M A T H L I N E ISSN 2502-5872 (Print)

JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA ISSN 2622-3627 (Elektronik)

Volume 8 Number 2, May 2023, 641-660

ANALYSIS OF MATHEMATICAL REASONING ABILITY IN

TERMS OF MATHEMATICAL SELF-EFFICACY
OF MAN 2 PEKANBARU STUDENTS

Masrianti Fadillah1*, Maimunah Maimunah2, Nahor Murani Hutapea3

1,2,3
Departement of Mathematics Education, Universitas Riau, Riau Province, Indonesia

*Correspondence: masrianti.fadillah6967@grad.unri.ac.id

ABSTRACT
The mathematical reasoning ability of each student is very important to be able to make them use
reasoning in patterns and traits, and perform mathematical tricks to produce valid generalizations,
proofs, and statements. The activity of generalizing, proving, and making valid statements requires
self-confidence. Confidence is in the form of Self-Efficacy and becomes an internal factor related
to mathematical reasoning abilities. describing mathematical reasoning abilities in terms of
students' mathematical self-efficacy is the aim of this study using a descriptive qualitative
approach. Data collection techniques were questionnaires to measure students' self-efficacy, written
tests to measure students' mathematical reasoning abilities, and interviews. The research subjects
were 30 students of class XII MAN 2 Pekanbaru. The results of the study found that: (1) 26.67% of
students with high mathematical reasoning abilities were accompanied by high or moderate self-
efficacy; (2) 56.67% of students with moderate mathematical reasoning abilities are accompanied
by high, medium, or low self-efficacy; (3) 16.67% of students with low mathematical reasoning
ability are accompanied by moderate or low self-efficacy; (4) 43.33% of students can perform
calculations based on certain rules; (5) 76.67% of students can do direct proof; and (6) 75.83% of
students can provide valid arguments. It can be concluded that the level of mathematical reasoning
ability is not always on the same level as students' self-efficacy, but the best mathematical
reasoning ability is always followed by good self-efficacy. So, students' self-efficacy needs to be
increased to be able to apply better mathematical reasoning abilities.
Keywords: Analysis of Mathematical Reasoning Abilities, Student Self-Efficacy, Limits of
Algebraic Functions

How to Cite: Fadillah, M., Maimunah, M., & Hutapea, N. M. (2023). Analysis Of
Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of MAN 2
Pekanbaru Students. Mathline: Jurnal Matematika dan Pendidikan Matematika, 8(2), 641-
660. http://doi.org/10.31943/mathline.v8i2.443

PRELIMINARY
In The 2013 curriculum and the independent curriculum, it is stated that learning
mathematics aims to form students' mindsets and mathematical reasoning. Patterns of
thinking and mathematical reasoning are part of students' ability to reason. Mathematical
reasoning ability can be interpreted as the ability to think by establishing strategies and
systematic steps in solving mathematical problems and finally obtaining a valid conclusion
based on mathematical concepts that have been found when solving non-routine
mathematical problems (Umaroh et al., 2020). The Regulation of the Minister of National
Education No. 22 of 2006 also lists the goals of learning mathematics, which include
applying mathematical reasoning to patterns and properties, performing mathematical

641
642 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

operations to conclude, gather data, or defend mathematical hypotheses and assertions

(Adetia & Adirakasiwi, 2022).
Researchers' observational data and interviews with students and math teachers
revealed that students' mathematical reasoning skills could not be fully developed while
learning mathematics and that students continued to struggle or hesitate to provide sound
arguments or provide direct proof using specific formulas when responding to questions
about math that were not commonplace. In addition to mathematics' abstract character, this
challenge is brought on by students' mistrust of their mathematical prowess. Due to this
circumstance, students experience anxiety when presenting concrete evidence and strong
arguments to support their explanations for how to solve a specific math problem. Low
student self-efficacy is a result of internal issues, including the students' lack of confidence
and fear. Self-efficacy is defined as an individual's self-confidence in his inherent skills
and abilities, which have an impact on his success in the learning process. (Adetia &
Adirakasiwi, 2022). Mathematics self-efficacy, which is related to studying mathematics,
can be defined as a student's self-confidence in the mathematical skills he possesses and
has an impact on whether or not he participates successfully in the learning process.
Similar claims have been made about how students' self-efficacy can help them accomplish
their goals and become one of the factors influencing their learning outcomes in
mathematics (Rizkiah et al., 2022);(Nuraisyah & Izzati, 2020); Ririk et al., 2018).
Thus, the self-efficacy that students develop in their mathematical abilities can
impact whether they achieve the intended learning outcomes of students in the form of
success or failure in learning mathematics (Utami & Wutsqa, 2017). Self-efficacy will
have a significant influence on deciding the appropriateness and correctness of students'
reasoning (Umaroh et al., 2020). Mathematical self-efficacy also makes a positive
contribution and plays an important role in the mathematics learning achievements that can
be achieved by students (Simatupang et al., 2020). This is because one of the psychological
factors that substantially determines students' performance in completing math tasks is the
self-efficacy that students develop based on their mathematical prowess (Jatisunda, 2017).
When students have high categories of mathematical self-efficacy, they will be
more motivated to be able to achieve the goals of learning mathematics, and when facing
challenges in the form of math assignments, they will choose to survive and try (Hartati et
al., 2021). As a result of this significant influence, mathematical reasoning abilities and
students' mathematical self-efficacy have a linear relationship. It is well recognized that
each student's motivation and approach to task completion varies, and this is related to how
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 643

