Mathematical Problem Solving Research Articles

Solving Mathematics Problems Based on Visual Information Processing

Solving mathematical problems involves a complex process and requires the ability to comprehend and manipulate visual information. When an individual encounters a problem, the ability to represent data, plan solution steps, and visualize relationships between variables is crucial. This research aims to explore in-depth how visual information is processed during mathematical problem-solving. The findings indicate that Subject S1, with high visual ability, adeptly represents the problem, articulates known and unknown elements, and exhibits a strong conceptual understanding. Students with robust visual conceptualization skills can plan and solve problems using elimination and substitution methods. By verifying results using different methods reflects a solid conceptual understanding. On the other hand, Subject S2, with low visual ability, struggles to represent the problem and tends to focus directly on the solution. This suggests a lack of conceptual understanding, limitations in visual representation, and deficiencies in verification skills. Finally, the visual representation only used visual representation with mathematical modeling. Further research should investigate similar studies involving other types of representations, such as diagrams and graphs. In conclusion, teachers need to enhance students’ conceptual understanding, metacognitive awareness, and practice verification skills to develop their mathematical problem-solving abilities

Analisis Kemampuan Pemecahan Masalah Matematis Siswa pada Penyelesaian Soal Cerita Pecahan di Sekolah Dasar

The ability to solve mathematical problems is the lowest ability in learning Math story problems in grade 5 at one of the public elementary schools in Kotabaru Subdistrict, Karawang Regency. This is the background for the researcher to conduct the study. This study aims to find out the extent of students' mathematical problem-solving abilities in solving addition and subtraction of fractions story problems, as well as the faktors that affect the success or failure of students in this case. This research is a case study with a qualitative method conducted by collecting data through tests and interviews with 5 student subjects. The results show that the average mathematical problem-solving ability of students is 57.6, which can be categorized as sufficient. Faktors affecting students' abilities include internal faktors such as intelligence, interest, talent, attitude, and communication skills, as well as external faktors such as the role of parents and teachers in guiding and teaching students.

ETHNOMATHEMATICS IN CACI DANCE OF MANGGARAI COMMUNITY AND ITS INTEGRATION IN MATHEMATICS LEARNING

Purpose: The purpose of this research is to describe the history and philosophy of the Caci Dance and describe the ethnomathematics contained in the Caci dance and develop learning tools for some of the mathematical concepts found. Theoretical reference: Ethnomathematics explores the relationship between mathematics and the diversity of human cultures, exploring the ways in which different groups of people use, understand and develop mathematical concepts in the context of their daily lives (Orey, 2011). It is important to understand that mathematics is not only an objective universal entity, but can also be influenced by the cultural context in which it develops (Bishop, 1988). Ethnomathematics seeks to overcome the traditional view of mathematics, which is often understood as a science that is neutral and separate from everyday life (François, 2010). One of the main aspects of ethnomathematics is the exploration of how different cultural groups develop systems of counting, number representation and mathematical problem solving in the context of their everyday lives (Rosa & Shirley, 2016). By understanding how to think about mathematics in a cultural context, ethnomathematics can provide deeper insights into the wealth of mathematical knowledge held by different communities (Stathopoulou et al., 2015). Teachers can use examples from students' culture to explain mathematical concepts, thus making learning more meaningful and relevant. This not only improves students' understanding of math but also helps them see the value and relevance of math in their daily lives (Polman et al., 2021). As technology and globalization evolve, ethnomathematics can also help in addressing the challenge of mathematical diversification (Orey, 2021). Many communities in the world have traditional mathematical systems that are rich in local knowledge and wisdom (Abas et al., 2022). Ethnomathematics provides a platform to document, value and preserve this knowledge from extinction. This approach is inspired by the belief that mathematics is not only universal, but can also be understood and taught through the lens of different cultures (Brandt & Chernoff, 2014). By incorporating cultural elements into mathematics learning, students can more easily relate mathematical concepts to their daily life experiences, thus making learning more meaningful and relevant (Acharya et al., 2021). Method:This research is a qualitative study using an ethnographic approach with four research subjects. The research instruments were interviews, observations and documentation and the data were analyzed by ethnography model. Results and Conclusion: The results of this study show that there are ethno mathematical activities in Caci Dance which include counting, localizing, designing, playing, and explaining activities. These activities are in accordance with mathematical concepts, namely addition, multiplication, number patterns, arithmetic sequence, geometry, mathematical logic, relations and functions. Thus, the concepts of school mathematics found in Caci Dance can be developed by designing appropriate learning tools to be applied in school learning. Implications of research: Mathematical concepts can be explained with cultural concepts found around students. The explanation of learning concepts with this cultural approach is better known as ethnomathematics. This approach emphasizes student culture-based learning related to mathematics. This can help teachers and students in understanding a certain concept that is considered difficult. In addition, students can easily understand the material because they know the problems presented by the teacher are related to their surroundings. Ethnomathematics can be applied in schools through the preparation of teaching materials. Originality/value: The novelty of this research is the formation of an ethnomathematics model of caci dance that can be integrated in mathematics learning in schools so that it can provide input for decision makers, in this case teachers and government or education observers to be more pro-active in implementing learning that is in accordance with the culture around students.

