11.1566. The calculated values of F

show that the Fy.x are significant at all levels. This shows that the adjusted

posttest scores in the two groups differ significantly in knowledge,

comprehension, application, and anidysis.

Analvsis of Data and RauNs

Table 5.56

Data and Results of the Test of Siqnificance of the Difference between Adiusted

Means for Posttest Scores in Achirzvement in Mathematics (Obiective-wise) of

Academicah Advantased Studelts and of Academicah Didvantased

Students in the b r i r n e n t a l (CAM1 Grou~.

Section Group N MK MY My.x Shy , t

AA- Knowledge CAM 145 8:74 23.21 23.27

0.23 15.34*** AD- CAM

123 6.52 19.75 19.69

Application AA- 145 4.40 16.29 16.28 CAM

0.22 6.06*** AD- CAM

123 4.?3 14.93 14.93

Analysis AA- CAM

145 5 . 3 17.17 17.17 0.26 10.59***

AD- CAM 123 5.(15 14.37 14.38

- '** p < 0.001

From table of t-ratio, t ,,, is 3.3289, t ,,, is 2.595 t ,,, is 1.969 for df =

265. The difference in means of the adjusted posttest scores were subjected to

test of significance .The obtained values oft are significant at 0.001 level.

This indicates that both the groups differ significantly. The adjusted

posttest means of the advantaged Group are comparatively higher than that of

the disadvantaged group in all levels. This shows that the academically

advantaged students in the experirrlental group scored higher than that of the

academically diiad~ntaged students in the experimental group at 0.001 level in

the four given objectives in the cognitive domain.

S1 Objectives Category Sourceof df SSx SSy SSxy SSy.x h4Sy.x SDy.x Fy.x Level off No Vuiation Significance 1 Total ADCAM m

AA-CAM 1 1583.18 9878.24 3954.62 6664.65 6664.65 4.02 411.46 R0.01

within Orouos

265 3226.45 4292.51 -23.09 4292.34 16.19

2 Knowledge & AA-CAM 1 325.25 802.56 510.91 673.95 673.95

within 1.84 199.16 P<0.001 . P onr -7 Lb5 1IYj . i i %C.ii -V=.LU o~".~, 2.29, Groups 3 Compre- ADCAM

AA-CAM 1 336.20 1389.96 683.5 925.63 925.63 hension 2.64 132.78 P<o.OOl

within Meals 265 1037.81 1863.39 128.78 1847.41 6.97

4 Application AD-CAM m AA-CAM Means I 0.522 122.35 7.99 121.33 121.33

1.76 39.09 P<0.001

265 900.16 825.75 53.96 822.51 Groups 3.10

5 Analysis AD-€AM Awong AA-CAM Mesas 1 7.27 516.03 61.25 511.65 511.64

W i n 2.09 117.68 P<0.001

Groups 265 959.84 1152.15 4.03 1152.13 4.35

Table 5.58 The Consolidated Results of Test of Siqnificance for Adiusted Means of Posttest Scores in Mathematics of Academically Advantaqed Students and Academically Disadvantaqed Students in the berimental Group - Total & Objective-wise

Objectives Categon. Group N Mx MY My.x SE, . t Level of No significance 1 Total AD CAM 123 21.39 70.15 70.15

AA CAM 145 26 28 82.33 82.34 0.5 1 23.93 P-cO.001

2 Knowledge AD CAM 123 6.52 39.75 19.69

A A CAM 145 8.74 23.21 23.27 6.23; i5.34 F.:u.uui

3 Comprchcnsion AD CAM 123 5.50 21.11 21.25

A A CAM 145 7.76 25.66 25.52 0.334 12.769 P<0.001

4 Application AD CAM 123 4.33 14.93 14.97

A A CAM 145 4.40 16.29 16.29 0.223 6.059 P<0.001

Analysis AD CAM 123 5 05 14.37 14.38 5

AA CAM 145 5.38 17.17 17.17 0.264 10.558 P<O.OOI


5.13.Cognitiue Abflfty: Cornparison of the Efictiueness of

Concept Attainment Model 04 Instruction on Cognitive Ability to

Academically Advantaged Students and Academically r

Msadvantaged Students.

In the experimental (CAbI) group 145 students were identified as

academically advantaged and 123 students were identified as academically

disadvantaged. The scores obtaiiczd by them in the cognitive ability test were

consolidated and analyzed statisticilly using the technique ANCOVA.

Before proceeding to the te:jt ANCOVA, ANOVA was done. The results of

the test ANOVA are given in Table 5.59

Table 5.59

Summaty of Analvsis of Variance of the Pretest and Posttest Scores in Coqnitive

s Ability Test of Academicallw Advantased Students and Academically

Disadvantaqed Students in the Experimental (CAM) Grou~ .