confident they feel about their abilities. Ningsih & Hayati (2020) argued that the
differences in self-efficacy for each student were found in three dimensions, namely: (1)
Magnitude or level of difficulty of the task. Students have different assessments and
attitudes in dealing with mathematical tasks. (2) Generality is closely related to the broad
field of behavior. Where a person feels confident in his abilities based on previous
experience, (3) strength, regarding the student's self-confidence about the extent to which
he believes he can complete the task properly and optimally.
Mathematical reasoning skills and mathematical self-efficacy appear to be closely
related, according to several earlier research. The results show that there is a positive
association between the two variables: mathematical reasoning ability increases as student
self-efficacy increases (Aprisal & Arifin, 2020). Another conclusion indicates that
students' learning outcomes in mathematics are positively correlated with their level of
self-efficacy in completing math tasks and setting math goals for developing attitudes and
reasoning is consistent with the findings (Disai et al., 2018). Mathematical self-efficacy in
students plays a significant role as one of the aspects and factors that affect the success of
learning mathematics in achieving the objectives of mathematical learning, namely the
formation of the thinking and reasoning students need to be able to apply during math
learning, sign the existence of a positive relationship produced by the ability to think
mathematically and mathematic self-efficacy.
The major goal of this study is to determine the relationship between students'
mathematical self-efficacy and their capacity for mathematical reasoning. In research
(‘Aini, 2020) it is said that students with high mathematical reasoning abilities have
moderate self-efficacy, students with moderate mathematical reasoning abilities have high
self-efficacy and students with low mathematical reasoning abilities have low self-efficacy
when tested on integer material. In this study, the authors will measure students'
mathematical reasoning abilities using algebraic limit function material and review them
with student self-efficacy accompanied by searching data through interviews at each level
of students' mathematical reasoning abilities. The interviews were aimed at knowing
students' self-efficacy verbally in giving opinions on learning mathematics and their own
perceived mathematical abilities. later the results of self-efficacy measurements and
research interviews will be able to describe students' mathematical reasoning abilities in
terms of self-efficacy compared to ability level categories and the interview results found.
644 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

METHODS
This research is descriptive qualitative research using case studies and aims to
describe students' mathematical reasoning skills in terms of their mathematical self-
efficacy. The subjects in this study were 30 students of Class XII MAN 2 Pekanbaru. Data
collection techniques in this study were carried out by testing mathematical reasoning
abilities, filling out students' mathematical self-efficacy questionnaires, and conducting
interviews with 15 students consisting of students with high, medium, and low
mathematical reasoning abilities. The first research instrument used was a mathematical
reasoning ability test sheet in which the six items had been tested to be valid and reliable,
the test results can be seen in Table 1. Instrument Prerequisite Test.
Table 1. Instrument Prerequisite Test
Validity Reliability
No. Difference Power Difficulty Level
Results Criteria Results Criteria
1 Valid Very High Very Good Difficult
2 Valid Enough Pretty Good Easy
3 Valid Enough Pretty Good Currently
Reliabel High
4 Valid High Pretty Good Currently
5 Valid Enough Good Currently
6 Valid Very High Very Good Difficult

