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.
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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
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
Efklides (2002) introduces
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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.
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.
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 .
The results are in tune with the findings of:
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
Metacognitive skills.
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
Metacognitive skills.
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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The results are in tune with the findings of:
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..
The results are in tune with the findings of:
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.
The results are in tune with the findings of:
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
Metacognitive skills.
The Mean score of Algebra with High Self Regulated Learning and Low
Metacognitive skills is higher than High Self Regulated Learning and High
Metacognitive skills.
The Mean score of Algebra with High Self Regulated Learning and High
Metacognitive skills is higher than Low Self Regulated Learning and Low
Metacognitive skills.
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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
Metacognitive skills.
The same has been depicted through graph in Fig. 2
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
Metacognitive skills is higher than Low Self Regulated Learning and Low
Metacognitive skills.
The Mean score of Geometry with High Self Regulated Learning and Low
Metacognitive skills is higher than High Self Regulated Learning and High
Metacognitive skills.
The Mean score of Geometry with High Self Regulated Learning and High
Metacognitive skills is higher than Low Self Regulated Learning and Low
Metacognitive skills.
The Mean score of Geometry with High Self Regulated Learning and Low
Metacognitive skills is higher than Low Self Regulated Learning and High
Metacognitive skills.
The same has been depicted through graph in Fig. 3
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
HSRL LSRL
Mea
n S
core
HMCS
LMCS
Journal of Information and Computational Science
Volume 10 Issue 1 - 2020
ISSN: 1548-7741
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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.
The results are in tune with the findings of:
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
24
25
26
27
28
29
30
31
32
HSRL LSRL
Mea
n S
core
HMCS
LMCS
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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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