CHAPTER – IV RESULTS AND DISCUSSIONshodhganga.inflibnet.ac.in/bitstream/10603/38474/9/chapter...

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CHAPTER – IV

RESULTS AND DISCUSSION

4.1. Introduction

According to Ferguson, G.A. (1981), “the process of interpretation is

essentially one of the statings what the results show, what do they mean,

what is their significance, what is the answer to the original problem”.

This chapter presents the analysis of the data (done through SPSS software).

The data were tabulated in descriptive tables prior to the statistical analysis

and presented in this chapter. Each research question is presented within the

statistical findings section. Each hypothesis was tested and verified through

statistical analysis. The results obtained through are discussed here

hypothesis-wise.

4.2. Hypotheses

1. There is no significant difference in the competency levels of the students

studying in different blocks (taluks).

2. Students studying in urban and rural areas do not differ significantly in

their competency scores.

3. Male and female students do not differ significantly in their competency

levels.

4. There is no significant difference between male and female students in

MLL attainment scores in Mathematics of schools of Shimoga District.

5. There is no significant difference between rural and urban students in MLL

attainment levels in Mathematics of schools of Shimoga District.

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6. There is no significant difference between control and experimental group

in the effect of diagnosis-based remediation programme in improving the

proportionate of students mastering each competency (percentage of

competency mastered) by the group of V standard students in the selected

(experimental) schools of Shimoga District.

4.3. Hypothesis 1: There is no significant difference in the competency

scores of the students studying in different blocks.

The investigator identified masters and non-masters based on pre-test and

the number of masters and non-masters found from each block are given in

table 4.3

Table 4.3 (a): Distribution of the sample by mastery and Blocks (taluks)

Students Blocks Non

masters Masters Total

Frequency 123 17 140 Soraba % 11.2% 4.7% 9.6% Frequency 147 15 162 Thirthahalli % 13.4% 4.2% 11.1% Frequency 78 78 156 Hosanagara % 7.1% 21.7% 10.7% Frequency 200 57 257 Bhadravathi % 18.2% 15.9% 17.6% Frequency 197 64 261 Shimoga % 17.9% 17.8% 17.9% Frequency 180 53 233 Sagar % 16.4% 14.8% 16.0% Frequency 173 75 248 Shikaripura % 15.8% 20.9% 17.0% Frequency 1098 359 1457 Total % 100.0% 100.0% 100.0%

CC=0.244; P<.000 (HS)

From the table 4.3 (a) it can be seen that out of the total 1457 students

selected from seven blocks of Shimoga district, Karnataka state for this study,

1098 students did not attain mastery and 359 of them were found to be having

mastery. The number of availability of masters and non-masters also varied

from one block to other. As in Hosanagara block, there were equal number of

masters and non-masters, whereas in Bhadravathi and Shimoga the number

of non-masters was more than masters. In other blocks the number of non

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masters was more as compared to less number of non-masters in Soraba and

Thirthahalli. Further, contingency coefficient (CC) test revealed a significant

association between blocks and mastery, where CC value of 0.244 was found

to be significant at 0.000 level. Hence hypothesis 1 stated as “There is no

significant difference in the competency levels of the students studying in

different blocks (taluks)” is rejected as the test statistics showed significant

difference in the competency levels of students studying in different blocks

(Fig. 4.3).

Figure 4.3: Distribution of the sample by mastery and blocks

According to Second half yearly monitoring report of the Institute of Social and

Economical change on SSA for Karnataka (2007) revealed that Hosanagara

has got more number of habitations though geographically it is a very small

block compared to other blocks of Shimoga district. The basic reason is that in

Hosanagara, the population (the communities) is scattered all over the block

whereas the population in other blocks of Shimoga District is concentrated.

And also literacy rate as per census reports showed that Hosanagara had an

average of 71.3 % literacy (Male=81.5%, female=64.7%). As blockwise

habitations and school access ratio (2007) results, it confirmed that

Hosanagara had highest access rate (99.90 %) in primary education among

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the blocks of Shimoga district. It is quite evident that differences in

geographical reasons and heterogeneity of the population influence over the

attainment levels so this influence is seen in the case of Hosanagara taluk in

the present study. Some of the studies revealed the reasons of the non

attainment of competency levels in mathematics. Van de Walle (2005)

observed, “the very fact that many students in grades 4 and 5 have not

mastered addition and subtraction and students in the middle and upper

grades do not have good command of their multiplication facts suggest that

this method simply does not work well.” Studies by Brownell and Chazal

(1935) concluded that children develop a variety of different thought

processes for basic facts regardless of the amount of drill they undergo (Van

de Walle 2005). They also found that children create and hold on to

procedures that develop from their own conception of numbers and that drill

does not help students develop any new or more efficient strategies (Van de

Walle 2005). However, drill can be used once a student has acquired an

efficient strategy. Premature drill (using drill before a student develops their

own understanding of numbers) will certainly be ineffective, waste valuable

time, and for many students contribute to a strong dislike and a faulty view of

learning mathematics (Van de Walle 2005). Overall, Van de Walle (2005)

suggested that drill can provide four things: an increased facility with a

strategy but only with a strategy already learned; a focus on a singular

method and an exclusion of flexible alternatives; a false appearance of

understanding; a rule-oriented view of what mathematics is about. In

conclusion, drill can only help students get faster at what they already know.

We feel that manipulatives have a place in the classroom but that children

learn through reflective thought and not through the manipulation of objects

(Colgan, 2007). We agree with Jon Van de Walle’s statement that you

‘cannot judge the value of an activity by the presence or absence of a physical

model’ and we feel that some problems are best solved without the assistance

of a manipulative (Colgan, 2007). Proof is and has been for long a

problematic area in the teaching of mathematics at the school level. While

proof remains central to the discipline of mathematics (articles like Horgan,

1993, notwithstanding), its pedagogic role at the school level remains unclear.

On perusing through the questions asked in the Math Forum site

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(http://mathforum.org/) one sees the demoralizing nature of the difficulties felt

by students.

A major contributory factor to this problem is surely that we introduce proofs at

too late a stage. Moreover, it is done in too abrupt, too formal, and too stylized

a manner. This results in a feeling of alienation for the child, who finds proofs

unmotivated and unnatural. This feeling is added to if what is being proved

looks obvious. And a majority of the early results encountered in geometry do

indeed look .obvious (Recall some of the results we meet early in the study of

geometry; e.g., the bridge of asses theorem). Whatever be the cause, the

problem challenges us to respond with some effective pedagogy. The cost of

not doing so is considerable. A child reaching the senior grades without a

significant exposure to the culture of proof has lost a valuable opportunity to

experience a central component of the discipline of mathematics.

Learning achievement surveys undertaken by National Council of Education

Research and Training (NCERT) and other agencies show that mathematics

pedagogy calls for more attention to help children acquire the basic skills in

mathematics. At present the attempt is to strengthen the early reading and

mathematics skill development programmes at the Primary level and

Mathematics teaching at Upper Primary level to prepare the students in a

better manner.

National Knowledge Commission (2008) on attracting students to maths and

science revealed that curriculum reform remains an important issue in almost

all schools. School education must be made more relevant to the lives of

children. There is need to move away from rote-learning to understanding

concepts, good comprehension and communication skills and learning how to

access knowledge independently.

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4.4. Hypothesis 2: Students studying in urban and rural areas do not differ

significantly in their competency scores.

Table 4.4 (a): Distribution of non-masters and masters selected from urban and rural areas for this study

Sectors

Non masters Masters Total

Frequency 208 51 259 Urban

% 80.3% 19.7% 100.0%

Frequency 890 308 1198 Rural

% 74.3% 25.7% 100.0%

Frequency 1098 359 1457 Total

% 75.4% 24.6% 100.0%

CC=0.053; P<.042 (S)

Area-wise comparison revealed a significant association between area and

mastery levels of the students where contingency coefficient of 0.053 was

found to be significant at 0.003 level. From the table it can be seen that more

students who found to be attaining mastery in MLL competencies assessed

through pretest were from rural area in comparison to urban area as 19.7%

of masters were from urban area whereas 25.7% masters were found from

rural area (Table 4.4 for more details). Hence, hypothesis 2 stated as

“Students studying in urban and rural areas do not differ significantly in their

competency scores “ is rejected, since the present study reveals that students

from rural area were found to be better than urban area students in the

mastery of competencies (Fig. 4.4 (i)).

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Figure 4.4 (i): The graph given shows the distribution of the sample by mastery and area

In this study sample included only government primary schools of Shimoga

district. The students in the rural sample were selected from government

schools. Usually students of all levels of mathematical ability have no option,

but to enroll themselves in government schools. Thus, the students from rural

areas present a more heterogeneous nature in mathematical ability than

urban students. Usually in urban areas, children of well to do families are

enrolled in private schools, which are perceived to be, and to an extent in

actual sense qualitatively better than government schools. Naturally in urban

areas, majority of students belongs to the higher ability group. In addition, in

urban areas many of the children studying in private institutions opt for

additional tuition classes than rural students. It is quite surprising that rural

students outshined urban students and hence shown better performance in

mathematics compare to rural students. In urban government schools almost

all students enrolled come from lower economic levels and impoverished

environment. Hence it is likely that they tend to be lower in their performance

in mathematics competencies. Many studies quoted above reported lower

mathematics achievement by urban students from government schools. In the

present study the sample from urban and rural area was drawn only from

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government schools. As a result the rural sample becomes more

heterogeneous having many higher ability students as well as lower ability

students for the reason mentioned above. But the urban sample becomes

more homogeneous which consisting students from first generation learners

and poor family support. This difference between rural and urban students is

due to these reasons.

