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SCHOLASTIC ACHIVEMENT IN MATHAMATICS OF

SENIOR SECONDARY SCHOOL STUDENTS IN

RELATION TO THEIR SELF REGULATED LEARNING

AND METACOGNITIVE SKILLS

Dr.Radha Arora1 , Dr.Pooja Arora2 Nikita Malhotra3

1Associate Professor, M.G.N. College of Education, Jalandhar, 144021, Punjab, India 2Assistant Professor, M.G.N. College of Education, Jalandhar, 144021, Punjab, India

3M.ED Student, M.G.N. College of Education, Jalandhar, 144021,Punjab, India

[email protected] /9646711883

Abstract: Student’s mathematical achievements in secondary school have an influential

effect on their performance in college and their future careers. Problems related to

mathematical achievement usually due to a combination of teaching and student factors

including language, cognitive, metacognitive skills, motor, social and emotional factors,

habits of learning, and previous experiences. Investigating the self-regulated learning

capabilities and Metacognitive skills of students is essential for understanding the

achievement in mathematics. This study is an applied research and the method is survey and

the data collection method was a quantitative research. The population consisted of

sr.secondary school students of10 Govt. and Private Schools from Jalandhar District so 300

students selected randomly by using random sampling technique as samples. The three

instruments were used to collect data from the respondents .Measurement tools are standard

questionnaire for self regulated learning and metacognitive skills. Mathematics achievement

test was prepared by the investigator keeping in view the universality of the various

branches – Algebra, Trigonometry and Geometry The results of two way analysis showed

that High Self Regulated Learning is necessary to achieve success in mathematics and

opportunity to communicate mathematically and to develop Self confidence to solve

Mathematical problem. High Metacognitive skills are necessary to achieve to obtain a

desired level of Learning in mathematics and control one’s own learning process. Students

having good Self Regulated Learning and Metacognitive skills can focus his or her

attention on Learning unit ; make a distinction between important and unnecessary

information; use effective strategies to keep the information in long term memory and

retrieve it when necessary and easily attain Mathematics Achievement. High Self Regulated

Learning is required to improve achievement in all three branches of mathematics i.e

Algebra, Trigonometry and Geometry. High Metacognitive skills are required to get

Mathematical Achievement in Algebra. Both High Self Regulated Learning & High

Metacognitive skills are significant to get Mathematical Achievement in Algebra and

Geometry

Key words- self-regulated learning Metacognitive skills, Mathematics Achievement

branches of Mathematics – Algebra, Trigonometry and Geometry, Senior Secondary School

Students.

Journal of Information and Computational Science

Volume 10 Issue 1 - 2020

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mailto:[email protected]

Introduction

In an era of ever-advancing science and technology, what is important in teaching is, to teach

students how to learn especially math and science. Math’s achievement at school is one of the

best predictors of success at tertiary level.. Mathematics means those quantitative techniques

which help in amplification and understanding things in order to transcend managing and

copying with the reality.

Kothari education commission (1964-1966) has wisely remarked that science and

mathematics should be taught to all pupils as a part of general education for first ten years of

schooling.[9] National policy of education (1986) has envisaged that Mathematics should be

visualized as the mode of communication, to train a child to think, to reason, to articulate and

to analyze logically[13]. National Council of teachers of Mathematics (NCTM) (2000)

recommended that new ideas strategies and research findings in mathematics should be

utilized in teaching in order to help students overcome their difficulties in learning

mathematics[12].

Self –regulated Leaning is a classroom management technique that reduces teacher

responsibility of student’s behaviour and puts the responsibility on the students. Zimmerman

(1989) defined self regulated learning as a multi-dimensional process involving personal

(cognitive and emotional), contextual, and behavioural components[20].

Omrod (1999) supported that self regulation was a reliable predictor of one’s educational

performance[14]. The results indicated that self regulation was a significant predictor of one’s

academic achievement. Zumbrunn et al. (2011) conclude, "It seems as though self-regulated

learning can make the difference between academic success and failure for many

students[21]." Vander Stoep et al., 1996 claim that self-regulated learning intertwines cognitive

strategies, metacognitive strategies, and motivational beliefs[18].