Source of df SSx S!$y MSx Fx FY Variation

-- - MSY

Among Means 1 1051.68 1126.39 1051.68 1126.39

233.13 69.03***

Within 266 1199.98 4340.43 4.511 16.32 Grouos

As per the results in Table 5.59, Fx is 233.13 and Fy is 69.03. From the

Table F, the values of F after in1:erpolation for df = li 266 are 3.8824, 6.7446

and 11.156 at 0.05, 0.01, 0.001 levels respectively. Hence it is clear that Fx is

7 significant at all levels (Fx = 233.13; p < 0.001) and Fy is also significant at all


levels (Fy = 69.03; p <0.001). This implies that the groups were different in

their pretest abilities and also in their posttest scores.

a The total sum of squares, adjusted mean square variance for posttest

scores and F ratio, were calculated They are presented in Table 5.60 along with

the results of analysis of covariance

Table 5.60

Summarv of Analvsis of Covariance of the Pretest Scores and Posttest Scores in

Coqnitive Ability Test of Academi*aUv Advantased Students and Academicallv

Diadvantased Students in the k~erirnental (CAM) Group.

Source of df SXY Sy.x MSy.x SDy.x Fy.x Variation

Among Means 1 1088.39 177.38 177.38

3.92 11.54*** Within Groups 265 566.79 4072.71 15.37

-- *** p < 0.001

From the Table F, for df = 11 265, the interpolated values of F at 0.05

level is 3.884, at 0.01 level is 6.745 and at 0.001 level is 11.1567. Here Fy.x

value is 11.54. Hence it is seen thet Fy.x is significant at all levels. This significant

ratio for the adjusted posttest scclres shows that the final mean scores of two

categories of students in the experimental group differ significantly after they

were adjusted for the differences irl their pretest means.

The significance of difference between the adjusted posttest means of the

z groups is tested by t test.

Analysis of Dma and Results

Table 5.61

The Data and Results of the Test of Sicmificance of Difference between the

Adjusted Means for Posttest Scores in Coqnitive Abilitv Test of Academicallv

A d v a n a d Students and Academically Didvantased Students in the

Ex~erimentai (CAM) Group. -

Group N Mx MY My .x S~I,.~ t

AA-CAM 145 13.12 19.87 19.95 0.497 4.53***

AD-CAM 123 9.16 15.75 15.88

k** p<0.001

From table of t-ratio, the mlues at 0.05 level is 1.969, at 0.01 level is

2.595 and at 0.001 level is 3.3289 lor df = 265. The results of the test contained

in Table 5.61 show that the difference is significant at aU levels. Hence it can be

concluded that the two groups diifer significantly in their posttest scores. This

implies that the performance of aczdemically advantaged students are in a better

position when compared to that c'f academically disadvantaged students when

both the groups were taught using Concept Attainment Model of instruction.

5.1 4. Comparison of Progress Made by the Groups.

The progress made by academically disadvantaged students and

academically advantaged studen* in their achievement in Mathematics and in

cognitive abilii is found out in order to establish the effectiveness of Concept

Attainment Model of instruction.

Analysis of Dota and Results

5.14.1. Comparison of Progress Made by Academically Disaduantaged

Students with tkat by Academically Adoamtoged Students in Thdr

Achievement in Mathematics.

The analysis of posttest scores indicate that both academically

advantaged students and academically disadvantaged students performed well in

the achievement test,though the mean scores adjusted for the pretest scores for

the first group is slightly higher than that of second group. It can be well

established if the progress made by Imth the groups is compared. The data and

the progress made by the academically advantaged group and academically

disadvantaged group taught under Concept Attainment Model of instruction and

Conventional Teaching Method is presented in Table 5.62

Table 5.62

Data and Proqress Made bv AcademicaUv Advantaqed and Academically

Didvantaqed Students in their Achievement in Mathematics Tauqht under

Conce~t Attainment Model and Conventional Teachins Method.

My.x(Posttest) Method

Academically Advantaged Academically Disadvantaged

CAM 82.32 70.18

CTM 70.118 42.34

Progress 11.tH 27.84

The results presented in Table 5.62 indicate that the academically

disadvantaged students had shown very good progress in their achievement in

Mathematics in comparison with academically advanthged students. This is 7

clearly shown in fig 5.6.

.. - _ . . - F

. . . , 'LA-

' (: I


5.14.2 Comparison of Progress Made by Academically Disadvantaged

Students with that by AcademioalEy Adoanhged Students in Cognitive

Ability.

A look at the posttest scores indicates that performance of both

academically advantaged students and academically disadvantaged students is

good in the cognitive ability test, though the mean scores adjusted for the pretest

scores for the first group is slightly higher than that of second group. If a

comparison is made on the progress gained by both the groups, this will be more

apparent. The data and the progress in cognitive ability made by the

academically advantaged group ar,d academically disadvantaged group taught

under Concept Attainment Model of instruction and Conventional Teaching

Method is presented in Table 5.63.

Table 5.63

Data and Prowess in Cmitive At- Made by Academicalh, Advanbaed and

Academicah Disadvantaqed Studsnis Tau& under Concept Attainment Model

and Conventional Teachma Method. ---

My.x(Posttest) Method - --

Academically Advantaged Academically Disadvantaged ---

CAM 19.95 15.872

CTM 13.459 11.296

Progress 3.491 4.576 --

The contents of Table 5.63 reveals that the progress in cognitive ability

made by the academically disadvantaged students is slightly greater in

comparison with that of academical'y advantaged students (vide Fig 5.7.).