Based on Table 1. So, all items are feasible to use and contain questions on the limits of
algebraic functions which consist of three indicators of mathematical reasoning ability,
namely: perform calculations based on certain rules or formulas; perform direct proof; and
develop valid arguments (Hendriana et al, 2017). The second instrument used in this study
was a student mathematics self-efficacy questionnaire consisting of 24 statement items, of
which there were 12 positive statement items and 12 negative statement items. The
dimensions of the students measured are (1) Magnitude with indicators of Difficult in
solving problems and Enthusiastic and trying to solve difficult problems; (2) Strength with
indicators of Convinced of having good math skills and having the hope of getting good
math results with the abilities they have; and last (3) Generalization with indicators Believe
it takes a lot of practice to get even better results and Making experience the basis for
increasing confidence (Sartika, 2019). The student mathematics self-efficacy questionnaire
used has also been tested to be valid and reliable.
The analysis was carried out in this study by analyzing the results of student
answers to mathematical reasoning ability questions about the limit of algebraic functions
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 645

using the assessment guidelines as presented in Table 2. Mathematical Reasoning

Assessment Criteria, as follows.
Table 2. Mathematical Reasoning Assessment Criteria
Skor Indicator of Mathematical Reasoning
4 Substantially correct and complete answer
3 The Answer contains one significant error or omission
2 Partly correct answers with one or more significant errors or omissions
1 Some answers are incomplete but contain at least one valid argument
0 Incorrect answer based on process or argument, or no response at all
Source: (Sulistiawati et al., 2015)

The items in the Mathematics Self-Efficacy questionnaire that students have filled in will
also be analyzed based on the scoring guidelines presented in Table 3. Criteria for Scoring
Student Mathematics Self-Efficacy, are as follows.
Table 3. Criteria for Scoring Student Mathematics Self-Efficacy
Score Positive Statement Negative Statement
4 Strongly Agree Strongly Disagree
3 Agree Disagree
2 Disagree Agree
1 Strongly Disagree Strongly Agree

The scores that students get will be summed up, compared to the total score, and
multiplied by 100 to get the final score. The final score that has been obtained and
processed will then be grouped according to the category of students' mathematical
reasoning ability or the category of students' mathematical self-efficacy, as presented in
Table 4. The Category of Students' Mathematical Reasoning Ability & Mathematical Self-
Efficacy is the following.
Table 4. The Category of Students' Mathematical Reasoning Ability
& Mathematical Self-Efficacy
Interval Category
The Final value ≥ Mean + SD High
Mean – SD ≤ The Final value < Mean + SD Medium
The Final value ≤ Mean + SD Low

Categorization of Mathematical Reasoning Ability and Mathematical Self-Efficacy

Students aim to be classified based on their level of mathematical reasoning ability and
their mathematical self-efficacy (Sartika, 2019). Thus, it will be seen how the level of
students' mathematical reasoning abilities relates to their mathematical self-efficacy.
To complete this research, the last data collection technique to support the results of
this research conducted by the author is to conduct interviews with students regarding their
views on mathematics learning and mathematics self-efficacy that they feel according to
646 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

their own experiences and perceptions. Relevant research will also be published along with
the results of the analysis that the author found to provide a clear description related to the
analysis of students' mathematical reasoning abilities in terms of their mathematical self-
efficacy.

RESULT AND DISCUSSION

Based on the results of students' answers to 6 items of mathematical reasoning
ability on the limited material of algebraic functions given, it is known that students have
diverse mathematical reasoning abilities, which are presented in Table 5. The Results of
the Mathematical Reasoning Ability Analysis are below.
Table 5. Results of Mathematical Reasoning Ability Analysis
Interval Frequency Percentage Category
The Final value ≥ or = 81.67 8 26.67% High
48.89 ≤ The Final value < 81.69 17 56.67% Medium
The Final value < 48.89 5 16.67% Low

In the data presented in Table 5, the results of the mathematical reasoning ability analysis
related to the limited problem of algebraic functions show that the test was given to 30
students of class XII MAN 2 Pekanbaru. The results of the mathematical reasoning ability
test classify students in the high, medium, or low category of mathematical reasoning
ability. It was found that the majority of the mathematical reasoning ability of Class XII
MAN 2 Pekanbaru students was in the category of moderate mathematical reasoning
ability, consisting of 17 students with a percentage of 56.67%. 8 out of 30 students, or
26.67%, have mathematical reasoning skills in the high category, and 5 students, or
16.67%, have low mathematical reasoning skills. The results of the analysis based on the
mathematical reasoning indicators contained in the mathematical reasoning ability test
instrument using algebraic function limit questions are presented in Figure 1. The results of
the analysis of Mathematical Reasoning Ability Indicators are as follows.
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 647