4.5 Hypothesis 3: Male and female students do not differ significantly in their

competency scores

For verifying this hypothesis, the investigator calculated contingency

coefficient test according to this the number of male and female masters were

found is given

Table 4.5 (a): Distribution of Sample by Mastery and gender

Mastery Gender Non masters Masters Total

Frequency 549 155 704 Male % 78.0% 22.0% 100.0% Frequency 549 204 753 Female % 72.9% 27.1% 100.0% Frequency 1098 359 1457 Total % 75.4% 24.6% 100.0%

CC=0.059; P<.025 (S)

A significant association was observed between gender and level of mastery.

Contingency coefficient of .059 was found to be significant at 0.025 level.

From the table it can be seen that the number of female students attaining

mastery more than male students (27.1% vs 22.0%). Hence hypothesis 3

stated as “Male and female students do not differ significantly in their

competency levels” is rejected as we find that female students excelled male

students in their competency level (Fig. 4.5 (i)).

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Figure 4.5 (i): Distribution of number of male and female students showing mastery level

Research evidence has consistently shown that female students in Hawai‘i

outperform males in mathematics. Brandon, Newton, and Hammond (1987),

who examined data from the 1982 and 1983 mathematics Stanford

Achievement Test (SAT) administered to Hawai‘i public school students in

grades four, six, eight, and ten, found that overall, females consistently

outperformed males across these grade levels. Brandon and Jordan (1994)

examined the 1991 SAT mathematics results for tenth graders in Hawai‘i and

confirmed that girls performed better than boys. A majority of studies found

that females perform better than males (DeMars 1998, 2000, Garner &

Engelhard, 1999; Myerberg, 1996; Zhang & Manon, 2000). Rastogi, S (1983)

attempted a study on diagnosis of weaknesses in arithmetic as related to the

basic arithmetic skills and their remedial measures and he revealed that one

of the important causes of backwardness in mathematics was the poor

command over basic arithmetic skills. Sastri, S.M (1984)studied on delay of

feedback and retention in rational understanding in mathematics and he found

that the retentive capacity of the girls was more than that of the boys, in the

following order, namely, decimals, arithmetic, numerals and geometry. The

girls possessed better understanding factors than boys in long-term retention.

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In memory ability there was a small but consistent sex difference, the girls

being higher than the boys over the entire range in all the three standards.

Chitkara, M. (1985) studied on the effectiveness of different strategies of

teaching on achievement in mathematics and she found that girls of average

ability scored significantly higher in mathematics than boys of average ability.

Rumki Gupta (2000) studied gender disparity in madhyamik examination

result and he revealed that difference in overall achievements i.e., average

percentage of pass of boys and girls of West Bengal is small. Marginally

higher percentage of girls passed the Madhyamik Examination than the boys.

Basic literary skills (reading and writing) are pre-requisites to mathematics

achievement. For instructional and learning purposes, increasing students’

verbal scores might assist in increasing their performance on mathematics

assessments. This is especially important for boys, whose lower linguistic

skills negatively influence their mathematics assessment.

Because gender differences exist in early literacy skills, mathematics

educators may need to consider gender-appropriate pedagogical approaches

for boys and girls. To benefit males and females, the instruction for males and

females might need to be differentiated. As Gambell and Hunter (2000)

stated, "Males are in trouble in literacy!” (p. 712). And as a result, boys are in

trouble with mathematics as well. While mathematics performance of males

might be improved by focusing on linguistic skills, for females beneficial

outcomes might be obtained by focusing on mathematics. Boys might benefit

from additional guidance in reading comprehension and verbalization along

with quantitative reasoning, whereas for girls the benefit might accrue from

focused practice with mathematics-specific semiotics, e.g., symbols, formulas,

and algorithms.

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4.6. Hypothsis 4: There is no significant difference between male and female

students in MLL attainment levels in Mathematics from selected schools of

Shimoga District.

Table 4.6 (a): Comparison of means on various competencies between male and female students and results of Independent samples‘t’ test

Competencies Gender Mean S.D ‘t’ value P valueMale 3.87 1.13 C1-Number

Female 3.84 1.13 0.397 0.692

Male 1.80 0.45 C2-Different numerals Female 1.83 0.40 1.308 0.191

Male 1.89 1.04 C3-Fundamental

operations

Female 2.03 1.11

2.318 0.021

Male 2.57 1.15 C4-Fractions, decimals, and percentages Female 2.68 1.13 1.846 0.065

Male 1.84 0.99 C5-Decimal’s fundamental operations Female 1.91 0.98 1.290 0.197

Male 2.01 0.99 C6-Decimals addition and subtraction with mixed operations

Female 1.99 1.02

0.384 0.701

Male 2.15 0.96 C7-Angles Female 2.06 0.97 1.763 0.078

Male 16.12 4.16 TOTAL Female 16.35 4.47 0.991 0.322

Only in Fundamental operationscompetency, significant difference was

observed between male and female students as the obtained ‘t’ value of 2.318

was found to be significant at 0.021 level where female students had high

scores (means 2.03 and 1.89 respectively). In rest of the components as well

as in total mathematics scores ‘t’ value revealed non-significant differences

between male and female students on the whole hypothesis 4 is accepted

where in all the competencies except one competency and in total

mathematics scores, the performance of male and female students had

statistically equal scores (Fig. 4.6 (i)).

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Figure 4.6 (i): Mean scores of male and female students on MLL Competency-Fundamental operations

4.7. Hypothesis 5: There is no significant difference between rural and urban

students in MLL attainment levels in Mathematics of schools of Shimoga

District

Table 4.7.(a): Comparison of means on various competencies of students hailing from urban and rural areas and results of Independent samples ‘t’ test

Competencies Area Mean S.D ‘t’ value P valueUrban 3.66 1.22 C1-Number

Rural 3.90 1.10 3.084 0.002

Urban 1.85 0.40 C2-Different numerals Rural 1.81 0.43 1.183 0.237

Urban 1.86 1.13 C3-Fundamental operations Rural 1.98 1.06 1.610 0.108

Urban 2.54 1.19 C4-Fractions, decimals, and percentages Rural 2.65 1.13 1.384 0.166

Urban 1.89 1.02 C5-Decimal’s fundamental operations Rural 1.87 0.98 0.237 0.812

Urban 1.77 1.05 C6-Decimals addition and subtraction with mixed operations

Rural 2.04 0.99

4.013 0.000

Urban 2.03 1.01 C7-Angles Rural 2.12 0.96 1.227 0.220

Urban 15.63 4.48 TOTAL Rural 16.37 4.27 2.490 0.013

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Only in number competency, different numeral competency and total

competencies overall performance of students on all the competencies it was

that significance differences between rural and urban areas were observed,

where ‘t’ values of 3.084, 4.013 and 2.490 were found to be significant at

0.002,0.000 and 0.013 levels respectively, where rural students had high

scores (means=3.8981, 2.6442 and 16.3689 and 3.66, 1.77 and 15.3

respectively) than urban students. In rest of the competencies ‘t’ value

revealed non significant differences between rural and urban students on the

whole hypothesis 5 is accepted where in all the conpetencies, except

numbers competency, Decimals addition and subtraction with mixed

operations and overall scores of all the competencies of rural and urban

students was found to be statistically equal scores.figure4.7(i)

Figure 4.7 (i): Mean scores of urban and rural students in numbers competency, Decimals addition and subtraction with mixed operations and overall scores of all the competencies

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Table 4.7 (b): Comparison of means on various competencies of students studying in different taluks and results of One-way ANOVA for competencies numbers, Different numereals, Fundamental operations, Fractions, decimals and percentages.

Competencies Taluks Mean S.D F value P value Soraba 3.32 1.20 Thirthahalli 3.70 1.00 Hosanagara 4.05 1.04 Bhadravathi 3.79 1.00 Shimoga 4.14 1.12 Sagar 4.03 1.13 Shikaripura 3.74 1.22

C1-Number Total 3.86 1.13

11.365 0.000

Soraba 1.80 0.42 Thirthahalli 1.81 0.48 Hosanagara 1.92 0.28 Bhadravathi 1.79 0.44 Shimoga 1.82 0.39 Sagar 1.81 0.47 Shikaripura 1.80 0.44

C2-Different numerals

Total 1.82 0.42

1.752 0.106


C3-Fundamental operations

Total 1.96 1.07

15.177 0.000


C4-Fractions, decimals, and percentages Total

2.63 1.14

3.965 0.001

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4.7.1. Numbers Competency

Table 4.7.1 (a): Results of Duncan’s Multiple Range Test for Competency: Number

Subset for alpha = .05 Taluks

N

1 2 3

Soraba 140 3.3214

Thirthahalli 162 3.6975

Shikaripura 248 3.7379

Bhadravathi 257 3.7899

Sagar 233 4.0343

Hosanagara 155 4.0516

Shimoga 261 4.1418

In the case of numbers competency significant difference was observed

between students studying in different taluks (F = 11.365; P = 0.000). The

mean numbers competency scores of Soraba, Thirthahalli, Hosanagara,

Bhadravathi, Shimoga, Sagar and Shikaripura were 3.32, 3.69, 4.05, 3.79,

4.14, 4.03 and 3.74 respectively. Further Duncan’s multiple range test

indicated that Soraba had least scores, Sagar, Hosanagar and Shimoga had

Highest scores, Thirthahalli, Shikaripura and Bhadravathi students had the

scores on competency numbers in between.