Heuristics and semantic spaces for the analysis of students’ work in mathematical problem solving

In this research, our objective is to characterize the problem-solving procedures of primary and lower secondary students when they solve problems in real class conditions. To do so, we rely first on the concept of heuristics. As this term is very polysemic, we exploit the definition proposed by Rott (2014) to develop a coding manual and thus analyze students’ procedures. Then, we interpret the results of these analyses in a qualitative way by mobilizing the concept of semantic space (Poitrenaud, 1998). This detailed analysis of students’ procedures is made possible by collecting audiovisual data as close as possible to the students’ work using an action camera mounted on the students’ heads. We thus succeed in highlighting three different investigation profiles that we have named explorer, butterfly, and prospector. Our first results tend to show a correlation with these profiles and the success in problem-solving, yet this would need more investigation.

Analyzing elementary students’ access to cognitive-oriented positions in mathematics

The effectiveness of group problem-solving in mathematics depends on the extent to which meaningful participation is distributed across all group members. One way to explore how participation is distributed within groups is by examining how students are positioned within group interactions. In this study, we explore the social instructional factors that cause elementary students to move in and out of positions that support cognitive engagement during collaborative problem-solving in mathematics. Using a case study analysis of three elementary students working in a group, we found five social instructional factors that caused students to move in and out of cognitive-oriented positions during group work in mathematics: (1) building an ally through common language, (2) physical access to the chalkboard and resources, (3) tone of voice, (4) teacher intervention, and (5) contestation from peers. The findings promote implications for effectively facilitating group work in mathematics.

Emibaru: Interactive E-Modules Based on Problem Solving Ability for Fifth Grade Students in Elementary School

Creating meaningful learning is crucial to accommodate students’ problems solving ability development. This research is motivated by the low problem-solving ability of elementary school students in solving mathematical word problems, hence the need for teachers to make an effort in developing teaching materials for students to improve their mathematical problem-solving abilities. This study aims to develop a spatial interactive e-module (Emibaru) and evaluate the problem-solving abilities of 5th-grade students in using the interactive e-module. The quantitative approach and quasi-experimental method with a pretest-post-test control group design were applied in this research. The sampling technique was simple random sampling with 12 students from the experimental group and nine from the control group. Data collection techniques are interviews, observations, and tests. The instruments used were interview sheets, observation sheets, and essay tests. The data analysis technique used the T-test assisted by the SPSS 23 application. The results based on the T-test analysis showed t 2.237 and the value of Sig. (2-tailed) is 0.037 at df 19 < 0.05. It was stated that the spatial interactive e-module (Emibaru) influenced problem-solving mathematical competence in geometric materials (cubes and blocks).