Percentage Diagram of Students' Mathematical Reasoning Ability

Indicator
Perform calculations based
43.33% on certain rules or formulas
75.83%
Perform direct proof

76.67% Develop valid arguments

Figure 1. The Results Of The Analysis Of Mathematical Reasoning Ability

Indicators
Based on Figure 1. Analysis Results of Mathematical Reasoning Ability Indicators,
it is known that the indicator of carrying out mathematical calculations based on certain
rules or formulas has a percentage of 43.33%. This percentage is the lowest indicator
percentage of the other 2 indicators of mathematical reasoning ability, namely that students
can do proof and compile valid arguments. These results conclude that most students still
have difficulty solving limit problems of algebraic functions related to calculations using
certain formulas or rules, so the popular score in this category is 0, which means that the
answers students present are empty or not filled in at all.
In the second indicator based on Figure 1. Results of Analysis of Mathematical
Reasoning Ability Indicators, namely carrying out direct proof, it is found that 76.77% of
students have succeeded in carrying out direct proof. Especially in question number 2,
most students got a perfect score of 4. In this second indicator, it can be said that many
students are skilled in mathematical reasoning ability to do direct proof related to the limit
problem of algebraic functions. The direct proof that students do is shown through the
presentation of graphs, derivation of formulas, and comparing one rule with other
mathematical rules to get a final mathematical decision.
As for the third indicator, it was found that 75.83% of students had also succeeded
in composing valid arguments. However, in the two questions containing the indicator of
constructing valid arguments, most students only got a score of 3 and did not achieve a
perfect score. This means that all students have difficulty being able to compile valid
arguments correctly without making the slightest mistake.
In Figure 1. The results of the Analysis of Mathematical Reasoning Ability
Indicators presented when viewed from the percentage of scores obtained by students as a
whole have a percentage score from lowest to highest of 17.8% for score 0, 3.9% for score
1, 8.3% for score 2, 39.4% for score 3, and 30.6% for score 4. The results of such data
648 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

explain that there are still many students who find it difficult when applying mathematical
reasoning skills, especially in indicators of performing mathematical calculations using
certain rules or formulas, and some students still have obstacles to carrying out proof
directly or in proposing a valid argument to draw a final mathematical conclusion. The
difficulties interpreted by students are, of course, different for each indicator of
mathematical reasoning ability. The results of the analysis of the application of indicators
of students' mathematical reasoning ability can be analyzed from the way students answer
mathematical reasoning ability questions on the material of limit algebraic functions in
difficult and easy categories presented in the following figures.

English Version:

Figure 2. Answers of Students with High Reasoning Ability on Difficult Problems

In Figure 2. Answers of Students with High Mathematical Reasoning Ability on

Difficult Problems, it can be seen that students with high mathematical reasoning abilities
try to answer the questions by providing valid arguments accompanied by direct evidence.
Direct proof is given in order to gain confidence in the correctness of the answers given by
students and shows that they are right in solving problems. Based on the results of the
interviews, it is known that students are trying to analyze the meaning of the problem and
solve it using the knowledge they have previously found, even though the problem is a
difficult limit of an algebraic function.
The results of the answers of students with moderate mathematical reasoning
ability on difficult problems are presented in Figure 3. below.
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 649

English Version:

Figure 3. Answers Moderate Reasoning Ability on Difficult Problems

Figure 3. Answers of Students with Moderate Mathematical Reasoning Ability on Difficult

Questions demonstrate how students who are capable of using mathematics to reason are
attempting to respond to the limit of algebraic functions given by using the knowledge and
understanding they have acquired along with an underlying justification. The student
answers presented also do not provide direct evidence that underlies their argument. In
student answers, there are also streaks in several parts, which can be interpreted as a form
of student doubt in answering the given limit of algebraic functions. The doubts felt by the
students were justified by the students themselves based on the interview results. In the
interview, students with moderate mathematical reasoning ability stated that they had
difficulty in stating some answers to the limit problem of algebraic functions due to
uncertainty about the formula or argument they gave. The difficulty of proving directly the
answer to the limit problem of algebraic functions is also based on the level of difficulty
presented by the problem. This makes students unsure of their mathematical abilities and
think they need to hone their mathematical skills again by practicing many problems. The
difficulty level of the problem fortunately does not make students with moderate
mathematical reasoning ability give up, most of them argue that such problems require
them to think harder and should not be left blank but must be answered based on their
abilities and analysis that they can do.
Students who have low mathematical reasoning ability also have characteristics in
solving mathematical reasoning problems regarding the given algebraic function limit
material. The following are presented the answers of students with low mathematical
reasoning ability in answering difficult questions as in Figure 4.
650 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