Metacognition is "cognition about cognition", "thinking about thinking", "knowing about

knowing", becoming "aware of one's awareness" and higher-order thinking skills. Leahey and

Harries (1997) defined that Metacognition is the knowledge, awareness and monitoring of

one’s own cognition[11].Brown (1978) defined that regulatory activities associated with

solving problems are calls metacognitive skills[2].

Efklides (2002) introduces

another aspect of it, one that serves the control of cognition, namely,

metacognitive skills. Since the components of metacognition serve the

monitoring rather than the control of cognition (Brown, 1978), one could refer

to this new aspect of metacognition as one which serves the control of

cognition






cognition




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cognition.






cognition.

SRL has become one of the most important research areas in educational psychology, and

many researchers proposed their theoretical model for the general learning.Extensive

number of studies has been conducted in education, which demonstrates that self –regulated

learning can enhance student’s academic achievement and facilitate learning motivation. self

regulated learning is the integration of “will “ and “skill” “will” refers to the learner’s goal

,values and expectation ands “skills “refers to the learners use of different strategies of

cognition, Metacognitive skills . So, metacognitive skills play a central role in learning and

achievement .Metacognitive skills are powerful tools for any discipline, inter discipline or

for learning in general maths play an important role in daily life .Students mathematics

achievement in secondary school have influential effect on their performances and future

carriers .Therefore, the present study will be formulated keeping in views the study of self

regulated learning and metacognitive skills to mathematics achievement in students. .

Because of the importance of mathematical education around the world, the present research

chose the mathematics subject to explore how aspects in SRL influenced the mathematics

performance.

The present study serves as a baseline study for students to identify the mathematics

Achievement of senior secondary school students in relation to their metacognitive skills and

self-regulated learning.

Methodology

Objectives

The study was design to attain the following objectives:

To study the mathematical achievement of senior secondary school students.

To study the mathematical achievement of senior secondary school students in relation

to self-regulated learning.

To study the mathematical achievement of senior secondary school students in relation

to Meta-cognitive skills.

Hypotheses

H1: There exists no significant difference in mathematical achievement of senior secondary

school students in relation to high Self Regulated Learning and low Self Regulated Learning.



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H2: There exists no significant difference in mathematical achievement of senior secondary

school students in relation to high Metacognitive Skills and low Metacognitive Skills.

H3: There exists no significant interaction effect between Self Regulated Learning and

metacognitive skills of senior secondary school students on the score of Mathematical

Achievement.

H4: There exists no significance difference in Mathematical Achievement of various branches

of mathematics (Algebra,Geometery&Trignometery) in relation to High, Average and Low Self

Regulated Learning of senior secondary school students.

H5: There exists no significance difference in Mathematical Achievement of various branches

of mathematics (Algebra, Geometery&Trignometery) in relation to High, Average and Low

Metacognitive Skills of senior secondary school students.

H6: There is no significant interaction effect between Self Regulated Learning and

Metacognitive Skills of senior secondary schoo students on the score of Mathematical

Achievement in various branches of mathematics(Algebra,Geometery&Trignometery).

Research design:

The investigator was used survey method for studying the problem. Quantitative approach is

applied in this study. Furthermore, quantitative research is about identifying relationships

between variables through the use of data collection and analysis.

Sample

In order to conduct the present study, 10 private schools from Jalandhar district were selected.

For their selection sample random technique was employed. Out of the selected schools,

investigation was carried out on 300 students of private & Government schools.

Design of the study

To test the proposed hypotheses the design of the present study was as follow:

Two way analysis of variance (ANNOVA) was employed on the score of Mathematics

Achievement and branches of mathematics (Algebra, Geometry& Trigonometry).Mathematics

Achievement and branches of Mathematics (Algebra ,Geometry& Trigonometry was dependent

variable. Self Regulated Learning (SRL) and Meta-cognitive skills (MCS) for classifying the

students viz-a-viz High self regulated (HSR) ,Low self regulated (LSR),High Metacognitive

Skills(HMC) ,Low meta cognitive (LMC) will be studied as independent variables.