4.7.2. Different numerals competency

In the case of Different numerals competency no significant difference was

observed between sectors as the observed ‘F’ value of 1.752 failed to reach

significance level criterion. In other words the mean values for students

studying in different taluks were statistically same.

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4.7.3. Fundamental operations competency

Table 4.7.3 (a): Results of Duncan’s Multiple Range Test for Competency: Fundamental operations

SECTOR N Subset for alpha = .05

1 2 3 4

Shimoga 261 1.6322

Soraba 139 1.7338 1.7338

Thirthahalli 162 1.8025 1.8025


Sagar 233 2.1073



In the case of Fundamental operations competency significant difference was

observed between students studying in different taluks (F = 15.177;

P = 0.000). The mean Fundamental operations competency scores of

students studying in Soraba, Thirthahalli, Hosanagara, Bhadravathi, Shimoga,

Sagar and Shikaripura were 1.73, 1.80, 2.47, 1.87, 1.63, 2.11 and 2.19

respectively. Further Duncan’s multiple range test indicated that students

studying in Shimoga , Soraba, Thirtahalli had least scores, Hosanagara had

highest scores, students studying in Bhadravathi, Sagara, Shikaripura taluks

had the scores in between.

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4.7.4. Fractions, decimals, and percentages competency

Table 4.7.4 (a): Results of Duncan’s Multiple Range Test for Competency: Fractions, decimals, and percentages


1 2 3


Soraba 140 2.5071 2.5071

Thirthahalli 162 2.5679 2.5679

Sagar 233 2.6180 2.6180


Shivmoga 261 2.6897


In the case of Fractions, decimals, and percentages competency significant

difference was observed between students studying in different taluks (F =

3.965; P = 0.001). The mean Fractions, decimals, and percentages

competency scores of students studying in Soraba, Thirthahalli, Hosanagara,

Bhadravathi, Shimoga, Sagar and Shikaripura were 1.08, 1.10, 1.0, 1.22,

0.96, 1.25 and 1.20 respectively. Further Duncan’s multiple range tests

indicated that students studying in Bhadravathi had least scores, Hosanagara

had highest scores, and students studying in Sagar, Shikaripura and Shimoga

had moderate scores.

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Table 4.7.4 (b): Comparison of means on various competencies of students studying in different taluks and results of One-way ANOVA for competencies Decimal’s fundamental operations, Decimals addition and subtraction with mixed operations, Angles and total scores

Competencies Taluks Mean S.D F

value P value Soraba 1.57 0.98 Thirthahalli 1.75 0.92 Hosanagara 2.18 0.86 Bhadravathi 1.85 1.08 Shimoga 2.02 0.86 Sagar 1.87 1.02 Shikaripura 1.81 1.04

C5-Decimal’s fundamental operations

Total 1.87 0.99

6.288 0.000


C6-Decimals addition and subtraction with mixed operations

Total 2.00 1.01

8.552 0.000


C7-Angles

Total 2.10 0.97

14.221 0.000


TOTAL

Total 16.24 4.32

11.574 0.000

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4.7.5. Decimals Fundamental Operations Competency

Table 4.7.5 (a): Results of Duncan’s Multiple Range Test for Competency: Decimals fundamental operations

SECTOR N Subset for alpha = .05 1 2 3 4 Soraba 140 1.5714 Thirthahalli 162 1.7531 1.7531 Shikaripura 248 1.8145 1.8145 Bhadravathi 257 1.8521 1.8521 Sagar 230 1.8696 1.8696 Shivmoga 261 2.0153 2.0153Hosanagara 156 2.1795

A significant difference was found between the students studying in different

taluks in the Decimals fundamental operations competency scores as the

obtained F value of 6.288 was found to be significant at .000 level. The

mean Decimals fundamental operations competency scores of students

studying in Soraba, Thirthahalli, Hosanagara, Bhadravathi, Shimoga, Sagar

and Shikaripura were 1.57, 1.75, 2.18, 1.85, 2.02, 1.87, 1.81 and 1.87

respectively. Further Duncan’s multiple range tests indicated that students of

Soraba and Thirthahalli had least scores, and students of Shimoga and

Hosanagar had highest and others in between.

4.7.6. Decimals Addition and Subtraction with Mixed Operations Competency

Table 4.7.6 (a): Results of Duncan’s Multiple Range Test for Competency: Decimals addition and subtraction with mixed operations

Taluks N Subset for alpha = .05 1 2 3 Thirthahalli 162 1.7963 Sagar 233 1.8069 Soraba 140 1.8214 Bhadravathi 257 1.9767 1.9767 Shivmoga 261 2.0000 2.0000 Shikaripura 248 2.1653 Hosanagara 156 2.3910

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In the case of Decimals addition and subtraction with mixed operations

competency, a significant difference was observed between students studying

in different taluks (F=8.552; P=0.000). The mean Decimals addition and

subtraction with mixed operations competency scores of students studying in

Soraba, Thirthahalli, Hosanagara, Bhadravathi, Shimoga, Sagar and

Shikaripura were 1.82, 1.80, 2.39, 1.98, 2.00, 1.80, 2.17 and 1.99

respectively. Further Duncan’s multiple range test indicated that students of

Thirthahalli, Sagar, Soraba had least scores, Hosanagar had highest scores,

and students of Bhadravathi, Shimoga, Sagar and Shikaripura had moderate

scores.

4.7.7. Angles competency

Table 4.7.7 (c): Results of Duncan’s Multiple Range Test for Competency: Angles


1 2 3 4

Sagar 233 1.6996

Thirthahalli 162 1.9877

Soraba 140 2.0214



Shimoga 261 2.2835 2.2835


In the case of Angles competency, a significant difference was observed

between students studying in different taluks (F=14.221; P=0.000). The mean

Angles competency scores of students studying in Soraba, Thirthahalli,

Hosanagara, Bhadravathi, Shimoga, Sagar and Shikaripura were 2.02, 1.98,

2.46, 2.23, 2.28, 1.69 and 2.04 respectively. Further Duncan’s multiple range

test indicated that students of Sagar had least scores, students of Shimoga

and Hosanagara had highest scores and other students in between.

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4.7.8. Total competency scores

Table 4.7.8 (a): Results of Duncan’s Multiple Range Test for total competency scores


1 2 3 4

Soraba 140 14.7857

Thirthahalli 162 15.4136 15.4136

Sagar 233 15.9142 15.9142

Bhadravathi 257 15.9416 15.9416


Shivmoga 261 16.5862


When total scores on all the competencies were verified, it was found that

students studying in different taluks differ significantly, as the obtained F value

of 11.574 was found to be significant at .000 level. The mean C7 scores for

Soraba, Thirthahalli, Hosanagara, Bhadravathi, Shimoga, Sagar and

Shikaripura were 14.79, 15.41, 18.42, 15.94, 16.59, 15.91 and 16.46

respectively. Further Duncan’s multiple range tests indicated that Sagar had

least scores, Shimoga and Hosanagar had highest scores, Thirthahalli,

Soraba, Shikaripura and Bhadravathi were in between.

Several studies have been conducted to compare achievement of mastery

level in mathematics by students studying in urban and rural schools. Singh

(2003) found significant difference in mathematic achievement between rural

and urban students. Santhosh Sharma (1999) also found the same results. A

study by Sharma (2000) found that teagarden school children (rural area)

lagged behind urban students. Dutta (2003) found that urban girls were better

in achievement in mathematics than rural girls. A study by Ramakalyani

(1993) showed that urban government school students were better than rural

137

government schools but they were inferior in mathematics achievements to

the private school children.

Some of the studies revealed that areas of study do not have significant

influence over achievement. Shailaja Shanbag (1992) reported that both rural

and urban schools fail to produce significant proportion of students who

attained required mastery level (80%). In mathematic competencies she did

not found significant difference in the proportion of mastery level students.

It can therefore be concluded that achievement pattern in mathematics

competencies among urban students is in a better position than compared to

rural students. The findings of the present study show the reverse pattern of

achievement as the rural students showed better performance .These results

can be explained in the following manner. The students in the rural sample

were selected from government schools. Usually students of all levels of

mathematical ability have no option, but to enroll themselves in government

schools. Thus, the students from rural areas present a more heterogeneous

nature in mathematical ability than urban students. Usually in urban areas,

children of well to do families are enrolled in private schools, which are

perceived to be, and to an extent in actual sense qualitatively better than

government schools. Naturally in urban areas, majority of students belonging

to the higher ability group go to private schools. In addition, in urban areas,

more number of students studying in private institutions opts for additional

tuition classes than the rural students. It is quite surprising that rural students

outshined urban students and hence shown better performance in

mathematics compare to urban students. In urban government schools almost

all students enrollment come from lower economic levels and impoverished

environment. Hence it is likely that they tend to be lower in their performance

in mathematics competencies. Many studies quoted above reported lower

mathematics achievement by urban students from government schools. In the

present study the sample from urban and rural area was drawn only from

government schools. As a result the rural sample becomes more

heterogeneous having many higher ability students as well as lower ability

students for the reason mentioned above. But the urban sample becomes

138

more homogeneous consisting of students from first generation learners and

poor family support. This difference of achievement between rural and urban

students occurred due to the above mentioned reasons.

4.8. Hypothesis 6

There is no significant difference between control and experimental group in

the effect of diagnosis-based remediation programme in improving the



(experimental) schools of Shimoga District.