-. Comparison of pmgness in sognitive ab'dity made by aedemid l j advantaged and academically disadvantaged students in the experimental and control .OU]


5.15. Influence of Sodo-economic Status and Intelligence on

Achievement in Mathemat:ics and Cognithe AMHty of

Academically Disadvantaged !Students.

Basically the school will have three types of students: students who can

learn on their own, students who need some help in learning, and students who

need a lot of help in learning. An effective teacher through his teaching strategy

should inculcate leaming in all the three types of students.

According to Kosc (1981) the factors like intelligence, cognitive ability,

learning and teaching strategies &:. influence students' thinking and also their

skills in mathematics. Intelligent thinking is dependent on their prior leaming.

Studies reportedly show that performance on intelligence tests is correlated with

school achievement (Neisser et.aI 1996, Perkins, 1995; Gardner and Hatch,

1990;Sattler, 1988; Brody, 1985). Shah and Kishan (1982) found that academic

achievement of students is positively correlated with intelligence. It can be

maintained that the intelledual atlilities of students appear to have a positive

association with their scholastic achievement

Socio-economic status is itnother important factor that affects school

achievement and has an influenu* on the academic disadvantage. Researchers

have noted that there is a close relationship between social class and school

achievement (Mansnerus, 1992;Slc:eter and Grant, 1991).

The classroom is the logiczil place to begin the process of reducing some

of the achievement differences that have been noted between lower SES and

Analysis of Daka andResults

upper SES students. An effective teacher should seek opportunities for getting

lower SES students to talk about their experiences. This is important for

encouraging learners to construct a ?d express understandings and meanings of

their own in a form that is most comfortable to them.

One of the main objective!, of the present study is to find out the

effectiveness of Concept Attainmerit Model of instruction on achievement in

mathematics of academically disadtmantaged students. It is very clear that if we

can prove the test scores of studctnts in mathematics achievement test and

cognitive ability test are independent of the factors like intelligence and socio-

economic status when a particular teaching strategy is used, then it can be

concluded that the teaching strategy s of good quality.

5.15.1. Socia-economic Status:, Achievement in Mathematics and

Cognitive Ability of the Academically Disadvantaged Students.

A popular socio-economic st2tus scale (revised) was administered to the

sample under study. Among the 50El students (total sample) 113 students from

experimental group (CAM) and 126 students from control group (CTM) were

identified as academically disadvantaged. The mean and standard deviation of

the socio-economic status scores of the academically disadvantaged students

(249 nos.) in the study were found out. The M+ 1/20 and M- 1/2a were

calculated. Students who scored below M- 112o were included in the low socio-

economic status group. Students who scored between M+ l/2oand M- 1/2a

were termed as average socio-econornic status group and students having score


above M+ 1/20 is termed as high socio-economic status group. Thus the

academically disadvantaged stude 7ts in the experimental group (CAM) were

categorized into high, average, lctw socio-economic status groups and their

corresponding achievement test scores and cognitive ability test scores were

grouped

5.1 5.1 . l . Sodo-economic Status and Achieuement in Mathematics of

the Academically Disadvantaged Students.

The post-test scores in ac7iewment in mathematics of academically

disadvantaged students included in the three SES groups in the experimental

group were adjusted to the difference in their pretest scores. The adjusted

posttest means in achievement in mathematics of the groups were in the

following Table 5.64.

Table 5.64

Number, Adjusted Posttest Mean, and Posttest Mean of the three SES Groups --

S1.No Group N MY M Y . ~

1 High SES 39 70 46 70 54

2 Average SES 3 7 69 84 69 79

3 Low SES 47 70 15 70 11

A perusal of the Table 5.64 makes it clear that the three groups have a

remarkable performance. The significance of the difference of adjusted posttest

means of the groups is found by czlculating the t-ratio. The data and results are

given in the Table 5.65.

.4nalysis of Data and Results

Table 5.65

Combination of Groups, Standard firor. and t Values

S1.No. Combination df t of Groups

1 1&2 LI 1.03 0.718 7"

From Tabk D, the values of .: for df = 73 is 1.9928 at 0.05 level, 2.645 at

0.01 level, 3.4293 at 0.001 level; for df = 83 is 1.9891 at 0.05 level, 2.6362 at

0.01 level, 3.4118 at 0.001 level; fcr df = 81is is 1.9897 at 0.05 level, 2.6374 at

0.01 level, 3.4146 at 0.001. A per~sal of the Table 5.65 makes it clear that the

three groups do not differ significantly in their adjusted posttest means. It is

surprising to find that socio-econornic status has least influence on achievement

of students when Concept attainment model is used

5.15.1.2. Sodo-economic Status and CognMue Ability of the

Academically Disadvantaged Students.

