Delta-Phi: Jurnal Pendidikan Matematika, vol. 3 (2), pp. 98-103, 2025
Received 15 Jan 2024 / Published 30 August 2025
https://doi.org/10.61650/dpjpm.v2i1.934

Improving Students' Mathematics
Learning Outcomes through Polya's
Computational Approach and ProblemSolving Approach
Risa Chusniah1, Ani Afifah2
1. Universitas PGRI Wiranegara Pasuruan, Indonesia
2. Universitas PGRI Wiranegara Pasuruan, Indonesia
E-mail correspondence to: fifa.ani@gmail.com

Abstract
This study aims to analyze the improvement of students' mathematics
learning outcomes through the application of the Computational
Thinking approach and the Polya problem-solving approach. This study
used a quasi-experimental method with a Non-Equivalent Control
Group Design. The subjects were 28 students of class VIII A of SMP
Negeri 4 Pasuruan as the experimental group and 23 students of class
VIII B as the control group. The instruments used were pretest and
posttest tests on the data centering material. Data analysis was carried
out using the Wilcoxon Signed Rank test because most of the data were
not normally distributed. The test results showed a significant
improvement in both groups after treatment. However, the
improvement achieved by students in the Computational Thinking
group was higher than that of the Polya group. This proves that
Computational Thinking is more effective in encouraging students to
think systematically, analytically, and reflexively in solving
mathematical problems.
Keywords: Learning outcomes, Computational Thinking, Improvement,
Polya, Wilcoxon Signed Rank

INTRODUCTION
Mathematics is a field of study that plays a significant role in
fostering logical, critical, and systematic thinking skills in students
(Gholami, 2024; Lenawati, 2022). However, many students still
struggle to understand mathematical concepts and solve problems
sequentially, particularly in organizing problem-solving steps,
writing down information obtained and asked questions,
transforming problems into mathematical models, solving
© 2024 author (s)

problems, and checking answers (Lein, 2020). This situation
highlights the need for a learning approach that can stimulate
systematic and structured thinking skills (Amalina & Vidákovich,
2023; Wolff, 2020).
A fairly popular and widely implemented approach is the Polya
problem-solving approach (Cheng, 2023; Yapatang & Polyiem,
2022). This approach emphasizes four stages of problem-solving:
understanding the problem (Risnawati, 2018), planning a strategy,
implementing the plan, and checking again (Anggraini & Fauzan,
2020; Reinke, 2022). Several studies have shown that implementing
Polya's stages helps students become more focused, directed, and
thorough in solving math problems (Ernawati, 2020; Yapatang &
Polyiem, 2022; Erna Yayuk & Husamah, 2020). Furthermore,
developments in 21st-century education have also introduced a new
approach, namely computational thinking (Lehmann, 2025).
Through this approach, students are trained to break down complex
problems into simpler components, recognize patterns, build
algorithms, and generalize (Papadakis, 2022).
Computational Thinking (CT) plays a crucial role in solving
mathematical problems because the problem-solving process
requires specific steps (Tsarava, 2019). By implementing CT,
students become accustomed to thinking abstractly and logically,
following algorithmic flows, and solving problems according to CTrelated indicators ((Jocius, 2021; Nouri, 2020; Tang, 2020). A
literature review found that approximately 20 research articles
demonstrated the positive influence of computational thinking on
students' mathematical problem-solving abilities, as well as
improving their mathematical reasoning and creativity.

Application of the TPACK Framework in Digital Assessment of Elementary School Students' Mathematical Communication Skills Based on Level of SelfConfidence

The demand for developing learning approaches that are expected
to help optimize students' abilities in the digital era strengthens
the relevance of comparing two approaches to solving
mathematical problems, namely Polya and computation
(Kampylis, 2023; J. Sung, 2022), as the basis for this research. This
comparison also opens up opportunities for the integration and
development of more effective and contextual approaches to
mathematics learning, resulting in learning designs that stimulate
students' critical, logical, and creative thinking skills (Atmojo,
2020; Olsson & Granberg, 2024; E Yayuk, 2020). This research
uses statistical material, specifically data centering. This material
is close to students' daily lives, such as reading data and drawing
conclusions from information (Aryanti, 2021). However, many
students still have difficulty organizing and interpreting data
correctly. Therefore, the application of the Polya approach and
computation to this material is considered highly relevant. The
research subjects focused on junior high school students, because
at this level students are in the development stage of thinking
from concrete to abstract, so it is important to provide an
approach that can guide them to think systematically. The
research location was a junior high school in Pasuruan City, taking
into account the teachers' need for various learning methods and
school support in improving the quality of education, especially in
mathematics.

