Delta-Phi: Jurnal Pendidikan Matematika, vol. 1, pp. 06–10, 2023
Received 18 Feb 2023 / published 30 Apr 2023
https://doi.org/10.61650/dpjpm.v1i1.19

Analysis of skills using pattern-finding
strategies in solving mathematical
problems given gender differences
M. Rizki Cahyadi1, Fitroh Ariansyah2, and Paulo Vitor da Silva Santiago3
1. Universitas Muhammadiyah Malang, East Java, Indonesia
2. SMP Islam Nurul Anwar, East Java, Indonesia
3. Federal University of Ceara (UFC), Brazil
E-mail correspondence to: mcahyadi24@gmail.com

Abstract
This study aims to describe the skills of using pattern-finding strategies in
solving mathematical problems in terms of gender differences. This
research is descriptive research with a qualitative approach. The subjects
of this study were students of class VIII SMP Baiti Jannati, Sunggal subdistrict, Deli Serdang district. The research subjects consisted of four
students with high mathematical abilities, two male and two female
students. The data collection technique used the problem-solving ability
essay test instrument, which amounted to two questions, and the non-test
instrument in the form of interviews. The data analysis technique in this
study uses the Miles and Huberman model, which consists of four stages:
data collection, data condensation, data presentation, and conclusions.
The results of this study indicate that both male and female students can
find and use patterns in solving mathematical problems. Based on these
results, there is no difference in skills in using pattern-finding strategies
between male and female students.

Keywords: Gender; Pattern finding; Problem-solving.

Introduction
Ability is a beneficial ability for students. The World Economic
Forum (WEF) also includes problem-solving as one of the skills
needed in the 21st century (Inganah et al., 2023; ND Safitri et al.,
2023; WEF, 2015). Students who have good problem-solving skills will
find it easier to overcome various difficulties encountered in
everyday life (Hu et al., 2018; Meryansumayeka et al., 2021;
Sekaryanti et al., 2023a). Therefore, it is essential to train students'
problem-solving abilities.
Problem-solving abilities are generally formed through learning
mathematics, often called mathematical problem-solving abilities
(Lai et al., 2020; Qomariyah et al., 2023; Sekaryanti et al., 2023b). The

National Council of Teachers of Mathematics (NCTM) states that
problem-solving is integral to mathematics (NCTM, 2000; Paloloang et
al., 2020). This shows the close relationship between problem-solving
abilities and learning mathematics. Memnun (2012) added that
problem-solving ability is a general goal of learning mathematics.
There are several problem-solving models, such as the Polya and
Ideal models (Brookman-Byrne et al., 2019; Darmayanti et al., 2022;
Fauza et al., 2022). Polya's problem-solving model was proposed by
George Polya in 1971 through his book " How to Solve It: A New Aspect
of Mathematical Method ". Polya offers four steps of problem-solving,
namely understanding the problem, devising a plan, carrying (Russell
et al., 2020) out the plan (Cundiff et al., 2020), and looking (Ismail et
al., 2021), back (Bossé et al., 2021; Polya, 1973).
The Ideal Model is a stage of problem-solving developed by John
D. Bransford and Barry S. Stein in their book entitled " The Ideal
Problem Solver " (Nayazik, 2017). The name Ideal is an acronym for
problem-solving steps, namely Identify problems and opportunities
(identify problems and opportunities) (Mulyono, 2017), Define goals
(define goals) (Yuntiaji, 2019), Explore possible strategies (explore
strategies) (Rahmawati et al., 2021), Anticipate outcomes and Act
(anticipate outcomes and act), and look back and Learn (looking back)
(Bransford & Stein, 1993).
These two problem-solving models have the same principles,
namely understanding the problem (Darmayanti, 2023; Syaifuddin et
al., 2022), planning a strategy (In’am et al. et al., 2023; Sugianto et
al., 2022), implementing it (Hasanah et al., 2022), and looking back at
the solution to solving the problem and understanding and
understanding a problem before acting or making a decision (Muniri
& Choirudin, 2022). A good understanding of the problem will
significantly assist in determining the strategy to be used in solving the
problem (Choirudin et al., 2021). Each problem has its characteristics,
so different approaches and strategies are needed to solve each
problem.

