A systematic review on visualization in mathematical problem-solving in secondary schools

This study aims to describe: (1) the mathematical problem-solving ability of Sleman Regency's JHS students, (2) whether there is a difference in students' mathematical problem-solving ability in terms of multiple intelligence, (3) whether there is a difference in students' mathematical problem-solving ability in terms of cognitive style, (4) whether there is a difference in students' mathematical problem-solving ability in terms of learning style, and (5) whether there is an interaction between multiple intelligences, cognitive style and learning style. The research method used is a survey method with a quantitative approach. The research population is JHS students in the 2023/2024 school year in Sleman. The sample is 434 students, determined using a stratified proportional random sampling technique. The instruments used were a mathematical problem-solving ability test, a GEFT test, a multiple intelligence questionnaire, and a learning style questionnaire. The data analysis is descriptive statistics to determine students' mathematical problem-solving ability level and inferential statistics using a three-way ANOVA test to describe students' mathematical problem-solving ability's differences in terms of multiple intelligence, cognitive style and learning style, and to describe the interaction between multiple intelligences, cognitive style and learning style. The analysis showed that: (1) the mathematical problem-solving ability average score of Sleman's JHS students is 53.49 which is in the moderate category, (2) there is no difference in students' mathematical problem-solving ability in terms of multiple intelligence, (3) there is a difference in students' mathematical problem-solving ability in terms of cognitive style, (4) there is no difference in students' mathematical problem-solving ability in terms of learning style, and (5) there is no interaction between multiple intelligence, cognitive style and learning style of students.

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.

The purpose of this study was to assess the contributions of mathematics teachers enhancing students’ critical thinking, reasoning, and creativity skills on enhancing students’ problem solving abilities in mathematics. The study used survey design with quantitative research method, and 102 teachers were selected using stratified random sampling based on the type of program, level of teaching and service year. The instrument used of the study was a Likert scale on enhancing students' critical thinking, reasoning, creativity skills and problem solving abilities in mathematics, and analyzed by mean, standard deviation, correlation, and multiple regression. The finding indicated that the perception of mathematics teachers enhancing students’ critical thinking, reasoning, creativity skills, and problem solving abilities in mathematics were above average. There is a significantly and positively associated between the perceptions of mathematics teachers enhancing students’ critical thinking, reasoning, and creativity skills in mathematics with enhancing problem solving abilities in mathematics; and enhancing students' reasoning skill was the highest and significantly contributor or predictor to enhancing problem solving abilities in mathematics; but the contribution of the mathematics teachers enhancing students' critical thinking and creativity skills were not significantly contributed or predicted to enhancing problem solving abilities in mathematics. Some of the recommendations were: training should be given to teachers on enhancing students’ critical thinking, reasoning and creativity skills, and mathematical problem solving ability; the curriculum and the textbook should designed to enable learners communicate their mathematical critical thinking, reasoning and creativity on mathematical problem solving.

The development of reflective thinking has been a highlight and important in the education of prospective mathematics teachers. It provides them with the opportunities to take a conscious and logical decision on the complex problems they faced. The quality of the problem solving and reflective thinking will differ between one student and another due to their characteristics. This study presents a description of reflective thinking skills of prospective teachers in solving mathematical problems based on the difference in cognitive style. The instruments used in this study consist of (1) GEFT cognitive-style test, (2) a mathematical problem solving task which is a non-routine and open-ended (3) the interview guidelines based on the reflective thinking component. By choosing analysis of qualitative approaches, the data of interviews that are in the form of interview's transcript based on mathematical problem solving results are gathered from two students of prospective mathematics teachers as research participants. One prospective teacher use cognitive field independent style (PTFI) and field dependent style (PTFD). Research findings show that PTFD tends to use the experience to be implemented in mathematical problem solving but PTFD cannot utilize the new information contained, so that PTFD has a reflective-dynamic characteristic. While PTFI tends to use the experience to utilize the new information contained in the problem in order to construct the problem solving strategy so that PTFI has reflective-generative characteristic. It is indicated that there are differences in the characteristics of reflective thinking process among prospective teachers based on difference of cognitive style.