The post-test scores in cognitive ability of academically disadvantaged

students included in the three SES groups in the experimental goup were

adjusted to the difference in their .~e t e s t scores. The adjusted posttest means in

cognitive ability of the groups were in the following Table 5.66

Analysis of Dda and Results

Table 5.66

Number. Posttest Mean and Adiustetl Posttest Mean of CMitive Ability Scores

of the Three SES Grouvs

SI.No. Group No MY My.x ~-

1 High SES 39 14.28 14.36

2 Average SES 37 16.03 16.08

3 Low SES 47 16.74 16.61

The adjusted posttest means of the groups and the significance of their

difference were found. The data and results were given in the Table 5.67

Table 5.67

Combination of Groups, Standard Error, and t Values

SI.No. Combination d f SED t of Groups

From Table D, the values oft For df = 73 is 1.9928 at 0.05 level, 2.645 at

0.01 level, 3.4293 at 0.001 level; fo~. df = 83 is 1.981 at 0.05 Level, 2.6362 at


0.01 level, 3.4146 at 0.001 level It is apparent that Groups 1&2 differ

significantly at 0.05 level and Groups 3&1 differ significantly at 0.01 level. The

results of the t test shows that there IS a significant difference between the High

.4nalysis of Data and Results

SES Group and the other two Groups in their adjusted post test scores in the

cognitive ability test.

5.1 5.2. Intelligence, Achievement in Mathematics and Cognitfue

Ability of the Acodemidy Disatiuantaged Students.

A standardized Non-Verbal Group Test of Intelligence (Raven's

Progressive Matrices Sets A, B, C, D ilnd E) was also administered to the sample.

The mean and standard deviation of the intelligence test scores of the

academically disadvantaged studenis in the study (249 Nos.) were found out.

Then M + ?h u and M - 'h u of the 249 students were also calculated. Students

who scored below M - ?h u were treated as ' Low Intelligence Group'. Those

who scored between M - % u and M+%u were categorized as 'Average

Intelligence Group' and those who got scores above M + % u were considered

as 'High Intelligence Group'. The i5cademically disadvantaged students in the

experimental group (CAM) were cateprized into 'high intelligence group',

'average intelligence group' and 'lo~v intelligence group' and their corresponding

achievement test scores and cognitive ability test scores were found

5.15.2.1. Intelligence und Aichfevement in Mathematics of the

Acadernicaliy Disadmmtaged Students.

The post-test scores in achievement in mathematics of the academically

disadvantaged students included in the three intelligence groups in the

experimental group were adjusted to the difference in their pretest scores. The

adjusted posttest means in achievement in mathematics of the three groups are

presented in the following Table 5.68

Analysis of Dutu and Results

Table 5.68

Number, Adiusted Posttest Mean, a ~ d Posttest Mean of the Three Intelliwnce

Groups.

SI. No. Group No MY My.x

1 High Intelligence

2 Average Intelligence 45 70.82 70.73

3 Low Intelligence 30 68.47 68.53

The adjusted posttest means in achievement in mathematics of the three

groups and the significance of their difference was found. The data and results

were given in the Table 5.69.

Table 5.69

Combination of Groups, Standard Error, and t Values.

SI.No. Combination df SED t of Groups

-- 1 I@ 90 0.91 -0.137

From Table D, the values of t for df = 90 is 1.987 at 0.05 level, 2.632 at



0.01 level, 3.4255 at 0.001 level. It i:; apparent that Group 3 differs significantly

at 0.05 level from Groups 2&1

Analysis of Dato and Results

5.15.2.2. Intelligence and Cognitive Ability of the Academically

Disdmmtoged Students.

The post-test scores in cqpitive ability were adjusted and the adjusted

C posttest means of the three inteuig~nce groups are presented in Table 5.70.

Table 5.70

Number, Posttest Mean. and Adiusted Posttest Mean in Gxmitive Abilitv of the

Three Intelliaence Groups.

S1.No. Group No MY My.x

1 High ~ntelli~ence-

2 Average Inteui~nce 45 16.36 16.15

3 Low Intelligence 30 14.73 15.10

The adjusted posttest means in cognitive ability of the three groups and

1; the significance of their difference is found. The data and results are given in the

Table 5.71

Table 5.77

Combination of Gmutx. Standard Error, and t Values

SI.No. Combination of d f SED t Groups

1 1& 2 90 0.779 -0.64

-- - From Table D, the values o f t for df = 90 is 1.987 at 0.05 level, 2.632 at

Irr 0.01 level, 3.402 at 0.001 level; for df = 72 is 1.9932 at 0.05 level, 2.646 at

Analysis of Dafo and Results

0.01 level 3.4312 at 0.001 level; for df = 75 is 1.992 at 0.05 level, 2.643 at

0.01 level, 3.4255 at 0.001 level. It is evident from the table that the three

groups do not differ significantly in their posttest.

Since the test scores of academically disadvantaged students in

Mathematics achievement test and Cognitive ability test are independent of the

factors like intelligence and socio-economic status when Concept Attainment

Model of instruction is used, then it can be judged that Concept Attainment

Model of instruction is of good quality with regard to teaching of academically

disadvantaged students.

5.15.3. Relationship of Sodo-economic Status and Intelligence on

Achieuement in Matftematics of Academically Disadvantaged Students.