Description of Students' Mathematical Problem Solving Ability on Flat Build Material Based on Gender Class VIII Mts Ar-Rahman Kaju

This research is a qualitative research with a descriptive approach which aims to determine the description of students' mathematical problem solving abilities in flat shapes material based on Gender Class VIII MTs Ar-Rahman Kaju which is arranged based on indicators of problem solving abilities, namely indicators of understanding problems, planning solutions, resolving problems and examining return. The data obtained is the result of interviews with 2 male students and 2 female students. The data collection methods used were observation, interviews and problem solving ability tests. The results in this study show that female students are better at solving mathematics problems than male students. It can be seen from this research that female students completed all four indicators of mathematical problem solving ability, while male students were only able to complete two of the indicators of mathematical problem solving ability.

Profile of Problem-Solving Abilities on Elementary School Teacher Education Students in The Basic Mathematics Course

This research aims to describe the mathematical problem-solving abilities of first-semester students in the Elementary School Teacher Education Program at STKIP Taman Siswa Bima. It employs a quantitative descriptive research design. The subjects consist of Class IE students selected through purposive sampling, comprising 29 female students and 13 male students. Data collection involves a test method utilizing a Mathematical Problem-Solving Ability Test consisting of three essay questions. Data analysis techniques include data reduction, data presentation, and drawing conclusions. The research results indicate that based on the analysis of the mathematical problem-solving ability test results, using the four-step Polya approach (understanding the problem, devising a solution plan, executing the solution plan, and reviewing the answer), students' ability to understand the problem falls into the "High" category with an average score of 82,10. Meanwhile, the ability to formulate problem-solving plans is categorized as "Medium" with an average score of 65,40. Furthermore, students' ability to execute formulated plans falls into the "Low" category with an average score of 58,80. The same holds for students' ability to review their answers, which also falls into the "Low" category with an average score of 50,48.

Technology-based learning interventions on mathematical problem-solving: a meta-analysis of research in Indonesia

<span lang="EN-US">Mathematical problem-solving is important for learning mathematics and is needed in the 21st century. In the 21st century, education technology has been complementing every learning activity. Research on learners’ mathematical problem-solving improvement increased rapidly over the last few decades. This study examined the effectiveness of technology-based mathematics learning interventions on learners’ mathematical problem-solving at all levels of education in Indonesia. The researchers only took meta-analysis research from 2015 to 2023 from indexing databases, such as Scopus, Web of Science, Google Scholar, and Science and Technology Index (SINTA) indexers. The collected research articles were from only national journals in Indonesia. The screened data became the research results, containing the mean, standard deviation, number of samples (N), and the scale used in the research. This research had 19 independent studies in this meta-analysis. The data analysis applied meta-analysis, specifically the mean effect size value. The results of data analysis using Jeffrey’s Amazing Statistics Program (JASP) software showed the effective implementation of innovative and fun technology-based mathematics learning interventions. These findings highlighted the importance of incorporating technology into mathematics education and its potential for improving learners’ problem-solving skills.</span>

Mathematical problem solving is modulated by word priming.

This study aimed to explore the influence of word priming on mathematical problem solving. In two experiments, participants were required to finish multiplication estimation tasks with a specified estimation strategy under different word priming conditions (Experiment 1: concrete words vs. Experiment 2: abstract words). The results showed that: (1) under the concrete word priming condition, in comparison to neutral, positive word priming improved accuracies (ACCs) when using a down-up strategy (e.g., doing 40 × 80 = 3200 for 43 × 78), while both positive and negative word priming reduced reaction time (RT); (2) under the abstract word priming condition, both positive and negative (vs. neutral) abstract word priming reduced RTs, while individuals' ACCs of completing the estimation task were not influenced by valence. The present study showed that whether concrete words or abstract words were adopted as experimental stimuli, participants' performance of completing mathematical problems was modulated by the valence of the priming word, which led us to develop a better understanding of how arithmetic performance is influenced by word processing.