structured based on the competency indicator grid for the material
focused on in the study. Before use, all questions are submitted to
expert judgment to determine content and construct validity.
Experts evaluate whether the items align with the indicators and
measurement objectives, and whether the language and context of
the questions are clear and appropriate for students. This expert
validation approach has been widely used in educational research,
for example, in the development of test instruments to measure
students' mathematical reasoning (Jannah & Rahayu, 2022).
2.3 Research Procedure
The research procedure involved three phases: Pre-Intervention,
Intervention, and Post-Intervention.
a. Pre-Intervention Phase: In the initial phase, both groups
(experimental and control) were given a pretest using a test
instrument validated by experts. This pretest served to
measure students' initial abilities and ensure that the initial
baseline of both groups could be compared validly and fairly.
b. Intervention Phase:
Following the pretest, treatment was administered according
to the research design. The experimental class received a
specific method/learning method aligned with the research
objectives, while the control class received conventional
learning without intervention. The treatment was
administered for a specified period according to the research
design.
c. Post-Intervention Phase: After the treatment was completed,
both groups were given a posttest using the same test
instrument. The results of this posttest then served as the
basis for evaluating improvements or differences in learning
outcomes between the experimental and control groups,
allowing for direct analysis of the intervention's effects
through changes in scores.
2.4. Data Analysis Techniques
In this study, data analysis was conducted by comparing the
pretest and posttest results between the experimental and control
classes. The collected data were first subjected to prerequisite
tests for normality and homogeneity. Hypothesis testing was then
conducted using the Mann-Whitney test to determine whether
there were significant differences between the two groups after
the treatment. This technique allows researchers to determine the
extent to which the treatment affected student learning outcomes
in a valid manner and in accordance with the characteristics of the
data obtained.

RESEARCH METHOD
This research is a quantitative research with an experimental
approach, specifically a quasi-experimental design (Leon, 2023).
The model used is an Unequal Control Group Design. The
characteristic of this design is the presence of two groups, Group
A and Group B, both of which are processed using pretests and
posttests (B. Sung, 2021; Yamada, 2024) quantitative. However,
the selection of subjects in each group is not random, but based on
pre-existing conditions.
2.1. Research Population and Sample
A population in research is defined as the entire area
encompassing objects or subjects with certain characteristics
determined by the researcher in accordance with the research
objectives, so that conclusions can be drawn from the population
(Siyoto & Sodikh, 2015). (Arikunto, 2010)
also explains that a population is all research subjects, while a
sample is a selected subset of the population considered
representative of the population's characteristics. Based on this
understanding, the population in this study is all eighth-grade
students of SMP Negeri 4 Pasuruan who possess characteristics
consistent with the research focus. A sample refers to a number of
individuals from the population selected through specific
procedures to represent the entire population.
Of the eight classes, two classes were selected with nearly identical
or similar average scores. The purpose of this selection was to
minimize initial differences between the two classes, thus
ensuring more objective and valid analysis results. The sample in
this study consisted of two classes: the class treated with Hsu's
computational thinking approach and the class treated with
Polya's problem-solving method as the control class. This study
used a purposive sampling collection technique, a sampling
technique that considers and determines specific criteria,
specifically based on students' relatively similar abilities, so that
differences can be observed after the treatment. The independent
variable, namely learning with a computational thinking approach,
and the bound variable, namely problem-solving skills. The test
used in this study was a written test consisting of descriptive
questions. The steps in implementing this test were a pretest,
administering the treatment by completing worksheets, and then
conducting a final assessment using a posttest.
2.2. Research Instrument
The research instrument consisted of a learning outcome test,
including a pretest and a posttest, to measure student achievement
before and after the treatment. The questions in this test were