To find out the relationship of socio-economic status and intelligence on

gain scores of achievement in mathematics, the Pearson coefficient of correlation

was calculated. The variable socio-economic status and intelligence were

categorised into High, Average and Low groups. The Pearson r corresponding

and its significance is presented in the Table 5.72

Analysis of Daka and Resulfs

Table 5.72

The Pearson r of Socioeconomic status and Intelliqence on Gain Scores in

Achievement in Mathematics of Aca,iemicalk Disadvantawd Students. pp

Number Variabks F'earson r d f Significance

1 High SES -3.025 37 0.394

2 Average SES -0.006

3 Low SES 11.029 45 0.375

4 High IQ -0.219 46 0.008

5 Average IQ 0.176 43 0.026

6 Low IQ 0.015 28 0.437

The tabk reveals that the %:orrelation coefficients except for High IQ and

Average IQ are not significant. We can infer that there is only a very low

correlation between gain in achievement in mathematics with socio-economic

status and intelligence. This may be the effect of the teaching strategy, namely

Concept Attainment Model of Instruction. Thus it can be concluded that the

Concept Attainment Model of Instruction reduces the effect of extraneous

variables like socio-economic sta..us and intelligence.

5.15.4. ReIatiomhip of Soc3o-economic Status and IntellEQence on

Cognitlue AMItty of Acodedcoliy Disaduentoged Students.

Pearson coefficient of omelation r between gains scores in cognitive

ability and the variables Like socio-economic status and intelligence were

calculated and tested for significance. The variable socio-economic status and

Analpis of Data and Results

intelligence were categorised into kigh, Average and Low groups. The Pearson r

corresponding and its significance is presented in the Table 5.73.

Table 5.73

The Pearson r of S&ioeconomi(: status and Intelliqence on Gain Scores in

Coqnitive Abilitv of Academically tjisadvanta~d Students.

Number Variables Pearson r d f Significance --

1 High SES -0.237 37 0.004

2 Average SES 0.067 35 0.232

3 Low SES 0.164 45 0.035

4 High IQ -0.047 46 0.301

5 Average IQ 0.069 43 0.223

6 Low IQ -0.031 28 0.366

The Table 5.73 reveals thal the correlation coefficients are significant only

for High SES and Low SES grou.3~. We can conclude that there is only a very

low correlation between gain in cognitive ability scores and the variables like

SES and Intelligence. This is the effect of the teaching strategy used. Hence we

can conclude that we can reduce the effect of SES and IQ on cognitive ability by

using Concept attainment Model c ~ f Instruction


5.15.5. Multiple Regression Anczlysis for the Relationship of SES and

IQ with Gain Scores in Achiewment in Mathematics of Academically

Disadvantaged Students in the thperimental Group.

To measure the strength of tile relationship between the variables (SES,

IQ, Cognitive abiltty and Achievenent in Mathematics) further, Regression

Analysis was done. Multiple Regress~on Analysis for the relationship of SES and

IQ with gain scores in achievement test scores is presented in the Table 5.74

Table 5.74

Results of Multi~k Recression Ar~alvsis for the Relatiinship of SES and

lntellictence on Gain Scores in Achievement in Mathematics --

Variables Parameter Standard Error t significance Estimates

Constant 50.684 1.137 44.577 0

High SES -1.153 1.326 0.089 0.386

Average SES -0.197 1.323 -0.015 0.882

Low SES Excluded

High IQ -4.016 1.443 -2.783 0.006

Average IQ Excluded

Low IQ -1.331 1.245 -1.069 0.287 - -. -- --

R square =0.063 Adjusted R square =0.031

R square is 0.063 and adjusted R square is 0.031 respectively. It indicates

that only 3.1% of variation in the ciain scores is explained by these variables.

Therefore it could be inferred that there is no significant relationship among SES,

Analysis of Duta andResults

Intelligence and gain scores in Acnievement in Mathematics of academically

disadvantaged students in the experimental group.

5.15.6. Mumpie Regression An~alysis for the Relationship of SES and

IQ with Gain Scores in Cognitive Ability of Academically


To measure the strength of h e relationship between the variables SES, IQ

and Cognitive ability further, Regression Analysis was done. Multiple Regression

Analysis for the relationship of SE; and IQ with gain scores in cognitive ability

test scores is presented in the Table 5.75

Table 5.75

Results of Multiple Remession Analysis for the Relationship of SES, Intelliaence

and Gain Scores in Coqnitive Abiliy

Variables Parameter Standard t significance Estimates Error

Constant 7.97 11.142 0 0.732

High SES -2.33 -2.793 0.006

Average SES -0.364

Low SES

High IQ

Excluded

Average IQ Excluded

Low IQ -0.585 0.801 -0.746 0.457

~~-p

R square=0.074 Adjusted R square=0.042

R square and adjusted R square are 0.074 and 0.042 respectively. This

indicates that only 4.2% of the change of gain scores in cognitive ability is

Analysis of Dala and Results

explained by the variables listed in the table. The table also reveals that there is

no significant relationship between the variables and the gain scores in cognitive

ability.

5.1 6. Tenab?iity of Hypotheses.

The main objedive of the study was to find out the effectiveness of

Concept Attainment Model of in:jtruction on achievement in mathematics of

academically disadvantaged students.