Table 4.8 (a): Mean pre- and posttest scores on total competency scores of male and female in experimental and control groups

Sessions

Pre-test Post-test Groups Gender

Mean S.D Mean S.D

Change/

gain

Male 15.27 2.62 15.50 2.44 0.23

Female 14.61 2.99 16.32 3.44 1.71 Control

Total 14.90 2.82 15.96 3.04 1.06

Male 14.18 2.61 19.64 2.16 5.46

Female 15.23 1.82 19.86 1.81 4.63 Experimental

Total 14.64 2.34 19.74 2.00 5.10

Male 14.66 2.65 17.82 3.08 3.16

Female 14.88 2.54 17.88 3.33 3.00 Overall

Total 14.77 2.58 17.85 3.19 3.08

139

Table 4.8 (b): Result of repeated measure ANOVA for Mean pre and posttest scores on total competency scores of male and female in experimental and control groups (within and between subject affects)

Source Sum of Squares df Mean

Square F value P value

Within subject effects Change 446.645 1 446.645 306.673 0.000Change* Group 205.038 1 205.038 140.782 0.000Change* Gender 1.338 1 1.338 0.919 0.340Change* Group* Gender 16.505 1 16.505 11.333 0.001Error (change) 139.817 96 1.456 Between subject effects Groups 160.157 1 160.157 13.489 0.000Gender 6.257 1 6.257 0.527 0.470Group* Gender 3.820 1 3.820 0.322 0.572Error 1139.823 96 11.873

Note: Change refers to difference between pre to post sessions irrespective of

the groups (E and C), Change* treatment refers to difference between pre to

post sessions for E and C groups (differential gains).

In the pretest on the whole irrespective of the groups, the total mean of pre-

test scores was 14.77 which increased to 17.85 in the post test. The gain of

3.08 scores was found to be statistically significant where as observed ‘F’

value of 306.673 was found to be significant at 0.000 level. Further when

change in the scores were verified against control and experimental groups,

the ‘F’ value of 140.782 (P=0.000) shows significant difference between

experimental and control groups. From the mean values and gain scores it is

clear that the control group has gained a mean of 1.06 scores (pre=14.9;

post=15.96) where as experimental group has gained 5.10 scores (pre=14.64;

post= 19.74). The substantial gain by experimental group can be attributed for

effectiveness of diagnostic based remediation programmes. Gender wise no

significant effect was observed as observed ‘F’ value of 0.919 failed to reach

a significance level criterion. Lastly the gain in the scores with respect to

gender and groups was found to be significant (F = 11.333; P= 0.001) where

as the male students of experimental group have gained maximum scores

(mean gain = 5.46) and males in the control group gained least (mean gain =

140

0.23). In between subject effects only between experimental and control

group significant difference was observed (F = 13.489; P = 0.000). Gender

wise comparison and interaction between gender and groups were found to

be non significant (Fig. 4.8 (i)).

Figure 4.8 (i): Mean of pre and post test scores of experimental groups on total competencies scores

Table 4.8 (c): Mean of pre and posttest scores on Competency (Numbers) scores of male and female in experimental and control groups

Sessions Pre-test Post-test Groups Gender

Mean S.D Mean S.D

Change/ gain

Male 3.73 0.88 3.91 1.07 0.18

Female 3.82 0.67 4.07 1.05 0.25 Control Total 3.78 0.76 4.00 1.05 0.22 Male 4.68 0.61 4.54 0.84

-0.14

Female 4.41 0.80 4.64 0.58 0.23 Experimental Total 4.56 0.71 4.58 0.73 0.02 Male 4.26 0.88 4.26 0.99

0.00

Female 4.08 0.78 4.32 0.91 0.24 Overall Total 4.17 0.83 4.29 0.95 0.12

141

In the case of Competency numbers, in the pre-test on the whole, irrespective

of the group the total mean pre-scores were 4.17 which increased 4.29. The

gain of 0.12 scores was found to be statistically not significant as observed ‘F’

value of 1.926 was fail to reach significance level criterion. Further when

change in the scores were verified against control and experimental groups

no significant effect was observed as the observed ‘F’ value of 0.872 fail to

reach significant level criterion. Gender wise no significant effect was

observed as observed ‘F’ value of 1.389 failed to reach significance level

criterion. Lastly, the gain in the scores with respect to gender and groups wise

was found to be not significant as observed ‘F’ value of 0.659 fail to reach

significance level criterion.

Table 4.8 (d): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Numbers) scores of male and female in experimental and control groups (within and between subject affects)



Within subject effects Change 0.821 1 0.821 1.926 0.168Change * Group 0.372 1 0.372 0.872 0.353Change * Gender 0.592 1 0.592 1.389 0.242Change * Group *Gender 0.281 1 0.281 0.659 0.419

Error (change) 40.907 96 .426 Between subject effects Groups 22.964 1 22.964 24.300 0.000Gender .024 1 .024 0.025 0.875Group * Gender .557 1 .557 0.590 0.444Error 90.719 96 .945

In between subject effects only between experimental and control group

significant difference was observed (F = 24.300; P = 0.000). Gender wise

comparison and interaction between gender and groups were found to be non

significant.

142

Table 4.8 (e): Mean of pre and posttest scores on Competency (Different numerals) scores of male and female in experimental and control groups


Mean S.D Mean S.D

Change/ gain

Male 1.68 0.48 1.77 0.43 0.09 Female 1.57 0.50 1.79 0.42 0.22 Control Total 1.62 0.49 1.78 0.42 0.16 Male 1.96 0.19 1.93 0.38 -0.03

Female 1.82 0.50 1.95 0.21 0.13 Experimental Total 1.90 0.36 1.94 0.31 0.04 Male 1.84 0.37 1.86 0.41 0.02


Table 4.8 (f): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Different numerals) scores of male and female in experimental and control groups (within and between subject effects)



Within subject effects Change 0.507 1 0.507 3.036 0.085Change * Group 0.129 1 0.129 .771 0.382Change * Gender 0.269 1 0.269 1.609 0.208Change * Group *Gender 0.007 1 0.007 .044 0.835

Error (change) 16.044 96 0.167 Between subject effects Groups 2.246 1 2.246 14.172 0.000Gender 0.146 1 0.146 .920 0.340Group * Gender 0.002 1 0.002 .010 0.920Error 15.213 96 0.158

In the case of different numerals, a non-significant change was observed from

pre to post test situation irrespective of the groups as the observed ‘F’ value

143

of 3.036 fail to reach significance level criterion. A change of 0.10 scores was

observed from pre to post test situation. Further when change in the scores

were verified against control and experimental groups, again a non- significant

change was observed as the observed ‘F’ value of 0.771 fail to reach

significant level criterion. Gender wise also no significant effect was observed

as observed ‘F’ value of 1.609 fail to reach significance level criterion. Lastly

the gain in the scores with respect to gender and groups wise was found to be

no significant as observed ‘F’ value of 0.044 fail to reach significance level

criterion. In between subject effects only between experimental and control

group significant difference was observed (f = 14.172; p = 0.000). Gender

wise comparison and interaction between gender and groups were found to

be non significant.

Table 4.8 (g): Mean of pre and posttest scores on Competency (Fundamental operations) scores of male and female in experimental and control groups


Mean S.D Mean S.D

Change/ gain

Male 1.64 0.58 2.23 1.11 0.59 Female 1.82 0.77 2.18 1.09 0.36 Control Total 1.74 0.69 2.20 1.09 0.46 Male 1.57 1.17 3.00 0.61 1.43



144

Table 4.8 (h): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Fundamental operations) scores of male and female in experimental and control groups (within and between subject affects)




Error (change) 71.688 96 0.747 Between subject effects Groups 2.195 1 2.195 2.290 0.134Gender 0.275 1 .275 0.287 0.594Group * Gender 1.006 1 1.006 1.049 0.308Error 92.019 96 0.959

In the case of fundamental operation competency on the pretest on the whole

irrespective of the group the total mean pre-scores were 1.69 which increased

2.47. The gain of 0.78 scores was found to be statistically significant where as

observed ‘F’ value of 38.581 was found to be significant at 0.000 level.

Further when change in the scores were verified against control and

experimental groups again we find a significant ‘F’ value of 5.572 (p = 0.020)

was found to be highly significant. From the mean values and gain scores it is

clear that the control group has gained a mean total of 0.46 scores (pre =

1.74; post = 2.20) where as experimental group has gained 0.90 scores (pre =

1.64; post = 2.74). The substantial gain by experimental group can be

attributed for effectiveness of diagnostic based remediation programmes. The

interaction between Gender and group was also found to be significant with

respect as the observed ‘F’ value of 3.965 was found to be significant at .049

level. We find that male subjects of experimental group gained maximum

compared to other groups. Lastly the gain in the scores with respect to

gender and groups wise was found to be non- significant as the observed ‘F’

value of 1.085 fail to reach significance level criterion. In between subject

effects only between experimental and control group, gender wise comparison

and interaction between gender and groups were found to be non significant

(Fig. 4.8 (ii)).