English Version:

Figure 4. Answers of Students with Low Reasoning Ability on Difficult Problems

Based on Figure 4. Answers of Students with Low Mathematical Reasoning Ability on

Difficult Problems. It can be seen that students answer as best they can. Students with low
mathematical reasoning do not try to find the right or best solution using direct proof or by
providing valid arguments supported by certain formulas so that the answers they give are
acceptable. Some answers from students with low mathematical reasoning ability also look
empty or deliberately ignore difficult problems related to the limited material of algebraic
functions. Based on the results of the interview, it is known that the reason students
deliberately leave blank answers is because of the difficulty of the problems given and
their ignorance of how to answer them, such as formulas or how to solve them. The
students also feel too dizzy to think about the solution, even though there is still working
time provided. In the end, students with low mathematical reasoning ability only fill in the
answers to difficult problems in a makeshift manner, seem haphazard, or choose not to
work on them at all. It is evident that in the difficult problem of the limit of algebraic
functions presented, many students' answer sheets are filled in blank and only present the
numbering of the problem without containing any mathematical problem-solving.

English Version:

Figure 5. Answers with High Mathematical Reasoning Ability on Easy Problems

 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 651

Analyzing Figure 5. Student Answers with High Mathematical Reasoning Ability on Easy
Problems concludes that students whose mathematical reasoning ability is high when
answering easy questions are correct and get a score of 4. Students whose mathematical
reasoning ability is high in answering easy questions are carried out by fulfilling each
indicator of mathematical reasoning ability, namely performing calculations with certain
formula rules, in this case, the limit of algebraic functions, and providing valid arguments
accompanied by direct proof. No problems or obstacles were felt when determining how to
solve this easy algebraic function limit problem by students with high mathematical
reasoning ability. The results of observations and interviews also found that students were
confident in the answers they gave and had no problem explaining the origin of the answer
to reach a valid conclusion.

English Version:

Figure 6. Answers of Students with Moderate Reasoning Ability on Easy Problems

Analyzing the results of students' answers with moderate mathematical reasoning

abilities on easy questions as presented in Figure 6. shows that the answers given by
students are not much different from those given by students who have high mathematical
reasoning ability. Students with moderate mathematical reasoning ability have also been
able to perform calculations with certain formula rules, in this case, the limit of algebraic
functions, and provide valid arguments accompanied by direct proof. It's just that in this
answer, students tend to skip some calculation steps or jump over the operation stages. The
interview results also found that students with moderate mathematical reasoning ability did
not find obstacles in solving easy algebraic function limit problems. After understanding
652 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

the meaning of the question, they can immediately answer it by first linking it to the
knowledge they have regarding the limit of algebraic functions.
English Version:

Figure 7. Answers of Students with Low Reasoning Ability on Easy Problems

The results of the answers of students with low category mathematical reasoning ability on
easy questions with limited algebraic function material and presented in Figure 7. obtained
a score of 1. This is because the arguments given by students are not valid and students are
wrong in using certain formulas or rules for the limit of algebraic functions. These errors
make it difficult for students with low mathematical reasoning ability to provide direct
proof. This difficulty is felt by students with low mathematical reasoning ability because of
the concept of limit that they have not understood and the many limit rules that make them
dizzy and lazy to think about it. The interview results also found student's statements in the
form of their dislike for mathematics because of things like this, namely the answers they
gave were always wrong.
The results of the analysis of student's answers to the limit problem of algebraic
functions to measure students' mathematical reasoning skills can be concluded that
students' mathematical reasoning skills still experience obstacles and difficulties in
realizing them. The obstacles and difficulties experienced by students include the level of
difficulty of the problem, the inability to answer by finding the right formula, doubts in
providing valid arguments, and not being able to do direct proof. Difficult problems have
the effect of different attitudes displayed by students, namely being enthusiastic or giving
up to work on and find solutions to their mathematical problems. Doubts in providing valid
arguments relate to students' lack of confidence in their mathematical abilities. This
uncertainty makes some students ignore difficult problems in the limit of mathematical
algebraic functions and get low results. Students' doubts in answering, lack of effort to
solve problems, and ignoring difficult problems are internal factors that affect students'
mathematical reasoning skills regarding students' mathematical Self-Efficacy. Based on the
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 653