The hypotheses given in Chapter I are converted into null hypotheses for

the purpose of statistical calculations.

Maior Hurwthesis.

The achievement in Mathematics and the cognitive ability of the

& d e m i d y disadvantaged students taught in Concept Attainment

Mo&l of instruction is wigniJicantly higher than that of the

academiwdly disadvantaged sf udents taught in Conuentiond Teaching

Method.

This hypothesis is converted into null hypothesis for the purpose of

stat ical calculations.

There is no sign@cant difference in the achievement in

mathematics and the cognitive ability of the academicaliy

disadvantcrged students when taught using Concept Attainment Model

of instructiolr and Conuentionol Teaching Method.


When the means of the gain scores of academically disadvantaged

students in the experimental (CAM) and control (CTM) groups were subjected to

test of significance of difference be t~een means, it was significant at 0.001 level

(mean for CAM =48.76, for CTM= 22.02, CR = 36.75; p< 0.001).

When the pretest and posttest scores were subjected to ANCOVA, it was

found that the academically disadmntaged students in CAM scored significantly

higher in mathematics than the academically disadvantaged students in CTM

(adjusted posttest mean for CAM= 70.18, for CTM=: 42.34, t= 42.97 for df =

246; p< 0.001).

The objectiw wise analysis by ANCOVA showed that CAM is significantly

effective than CTM.

i. Knowledge : Adjusted posttest means for CAM =19.74, for

CThl = 12.83, t=26.89 for df = 246; p <

o.OC1. .

ii. Comprehension : Adj~~sted posttest means for CAM = 21.19, for

CThI = 13.16, t=23.35 for df = 246; p <

0.001.

: Adj~sted posttest means for CAM = 14.94, for

CTM = 7.67, t=29.53 for df = 246; p < 0.001.

: Adjusted posttest means for CAM = 14.47, for

CTNI = 12.17, t=7.56 for df = 246; p < 0.001.

iii. Application

iv. Analysis.

Analysis of Dato and Resuhs

The academically disadvantaged students in the experimental group

(CAM) scored significantly higher .:ban those in the control group (CTM) in

achievement test in mathematics.

From the results obtained above, it is obvious that CAM is more effective

in teaching mathematics.

In the case of cognitive ability test scores, when the means of the gain

scores of academically disadvantaged students in the experimental (CAM) and

control (CTM) groups were subjected to test of significance of difference between

means, it was significant at 0.001 Lwei (for CAM =6.59, for CTM= 1.91, CR =

12.85; p< 0.001).

Resultsof the Covariance analysis of the pretest and posttest scores in

cognitive ability of the academically &sadvantaged students shows that the

Concept Athinment Model of teaching is more effective than Conventional

Teaching Method. (Adjusted posttest mean for CAM= 15.88, for CTM= 12.21,

t= 9.24 for df = 2%; p< 0.001).

Therefore the null Hypothesis is not accepted.

Hvtlothesls I.

There ?s no sign@umt Werence in the achfwement in

Mathematics and in the cognitiue ability of the academically

& A t a g e d and of the academically adwntclged students when they

are taught using Concept Atttlnment Model of instruction.

Analysis of Data and Resultr

The achievement test scores in mathematics of academically advantaged

students were significantly higher than that of academically disadvantaged

students when both of them learned in CAM. (Adjusted posttest mean for

academically advantaged students in CAM= 82.34, for academically

disadvantaged students in CAM = 73.14, t= 23.93 for df = 265; p<0.001).

The cognitive ability the aedemically advantaged students were better

than that of the academically disadvantaged students when both the groups

were taught in CAM. (Adjusted p~sttest mean for academically advantaged

students in CAM= 18.93, for acad~?mically disadvantaged students in CAM =

16.68, t= 4.53 for df = 265; p<0.0f)l).

Therefore the null hypothesis cannot be accepted.

Hvwthesis 11.

The relatiue progress in achievement in Mathematics and in the

cognitive aMHty when taugbt using Concept Attainment Model of

instruction and Conventional Teaching Method is higher for the

academically tiisadoantaged students than the academically

advantaged students.

This hypothesis is convertecl into null hypothesis for the purpose of

statistical calculation.

There is no stgnyicant tlifference in the relatiue p r o m in

achievernent in mathematics m.~d in cognitiue ability when Concept

Analysis of Dara andAesuhs

Attainment Model of instruction and Conventional Teaching Method

were used for teaching of academically disadutrntoged m d advantclged

students.

1 . Achisuement in Mahmafics

(a) Progress made by academim1Iy Cusadvantaged students.

Adjusted posttest mean of experimer~tal group (CAM) is 70.18.

Adjusted posttest mean of control grcup (CTM) is 42.34.

Progress made by academically disadvantaged students is 27.84.

(b) Progress made by academfcalfy advantaged students.

Adjusted posttest mean of experimental group (CAM) is 82.32.

Adjusted posttest mean of control group (CTM) is 70.48.