Purpose - Mathematical literacy and mathematical problemsolving are crucial abilities that link mathematics content to real life applications, facilitating both mathematics understanding and mathematical processes. The present study aimed to investigate the effectiveness of the STEMEN (STEM and educational neuroscience) teaching model in enhancing mathematical literacy and problem-solving skills. Methodology - This study adopted a pre-test and post-test control group design. Among 156 Grade 9 students from a secondary school in Phayao, Thailand, 70 were randomly selected. The STEMEN teaching model was implemented in the experimental group, while the 5E teaching model, typically used in a normal classroom was employed in the control group. Two types of tests, namely the mathematical literacy test and the mathematical problem-solving test, were used as research instruments. Pre and post-data were collected from both the experimental and control groups. Repeated measures ANOVA with Wilks’ lambda was employed to analyze the mean comparison for mathematical literacy and mathematical problem-solving. Findings - The findings revealed that the mean scores for mathematical literacy and mathematical problem-solving were relatively higher in the STEMEN teaching model group compared to the 5E teaching model group. These results provide insights into the effectiveness of the STEMEN teaching model in enhancing learning outcomes, particularly mathematical literacy and problem-solving in mathematics. Significance – The results of this study showed that the STEMEN teaching model was effective in increasing learning outcomes, including mathematical literacy and problem-solving. These outcomes should enable teachers to design effective and efficient instructional strategies for enhancing mathematical literacy and problem-solving in classrooms.

The study aimed to analyze the interaction effect teaching models and cognitive style field dependent (FD)-field independent (FI) to students’ mathematical problem-solving ability (MPSA), as well as students' MPSA differences based on teaching models and cognitive styles. Participants in this study were 145 junior high school students, with details of 50 students learning through the Connect, Organize, Reflect, and Extend Realistic Mathematics Education (CORE RME) model, 49 students use the CORE model, and 46 students use the Conventional model. Data collection tools used are the MPSA test, and the group embedded figure test (GEFT). The MPSA test finds out that there are interaction effect teaching models and cognitive styles on students' MPSA, as well as a significant difference in MPSA students who study through the CORE RME model, CORE model, and Conventional model. Based on cognitive style, between students who study through CORE RME model, CORE model, and Conventional model found that there was no significant difference in MPSA between FI students. Furthermore, there were significant differences in MPSA between FD students and also MPSA of FI students better than MPSA FD students. Therefore, teaching models and student cognitive styles are very important to be considered in the learning process, so students are able to solve mathematical problems.

The objective of this study is to determine the effect of cognitive style on students’ mathematical problem-solving ability. This study used the survey method with a quantitative approach. One class consisting of 32 students was selected by purposive sampling for the study sample. A total of 17 students have a field-dependent (FD) cognitive style, while 15 other students have a field independent (FI) cognitive style. GEFT and mathematical problem-solving ability test instruments were used to collect research data. Data were analyzed using Pearson Product Moment correlation test and a simple regression test. The research results found that there is a strong positive relationship between cognitive style and students’ mathematical problem-solving ability, indicated by correlation coefficient r = 0,636. In addition, cognitive style has an effect on students’ mathematical problem solving ability of 40,5% through a linear relationship Ŷ = 3,703 + 0,512X.

The aim of this research is to determine the effect of cognitive style and gender on mathematical problem solving ability. This research is an expost facto research. The students of Mathematics Education Department of Universitas Sulawesi Barat who program the trigonometric course were made population in this research. Data were collected by documentation dan test techniques. Documentation was used to obtain data of gender. GEFT test and problem solving ability test were used by researcher. The technique of data analysis used multiple linear regression analysis. The results showed that (a) cognitive style influenced the mathematical problem solving ability with significantly; (b) gender has no effect on the mathematical problem solving ability; (c) cognitive and gender styles together have a significant effect on mathematical problem-solving ability. Keywords: Cognitive Style, Gender, Mathematical Problem Solving Ability

This research aims were to (1) test the effectiveness of the Flipped Classroom learning model assisted by the Sevima Edlink on students' mathematical problem-solving abilities, and (2) describe students' mathematical problem-solving abilities based on cognitive style in the Flipped Classroom learning model assisted by the Sevima Edlink. This research was a mixed methods type of sequential explanatory design. Quantitative methods were used to test the effectiveness of using the Flipped Classroom learning model on students' mathematical problem-solving abilities while qualitative methods were used to describe students' mathematical problem-solving abilities based on cognitive style in the Flipped Classroom learning model assisted by the Sevima Edlink. Data collection was carried out using problem-solving ability tests, GEFT tests (cognitive style tests), and interviews. The population of this study were all class VIII students of SMP N 1 Pecangaan for the 2022/2023 school year. The samples used were students of class VIII E as the experimental group and class VIII G as the control group. The results of the research conducted showed that (1) the Flipped Classroom learning model was effective in increasing students' mathematical problem-solving abilities, (2) students' mathematical problem-solving abilities in terms of cognitive style were divided into two categories, namely FI (7) and FD (15). The FI category is divided into 3 patterns of problem-solving abilities while students with the FD category are divided into 5 patterns.