145

Figure 4.8 (ii): Mean pre and post test scores of experimental and control groups on Competency (Fundamental operations)

Table 4.8 (i): Mean pre and posttest scores on Competency (Fractions, decimals and percentages) scores of male and female in experimental and control groups

Sessions


Mean S.D Mean S.D

Change/ gain

Male 2.41 0.85 1.77 1.11

-0.64

Female 2.68 0.72 1.75 0.84 -0.93 Control

Total 2.56 0.79 1.76 0.96 -0.80

Male 1.50 0.84 2.96 0.79

1.46


Total 1.56 0.81 3.08 0.75 1.52

Male 1.90 0.95 2.44 1.11

0.54

Female 2.22 0.91 2.40 1.07 0.18 Overall

Total 2.06 0.94 2.42 1.08 0.36

146

Table 4.8 (j): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Fractions, decimals and percentages) scores of male and female in experimental and control groups (within and between subject affects)




Error (change) 67.615 96 0.704 Between subject effects Groups 1.586 1 1.586 2.312 0.132Gender 1.286 1 1.286 1.875 0.174Group * Gender 0.072 1 0.072 0.105 0.747Error 65.843 96 0.686

In the case of Fractions, decimals and percentages competency, on the whole

irrespective of the groups, the total mean pre-scores of 2.06 which increased

to 2.42 in the post test. The gain of 0.36 scores was found to be statistically

significant, as the observed ‘F’ value of 9.712 was found to be significant at

0.002 level. Further when change in the scores were verified against control

and experimental groups, again we find a significant ‘F’ value of 93.344 (P =

0.000). From the mean values and gain scores it is clear that the control

group has gained a mean total of 1.06 scores (pre = 2.50; post = 1.76) where

as experimental group has gained 1.52 scores (pre = 1.56; post = 3.08). The

substantial gain by experimental group can be attributed for effectiveness of

diagnostic based remediation programmes. Gender wise no differential

change was observed as observed ‘F’ value of 0.120 failed to reach

significance level criterion. The gain in the scores with respect to gender and

groups wise was found to be non- significant as observed ‘f’ value of 0.767

failed to reach a significance level criterion. In between subject effects only

between experimental and control group, gender wise comparison and

interaction between gender and groups were found to be non significant (Fig.

4.8 (iii)).

147

Figure 4.8 (iii): Mean pre and post test scores of experimental and control groups on Competency (Fractions, decimals and percentages)

Tests of Between-Subjects Effects

Table 4.9 (a): Mean pre and posttest scores on Competency (Decimals fundamental operations) scores of male and female in experimental and control groups


Mean S.D Mean S.D

Change/ gain

Male 2.18 0.85 1.59 0.73 -0.59 Female 1.54 0.96 1.82 1.02 0.28 Control Total 1.82 0.96 1.72 0.90 -0.10

Male 1.43 0.74 2.11 0.88 0.68

Female 1.86 0.64 2.41 0.50 0.55 Experimental Total 1.62 0.73 2.24 0.74 0.62

Male 1.76 0.87 1.88 0.85 0.12 Female 1.68 0.84 2.08 0.88 0.40 Overall Total 1.72 0.85 1.98 0.86 0.26

148

Table 4.9 (b): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Decimals fundamental operations) scores of male and female in experimental and control groups (within and between subject affects)





In the case of decimals fundamental operation competency, on the whole

irrespective of the group the total mean pre-scores were 1.72 which increased

to 1.98. The gain of 0.26 scores was found to be statistically significant as the

observed ‘F’ value of 6.045 was found to be significant at 0.016 level. Further

when change in the scores were verified against control and experimental

groups again we find a significant ‘F’ value of 16.743 (P = 0.000). From the

mean values and gain scores it is clear that the control group has gained a

mean total of 0.16 scores (pre = 1.82; post = 1.72) where as experimental

group has gained 0.62 scores (pre = 1.62; post = 2.24). The substantial gain

by experimental group can be attributed for effectiveness of diagnostic based

remediation programmes. The interaction between Gender group was also

found to be significant with respect to change as observed ‘F’ value of 3.958 (

P=0.049) .The scores where as it was found that male students gained

maximum (mean gain = 0.68) scores (pre = 1.43 ; post = 2.11) where gain in

female subjects gained least(mean gain = 0.55) scores (pre = 1.86 ; post =

2.41). The gain in the scores with respect to gender and groups was found to

be significant (F = 7.300; P = 0.008) where we find that male students of

experimental group have gained maximum (mean gain = 0.68) and males in

149

the control group gained least (mean gain = 0.59). In between subject effects

only between experimental and control group, gender wise comparison and

interaction between gender and groups were found to be non significant

(Fig.4.9 (i)).

Figure 4.9 (i): Mean of pre and post test scores of experimental and control groups on Competency (decimals fundamental operation)

Table 4.9 (c): Mean pre and posttest scores on Competency (Decimals, additions subtraction with mixed operations) scores of male and female in experimental and control groups

Sessions


Mean S.D Mean S.D

Change/ gain

Male 1.68 1.00 1.68 0.72 0.00

Female 1.68 0.98 1.82 0.98 0.14 Control

Total 1.68 0.98 1.76 0.87 0.08

Male 1.00 0.72 2.14 0.85 1.14


Total 1.14 0.70 2.18 0.75 1.04

Male 1.30 0.91 1.94 0.82 0.64

Female 1.52 0.86 2.00 0.86 0.48 Overall

Total 1.41 0.89 1.97 0.83 0.56

150

Table 4.9 (d): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (Decimals, additions subtraction with mixed operations) scores of male and female in experimental and control groups (within and between subject affects)





In the case of Fractions, decimals and percentages, on the whole irrespective

of the group the total mean pre-scores were 1.41 which increased 1.97. The

gain of 0.56 scores was found to be statistically significant, as observed ‘F’

value of 34.456 was found to be significant at 0.000 level. Further when

change in the scores were verified against control and experimental groups

again we find a significant ‘F’ value of 26.069 (P = .000). From the mean

values and gain scores it is clear that the control group has gained a mean

total of 0.08 scores (pre = 1.68; post = 1.76) where as experimental group has

gained 1.04 scores (pre = 1.14; post = 2.18). The substantial gain by

experimental group can be attributed for effectiveness of diagnostic based

remediation programmes. Gender wise no significant effect was observed as

observed ‘F’ value of 0.059 fails to reach significance level criterion. The gain

in the scores with respect to gender and groups wise was found to be no

significant as observed ‘F’ value of 1.015 fail to reach significance level

criterion.In between subject effects only between experimental and control

group, gender wise comparison and interaction between gender and groups

were found to be non significant (Fig.4.9 (iii)).

151

Figure 4.9 (ii): Mean of pre and post test scores of experimental and control groups on Competency (Decimals, additions subtraction with mixed operations)

Tests of Between-Subjects Effects

Table 4.10 (a): Mean of pre and posttest scores on Competency (Angles) scores of male and female in experimental and control groups


Mean S.D Mean S.D

Change/ gain

Male 1.95 0.49 2.55 0.60 0.60 Female 1.50 0.75 2.89 0.42 1.39 Control Total 1.70 0.68 2.74 0.53 1.04 Male 2.04 1.26 2.96 0.19 0.92



152

Table 4.10 (b): Result of repeated measure ANOVA for Mean pre and posttest scores on Competency (angles) scores of male and female in experimental and control groups (within and between subject affects)



Within subject effects Change 33.978 1 33.978 89.157 0.000Change * Group 1.286 1 1.286 3.374 0.069Change * Gender 0.246 1 0.246 .645 0.424Change* Group *Gender 5.378 1 5.378 14.112 0.000Error (change) 36.586 96 0.381 Between subject effects Groups 1169.221 1 1169.221 2508.364 0.000Gender 8.881 1 8.881 19.052 0.000Group * Gender 0.721 1 0.721 1.546 0.217Error 1.501 1 1.501 3.220 0.076

In the case of angles competency, on the whole irrespective of the group the

total mean pre-scores were 1.99 which increased 2.86. The gain of 0.87

scores was found to be statistically significant as the observed ‘F’ value of

89.157 was found to be significant at 0.000 level.Further, when change in the

scores were verified against control and experimental groups no significant

effect was observed as the observed ‘F’ value of 3.374 fail to reach

significant level criterion. Gender wise no significant effect was observed as

observed ‘F’ value of 0.645 fail to reach significance level criterion. The gain

in the scores with respect to gender and groups was found to be significant

(F= 14.112; P = 0.000) where it was found that male students of experimental

group have gained maximum (mean gain = 0.92) and males in the control

group gained least (mean gain = 0.60).In between subject effects only

between experimental and control group significant difference was observed

(F = 19.052; P = 0.000). Gender wise comparison and interaction between

gender and groups were found to be non significant (Fig. 4.10 (i)).

153

Figure 4.10 (i): Mean pre and post test scores of experimental and control groups on Competency (Angles)

Table 4.10 (c): Distribution of the sample by groups and mastery level (total scores) in the post test and the results of contingency coefficient test

Groups Mastery level Control Experimental Total

Frequency 38 13 51 Non-masters percent 76.0% 26.0% 51.0%

Frequency 12 37 49 Masters percent 24.0% 74.0% 49.0%

Frequency 50 50 100 Total percent 100.0% 100.0% 100.0%

Contingency Coefficient=.447; P=0.000 (S) In the case of total seven(overall) competencies, both in experimental and

control groups there were 100 non masters (50 each) in the pretext after the

remediation program when the posttest was applied, we find that in

experimental group out of 50 non masters 37 became masters (74%) as

against only 12 in the control group became masters (24%). When

contingency coefficient tests were applied for mastery level and groups

154

contingency coefficient of 0.447 was found to be significant at 0.000 level. In

other words in comparison with control group 50 % of the experimental group

became masters that can be attributed to effectiveness of diagnosed based

remediation programme (Fig. 4.10 (ii)).