RESULT AND DISCUSSION
Result
This section presents the results of quantitative and qualitative data
analysis, followed by an in-depth discussion of the effect of the
Computational and Polya Problem-Solving Approaches on
Improving Student Mathematics Learning Outcomes.
3.1. Descriptive Analysis Results, Prerequisite Tests, and
Hypothesis Test Results (Effectiveness Comparison)
This research was conducted at SMP Negeri 4 Pasuruan, involving
two classes. This research was conducted at SMP Negeri 4 Pasuruan,
involving two sample classes. Class A consisted of 28 students who
received computational thinking-based learning, while Class B
consisted of 23 students who were taught using the Polya problemsolving approach. The research data consisted of pretest and
posttest results, which were analyzed according to the indicators of
each variable.
Before conducting the hypothesis testing, the data were first tested
for normality using the Shapiro-Wilk test, because the sample size
was less than 50 and the data were on an interval scale. The analysis
results showed that in class A, both the pretest (W = 0.9089 < 0.924)
and posttest (W = 0.7912 < 0.924) were not normally distributed.
Conversely, in class B, the pretest data (W = 0.9256 > 0.914) were
normally distributed, but the posttest data (W = 0.0209 < 0.914)
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were not normally distributed. Thus, only class B's pretest met the
assumption of normality. Because most of the data were not normal,
hypothesis testing continued using nonparametric statistics.
Meanwhile, for class B, which was taught using the Polya problemsolving method, the pretest normality test results showed that the
calculated W value was 0.9256, while the table W value was 0.914.
Because the total W value was greater than the calculated W value
(W count > W table), it can be concluded that class B's pretest data
was normally distributed. However, unlike the posttest, the test
results showed that the calculated W value was 0.0209, lower than
the W table value of 0.914, indicating that the posttest data for Class
B were not normally distributed. From these four results, it can be

concluded that only one group of data was normally distributed,
namely the Class B pretest. The other three groups of data (Class A
pretest and posttest, and Class B posttest) were not normally
distributed. Therefore, in subsequent hypothesis testing, nonparametric statistics were used, as they did not meet the
assumption of normality.
The next step was to conduct a Wilcoxon signed-rank test. The
Wilcoxon signed-rank test was conducted first to analyze changes
in pretest and posttest scores in each group separately. This aimed
to ensure that the treatment provided improved mathematical
problem-solving skills within the groups.

Table 1. Wilcoxon Signed-Rank Test for the Computational Approach Group

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Table 2 Wilcoxon Signed-rank Test for the Polya Approach Group

Discussion

calculation process and final results. Although the Polya group also
improved, errors were still found, such as incorrect data
substitutions by Arya DRM and Nadiah AZ. Quantitatively, the
computational group's posttest average was higher (86.1) than the
Polya group's (73.6). These results support Supiarmo (2021) who
stated that computational thinking can improve students' accuracy
and logic in problem-solving.
The calculation ability indicator also improved in both groups. The
computational group improved from a pretest average of 50.5 to
86.1 on the posttest, while the Polya group's score increased from
45.6 to 73.6. This improvement was not only demonstrated
quantitatively; Aira QM and Ayu DL, who initially only wrote the
median, were able to complete all calculation components by the
posttest: mean, median, mode, and percentage. On the other hand,
in the Polya group, some students, such as Rasyafa KA and Rebecca
GAP, only partially completed the problem components. Research
by Hsu (2018) supports this finding, stating that computational
thinking can help students develop more accurate and
comprehensive mathematical calculation skills.
In the reflection indicator, pretest results indicated very low
proficiency because only a few students were able to reassess the
solution steps. After treatment, the computational group showed
significant improvement. Many students, such as M Zamroni and
Nadira AP, began to explain whether the strategies they used could
be applied to other problems. Meanwhile, in the Polya group,
despite some improvement, some students still struggled to
evaluate the lengthy and procedural solution steps. These results
are supported by the opinion of Markandan (2022) who
emphasized that computational thinking can foster metacognitive
awareness so that students are better able to assess the chosen
solution strategy.
Error analysis also supported the previous results. In the
computational group, errors in writing the sequence of steps and
performing calculations decreased significantly after treatment.
Conversely, in the Polya group, although the number of errors
decreased, many students still made errors calculating percentages,