© 2023 Cahyadi et al., (s). This is an open-access article licensed under the Creative Commons Attribution License 4.0.
(http://creativecommons.org/licenses/by/4.0/).

Cahyadi et al.: Analysis of skills using pattern finding... Delta-Phi: Jurnal Pendidikan Matematika, 1, 06–10, 2023
Posamentier & Krulik, (2009) offers several strategies for
solving mathematical problems, including organizing data (Yan et
al., 2022), guessing and testing (Gray et al., 2020), solving simpler
similar problems (Manzano-León et al., 2021), simulating actions
(Björn et al., 2019), working backward (Baiduri, 2019), finding
patterns (AN Vidyastuti et al., 2022), logical reasoning (Rizki et al.,
2022), making pictures (Darmayanti et al., et al., 2022), and
adopting different points of view. Among these strategies, finding
patterns is the most frequently used in solving mathematical
problems because mathematics is about looking for and finding
patterns (Resnik, 1981).

instruments in the form of interviews were conducted to add and
explore deeper information related to the pattern-finding
strategies used by students to solve problems. The data analysis
technique in this study used the Miles and Huberman interactive
analysis model, which consisted of four stages: data collection, data
condensation, data presentation, and conclusions (Miles &
Huberman, 1994).

Results and Discussion
This research is descriptive research with a qualitative
approach. This type of descriptive research aims to describe a
phenomenon's condition or state (Creswell, 2010). A qualitative
approach is used because the object of this research is a work
process (In’am et al. et al., 2023; Rofiah et al., 2023), namely the
process of using pattern-finding strategies in solving mathematical
problems regarding gender differences.

A pattern is a model or arrangement with regularity in which
the pattern-forming elements are arranged according to specific
rules to predict the continuation (Mustakim et al., 2023; Safitri et
al., 2023). Patterns can appear in various situations in systematic
sequences of numbers, pictures, lists, or tables. Pattern finding
simplifies and saves the troubleshooting process. So, students or
individuals need to master identifying and finding patterns.

The following are the results of students' mathematical
problem-solving tests:

Each student certainly has a different mastery of patternfinding skills in solving mathematical problems. Gender or gender
differences are one of the factors that influence problem-solving
abilities (Mefoh et al., 2017; Utomo et al., 2021). Male students are
superior in visual-spatial problems than female students (Awalah et
al., 2019; Santrock, 2008). Meanwhile, female students excel in
verbal skills and memory tasks compared to male students (Akbar
et al., 2020; Maccoby & Jackline, 1974).

Figure 1. Answers of male students 1 question no 1

Figure 1 is the work of male student 1 (L1) on question no 1. L1
immediately answered with "10 x 5 = 50" and "4 x 5 = 20" and
concluded that the result was 70. If referring to the Polya problemsolving stage, L1 did not explicitly show the stage of problemsolving through writing, but that does not mean he did not do it.
The researcher then interviewed L1 students to dig deeper into
information regarding the problem-solving process that L1 did.

The results of previous studies related to problem-solving show
that female students have better problem-solving abilities than
male students (Kusumaningsih et al., 2020; Nurfitri & Jusra, 2021;
Tunnajach & Gunawan, 2021; Yerizon et al., 2021). This happens
because female students are more thorough and structured in
solving problems (Kusumaningsih et al., 2020; Subekti & Krisdiani,
2021). Apriani et al. (2017)revealed that male students experience
difficulties understanding questions and making mathematical
models compared to female students.

Researcher: "How did you get this '10 x 5'?"
L1
: "Look, sir — those asked for eggs on Friday
multiplied by five packs.
10 is many eggs."
Researcher
: "Then where does this 4 x 5 come from?"
L1
: "Every day it increases by 4 Sir, so multiply it
by five as well."