Measures

The three instruments were used to collect data from the respondents. They include

TOOL-I: MATHEMATICAL ACHIEVEMENT SCALE CONSTRUCTED BY THE

INVESTIGATOR:

In order to develop Mathematical Achievement Scale following steps were followed:

Step 1:- Planning

Mathematics achievement test was prepared keeping in view the universality of the various

fields – Algebra, Trigonometry and Geometry. Also the investigator herself checked the

problems, conceptual questions and reasoning questions solved by the students. So by thorough

checking of the errors committed by students in the selected fields and discussion with the



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teachers, the investigator was able to collect relevant information about the types of errors

committed by the students in the selected field.

After identification of students deficiencies few topic from the ―Central board of secondary

school syllabus of class 11th and 12th mathematics subject were analyzed where Meta cognitive

skills and self regulated learning are mostly used. The investigator consulted the syllabus of

mathematics subject prescribed for class 11th and 12th and selected few topics from algebra,

trigonometry and geometry. In algebra selected topics were Principal of mathematical

induction, Polynomials, Linear equation, inequalities, Exponent and square roots, Geometric

measurement& Quadratic equation. In Geometry selected topics were Points, Lines ,Planes ,

Angles ,Proofs, Triangles, Similarity, Quadrilaterals, Circles and Areas of different geometrical

figures. In Trigonometry selected topics were Sine ,Cosine and Tangents, Congruent and

Similar, Trigonometry functions and ratios, Trigonometry identities, Trigonometric ratios of

specific angles, Inverse trigonometric ratios.

Step:-2 Designing and Construction

The analysis of the content was done. Then the test items were written according to specific

objectives. In total 120 questions were selected. The questions were carefully written. The

mathematical achievement test thus, constructed was checked by the supervisor, with little

modification in the language of test items.

Step:-3 Preparation of Preliminary Draft Of Test

Originally a comprehensive test was prepared including the different types of questions as

indicated by the subject teachers to be problematic. This test consisted of 120 items involving

the following three major fields

The test comprised of objective type items, short answer type, extended response questions, fill

in the blanks and true/false. The preliminary draft of the test was given to randomly select 300

students of XI and XII class. The purpose of the preliminary draft of the test was to find out

very easy and very difficult items and also to examine the functioning of the item and

distracters of multiple choice items.

Step:-4 Preparation of Final Draft

A careful scrutiny was made for the functioning of various distracters; Dead distracters were

modified and replaced with more appealing and new ones. The final test comprised of 90 items.

While eliminating any item, care was taken that no basic concept is eliminated from the final

draft of the test. The items of the final draft were distributed in the same manner as the

preliminary draft. The comparative picture of the number of items selected in first draft and the

final form of the test is being reported in table 1.2

Table 1.2

The distribution of the items in the final draft

Preliminary Draft 40 40 40

Final Draft 30 30 30

For determining the reliability the test was administered to 300 students of 11th and 12th class.

The present test has content validity and test presented in fairly manner. In total 90 items were

selected. 50 marks were distributed to different questions in each field i.e. 1 mark and 2 marks

depending upon the difficulty level of the items



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Self-Regulated Learning Questionnaire: (Dr. Madhu Gupta and Ms. Dimple Mehtani,

2017).