Using Gardner's Three-Squares Problem for a Group Project in a Mathematical Problem Solving Module

Using Gardner's Three-Squares Problem for a Group Project in a Mathematical Problem Solving Module

PENGARUH PROBLEM SOLVING BERBANTUAN LEAD ADVERSITY QUOTIENT TERHADAP PENINGKATAN KEMAMPUAN PEMECAHAN MASALAH SISWA SD

This research aimed to determine the effect of using the Problem-Solving model assisted by LEAD Adversity Quotient on students' mathematical problem-solving abilities. The type of research conducted was quasi-experimental research. The sampling technique used was purposive sampling. The population of this study was all students of Bawen 01 Public Elementary School, and the sample selected for the research was the fourth-grade class of Bawen 01 Public Elementary School. Data were collected using test techniques (pretest, posttest) and non-test techniques (observation, documentation, questionnaire). The data analysis techniques included normality test, homogeneity test, simple linear regression test, and independent sample t-test. The research results revealed the following: (1) There was a significant difference between the control group and the experimental group in terms of mathematical problem-solving abilities, as evidenced by the significance level Sig. (2-tailed) of 0.019 < 0.05 using the independent sample t-test. (2) The implementation of the Problem-Solving model assisted by LEAD Adversity Quotient on students' mathematical problem-solving abilities was proven with a calculated t-value of 6.929 > t-table of 2.120 and a significance value of 0.000 < 0.05 using the simple linear regression test. In conclusion, the Problem-Solving model assisted by LEAD Adversity Quotient has a significant impact and difference in improving students' mathematical problem-solving abilities

Exploring junior high school students' geometry self-efficacy in solving 3D geometry problems through 5E instructional model intervention: A grounded theory study

Geometry self-efficacy is an essential affective aspect that will influence students in solving mathematics problems, especially geometry material. Therefore, teachers must be able to develop learning instructions that not only affect students' mathematical abilities but also strengthen students' affective aspects. This research explores students' geometry self-efficacy when learning to solve three-dimensional geometry problems through the 5E Instructional Model intervention. A grounded theory design was used to reveal the aims of this research. Participants in this research were one mathematics teacher and 22 students (12 girls and 10 boys) in class VIII at a state Junior High School in Indramayu Regency, Indonesia. The research involved the qualitative analysis of gathered data obtained through observation, questionnaires, interviews, and documentation, employing grounded theory analysis techniques, including open coding, axial coding, and selective coding. The findings revealed that students with high self-efficacy in geometry display confidence in describing and calculating the surface area and volume of three-dimensional geometric objects. Those with moderate self-efficacy in geometry are self-assured in addressing straightforward assignments but may need more confidence in tackling more complex tasks. Conversely, students with low self-efficacy in geometry tend to need more confidence and are prone to giving up easily. Therefore, this research emphasizes that the geometry self-efficacy level can influence how students act and complete 3D geometry tasks given by teachers in learning, especially 3D geometry learning.

Analysis of The Mathematical Problem-Solving Ability on Two-Variable Linear Equation System Material In Grade VIII Students

This study aims to describe the ability to solve mathematical problems on two-variable linear equation system material based on the locus of control in grade VIII students. This study used qualitative methods to obtain a sample of 72 students using purposive sampling. Data collection techniques use locus of control questionnaire instruments and problem-solving ability test questions. The results of this study showed that students with a strong external locus of control were only able to reach a step of understanding the problem. Meanwhile, students with a balanced internal and external locus of control can reach two steps namely, understanding the problems and devising a strategy. This happens because, students with a strong external locus of control, as well as students with a balanced internal and external locus of control, are less trying and less active in seeking information related to the problems at hand, and are easily influenced by others. Meanwhile, students with a strong internal locus of control can reach three steps namely, understanding the problems, devising a strategy, and carrying out the strategy. This happens because students have a strong internal locus of control easily satisfied with the results they get with the effort they make.