Self-Efficacy questionnaire items that students have answered, the following results are
obtained.
Table 6. Results Of Self-Efficacy Analysis Of Students' Mathematics
Interval Frequency Percentage Category
The Final value ≥ 77.44 5 16.67% High
59.25 ≤ The Final value < 77.44 19 63.33% Sedang
The Final value < 59.25 6 20% Low

Based on Table 6. Results of Student Self-Efficacy Analysis can be seen that only
16.67% or 5 out of 30 students have high mathematics selfefficacy. The rest, 63.33% or
19 students have moderate math Self-Efficacy, and 20% or 6 students have low math Self-
Efficacy. In simple terms, it can be concluded that the majority of students in class XII
MAN 2 Pekanbaru have a moderate level of mathematics Self-Efficacy. The results of the
analysis of students' mathematics Self-Efficacy indicators are presented in Table 7.
Table 7. Results of Analysis of Students' Mathematics Self-Efficacy Indicators
Dimensions Indicators Percentage Average
Difficult in solving problems 45%
Magnitude Enthusiastic and trying to solve difficult 50.84%
56.67%
problems
Convinced of having good math skills 39.17%
Strength have the hope of getting good math results 44.17%
49.17%
with the abilities they have
Believe it takes a lot of practice to get even
63.33%
better results
Generalization 62.08%
Making experience the basis for increasing
60.83%
confidence

Based on Table 7. Results of the Analysis of Student's Mathematical Self-Efficacy

Indicators found that the Magnitude dimension has a percentage of 45% related to students'
recognition of the difficulty in doing math tasks, and 56.67% of students will be
enthusiastic and think hard in solving difficult or easy math tasks. The average for the
Magnitude dimension is 50.84%. In the Strength dimension, 39.17% of students believe
they have good enough math skills and 49.17% of students have hopes that their math
skills will make them able to solve math problems even better, so the average in the
strength dimension is 44.17%. In the Generalization dimension, it was found that 63.33%
of students believed that they would get better results when they often practiced and
studied harder, and 60.83% of students believed that the practice and study they had done
so far helped improve their mathematics skills.
However, based on interviews, there were also comments from students who felt
that they were not good at math at all, so whether they studied or not they would have the
654 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

same low results. Their attitude toward learning mathematics as a result exhibits hesitation,
discontent, and laziness. This statement was also confirmed by the mathematics teacher
who taught them. This statement is in contrast to students who are known to be smart and
are recognized by mathematics teachers as having good mathematical abilities; namely,
learning mathematics that they do at school and practicing it at home will help them
improve their math skills. Even these students are not afraid to present themselves and
confidently give the mathematical solution proposed by the teacher. They also do not
hesitate to discuss difficulties and obstacles during mathematics learning with the
mathematics teacher so that they can understand learning better.
Thus, it can be realized that students' mathematical self-efficacy affects how they
behave and act when faced with math problems and how they generate and optimize their
mathematical abilities, including exploring their reasoning power. Analyzing students'
mathematical reasoning abilities and reviewing them with students' mathematical self-
efficacy found a comparison as presented in Table 8. Analysis of criteria for mathematical
reasoning abilities and students' mathematical self-efficacy. The following.
Table 8. Analysis of criteria for mathematical reasoning abilities and self-efficacy
Mathematical Reasoning Ability Self-Efficacy Frequency Total
High 3
High 8
Medium 5
High 2
Medium Medium 13 17
Low 2
Medium 1
Low 5
Low 4
Total 30 Students

In Table 8. Analysis of Criteria for Mathematical Reasoning Ability and Students'