Progress made by academically advantaged students is 11.84

It is obvious that the progress in achievement in mathematics made by

academically disadvantaged students is unequivocally higher than that of

academically advantaged students

2. C o q n W AM&.

(a) Progress made by academically disadwntaged students.

Adjusted posttest mean of experimental group (CAM) is 15.872.

Adjusted posttest mean of control group (CTM) is 11.2%

Progress made by academically disadvar~taged students is 4.576.

(b) Progress made by academically trduantaged students.

Adjusted posttest mean of experimental goup (CAM) is 19 95.

Analysis of Data andResuhs

Adjusted posttest means in control group (CTM) 16.459.

Progress made by academically ad!mntaged students is 3.491.

It is clear that the progre:s in cognitive ability test scores made by

academically disadvantaged studer~is is slightly higher than that of academically

advantaged students.

Therefore the null hypothesis cannot be accepted.

Hwothesis 111.

The hrtelligence and sc~cio-economic status of academically

disadvantaged students who learned mathematics using Concept

Attainment Modal of instructioia hooe only minimal influence on their

achievement in mathematics ancf also on cognitive ability.

This hypothesis is converted into null hypothesis for the purpose of

statistical calculation.

The intelligence and smSo-economic status of academically

disadvantaged students who learned mathematics using Concept

Attainment Model of instruction have no infhrence on their

achievement in mathematics and also on cognitive obifity.

The adjusted posttest means in achievement in mathematics of the three

groups of academically disadvantaged students based on their intelligence level

(High, Average, and Low) have no diflerence between High and Average groups

but have significant difference when low intelligence group is compared with

other two groups. (My.x for high intelligence group is 70.61, My.x for average


intelligence group is 70.73, and My.x for low intelligence group is 68.53), t (for

high & average intelligence groups) is -0 137 for df = 90, p > 0.05, t (for low &

average intelligence groups) is -2.12 for df = 72; p < 0.05, t (for low & high

intelligence groups) is -2.03 for df = 75; p< 0.05).

The adjusted posttest mears in achievement in mathematics of the three

groups(High, Average, and Low) of academically disadvantaged students based

on their socio-economic status (SES) have no difference. (My.x for high SES

group is 70.54, My.x for average SES group is 69.79, and My.x for low SES

group is 70.11), t (for high & average SES groups) is 0.718 for df = 73; p >

0.05, t (for low &average SES grctups) is 0.321 for df = 81; p > 0.05, t (for low

& high SES groups) is -0.435 for df = 83, p> 0.05).

The adjusted posttest means in cognitive ability of the three groups (High,

Average, and Low) of academically disadvantaged students based on their

intelligence level have no difference. (My.x for high intelligence group is 15.65,

My.x for average intelligence group is 16.15, and My.x for low intelligence group

is 15.1). t (for high &average intelligence groups) is -0.64 for df = 90, p > 0.05,

t (for low & average intelligence gmups) is -1.18 for df = 72; p > 0.05, t (for low

& high intelligence groups) is -0.62 for df = 75; p> 0.05).

The adjusted posttest means in cognitive ability of the three groups (High,

Average, and Low) of academically disadvantaged students based on their socio-

economic status (SES) have sign ficant difference between Average and Low

groups but no difference in the other combinations. (My.x for high SES group is

Analysis of D m and Results

14.36, My.x for average SES group is 16.08, and My.x for low SES group is

16.61). t (for high &average SES groups) is -2.06 for df = 73; p c 0.05, t (for

low & average SES groups) is 0.66 for df = 81; p > 0.05, t (for low & high SES

groups) is 2.86 for df = 83; pi0.01).

Pearson r calculated for different levels of intelligence, different levels of

SES with gain in achievement test scores and cognitive ability test scores were

not significant. R square is 0.63. Adjusted R square is 0.031 for gain scores in

achievement in mathematics. R square is 0.074; Adjusted R square is 0.042 for

gain scores in cognitive ability test.

Thus the null hypothesis is proved to be true for SES and partially true for

intelligence with respect to achievement in mathematics, and the null hypothesis

is proved to be true for intelligence* and partially true for SES with respect to

cognitive ability.

The conclusions arrived at in this regard are presented in summary form

in Table 5.76

Table 5.76

Hv~otheses Formulated for the Studv and Their Tenabilitv

SI.No. Hypotheses formulated(as given in Chapter I) 7 Tenability Hypotheses o r ] I

1- I cognitive ability. 1

I

1.

2. 1

3.

4.

1 instruction have only minimal influence on their achievement in mathematics and also on

Major Hypothesis: - The achievement in mathematics and the cognitive ability of the academically disadvantaged students taught in Concept Attainment Model of instruction is significantly higher than that of the academically disadvantaged students taught in Conventional Teaching Method. Hypothesis I : - There is no significant difference in the achievement in mathematics and in the cognitive ability of the academically disadvantaged and of the academically advantaged students when they are taught using Concept Attainment Model of i . .*k*.rUrm ,,I* L.LaW.&"...