The effects of functional moves in teacher questioning on students’ contextualization of mathematical word problem solving

AbstractPosing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that the implementation of task clarification (TC) moves effectively enhanced contextualization only when students possessed a relatively strong sense of agency while solving word problems. Furthermore, when students’ attentional focus was not appropriately redirected by the functional moves, including procedural understanding (PU), making connections (MC), the rationale behind a strategy (RA), and an alternative strategy (AS), their understanding of the contextual features and construction of mathematical relationships in word problem solving could not be refined. Implications for field experience design and future research on the quality of teacher questioning in mathematics teacher education programs are discussed.

Analysis of Problem-Solving Abilities in Completing Story Problems on Combination Material Based on Student Learning Styles

Analysis of mathematical problem-solving abilities is a detailed observation effort of students' abilities in solving mathematical problems. Combinations in mathematics cause difficulty in understanding information and getting the main idea of sentences; therefore, knowing students' learning styles helps them choose an appropriate approach. This research aims to describe problem-solving abilities in solving combination material story problems based on the visual, auditory, and kinesthetic learning styles of class XII MIA students. This research uses qualitative methods with research instruments consisting of learning-style questionnaire sheets, test sheets, interview transcripts, and member check sheets. The research subjects consisted of a visual, an auditory, and a kinesthetic student. The research results show problem-solving abilities: 1) visual students understand problems, formulate plans, arrange to problem-solve, and review the results; 2) auditory students understand problems, prepare plans, arrange problem-solving, and review the results; 3) kinesthetic students understand problems, make plans, organize problem-solving, and not check the results. These results show that visual and auditory subjects can answer mathematical problems well and correctly. However, the kinesthetic subject is unable to solve mathematical problems. In conclusion, these results provide a detail that increases students' and teachers' awareness that kinesthetic students need extra support to improve their problem-solving ability.

The use of augmented reality to improve students' geometry concept problem-solving skills through the STEAM approach

This research develops learning media with a Science, Technology, Engineering, Art, Mathematics (STEAM) approach based on Augmented Reality (AR) to improve students' mathematical problem-solving abilities on geometric concepts. This method uses design-based research (DBR). The development stages consist of needs assessment and literature review, design and development, user testing to analyze user responses and evaluation and examination of the media devices being developed. The research subjects for expert tests included media experts and education experts, practicality tests for teachers, response tests for ten high school students, and examination stage tests for 30 high schools in Indonesia. The instruments used were media expert questionnaires, education expert questionnaires, practicality questionnaires, and tests. The media developed is called Augmented Reality Mathematics (ARM). The results of this research are 1) ARM media expert test in the very good category, 2) ARM educational media expert test in the very good category, 3) ARM media practicality test in the good category, 4) responses from students who use ARM media in the very good category, and 5) ARM media can improve mathematical problem-solving abilities in the moderate category. The findings of this research are that AR media is effectively used to improve students' problem-solving abilities in medium-category geometry concepts using the STEAM approach. This research concludes that using ARM media with STEAM learning can improve problem-solving abilities in geometric concepts.