Research on students' problem-solving abilities regarding
gender differences has been done a lot. In addition to the several
studies above, there are also studies (Lestari et al., 2021) that
(Oemolos & Mampouw, 2021) discuss mathematical problemsolving abilities regarding gender differences. These studies only
discuss problem-solving abilities from the problem-solving stage,
not yet discussing the strategies used in problem-solving in more
detail. Based on that, this study seeks to discuss more deeply the
ability to solve mathematical problems using pattern-finding
strategies regarding gender differences. Through this research, the
authors hope that students will be able to solve problems and be
critical in determining effective and efficient strategies for solving
these problems.

Based on the interview, it is known that L1 has been able to
identify the elements of the problem but is mistaken in
understanding the expected problem-solving objectives. L1
understands that Zidan's chickens produce at least ten eggs daily.
L1 also understands that Friday is the fifth day and applies it to the
number 5. These two elements ultimately result in the
multiplication “10 x 5 = 50”. This concept is also used to find the
number of eggs added to produce the multiplication "4 x 5 = 20".
In this problem, L1 has found a rule or pattern of egg addition, but
L1 has not been able to use this pattern to solve the given problem.

Research Methode
This research is descriptive research with a qualitative
approach. This type of descriptive research aims to describe a
phenomenon's condition or state (Creswell, 2010). A qualitative
approach is used because the object of this research is a work
process, namely the process of using pattern-finding strategies in
solving mathematical problems regarding gender differences.

Figure 2. Answers of male students 1 question no 2

This research was conducted at Baiti Jannati Middle School,
Sunggal sub-district, Deli Serdang district. The subjects in this study
were students with high mathematical abilities who were selected
according to input from the mathematics teacher to fulfill the
objectives of this study. The research subjects consisted of four
male students and two female students whose aim was to fulfill the
constancy of the data.

In question number 2, the problem is how many eggs are
produced in a week if Monday produces six eggs and only adds two
eggs the next day. In this problem, L1 arranges and totals the
number of eggs produced daily for a week. Based on these answers,
it can be seen that L1 has been able to find patterns from the
problems given. This can be seen from how he correctly recorded
the number of eggs for a week. L1 has also used this pattern to
solve problems by adding all the eggs produced.

Data collection was carried out using test and non-test
instruments. The test instrument used is in the form of an essay test
of problem-solving abilities, totaling two questions that are
constructed to work with a pattern-finding strategy. Non-test

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Cahyadi et al.: Analysis of skills using pattern finding... Delta-Phi: Jurnal Pendidikan Matematika, 1, 06–10, 2023
Based on the results of the interviews conducted, it is known
that P1 understands the problem as one of the material problems
of the number pattern that he has studied, so P1 solves this
problem with the rules/formula of the Un number pattern. This
shows that P1 has been able to understand the characteristics of a
problem, can choose the right strategy, namely finding patterns,
and can carry out this strategy properly and correctly.

Figure 3. Answers of male students 2 Question No. 1

Figure 3 is the work of male student 2 (L2) on question no 1.
Like L1, L2 does not explicitly show the stages of solving Polya's
problem through writing. However, based on the results of the
interviews, it can be seen that L2 already understands the problems
given.
Researcher: "What does this '4 x 4' mean?"
L2
: "The number of eggs has increased, sir. The eggs
will increase from Tuesday, then Wednesday,
Thursday, and Friday, so four days, sir."
Researcher : "Okay. Then why is this added 10?”
L2
: "There were still many eggs added, sir. Continue
adding 10, the principal amount, the eggs
produced daily."

Figure 2. Female student answer 1 question no 2

In question no. 2, P1 could write down the information and
identify the problem, but an error occurred in solving it. P1 solves
the problem using the same method as question no 1. Similar to L2,
P1 also assumes that the intent and purpose of this problem is to
determine the number of eggs produced on Sunday.

L2 understands that the goal of the problem is to find the
number of eggs laid on Friday. L2 can also find patterns of egg
addition from Monday to Friday, which is written as “4 x 4 = 16,”
which means that on Friday, there will be four times the addition
of 4 eggs. Then L2 adds it by 10, the principal number of eggs
produced each day.