Figure 4.10 (ii): Distribution of the sample by groups and mastery level (total scores) level in the post test

Table 4.10 (d): Distribution of the sample by groups and mastery level (Numbers) in the post test and the results of contingency coefficient test

Groups Mastery level

Control Experimental Total Frequency 11 5 16Non-masters

percent 22.0% 10.0% 16.0%Frequency 39 45 84Masters

percent 78.0% 90.0% 84.0%Frequency 50 50 100Total

percent 100.0% 100.0% 100.0%

Contingency Coefficient=. 162; P=.102(NS)

155

In the case of Numbers competency, contingency coefficient test revealed a

non- significant association between mastery level and groups, where, after

the post test irrespective of the groups we find 84 out of 100 became masters

and this trend was found to be similar for both experimental and control group

(90% and 78% respectively). However comparatively we can see more

number of students became masters in the experimental group than control

group.

Table 4.10 (e): Distribution of the sample by groups and mastery level (Different Numerals) in the post test and the results of contingency coefficient test





percent 100.0% 100.0% 100.0%

Contingency Coefficient=. .259; P=. 007 (S)

In the case of different numerals competency, both in experimental and

control groups there were 100 non masters (50 each) in the pretest. After the

remediation program when the posttest was applied, we find that in

experimental group out of 50 non masters, 48 became masters (96%) as


contingency coefficient tests were applied for mastery level and groups,




remediation programme over different numerals (Fig. 4.10 (iii)).

156

Figure 4.10 (iii): Distribution of the sample by groups and mastery level (Different Numerals) level in the post test

Table 4.10 (f): Distribution of the sample by groups and mastery level (fundamental operations) in the post test and the results of contingency coefficient test


Frequency 31 15 46 Non-masters percent 62.0% 30.0% 46.0%

Frequency 19 35 54 Masters percent 38.0% 70.0% 54.0%

Frequency 50 50 100 Total percent 100.0% 100.0% 100.0%

Contingency Coefficient=.306; P=. 001 (S)

In the case fundamental operations competency, both in experimental and

control groups there were 100 non masters (50 each) in the pretext after the

remediation program when the posttest was applied we find that in

experimental group out of 50 non masters 35 became masters (70%) as


contingency coefficient tests were applied for mastery level and group’s




remediation programme over fundamental operations (Fig. 4.10 (iv)).

157

Figure 4.10 (iv): Distribution of the sample by groups and mastery level (fundamental operations) level in the post test

Table 4.10 (g): Distribution of the sample by groups and mastery level (Fractions, decimals and percentage) in the post test and the results of contingency coefficient test


Control Experimental Total Frequency 40 10 50 Non-masters

percent 80.0% 20.0% 50.0% Frequency 10 40 50 Masters

percent 20.0% 80.0% 50.0% Frequency 50 50 100 Total

percent 100.0% 100.0% 100.0%

Contingency Coefficient=. 514; P=0.000 (S)

In the case Fractions, decimals and percentage competency, both in

experimental and control groups there were 100 non masters (50 each) in the

pretext after the remediation program, when the posttest was applied we find

that in experimental group out of 50 non masters 40 became masters (80%),

as against only 10 in the control group became masters (20%). When


158




remediation programme over Fractions decimals and percentage

(Fig. 4.10 (v)).

Figure 4.10 (v): Distribution of the sample by groups and mastery level (Fractions, decimals and percentage) level in the post test

Table 4.10 (h): Distribution of the sample by groups and mastery level (Decimals fundamental operations) in the post test and the results of contingency coefficient test


Frequency 40 30 70Non-masters percent 80.0% 60.0% 70.0%

Frequency 10 20 30Masters percent 20.0% 40.0% 30.0%

Frequency 50 50 100Total percent 100.0% 100.0% 100.0%

Contingency Coefficient=0 .213; P=0.029 (S)

159

In the case competency 5 (Decimals fundamental operations), both in

experimental and control groups there were 100 non masters (50 each) in the

pretest. After the remediation program, when the posttest was applied we find

that in experimental group, out of 50 non masters 20 became masters (40%)

as against only 10 in the control group became masters (20%). When





remediation programme over Decimals fundamental operations

(Fig. 4.10 (vi)).

Figure 4.10 (vi): Distribution of the sample by groups and mastery level (Decimals fundamental operations) level in the post test

Table 4.10 (i): Distribution of the sample by groups and mastery level (Decimals addition and subtraction with mixed operations) in the post test and the results of contingency coefficient test


Frequency 40 32 72Non-masters Percent 80.0% 64.0% 72.0%

Frequency 10 18 28Masters Percent 20.0% 36.0% 28.0%

Frequency 50 50 100Total Percent 100.0% 100.0% 100.0%

Contingency Coefficient=0 .175; P=0.075 (NS)

160

In the case of Decimals addition and subtraction with mixed operations

competency, contingency coefficient test revealed a non-significant

association between mastery level and groups, where, after the post test

irrespective of the groups we find 28 out of 100 became masters and this

trend was found to be similar for both experimental and control group (36%

and 20%) respectively. However comparatively we can see more number of

students became masters in the experimental group than control group.

Table 4.10 (j): Distribution of the sample by groups and mastery level (angles) in the post test and the results of contingency coefficient test





percent 100.0% 100.0% 100.0%

Contingency Coefficient=0 .294; P=0.002 (S)

In the case angles competency, both in experimental and control groups there

were 100 non masters (50 each) in the pretest. After the remediation program

when the posttest was applied, we find that in experimental group out of 50

non-masters 49 became masters (98%) as against only 39 in the control

group became masters (78%). When contingency coefficient tests were

applied for mastery level and groups’ contingency coefficient of 0.294 was

found to be significant at 0.002 level. In other words in comparison with

control group 20 % of the experimental group became masters that can be

attributed to effectiveness of diagnosed based remediation programme over

angles (Fig. 4.10 (vii)).

161

Figure 4.10 (vii): Distribution of the sample by groups and mastery level (angles) level in the post-test

Table 4.10 (k): Distribution of the sample by groups and mastery level of overall competencies in the post-test and the results of rank difference

Maximum masters converted in competency 4 (Fractions, decimals and

percentage) followed by competency 3 (fundamental operations), competency

5 (Decimals fundamental operations), competency 2 (different numerals),

competency 6 (Decimals addition and subtraction with mixed operations),

competency 1 (Numbers), competency 7 (angles) respectively.

In the pretest on the whole irrespective of the group the total mean pre-scores

were 14.77 which was increased 17.85. The gain of 3.08 scores was found to

be statistically significant. Further, experimental group has gained 5.10 scores

(pre=14.64; post= 19.74) compared to control group, which has gained a low

c Ctrl Exptl Diff Rank 1 78 90 12 6 2 78 96 18 4 3 38 70 32 2 4 20 80 60 1 5 20 40 20 3 6 20 36 16 5 7 39 49 10 7

162

mean of 1.06 scores (pre=14.9; post=15.96). The substantial gain by

experimental group over control group can be attributed for effectiveness of

diagnostic based remediation programmes. Hence hypothesis 6 formulated

as “There is no significant difference between control and experimental group

in the effect of diagnosis-based remediation programme in improving the



(experimental) schools of Shimoga District’ is rejected.

Several studies have been conducted in India and abroad relating to the

effectiveness of various strategies of teaching mathematics and remedial

programmes designed in many ways by researchers. Gusky and Gates

(1986) surveyed 46 research studies relating to the effectiveness of blooms

mastery learning approach and found that in most of the studies mastery

learning approach was beneficial. It is significant to note the positive effects of

this approach were more in language and arts than in mathematics and

science. Airasian (1967) and Colins (1969) found that the mastery learning

approach was better than conventional method of teaching. Similarly Reese

(1976) reported positive effectiveness of remedial teaching over conventional

teaching in learning algebra. Block (1970), Reed (1993), Kersh (1990),

Meverrech (1986), Kulik et. al. (1990) have reported beneficial effects of

mastery in learning approach on learning mathematics.

In India also several studies have been conducted on the effectiveness of

several kinds of intervention programmes. Archana Srivastava (2004) showed

better achievement level was observed on the part of students with

mathematical disability after teaching them with the help of remedial

programme. Sullivan (1987) found in his study that students who were thought

through mastery learning method scored significantly higher in mathematics

than students taught through traditional method. Kumar, Surinder, Susma

and Harizuka (1996) found significant difference between experimental and

control groups after teaching mathematics through cooperative learning. They

found positive interaction among students. Amruthavalli Devi (2008) studied

the effectiveness of strategy of teaching mathematics developed by her based

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on Piaget and Vigotski’s views. She found significant difference between

pretest and posttest scores in all the four variables studied namely

mathematical thinking, creative thinking, intelligence and mathematics

achievement. The above studies have shown positive effect of well designed

intervention programme (including remedial programmes and new teaching

strategies like discovery method, cooperative teaching, etc). Rastogi (1983)

attempted a study on diagnosis of weaknesses in arithmetic as related to the

basic arithmetic skills and their remedial measures and he revealed that basic

arithmetic skills could very quickly and conveniently be mastered through the

course of self-help in basic arithmetic skills as developed during the study.

Vyas (1983) attempted a study on development of symbol picture logic

programme and to study its effect on mathematics achievement the students

of the experimental group who were given a treatment of the SPLP showed

better achievement in mathematics than the control group students. Yadav

(1984) found that after the experimental treatment, the experimental group of

pupils exhibited a significantly higher achievement in mathematics than the

control group of pupils and higher gain scores of achievement in mathematics

and different percentile achievement scores of the experimental group of

pupils were found to be significantly higher than those of the control group of

pupils at post-test stage. Das and Barua (1986) studied on effect of remedial

teaching in arithmetic among grade IV pupils and they revealed that the major

conclusion of the study was that remedial teaching had definitely improved

significantly the achievements in arithmetic. Dutta (1986) attempted on

learning disabilities in the reasoning power of the students in geometry-

diagnosis and prevention and he found that the experimental groups taught by

audio-visual materials and techniques achieved significantly more than the

controlled groups taught by conventional methods.