It has 65 items with six dimensions. Scale was done by giving a score 5, 4, 3, 2 or 1 and for

negative items 1,2,3,4 &5.The total score of an individual respondent varied from 48 to 240

showing extremely high level of self-regulated learning to extremely low level of self-regulated

learning. It has Test-Retest Reliability .The coefficient of correlation got was 0.982, which is

significant at 0.1 level of significance. Construct validity of the scale has also been measured

Meta-Cognition Inventory (PROF. DR. MADHU GUPTA AND MS.SUMAN)

This Meta cognitive skills scale is designed to assess Meta cognitive skills of secondary &

Senior Secondary School students and under graduation college students. To obtain a desired

level of learning it is necessary to improve Meta cognitive skills which control once on

learning process. The final form of a scale compressed of 42 items in all based on four

different dimensions of Meta cognitive skills i.e. planning skill, implementation skill

monitoring skill and evaluation skill. Likert Type 5 point scale was used for scoring.

Reliability of the scale has been measured by test retest method and split half method by

administering the scale on a sample of hundred students. The coefficient of correlation

through test-retest method was 0.76 3. Split half reliability was found 0.949 which has been

made by Spearman- Brown prophecy formula. The validity of Meta cognitive scales was

calculated on the basis of face validity and content validity. To assess the face validity the

maces scales was presented to 15 experts for their opinions. Content validity was of primary

importance for this scale where issues of overlap between items were addressed by experts

and also system relevancy of the items to the category to which they belong. Intel

Correlations among different dimensions of a scale have been found to be a significantly high

through Pearson product moment correlation.

Procedure

In order to conduct the study, 10 secondary schools of Jalandhar city were selected. A,

sample of about 300 students from 12th class were selected. Meta cognitive style inventory

was administrated on selected students. Further the selected sample was segregated under two

categories viz-a-viz High Meta-cognitive skills and Low Meta-cognitive skills. Again self-

regulated learning scale was administered on the segregated students under two categories viz

a-viz High self-regulated learning and Low self-regulated learning. The Mathematical

Achievement Scale was administered. The score of Mathematics Achievement & its various

fields – Algebra, Trigonometry and Geometry of these groups were taken. Further the data

was given statistical treatment.

Statistical technique: The data was analyzed using two ways analysis of variance to find out

the significant differences between groups. Mean and standard deviation of various subgroups

was computed to understand the nature of data

The Data Obtained has been analyzed under the following headings:

Results and discussion

The data Obtained has been analyzed under the following headings:

Self-efficacy in relation to their self-regulated learning and metacognition



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The Mean and standard deviation of Sub Groups of 2x2 Factorial Design on the Score of

Mathematical Achievement have been calculated and presented below in Table 1

Table 1:

Means & Standard Deviation Of Sub Groups Of Anova Of 2x2 Factorial Design On The

Score Of Mathematical Achievement.

MCS

SRL LOW AVERAGE HIGH TOTAL

LSRL

N=20

M=86.35

S.D=7.492

N=46

M=85.87

S.D=8.609

N=21

M=89.57

S.D =8.213

N=87

M=86.87

S.D=8.322

ASRL

N=29

M=83.66

S.D=12.602

N=49

M=85.57

S.D=9.298

N=52

M=88.21

S.D=9.752

N=130

M=86.20

S.D=10.367

HSRL

N=32

M=85.38

S.D=7.170

N=42

M=85.87

S.D=8.268

N=9

M=88.20

S.D=9.103

N=83

M=86.27

S.D=7.871

TSRL

N=81

M=85.00

S.D=9.487

N=137

M=85.87

S.D=8.702

N=82

M=88.20

S.D=9.297

N=300

M=86.27

S.D=9.136

In Order to analyze the variable, the obtained scores were subjected to Anova. The Results

have been presented in Table 2

Table 2

Summary of Anova of 2x2 Factorial Designs on the Score of Mathematical

Achievement.