Students’ Mathematical Thinking in Movement

AbstractMathematics education research is increasingly focused on how students’ movement interacts with their cognition. Although usually characterized as embodiment research, movement research often theorizes the body in diverse ways. Ingold (Making: Anthropology, archaeology, art and architecture, 2013) proposes that thinking and knowing emerge from the entwined, dynamic flows of human and non-human materials in a process called making and, following Sheets-Johnstone (The primacy of movement (Vol. 82), 2011), contends that humans think in movement. The study that this paper draws on employs Ingold’s making to study students’ movement during mathematical problem solving. In this paper I also recruit Laban’s movement elements (Laban & Ullmann, 1966/2011) as a framework to describe and analyse how the body moves in space and time and to incorporate the often-forgotten dynamic qualities of movement. This paper investigates the movement of a small group of tertiary students as they engage with a mathematical prompt (a task in Abstract Algebra), using thick description, to answer the questions: (1) How do students think mathematically in movement? (2) How do Laban’s elements help inform research into students’ movement? Through the lens of Laban’s movement elements, my analysis demonstrates that students think mathematically in movement. These findings suggest that mathematics educators may be overlooking valuable instances of students’ mathematical thinking and knowing: the thinking and knowing in movement which may not be available through verbalizations or artefacts. Although thinking in movement does not fit a traditional conceptualization of undergraduate mathematics, which privileges written communication heavily reliant on notation, to understand students’ mathematical cognition more comprehensively, mathematics educators need to reconsider and appreciate students’ mathematical thinking in movement.

The Peer Tutor Model with Cognitive Conflict Strategies in Collaborative Learning Mathematical Problem Solving and Its Effect on Individual Achievement.

Cognitive conflict is a condition where students encounter new experiences that are not neatly arranged in their cognitive structure. The process of assimilation between old and new concepts in students' cognition. The assimilation process is more effective when done together with peer tutors. The purpose of this study was to see the effect of cognitive conflict on collaborative mathematical problem solving and its effect on individual learning success. Case study research methods, descriptive qualitative and quantitative. Learning is carried out to 28 semester II students collaboratively in solving integral problems. Pretest knowing the initial ability of mathematics, given the problem of integral functions of fractional powers. Given posttest independently. In the learning process students with low initial abilities and difficult to ask questions with peer tutors dare to ask information that has just been received with the help of students with moderate and high initial abilities. Cognitive conflict strategies with peer tutors are very useful. The impact of the experience of peer tutors, posttest results is very significant. This means that the posttest results increased significantly for the material of integral functions of fractional powers and motivation to learn for the better.

Using lesson study to help mathematics teachers enhance students’ problem-solving skills with teaching through problem solving

As a central objective, problem-solving skills are important in the mathematics curricula of many countries. However, such skills tend to receive limited and rarely systematic attention in mathematics lessons, including in the Netherlands. To address this gap, the authors adopt a specific approach that defines problem solving as integral to mathematics: Teaching mathematics Through Problem solving (TTP). In Japan, teachers often learn about TTP by performing Lesson Study (LS), an approach in which teachers work in teams to design and conduct a research lesson that allows them to learn collectively about students’ learning processes. TTP offers a promising, structured, didactical approach to introducing problem solving in mathematics lessons, and LS appears to represent an effective means for teachers to learn about TTP. To test this proposition, the current study entails a TTP- and LS-based intervention implemented in two secondary schools in the Netherlands, with an explicit focus on problem-solving skills. The central research objective for this study is to determine whether this TTP-LS-intervention helps mathematics teachers incorporate problem-solving skills into their lessons and how design characteristics and mechanisms of the intervention affect the outcomes. Interviews with teachers provide insights into which characteristics of the TTP-LS intervention fostered the implementation of problem solving in their teaching practice, as well as which did not. The collected data show that the teachers regard TTP as a valuable pedagogy to teaching mathematical problem solving. They report that the joint development, implementation, and evaluation of TTP lessons in the LS cycles, and especially observations of students, has given them more tools for applying TTP pedagogy and that they use these tools to promote problem-solving skills. Elements of the TTP lessons that the teachers perceived as difficult were the lesson phases that featured discussions on solution strategies rather than finding the “right” answers. Teachers regarded LS as a suitable approach for learning about TTP. Some points for improvement also emerged from the data. For example, more support should be given to TTP-LS-teams to explain the problem-solving skills they want to target in their lessons, and to practice especially the classroom discussion and summary phase.