Figure 3. Female students answer two questions no 1

Figure 7 shows female student 2 (P2) answers to question no
1. P2 worked on the questions by writing down the information
he could receive, but there was a mistake in receiving and
understanding the information. This results in errors in finding
solutions to troubleshooting. Even so, there are exciting things
from the work process carried out by P2. P2 compiles and records
egg yields every day according to predetermined rules. This shows
that P2 understands and succeeds in finding patterns from the
problems given. P2 is also able to apply the pattern rules. It is just
that P2 is wrong in setting the goal of solving the problem.

Figure 4. Answers of male students 2 Question No. 2

In question no. 2, L2 experienced a mistake in understanding
the intent and purpose of the question. L2 considers question
number 2 the same as question number 1, so they do it similarly.
Researcher : "Why did you work on this problem the same as
number 1?"
L2
: "It is the same, sir. The difference is that it is
Sunday."
Researcher : "Try rereading it because it is more thorough!"
L2
: "Oh yes, sir. For a week, sir."
Researcher : "That is right. You are not careful enough."
L2
: "Yes, sir, in a hurry, sir."

Knowing there was a mistake in understanding P2, the
researcher tried to help straighten the understanding of P2.
However, unfortunately, P2 crossed out his work and imitated the
work of his friends.

Based on the interviews, L2 admitted that he was in a hurry to
read the questions, so he was not thorough. L2 considers that the
intent and purpose of this problem is to determine the number of
eggs produced on Sunday.

Figure 4. Female students answered two questions no 2

In question no. 2, P2 immediately answered by collecting data,
compiling the number of eggs produced daily for a week, and then
adding them up. Based on the answers, P2 already understands the
intended and purpose of the problems. P2 can record and arrange
patterns according to the rules given in the problem.

Figure 5. Female student answer 1 question no 1

Figure 5 shows the work of female student 1 (P1) on question
1. P1 writes down the stages of problem-solving, from problem
identification to completion. However, there were several
completion steps that P1 did not write down, so an interview was
conducted about how the P1 process solved the problem.

Selection and use of the right strategy will provide optimal
results in solving problems. Based on the results of the
mathematical problem-solving test, it is known that both male and
female students can apply pattern-finding strategies in solving
mathematical problems. Students can find specific rules of
patterning on a given problem. Students are also able to use these
rules to obtain solutions to problem-solving.

Researcher : "Where did this 10 +16 come from?"
L2
: "Formula, sir. 10 is the first term. 16 of 4 times
4.”
Researcher: "Where do four times four come from?"
L2: “From Tuesday to Friday, four days. Then multiply it by
four because the difference is four, sir."

Even though students can use pattern-finding strategies,
students are often not careful and do not understand the intent

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Cahyadi et al.: Analysis of skills using pattern finding... Delta-Phi: Jurnal Pendidikan Matematika, 1, 06–10, 2023
and purpose of the problems given. Both male and female students
experience mistakes in understanding the problem, so they are
wrong in problem-solving. This is inversely proportional to the
results of research (Peranginangin & Surya, 2017), which show that
the problem identification indicator has the highest percentage
compared to other indicators. So, students should be able to
identify the problem well.

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If you look at all aspects of problem-solving, the work of female
students is more organized and structured than male students. This
result aligns with research (Akbar et al., 2020), which reveals that
female students are more organized in problem-solving. Several
other studies have also revealed that the problem-solving abilities
of female students are better than male students (Nurfitri & Jusra,
2021; Tunnajach & Gunawan, 2021; Yerizon et al., 2021). Male
students tend to be lazy to write down information on the
problems given and prefer to act directly according to their
reasoning and understanding of the problem.

Conclusion
Based on the results and discussion, it can be concluded that
there is no difference in the skills of using pattern-finding strategies
between male and female students. Students can find specific rules
of patterning on a given problem. Students are also able to use
these rules to obtain solutions to problem-solving. Based on the
results of this study, the researcher suggests that further research
can provide more complex problems so that the pattern-finding
process by students can be seen. In addition, research subjects can
also be added so that the differences in skills in using patternfinding strategies between male and female students can be seen
clearly.

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