Sources Sum of squares df Mean square F

SRL(A) 1130.511 2 565.2555 6.788**

MCS(B) 583.664 2 291.832 3.50*

Interaction(AXB) 1182.125 4 295.531 3.54*

Within 24257.595 291 83.359

Total 27153.895 300

** Significant at .01 level of confidence

* Significant at .05 Level of Confidence

MAIN EFFECT

Self-Regulated Learning (A)

From the results inserted in the table 2 revealed that the variance ratio or F is 6.78 the

degree of Freedom between means is 2 and among groups is 291. Entering table F with these

degree of Freedom, It may be observed that F of magnitude 6.78> 4.71 at .01 level of

confidence. So F-ratio for the difference in the means of Mathematical Achievement with

three groups of Self Regulated Learning (High, Average & Low Self Regulated) was found to



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be significant at .01 level of confidence. Hence, the data provide sufficient evidence to reject

the hypothesis H1 namely. “There exists no significant difference in Mathematical

Achievement of senior secondary school students in relation to High, Average & Low Self

Regulated Learning.

Further the mean table 4.1 revealed that students having High Self Regulated Learning has

High Mathematical Achievement as compare to Average & Low Self Regulated Learning and

students having Low Self Regulated Learning has Low Mathematical Achievement as

compare to High and Average Self Regulated Learning.

The results are in tune with the findings of:

Boekaerts, M. (1995). found that students’ mathematics scores would increase once the

students were taught using a Self-Regulated Learning structure. The research indicated that

when using Self-Regulated Learning procedures, students’ scores in school would improve.

However, study showed a positive effect of Self-Regulated Learning on mathematic

Achievement[1].

Kistner, Saskia & Rakoczy, Katrin & Otto, Barbara & Dignath, Charlotte & Büttner, Gerhard

& Klieme, Eckhard. (2010) investigates teachers’ direct and indirect promotion of self-

regulated learning and its relation to the development of students’ mathamatics

performance. Tha results revealed thtaThe instruction of organisation strategies and some

features of the learning environment (constructivism, transfer) relate positively to students’

performance development. In contrast to implicit strategy instruction, explicit strategy

instruction was associated with a gain in performance[8].

Tavakolizadeh (2012) found that Self-Regulated Learning strategies have a positive effect on

psychological well being condition of the students and Mathematical Achievement[16].

Metacognitive Skills (B)

From the results inserted in the table 2 revealed that the variance ratio or F is 3.50. The

degree of Freedom between means is 2 and among groups are 291. Entering table F with

these degree of Freedom, It may be observed that F of magnitude 3.50>3.04 at .05 level

confidence .So F-ratio for the difference means of Mathematical Achievement with three

groups of Metacognitive skills(High, Average & Low Metacognitive skills) was significant

at .05 level of confidence. Hence, the data provide sufficient evidence to reject the hypothesis

H2 namely. “There exists no significant difference in Mathematical Achievement of

secondary school students in relation to their High, Average and Low Metacognitive skills.

Further the mean table 1 revealed that students having High Metacognitive skills has High

Mathematical Achievement as compare to Average & Low Metacognitive skills and students

having Low Metacognitive skills has Low Mathematical Achievement as compare to High

and Average Metacognitive skills .


Flavell (1976) considered metacognitive skills as a very powerful predictor of learning

performance in mathematics[6].



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Two Order Interaction (A×B)

From the results inserted in the table 2 revealed that the variance ratio or F is 3.54. The

degree of Freedom between means is 2 and among groups is 291. Entering table F with these

degree of freedom, it may be observed that F of magnitude 3.54>3.05 at .05 level of

confidence. So F-ratio for the interaction between Self Regulated Learning & Metacognitive

skills on the score of Mathematical Achievement found to be significant at .05 level of

confidence. Hence, the data provide sufficient evidence to reject the hypothesis H3 namely,

“There exists no significant interaction effect between Self Regulated Learning &

Metacognitive skills of senior secondary school students on the score of Mathematical

Achievement.

Further the examination of Mean table 1 revealed that.

The mean score of Mathematical Achievement of Low Self Regulated Learning and

High Metacognitive skills is lower than High Self Regulated Learning and High

Metacognitive skills.

The mean score of Mathematical Achievement of High Self Regulated Learning with

Low Metacognitive skills is lower than High Self Regulated Learning and High


The mean score of Mathematical Achievement of High Metacognitive skills with

High Self Regulated Learning is higher than Low Metacognitive skills and Low Self-

Regulated Learning.