Mathematical Self-Efficacy, it can be seen that students with high mathematical reasoning
abilities totaled 8 students, with 3 students having high category mathematical self-efficacy
and 5 students having moderate mathematical self-efficacy. Another result is that students
with high mathematical reasoning abilities do not have low mathematical self-efficacy.
This is because students' high mathematical reasoning abilities give them good confidence
in their mathematical abilities. So the mathematical self-efficacy possessed by students
with high mathematical reasoning abilities gives birth to motivation, tenacity, persistence,
and an attitude of never giving up on solving math problems. This statement is justified by
(AR, et al., 2022) who have shown that studying student self-efficacy is essential,
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 655

particularly while learning mathematics, to prevent pupils from ignoring issues they
perceive to be difficult.
Table 8. Analysis of Criteria for Mathematical Reasoning Ability and Student Self-
Efficacy also presents that of the 17 students with medium mathematical reasoning
abilities, 2 have high mathematical self-efficacy, 13 are in the medium category, and 2 are
in a low category. In simple terms, it can be concluded that 17 Students with medium
mathematical reasoning skills often have medium mathematical self-efficacy. This
concludes that the student's mathematical reasoning abilities that they display are in tune
with the mathematical self-efficacy they have. In other words, students with medium
mathematical ability to reasoning perpetually struggle and needed to develop their
mathematical reasoning skills so that they no longer experience doubts or worries while
completing some mathematical activities that need high-level thinking.
As for analyzing the mathematical reasoning abilities of low-category students by
reviewing students' mathematical self-efficacy from Table 8. Analysis of Criteria for
Mathematical Reasoning Ability and Students' Mathematical Self-Efficacy found that 5
students had mathematical reasoning abilities in the low category, including having
moderate mathematical self-efficacy as much as 1 student and having low category
mathematics self-efficacy for 4 people. It can be concluded that students with low
mathematical reasoning abilities also tend to have low mathematical self-efficacy. This
creates fear in students and lowers their self-confidence when facing problems related to
mathematics (Tatiriah et al., 2017). Therefore, it is not surprising to hear that some
students continue to avoid and even seem to ignore learning mathematics. They lack the
desire and enthusiasm to learn mathematics as a result of their low mathematical reasoning
abilities. Because their self-efficacy is also low, students do not take advantage of the
teacher's help, namely asking the teacher when they have difficulty learning mathematics.
They feel it won't help either because their math results are still low. Consequently, some
of these children decide to do their homework by surfing the internet or copying the results
of their peers.
Analyzing students' mathematical reasoning abilities and reviewing students'
mathematical self-efficacy shows that each student's mathematical reasoning abilities
produce and are built with different mathematical self-efficacy. As it is known, students
with high reasoning abilities have high or moderate mathematical self-efficacy. Students
with moderate mathematical reasoning abilities have high, medium, or low categories of
mathematical self-efficacy. As for students who have low-category mathematical reasoning
656 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

abilities, they have moderate or low-category mathematical self-efficacy. This means that
not all students who have high mathematical reasoning abilities also have high
mathematical self-efficacy, as found by other researchers. Therefore, mathematical self-
efficacy is not always a reference for the level of mathematical reasoning ability because
there are students who have low mathematical self-efficacy but have good mathematical
reasoning abilities (Nurussalamah & Marlina, 2022).
Based on the previous statement, mathematical self-efficacy is not always a
reference for concluding the level of mathematical reasoning ability, but mathematical self-
efficacy still influences the level of students' mathematical reasoning ability. The effect is
that it can raise and train students' mathematical reasoning abilities. This influence is felt in
how students behave and try to overcome difficult situations, such as math assignments
(Zakiyah et al., 2018). For students with high categories of Self-efficacy mathematics will
result in the emergence of self-confidence in the abilities that exist within them to be able
to do something to achieve success. In contrast, students with low math self-efficacy will
have the perception that they are not able to do all the tasks that exist during the process of
learning mathematics (Monika & Adman, 2017). The proof is that students with high
mathematical self-efficacy are in the high category or have good learning outcomes and
mathematical reasoning abilities. This is because students who can optimize self-efficacy
in themselves will try more optimally to deal with difficulties when learning mathematics,
which requires a lot of effort, perseverance, and calmness to complete the task (‘Aini,
2020).
Students who have high Self-Efficacy will better prepare themselves to study well
to obtain good learning outcomes as well (Wahdaniah et al., 2017). When compared to
students with low self-efficacy, who have comprehension difficulties or cannot find the
proper formula for mathematical modeling, students with high self-efficacy are better able
to comprehend problems thoroughly and plan and apply problem-solving strategies
effectively (Imaroh et al., 2021). Thus, one of the elements that have a significant impact
on math behavior is mathematics self-efficacy. This behavior affects students' perspectives
on studying mathematics and develops their mathematical skills (Auliya & Munasiah,
2016). It is not unexpected that kids who have high levels of self-efficacy also have high
levels of confidence in their aptitude for mathematics. This notion developed as a result of
their perception that completing math issues presented challenge for them. They can
because they pay attention to the teacher's explanation and repeat the activity at home.
When students run into challenges with math, they don't afraid about asking the teacher for
 Masrianti Fadillah, Maimunah Maimunah, Nahor Murani Hutapea 657