Hypothesis 11: - The relative progress in achievement in mathematics and in the cognitive ability when taught using Concept Attainment Model of instruction and Conventional Teaching Method is higher for the academically disadvantaged students than the academically advantaged students. Hypothesis 111: - The intelligence and socio-economic status of academically disadvantaged students who learned mathematics using concept attainment model of

Sustained

I

Not Sustained 4 I I i

Sustained 1

Sustained


5.1 7. Discussion ojResu1t.s.

Learning any subject or discipline of formal education primarily involves

the learning of concepts, which is undoubtedly basic to all scholastic

achievements. As concepts in each discipline are arranged in a hierarchy, the

acquisition of lower order concepts aids in acquiring higher order concepts.

Mathematics is the prime vc hicle for developing students' logical thinking

and higher order cognitive skills. It is one of the most important subjects in the

curriculum of all counkies. Still it is commonly seen as one of the most difficult

subjects. Several studies support this (Bynner and Steedman, 1995; Byner and

Parsons, 1997).

If learning to be meanin~lful, instruction should help the learner in

building a strong network of concepts to facilitate efficient acquisition and use of

information (Beddoe and Seepersad, 1976; Bernard, 1974). Sherris (1980) also

explained that meaningful learning involves linking of new ideas to existing

concepts and principles in a learner's knowledge structure.

Concept Attainment Model is a means of teaching concepts inductively,

that is, the learner begins with examples and develops the concepts. The model

is implemented by presenting pjitive and negative examples of the concept.

The students analyse hypothesis, ].ejecting those which have become inaccurate

in the light of the examples and forming additional hypotheses based on new

information. The cycle of data-iinalysis, hypothesis-examination, hypothesis-

generation continues until the con'zpt is attained and the teacher brings closer to


the lesson by having the students identified the concept's characteristics and

stating a definition.

In this study, the Concept Attainment Model of Instruction has been

found to beneficial to the learners .n raising their achievement in mathematics

and cognitive ability. This finding i:j supported by the results of earlier studies

(Byers, 1x1; Gagne &Brown, I%:[; Lemke, 1%5; Cook, 1981; Pandey, 1981;

Chitrive, 1983; Antimadas, 1986; Bihari, 1986, Sharma, 1986; Gangrade, 1987;

Sushama & Singh, 1987; Siddiqui, 1993; Anuradha & Anand, 1993; Pritchard,

1994; Nelson & Pan, 1995, Ayishabi, 1996; Prabhakaran & Rao, 1998;

Krishnakumari, 2002).

The results of the study prc've that the Concept Attainment Model of

Instruction is more effective when compared to Conventional Teaching Method

in teaching mathematics to academically disadvantaged students also. It has

been found (by Schub, 1x9; Herrkin, 1977; Rottavina, 1977; and Nuzum,

1983;) that the concept attainment 5trategies were also responsive to the needs

of exceptional children like learn in!^ disabled in problem solving and in the

attainment of several concepts in teaching-learning process.

The findings of the study clearly exhibit that the progress made by

academically disadvantaged students is far higher than by the academically

advantaged students both in mathematics achievement and in cognitive ability.

This is supported by the earlier studies (Paour et al., 1993; Haywood, 1995;

Tzuriel et al., 1999; Pena & Gillam, 2000; Tzuriel, 2001.).

Analysis of Dato and Results

The present study also revealed that the academically disadvantaged

students' intelligence and socio-economic status do not play any significant role

in the achievement in mathematics is well as in cognitive ability. A similar result

was found by Agarwal (2000). Sh,? found that students' sex, socio-economic

status and even intelligence had no influence in the learning speed of students in

concept learning through program instruction method. Since most students in

our school belong to low- or average- socio-economic status and intelligence

group, this result is ve y significant.

Scam (1981) indicated that many factors, in addition to IQ, will contribute

the learner's success: their motivat~on, support from parents, prior knowledge,

health, appropriate use of learning strategies, and quality of instruction. About

25% of school achievement only are attributed to Intelligence

Concept Attainment Model has tremendous promise and potential for

future as the schools of future will increasingly ask to prepare children to face

emergencies and uncertainties in the complex society of tomorrow. Concept

Attainment Model of Instruction i j a way of teaching the subject matter and

critical thinking skills in a reliable and effective way to engage in learning

simultaneously content and process. As students progress through the model,

they engage in a cycle of inductit,e and deductive thinking and strengthen the

particular khiiking skills, which comprise inductive and deductive reasoning.

Teachers and students will find great satisfaction in using concept attainment

model to affirm the intimate intern?lationship between knowing and thinking.


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Beddoe, I. & Seepersad, K. (1976). Concepts as organising centres for social studies content. Sociil Studies Edu(&, 8,36-41.

Bernard, L. (1974). Problems and practical solutions of social studies teaching in junior secondary schools. Social Studies Education, 2, 13-15.

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Chitrive, U.G, (1988). Ausubel Vs Bruner model for teachins mathematics. Bombay: Himalaya Publishing Ccmpany.

Cook, Willie Clance. (1981). The concept of negative and positive instances in 7 teaching mathematics concepts to fresh men at Florida University. Dissertation

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ANALYSIS OF DATA AND RESULTS. - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/6637/13/13_chapter 5.pdf · ANALYSIS OF DATA AND RESULTS. The present study was intended to test