The mean score of Mathematical Achievement of High Metacognition with Low Self-

Regulated Learning is higher than Low Self-Regulated Learning and Low


The same has been depicted through graph in Fig. 1

Fig. 1: 2x2 Interaction Graph on the Score of Mathematical Achievement in

Relation to Self Regulated Learning and Metacognitive Skills.

.

80

81

82

83

84

85

86

87

88

89

90

91

HIGH AVERAGE LOW

Me

an S

core

s

Self Regulated Learning

HMCS

AMCS

LMCS



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Tian, Y., Fang, Y., & Li, J. (2018). results suggested that the mathematics performance could

be predicted by MK, self-efficacy and intrinsic motivation The findings highlight the

psychological mechanism in the mathematics of Chinese students and will help teachers to

improve students’ mathematical learning in SRL framework more effectively. Implications

for education and further studies are discussed[17].

Dornyei (2005) found that Self regulation in the academic contexts entails a

“multidimensional construct, including cognitive, Metacognitive, motivational, behavioural

and environmental processes that learns can apply to enhance mathematics Achievement.

Branches of Mathematical Achievement in relation to Self Regulated Learning and

Metacognitive skills[3].

Various Branches of Mathematical Achievement, Self Regulated Learning and

Metacognitive Skills

Table 3

2x2 Analysis of Variance on the Score of Various Branches of Mathematics in Relation

To Self Regulated Learning and Metacognitive Skills

HMCS LMCS TOTAL

B(I)

ALGEBRA

HSRL

N=9

M=26.33

S.D=5.937

N=32

M=28.34

S.D=5.084

N=41

M=27.90

S.D=5.272

LSRL

N=21

M=30.76

S.D=4.158

N=20

M=29.40

S.D=4.185

N=41

M=30.10

S.D=4.176

TOTAL

N=30

M=29.43

S.D=5.090

N=52

M=28.75

S.D=4.744

N=82

M=29.00

S.D=4.853

B(II)

TRIGNOMETRY

HSRL

N=9

M=30.00

S.D=3.500

N=32

M=29.19

S.D=4.351

N=41

M=29.37

S.D=4.152

LSRL

N=21

M=27.62

S.D=5.015

N=20

M-28.70

S.D=5.440

N=41

M=5.181

S.D=27.17

TOTAL

N=30

M=28.33

S.D=4.686

N=52

M=28.23

S.D=4.901

N=82

M=28.00

S.D=4.795

B(III)

GEOMETRY

HSRL

N=9

M=28.56

S.D=4.876

N=32

M=27.84

S.D=4.104

N=41

M=28.00

S.D=4.231

LSRL

N=21

M=31.19

S.D=3.140

N=20

M-30.25

S.D=3.823

N=41

M=30.73

S.D=3.479



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TOTAL

N=30

M=30.40

S.D=3.856

N=52

M=28.77

S.D=4.133

N=82

M=29.37

S.D=4.087

In order to analyse the variables the obtained scores were subjected to Anova. The results

have been presented in table 4

Table 4

Summary of Anova for 2×2 Factorial Designs of the Scores on the Various Branches of

Mathematics

Branches of

Mathematics

Self

Regulated

Learning

Meta

Cognitive

skills

Interaction

AXB SSW TSS

Algebra MSS 125.357 101.753 47.390

1761.828* 70970.00 F RATIO 5.550* 4.50* 2.098

Geometry MSS 105.898 11.376 71.218

1187.429 72137.00 F RATIO 6.956* .747 4.68*

Trignometry MSS 98.766 12.494 .047

1750.027 67388.00 F RATIO 4.402* .557 .002

*Significant at .05 Level of Confidence

**Significant at .01 Level of Confidence

MAIN EFFECTS

Branches of Mathematics with Self Regulated Learning (A)

It may be observed from the Table 4 that F ratio for the difference between means of various

Branches of Mathematics viz a viz B(I) Algebra , B(II) Trigonometry , B(III) Geometry are

found to be significant at .05 level of confidence. This indicates that B (I), B (II), B (III) of

Mathematics is significantly different in relation to High Self Regulated Learning and Low

Self Regulated Learning. Thus the data provide Sufficient evidence to reject the Hypothesis

in case of B(I),B(II),B(III) namely H4,” There exists no significant difference in

Mathematical Achievement of various Branches of Mathematics in relation to High ,Average

and Low Self Regulated Learning of senior secondary school students”.

