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 6 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 7 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. (2021). Pengembangan LKPD Matematika Berbasis Kaligrafi dengan Pendekatan Guided Discovery Learning. Jurnal Pendidikan Matematika (JPM), 7(1), 52. https://doi.org/10.33474/jpm.v7i1.6738 Creswell, J. W. (2010). Research Design Pendekatan Kualitatif, Kuantitatif, dan Mixed. Pustaka Pelajar. Cundiff, P. R., McLaughlin, O., Brown, K., & Grace, K. (2020). In Search of Greater Understanding: The Impact of Mastery Learning on Social Science Education. Teaching Sociology, 48(2). https://doi.org/10.1177/0092055X20907979 Darmayanti, R. (2023). 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Profil Berpikir Aljabar Siswa SMP dalam Pemecahan Masalah matematis Ditinjau dari Gaya Kognitif dan Gender. JIPMat, 5(1). https://doi.org/10.26877/jipmat.v5i1.5574 Lai, C. P., Zhang, W., & Chang, Y. L. (2020). Differentiated instruction enhances sixth-grade students’ mathematics self-efficacy, learning motives, and problem-solving skills. Social Behavior and Personality, 48(6). https://doi.org/10.2224/sbp.9094 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. Reference Akbar, M., Sa’dijah, C., & Sisworo. (2020). Profil Siswa Dalam Memecahkan Masalah Matematika Berdasarkan Gaya Kognitif Dan Gender. 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