help. They have a strong conviction that mathematics always finds a solution to its issues.
These results prove Somakim's statement, that is, that students who have good self-efficacy
will have independence, work hard, and always try not to give up easily when solving a
math problem (Auliya & Munasiah, 2016).
Students with self-efficacy are in the middle category when solving difficult
questions, and they don't give up easily but create a feeling that they need to study harder
to hone their abilities. The self-efficacy that they have requires them to find other strategies
for improving their abilities, meaning that mathematical self-efficacy can be linked to the
ability to set strategies for solving problems (Kurnia et al., 2018).
Students with low self-efficacy have displeasure with the math assignments given.
They tend to leave out difficult math problems. Many students with low math self-efficacy
say that their math results are not satisfactory enough, even though they have studied
before. They also feel that they are not good at math. Such attitudes and feelings make
their self-efficacy low compared to their abilities and cause students to develop an attitude
of indifference and reluctance to learn (Wahyuningtyas & Febrianingsih, 2018). According
to the findings of student interviews, many students feel that mathematics is the most
difficult subject to understand because it requires strong thinking. In addition, it can be
seen that the majority of children perceive mathematics as a challenging and frightening
topic (Muhsana & Diana, 2022). However, the ability to trust in oneself to finish answering
difficult math problems is something that pupils should have (Rahmawati et al., 2021).
Such belief can renew and maximize students' mathematical abilities. As
mentioned, self-efficacy is a strong factor in influencing students' mathematics learning
outcomes (Ningsih & Hayati, 2020). This statement is relevant to the results of research
conducted by Lestari and friends that the presence of mathematical self-efficacy in students
of IT IQRA High School Bengkulu City, SMA Negeri 11 Bengkulu City, and Idhata High
School Bengkulu City has a direct effect on students' mathematical reasoning abilities
(Lestari et al., 2022). Mathematical reasoning abilities will also increase when students'
self-efficacy is increased, so they will not avoid doing math assignments (Hadiat &
Karyati, 2019). This can be proven by the data found that 8 students with high
mathematical reasoning abilities have high or moderate Self-Efficacy, meaning that
difficulties in the problem will be encouraged to find a solution strategy. Meanwhile, 5
students who have a low dominant category of mathematical reasoning ability have low
self-efficacy, which results in them losing motivation and confidence in their ability to find
solutions to solving math tasks.
658 Analysis Of Mathematical Reasoning Ability in Terms of Mathematical Self-Efficacy of
MAN 2 Pekanbaru Students

The results of this study are different from the research conducted (‘Aini, 2020)
which found that high mathematical reasoning abilities have moderate self-efficacy,
moderate mathematical reasoning abilities have high self-efficacy, and low mathematical
reasoning abilities have low self-efficacy. Comparing the results of Aini's research with the
results of this study it was found that (1) the majority of students with high mathematical
reasoning abilities had moderate self-efficacy due to the opinion that there was still a lot of
mathematical material that they did not understand well, (2) the majority of students with
low mathematical reasoning abilities also have low math self-efficacy, and (3) students
with high mathematical reasoning abilities have high or moderate self-efficacy, in this
study, the majority have moderate math self-efficacy.

CONCLUSION
Based on the analysis carried out oin this study, it was found that: (1) the
mathematical reasoning ability of students in class XII MAN 2 Pekanbaru the majority
category is medium or equal; (2) students with high mathematical reasoning abilities have
high or medium mathematical self-efficacy; (3) students with mathematic reasoning
abilities are likely to have medium-sized mathematical self-efficacy; and (4) students who
have low-category mathematical reasoning abilities tend to have low mathematical self-
efficacy.
Thus, the student's mathematical reasoning ability is not necessarily equal to the
self-efficacy of mathematics that the student possesses, due to different experiences and
environments, but for students who have a good ability to mathematically reason along
with having good mathematical self-efficacy. This research is limited to mathematical
reasoning abilities in terms of students' mathematical self-efficacy. many other affective
assessments can be measured as a review of students' mathematical reasoning abilities,
such as self-anxiety, fear, and others that can be used as further research so that students'
mathematical reasoning abilities can be measured even better as an effort to help maximize
students' abilities.

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