However, some of the studies indicated non-effectiveness of intervention

programmes. Kirikire (1981) studied the impact of objective based lesson

plans on the class room verbal interaction of behaviour but he did not find any

significant effect. Wagh S K (1981) developed a multimedia instructional

system for remedial teaching about fractional numbers but did not find

significant difference in the achievement of the experimental and control

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groups. Multimedia system and traditional system both were effective to the

same extent. Elfar (1982) evaluated two procedures – diagnostic and

prescriptive in terns of proportion of students achieving mastery level in

learning algebra but he did not find any significant difference between these

two procedures. But he found significant difference between the two

experimental groups (treatment 1 and 2) and the control group.

In the present study also the experimental group gained significantly higher

competencies in total scores than the control group, Male students of

experimental group gained most but if we analyze competency wise the

experimental group significantly gained more than the control group in

competencies ”fundamental operations“, “fractions, decimals and

percentages”, “decimal fundamental operations” and “decimals addition

subtraction with mixed operation”. In other competencies like “numbers”,

“different numerals” and “angles” the gain of the experimental group was

moderately observed over the control group. So it indicates that the remedial

teaching programme with reference to these competencies needs to be

revised and strengthened. It is significant to note that the male students

gained more than the female students in competencies like “fundamental

operations”, “decimal fundamental operations” and “angles” and in total

competency scores. So in conclusion it may be said that the effect of remedial

programme was not uniform across the competencies in mathematics and it

needs to be further modified.

Let us return to the classroom and try to gain insight by seeing how these

ideas work out in a school setting. If we consider our example of the teaching

of fractions, a subject is thought to be difficult for most children to apprehend

because the material is "so abstract." Indeed fractions are an appropriate

example for study, since one of the primary difficulties in understanding

fractions is in grasping that the fraction expresses a relationship between a

part and a whole (e.g., Harel, 1988). The difficulty lies in the child's confusion

about what the whole is, the very same difficulty we encountered when trying

to define concrete. The traditional approach to teaching the manipulation of

fractions is to give rules for each operation, rules such as "to add fractions,

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make a common denominator," "to divide fractions, invert and multiply."

These rules are given as if they were definitions: they are supposed to serve

as the meaning of their corresponding operations. They are not connected to

each other, nor to previous knowledge about fractions. Indeed, studies have

shown that, in the case of dividing fractions, no connection is made between

the notion of division in fractions and familiar division of whole numbers (e.g.,

Ball, 1990; Wilensky, 1989). These practices lead to a disconnected knowing,

a knowledge of fractions that can only bear up if one is given problems that

just call for application of these rules. The solution to this problem, however,

is not to avoid abstract objects like fractions, or even to replace rules for

manipulating them with situated practices such as suggested by Lave (1988).

These solutions use the old mistaken notion of concrete, a notion of concrete

as a property of certain objects but not others, in order to restrict the domain

of learning. Rather, we must present multiple representations of fractions,

both sensory (pies, blocks, clocks) and non-sensory (ratios, equivalence

classes, binary relations), and give opportunities for the child to interact with

all of these and establish connections between them. This kind of enrichment

of the relationship between the child and the fraction will make the fraction

concrete for the child and provide a robust and meaningful knowledge of

fractions. By establishing this kind of complex and multifaceted relationship

with the fraction, the child may still not fall in love with fractions as Papert did

with the gears of his childhood (Papert, 1980), but at least fractions will be

brought into the "family" thus enabling a lifelong relationship with them. With

long term use of manipulatives in mathematics, educators have found that

students make gains in the following general areas (Heddens and Piccioto,

1998; Sebesta and Martin, 2004). These areas are verbalizing mathematical

thinking, discussing mathematical ideas and concepts, relating real world

situations to mathematical symbolism, working collaboratively, thinking

divergently to find a variety of ways to solve problems, expression problems

and solutions using a variety of mathematical symbols, making presentations,

taking ownership of their learning experiences, gaining confidence in their

abilities to find solutions to mathematical problems using methods that they

come up with themselves without relying on directions from the teacher.

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The use of manipulatives helps students hone their mathematical thinking

skills. According to Stein and Bovalino (2001), “Manipulatives can be

important tools in helping students to think and reason in more meaningful

ways. By giving students concrete ways to compare and operate on

quantities, such manipulatives as pattern blocks, tiles and cubes can

contribute to the development of well grounded, interconnected

understandings of mathematical ideas. Studies have shown that students

using manipulatives in specific mathematical subjects are more likely to

achieve success than students who don’t have the opportunity to work with

manipulatives. Following are some specific areas in which research shows

manipulatives are especially helpful: Counting, some children need to use

manipulatives to learn to count (Clements, 1999). Place Value, using

manipulatives increases students’ understanding of place value (Phillips,

1989). Computation, students learning computational skills tend to master and

retain these skills more fully when manipulatives are used as part of their

instruction (Carroll and Porter, 1997). In case of Problem Solving, using

manipulatives has been shown to help students reduce errors and increase

their scores on tests that require them to solve problems (Carroll and Porter,

1997, Clements, 1999, Krac, 1998). In Fractions, students who have

appropriative manipulatives to help them learn fractions outperform students

who rely only on textbooks when tested on these concepts (Jordon, Miller and

Mercer, 1998; Sebesta and Martin, 2004). In case of Ratios/Percentages, students who have appropriate manipulatives to help them learn fractions also

have significantly improved achievement when tested on ratios as compared

to students who do not have exposure to these manipulatives (Jordon, Miller

and Mercer, 1998). Manipulatives have also been shown to provide a strong

foundation for students mastering the following mathematical concepts (The

Access Center, October 1, 2004). They are, namely, Number relations,

Measurement, Decimals, Number bases and Percentages.

Well known math educator Marilyn Burns considered manipulatives essential

for teaching math to students of all levels. She found that manipulatives help

make math concepts accessible to almost all learners, while at the same time

offering ample opportunities to challenge students who catch on quickly to the

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concepts being taught. Research indicates that using manipulatives is

especially useful for teaching low achievers (Marsh and Cooke, 1996; Ruzic

and O’connell, 2001). Reseach also indicates that using manipulatives helps

improve the environment in math classrooms. When students work with

manipulatives and then are given a chance to reflect on their experiences, not

only is mathematical learning enhanced, but math anxiety is greatly reduced

(Cain-Caston, 1996, Heuser, 2000). Exploring manipulatives, especially self

directed exploration, provides an exciting classroom environment and

promotes in students positive attitude towards learning (Heuser, 1999, Moch,

2001). Among the benefits several researchers found for using manipulatives

was helpful in making the learning fun (Moch, 2001; Smith et.al, 1999).

How do we foster the concretion process? What kind of learning environment

nurtures it and promotes its growth? Clearly, much more research is needed

to explore the many facets of this question. Here we point to only one: the

constructionist paradigm for learning (Harel & Papert, 1990). When we

construct objects in the world, we come into engaged relationship with them

and the knowledge needed for their construction. It is especially likely then

that we will make this knowledge concrete. When Harel's fourth and fifth

graders (Harel, 1988) construct a computer program for representing and

teaching fractions, they have the opportunity to meet and connect multiple

representations of fractions and to construct their own idiosyncratic

relationships with and between them.

The number and math symbol cards facilitate the translation of words to

numbers and symbols. This critical connecting step helps students to bridge

the gap between the concrete and the abstract. This product is designed for

use with partners, in small groups, in centers, or with whole group instruction.

Grouws and Cebulla (2000) stated that long-term use of concrete materials is

positively related to increase mathematics achievement in the report,

“Improving Student Achievement in Mathematics.” This finding suggested that

teachers use manipulative materials in mathematics instruction regularly in

order to provide students hands-on experience that enables them to construct

useful meanings for the mathematical ideas that they are learning. Grouws

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and Cebulla (2000) found that using small groups of students to work on

activities, problems and assignments can increase student mathematics

achievement. These researchers noted that using whole-class discussion

following individual and group work improves student achievement.

Research reflects the importance of whole-class discussion following student

work on problem-solving activities. Findings indicate that such discussion

following individual and small group work improves student achievement

(Grouws and Cebulla, 2000). The use of multimedia learning environments

may offer ways to overcome these difficulties (Mayer, 2001). In multimedia

learning environments, information presentation can be accomplished by

using different representational formats (textual and pictorial) which maybe

processed in different sensory channels (auditory and visual). Additionally,

information presentation is not restricted to static displays (e.g., diagrams,

pictures, written text), but the representations used can involve changes over

time (e.g., dynamic visualizations, spoken text).