Further the examination of mean table revealed that the Mean Score of Algebra,

Trigonometry and Geometry with High Self Regulated Learning is higher than Low Self

Regulated Learning..


Veenman, Kok, & Blöte(2006) concluded that Metacognitive skills of monitoring and

evaluation facilitate students to avoid or repair errors during the math problem-solving

process, detect progression being made and compare the answer given against the problem

statement[19].



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Branches of Mathematics with Metacognitive skills (B)

It may be observed from the Table 4 That F ratio for the difference between means of various

Branches of Mathematics viz a viz B (I) Algebra are found to be significant at .05 level of

confidence. This indicates that B (I) of Mathematics are significantly different in relation to

High Metacognitive Skills and Low Metacognitive skills . Thus the data provide Sufficient

evidence to reject the Hypothesis in case of B (I) namely H5,” There exists no significant

difference in Mathematical Achievement of various branches of mathematics in relation to

High, Average and Low Metacognitive skills of Senior Secondary School students “.

Further the examination of mean table revealed that the Mean Score of Algebra with High

Metacognitive skills is higher than Low Metacognitive skills. So, High Metacognitive skills

are required for getting Mathematical Achievement in Algebra.


Eluemuno and Azuka-obieke (2013) found that there is positive relationship between meta-

cognitive skills and Mathematical Achievement in algebra of senior secondary school

students[5].

Interaction (A×B)

It may be observed from the table 4 that the interactions between Self Regulated Learning

and Metacognitive skills were found to be significant at .05 level of confidence on B (I)

Algebra, B (III) (Geometry). This indicates that B (I) (Algebra) and B (III) (Geometry) are

significantly different in relation to Self Regulated Learning and Metacognitive skills. Hence

the data provide sufficient evidence to reject the hypothesis (H6) namely,‘There exists no

significant difference interaction effect between Self Regulated Learning and Metacognitive

skills of senior secondary school students on the score of various branches of mathematics

whereas the hypothesis (H6) is not rejected in case of B(II).

Kramarski & Mevarech, (2003) investigated the effects of self-metacognitive questioning

training on Year 3 students’ (a) mathematical problem solving; (b) mathematical anxiety; and

(c) on problem solving and anxiety of mathematics of higher and lower achievers is reported.

The metacognitive training was based on to improve self-questioning method[10].

Further the examination of the corresponding means from the table 3 suggested that In

case of B(I) Algebra of Mathematics :

The Mean score of Algebra with Low Self Regulated Learning and High

Metacognitive skills is higher than Low Self Regulated Learning and Low


The Mean score of Algebra with High Self Regulated Learning and Low

Metacognitive skills is higher than High Self Regulated Learning and High


The Mean score of Algebra with High Self Regulated Learning and High





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The Mean score of Algebra with High Self Regulated Learning and Low

Metacognitive skills is Higher than Low Self Regulated Learning and High



Fig.2: 2x2 Interaction Graph on the Score of Algebra (BI) of Mathematical

Achievement in Relation to Self Regulated Learning and Metacognitive Skills.

In case of B (III) Geometry of Mathematics:

The Mean score of Geometry with Low Self Regulated Learning and High



The Mean score of Geometry with High Self Regulated Learning and Low

Metacognitive skills is higher than High Self Regulated Learning and High


The Mean score of Geometry with High Self Regulated Learning and High



The Mean score of Geometry with High Self Regulated Learning and Low

Metacognitive skills is higher than Low Self Regulated Learning and High



0

0.5

1

1.5

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Fig.3: 2x2 Interaction Graph on the Score of Geometry B (III) of Mathematical

Achievement in Relation to Self Regulated Learning and Metacognitive Skills.