4.1 Analysis of Improvement in the Polya and Computational
Approaches
Pretest and posttest results show that both approaches positively
impacted student learning outcomes. However, the improvement
achieved by students using the computational thinking approach
was more pronounced. For example, in the aspect of problem
identification, many students initially struggled to detail the
question's question, but after learning with the computational
approach, they were able to write down relevant information and
connect it to solution strategies. In the Polya group, this ability also
improved, but not as strongly as in the computational group
(Tsarava, 2019).
The ability to identify problems remained a challenge for most
students in both groups initially. Some students, such as Aira QM
and Ayu DL in the computational group, were unable to accurately
detail the question in the pretest. After the treatment, the
computational group experienced significant improvement,
indicated by students' ability to write down the questions, select
relevant data, and connect them to the solution steps. This aligns
with the opinion (Cousins, 2020; Nurbaya, Hudi, Nurmalasari, &
Amalia, 2021) that the first step in problem solving is to understand
the problem properly, because without a clear understanding,
students will have difficulty moving on to the next stage. In the
Polya group, identification skills also improved, although not as
significantly as in the computational group. Some students, such as
M Billy SS and M Faqih A, still struggled due to the burden of lengthy
solution procedures. Therefore, it can be concluded that the
computational approach resulted in more equitable problem
identification.
Regarding accuracy indicators, pretest results showed that students
in both groups still frequently mis-written percentages or skipped
steps in calculating averages and medians. After treatment, the
computational group experienced significant improvements in
accuracy, as demonstrated by Abira KZ and Andini C, who were able
to be more careful in selecting data and correctly writing down the
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copying data, or failing to complete all problems. Therefore, the
computational-based approach was more effective in minimizing
errors while encouraging students to solve problems
comprehensively.
In general, both approaches successfully improved students'
mathematics learning outcomes. However, the computational
approach demonstrated superiority in almost all aspects, from
precision, systematic steps, completeness of answers, reflection,
and error reduction. These results align with research by Augie, A.,
Nurhayati, N., & Susanti, D (Mirheidari, 2019; Yu, 2021), which
emphasized the need for teachers to implement learning strategies
that involve computational thinking skills because they can train
students to think systematically and analytically and solve complex
problems in mathematics.
4.2 Comparison with Conventional Learning
The results showed that both the computational thinking approach
and conventional learning improved student learning outcomes,
but the improvement was significantly stronger in the group
learning with the computational approach. While conventional
learning, which generally relies on procedural explanations and
practice exercises, such as in the Polya siswa model (Ernawati,
2020; Riyadi, 2021), does experience progress, it is not as dramatic
as that seen in the group guided through the computational stages.
For example, in problem identification skills, students in the
conventional learning group still tend to struggle to detail
important information and connect it to problem-solving strategies,
while students in the computational group experienced a significant
jump in ability. The conventional approach, which emphasizes
lengthy, procedural steps, leaves some students confused about
determining what to ask, as seen in students like M Billy SS and M
Faqih A. The computational group, on the other hand, was able to
write down relevant information more systematically.
In terms of accuracy, conventional learning also showed
improvement, although common errors such as incorrect data
substitution or missed calculation steps remained. This contrasted
with the computational group, which showed significantly higher
accuracy gains, bolstered by the achievements of students like Abira
KZ and Andini C, who began to be more careful in selecting data and
consistently write down their calculation processes. Quantitatively,
the computational group's posttest average reached 86.1, while the
conventional learning group only achieved 73.6. A similar pattern
was seen in arithmetic skills: although both groups improved,
conventional learning still left students unable to complete only

partial problem components, in contrast to the computational
group, where almost all students were able to complete the mean,
median, mode, and percentage.
A striking difference was also evident in reflection skills. In
conventional learning, students did show progress, but still
struggled to reassess lengthy and procedural solution steps.
Meanwhile, students in the computational group demonstrated
more mature reflection skills, as illustrated by M Zamroni and
Nadira AP, who began to relate the strategies they used to other
problems. Furthermore, error analysis clarified that the
conventional approach still resulted in various errors in calculating
percentages, copying data, and solving problems completely, while
the computational approach significantly reduced errors due to its
more structured and systematic thinking process.
Overall, conventional learning still had a positive impact on learning
outcomes, but it was not as effective as the computational thinking
approach, which proved superior in improving accuracy,
completeness, reflection, and reducing student errors in completing
math assignments. This finding aligns with research by Augie,
Nurhayati, and Susanti (2023), which emphasized that integrating
computational thinking skills into learning helps students think
more systematically, analytically, and effectively in solving complex
problems advantages not fully achieved through conventional
learning.

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CONCLUSION
Based on the results of a study conducted on eighth-grade students
at SMP Negeri 4 Pasuruan, it can be concluded that there was a
significant improvement in mathematics learning outcomes in both
groups, both those taught using the Computational Thinking
approach and those taught using the Polya problem-solving
approach. Therefore, the alternative hypothesis (H₁), which states
that there is an improvement in learning outcomes between
students' pretest and posttest scores, is accepted.
The improvement in learning outcomes was more pronounced in
the Computational Thinking group, indicating that this approach is
more effective in training students to think systematically,
analytically, and reflectively than the Polya approach. Therefore,
the application of Computational Thinking is recommended as a
mathematics learning strategy to improve students' problemsolving abilities.

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High School Students in Biology Learning: Preliminary
Research. Journal of Physics Conference Series, 1842(1).
http://doi.org/10.1088/1742-6596/1842/1/012080
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on students’ creative-thinking skills: Case on the topic of
simple food biotechnology. International Journal of
Instruction, 13(3), 329–342.
http://doi.org/10.29333/iji.2020.13323a
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