Hodes (1992) compared the effectiveness of imagery instructions and

instructional visuals for fact recall and understanding. Both the instructional

methods were helpful in inducing an imagery strategy and in improving post-

test performance; however, for some performance measures, achievements

due to presenting external visuals were larger than for the imagery

instructions. Ginns, Chandler and Sweller (2003) showed that imagining

procedures (vs. studying text-based materials) was only helpful for learners

possessing sufficiently high prior knowledge in the domain. This replicates

findings of Cooper, Tindall-Ford, Chandler, and Sweller (2001) who found

interactions between domain-specific abilities and the type of instruction

given. For students who can read, most textbooks are not very helpful when it

comes to teaching students how to solve math problems. They typically

provide a four-step formula: (a) read the problem, (b) decide what to do,

(3) compute and (4) check your answer. “Read” the problem for

understanding is the first step. Understanding involves a representation of the

relationship between numbers, words and symbols in the problem. This

representation provides the basis for deciding what to do to solve the

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problem. From early on, most students acquire the skills and strategies

needed to “read the problem” and “decide what to do” to solve it. Many

students who are nonmasters, however, do not easily acquire these skills and

strategies. Therefore, they need explicit instruction in mathematical problem-

solving skills and strategies to solve problems in their math textbooks and in

their daily lives. Problem types should be introduced beginning with the

easiest problem type, and after mastery, move to the next level of difficulty

(García, Jiménez and Hess, in press, for a taxonomy of the difficulty levels of

the four types of addition and subtraction problems for students with

mathematical difficulties).

Effective visual representations, whether with manipulatives, with paper and

pencil, or in one’s imagination, show the relationships among the problem

parts. These are called schematic representations (van Garderen &

Montague, 2003). Cognitive processes and strategies needed for successful

mathematical problem solving include paraphrasing the problem, which is a

comprehension strategy, hypothesizing or setting a goal and making a plan to

solve the problem, estimating or predicting the outcome, computing or doing

the arithmetic, and checking to make sure the plan was appropriate and the

answer is correct (Montague, 2003; Montague, Warger and Morgan, 2000).

Good problem solvers use a variety of processes and strategies as they read

and represent the problem before they make a plan to solve it (Montague,

2003). Visualizing or drawing a picture or diagram means developing a

schematic representation of the problem so that the picture or image reflects

the relationships among all the important problem parts. Using both verbal

translation and visual representation, good problem solvers not only are

guided toward understanding the problem, but they are also guided toward

developing a plan to solve the problem. This is the point at which students

decide what to do to solve the problem. They have represented the problem

and they are now ready to develop a solution path. They hypothesize by

thinking about logical solutions and the types of operations and number of

steps needed to solve the problem. They may write the operation symbols as

they decide on the most appropriate solution path and the algorithms they

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need to carry out the plan. They ask themselves if the plan makes sense

given the information they have.

Why is it so difficult to teach students to solve math problems?

Students who are poor mathematical problem solvers, as most students who

are non-masters are, do not process problem information effectively or

efficiently. They lack or do not apply the resources needed to complete this

complex cognitive activity. Generally, these students also lack meta-cognitive

or self-regulation strategies that help successful students understand,

analyze, solve and evaluate problems. To help these students become good

problem solvers, teachers must understand and teach the cognitive processes

and meta-cognitive strategies that good problem solvers use. This is the

content of math problem-solving instruction. Teachers must also use

instructional procedures that are research-based and have proven effective.

These procedures are the basis of cognitive strategy instruction, which has

been demonstrated to be one of the most powerful interventions for non

master students (Swanson, 1999).

Visualization Visualization is critical to problem representation. It allows students to

construct an image of the problem on paper or mentally. Students must be

shown how to select the important information in the problem and develop a

schematic representation. To do this, teachers model how to use

manipulatives to represent a problem, and then how to draw a picture or make

a diagram that shows the relationships among the problem parts using both

the linguistic and numerical information in the problem. These three-

dimensional and two-dimensional visual representations can take many forms

and will vary from student to student. As students become better problem

solvers, they will use a variety of visual representations including

manipulatives, pictures, tables, graphs, or other types of displays. Initially,

students must be shown how to use the manipulatives and also how to

translate the results of their manipulations with concrete objects to more

symbolic representations using paper and pencil, e.g., the problem type

diagrams. Later, as students become more proficient, they will progress to

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mental images. Interestingly, if the problem is novel or challenging, they

frequently return to conscious application of processes and strategies, which

is typical of good problem solvers.

The above studies showed that the improvement of mastery level in the

competencies ”fundamental operations“, “fractions, decimals and

percentages”, “decimal fundamental operations” and “ decimals addition

subtraction with mixed operation” is due to the use of adequate

manipulatives, so in the present study also investigator used adequate

manipulatives wherever necessary in his intervention programme. Hence it

can be stated that the adequate use of manipulatives and appropriate

strategies can improve the mastery level in attainment of the above

competencies.

4.9. Main findings of the study

4.9.1. Survey findings

1. Male and female students had statistically equal scores on all the

competencies and also on overall performance, except for ‘fundamental

operations’ where female students excelled male students.

2. Rural and urban area-wise comparisons revealed that rural students

scored high in ‘Numbers’, ‘Decimals addition and subtraction with mixed

operations’, and in ‘total scores’, than the urban students and in rest of the

components students from urban and rural areas had statistically equal

scores.

3. Block-wise comparison revealed that in numbers competency students

from Sagar, Hosanagar and Shimoga had Highest scores, and Soraba

taluk had least scores (Table 4.7.1).

4. In ‘fundamental operations’ competency, students studying in Hosanagara

taluk had highest scores and students in Shimoga, Soraba, and Thirtahalli

taluks had least scores (Table 4.7.3).

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5. In ‘Fractions, decimals, and percentages competency, students studying in

Hosanagara taluk had highest scores and students studying in

Bhadravathi had least scores (Table 4.7.4).

6. Students of Shimoga and Hosanagar taluks scored highest in ‘Decimals

fundamental operations’ competency, where as students of Soraba and

Thirthahalli taluks scored least (Table 4.7.5).

7. In ‘Decimals addition and subtraction with mixed operations’ competency,

Hosanagar taluk students had highest scores and students of Thirthahalli,

Sagar, and Soraba taluks had least scores (Table 4.7.6).

8. Students of Shimoga and Hosanagara taluks scored highest in ‘Angles’

competency, where as students of Sagar taluk had least scores (Table

4.7.7).

9. In overall performance on ‘Total competencies scores’ students of

Shimoga and Hosanagar taluks excelled maximum and students of Sagar

taluk had least scores. The students studying in Thirthahalli, Soraba,

Shikaripura, and Bhadravathi taluks performed moderately in between the

above mentioned taluks (Table 4.7.8).

4.9.2. Effect of remedial teaching

1. Experimental group had gained significantly higher in general on all the

competencies and also overall performance scores than the control group.

Further, male students of experimental group had substantial gain in

comparison to all other groups.

2. Competency-wise, in ‘fundamental operations’, ‘Fractions, decimals and

percentages’, ‘Decimals fundamental operations’, and in ‘Decimals,

additions subtraction with mixed operations’ experimental group found to

be better significant as there is gain in comparison control group whereas

other competencies – ‘numbers’, ‘different numerals’ and for ‘angles’, the

effect of remedial teaching showed no significant effect on the

experimental group.

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3. Male subjects gained more than female students in competencies like-

Fundamental operations, Decimals fundamental operations and in ‘angles’

and also on total competencies than female students.

4. The diagnosis-based remediation programme had maximum effect on

competency (Fractions, decimals and percentage) where most of the non-

masters became masters in experimental group.

The main findings are discussed along with verification of the hypothesis in

the light of previous findings and suggestions offered by the experts.

4.10. Implications 1. Present remediation programme can be used by the teachers to improve

mathematics achievement in schools.

2. The MLL strategy of the present study can be useful in implementing

constructivistic approach in teaching learning.

3. A teacher in group based context of teaching should keep in mind that the

instructional time required for mastery of competencies is not uniform

across learners. Hence there could be additional time required for some

learners when class is heterogeneous. Also, even in a group based

instructional program remediation is a necessary condition for mastery.

4. It was found out from the present study that diagnosis based remediation

programme leads to mastery of competencies in mathematics among non

masters, but time taken for mastering competencies by all non-masters

was higher than the time allotted in the school for teaching. In the rigid

time frame of an academic year it would then be necessary that the

competencies that are difficult for the students may be identified and

shifted to the bridge course. This will be the requirement for the diagnosis

based remediation programme prescribed for a grade to be appropriate for

the learners and for ensuring universal achievement of a comparable

standard by all learners.

5. The curriculum planners can design the curriculum based on concrete to

abstract learning continua in mathematics by providing concrete, semi-

abstract and abstract activities and games and live experiences in and

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around the pupils daily life activities which will lead to high level of

attainment of MLL competencies.

6. Training programme can be designed for training the primary school

teachers in adopting diagnosis based remediation programme for teaching

mathematics at the primary level.

7. Teachers can use the diagnosis based remediation programme to achieve

mastery of MLL competencies in mathematics and can also create an

interest among the students to learn mathematics.

8. Findings of this study demand that teachers must try to improve the quality

of teaching so that abilities of attaining MLL competencies of mathematics

can be developed among children.. Teachers with the help of this study

can develop their own teaching strategies to teach different subjects

interestingly and innovatively.

9. The diagnosis based remediation program is useful for students who lag in

decimals, percentage and fractions where one can expect better results.

4.11. Suggestions 1. Present remediation programme can be extended to other classes.

2. New methods like discussion method, guided discovery method, mastery

learning and co-operative learning can be attempted by teachers.

3. This study can be extended in government aided and private schools in

urban and rural areas.

4. Studies may be conducted in other curricular areas using diagnosis based

remediation programme to study the effectiveness of the strategy.

5. The effectiveness of the diagnosis based remediation programme to be

verified for a full academic year.

6. A study involving other variables that may be intervening with attainment

levels could be conducted for greater understanding of the effectiveness of

diagnosis based remediation programme.

7. Further validation of effectiveness needs to be done when the strategy is

implemented on a larger scale and in different contexts of school

education, especially the multigrade context.

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