Focant et al. (2006) found positive and significant relations between Self Regulated leraning

and Metacognitive skills on the one hand, and Mathematics Achievement, on the other.

They also found that most children were able to correctly specify the goals of an arithmetical

problem at the end of elementary school. On the other hand, they found that most children,

although possessing sufficient content knowledge, did not succeed in detecting their errors.

Apparently, monitoring and evaluation are more abstract Metacognitive skills and Self

Regulated Learning that arise later in the developmental trajectory[7].

Pintrich and de groot (1990) found that Self Regulated Learning conjoins three major

constructs; students Metacognitive skills for planning ,monitoring and regulation, students’s

management and control of their efforts on Mathematical Achievement and cognitive

stratergies that students used to learn, remember and understand the Mathematical

problems[15].

Finally, it was found that Self-Regulated Learning is linked to Metacognitive skills such as

planning, monitoring, evaluation and concentration.

FINDINGS OF THE STUDY

The finding of the study were

High Self Regulated Learning is necessary to achieve success in mathematics and

opportunity to communicate mathematically and to develop Self confidence to solve

Mathematical problem

High Metacognitive skills are necessary to achieve to obtain a desired level of

Learning in mathematics and control one’s own learning process.

students having good Self Regulated Learning and Metacognitive skills can focus his

or her attention on Learning unit ; make a distinction between important and

unnecessary information; use effective strategies to keep the information in long term

memory and retrieve it when necessary and easily attain Mathematics Achievement

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High Self Regulated Learning is required to improve achievement in all three

branches of mathematics i.e Algebra, Trigonometry and Geometry

High Metacognitive skills are required to get Mathematical Achievement in Algebra.

Both High Self Regulated Learning & High Metacognitive skills are required to get

Mathematical Achievement in Algebra and Geometry.

Educational Implications of the Study

Research has shown students having more metacognitive skills means, more likely to plan,

monitor, and regulate themselves and high Self regulation in classroom has more

Mathematical Achievement. An alternative explanation may be a result of students’

overestimating their capabilities resulting in higher mathematical achievement. So role of

teacher is very important to develop metacognitive skills and Self Regulated Learning.

Teacher should encourage and support students when their Self Regulated Learning

strategies have been misused or ineffective. Students who have difficulty with SRL

strategies must be provide with personal and academic support .Teacher should

always encourage their student that they can accomplish their goals when their

strategies are proven ineffective.

Teacher should also apply their metacognitive skills in anticipating questions their

students may have when introducing different types of activities, this will be better

prepared to answer and help facilitate the desired activity.

Metacognitive Skills and Self Regulated Learning help students to transfer what they

have been learnt from one context to the next, or from a previous task to a new task

when teacher provide proper knowledge of these skills.

Teacher should provide knowledge of Wrappers to student’s .Wrappers is a quick and

easy tool for monitoring and evaluating meta cognitive activity.this activity surrounds

pre –existing learning or assessment task and fosters students Metacognitive Skills

and Self Regulated Learning.

School coordinator and teachers should impart the curriculum with such kind of

pedagogies the mathematical achievement and ultimately lead to better Self Regulated

Learning.

Teacher should integrate their subjects with hearts and some brainstorming exercises

which lead to mathematical achievement to self-learning and metacognition.

Co curricular activities like sports transmission proficiency self confidence and self

attitude dimensions work on petaorganization and results in mathematical

achievement.

Lesson plans also promote mathematical achievement and outcome expectation.

So Teachers may need to incorporate learning activities in curriculum that promote

cognitive and metacognive strategies to more effectively engage the learner in the content

of the discipline. It may also be advantageous to ask if the promotion of mathematical

achievement in the curriculum detracts from integrating cognitive and metacognitive

approaches.



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References

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