This study aims to describe students' mathematical problem solving skills in solving word problems. The population in this study were all fourth grade students at SD 4 Dersalam with a total sample of 24 students. The research method used is a qualitative approach with descriptive methods. The research instrument used was in the form of test questions (essays) and interview for mathematical problem-solving abilities in diagrammatic material. The data collection technique in this study has three stages of procedure namely; 1) preparation stage, 2) implementation stage, 3) final stage. Based on the results of the tests that have been given, the ability to solve mathematical problems in the good category is 14 students (58.3%), the medium category is 4 students (16.6%) and the low category is 6 students (25%). Based on the categories of mathematical problem solving abilities, namely good, sufficient and insufficient, it can be described as follows: 1. Students' Mathematical Problem Solving Ability in the Good Category 2. Students' Mathematical Problem Solving Ability in the Enough Category 3. Students' Mathematical Problem Solving Ability in the Poor Category.

This article discusses the relationship between students' cognitive style and mathematical problem-solving abilities in the number pattern material carried out at SMP Negeri 1 Botupingge in the odd semester of the 2021/2022 academic year. The research method used is a survey method with a correlational approach, with a questionnaire instrument to determine students' cognitive style and problem-solving tests to measure students' mathematical problem-solving abilities. The results showed that the correlation coefficient between students' cognitive styles and mathematical problem-solving abilities was 0.60, which means that there is a relationship between students' cognitive styles and mathematical problem-solving abilities at a high level. The coefficient of determination of 0.36 indicates that 36% of the contribution of cognitive style to the improvement of mathematical problem-solving abilities, and the remaining 64% is determined by other factors.

Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development - Young Seh Bae - This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically developing students in fourth and fifth grade, who were comparable on age and IQ (greater than 80). The factors examined in the study were: word problem solving accuracy; word reading/decoding; sentence comprehension; math vocabulary; arithmetic computation; everyday math knowledge; attitude toward math; identification of problem type schemas; and visual representation. Results indicated that the students with typical development significantly outperformed the students with ASDs on word problem solving and everyday math knowledge. Correlation analysis showed that word problem solving performance of the students with ASDs was significantly associated with sentence comprehension, math vocabulary, computation and everyday math knowledge, but that these relationships were strongest and most consistent in the students with ASDs. No significant associations were found between word problem solving and attitude toward math, identification of schema knowledge, or visual representation for either diagnostic group. Additional analyses suggested that everyday math knowledge may account for the differences in word problem solving performance between the two diagnostic groups. Furthermore, the students with ASDs had qualitatively and quantitatively weaker structure of everyday math knowledge compared to the typical students. The theoretical models of the linguistic approach and the schema approach offered some possible explanations for the word problem solving difficulties of the students with ASDs in light of the current findings. That is, if a student does not have an adequate level of everyday math knowledge about the situation described in the word problem, he or she may have difficulties in constructing a situation model as a basis for problem comprehension and solutions. It was suggested that the observed difficulties in math word problem solving may have been strongly associated with the quantity and quality of everyday math knowledge as well as difficulties with integrating specific math-related everyday knowledge with the global text of word problems. Implications for this study include a need to develop mathematics instructional approaches that can teach students to integrate and extend their everyday knowledge from real-life contexts into their math problem-solving process. Further research is needed to confirm the relationships found in this study, and to examine other areas that may affect the word problem solving processes of students with ASDs.

Teacher knowledge and beliefs are known to play crucial roles in shaping teacher teaching practice regarding mathematical problem-solving. Thus, assessing the teacher’s quality of mathematical problem-solving can be traced through such three factors. This paper aimed at exploring the elements of mathematics-related beliefs, mathematics problem-solving knowledge for teaching, and problem-solving-based teaching practice needs to be improved by mathematics teachers. Some empirical findings of assessing those three factors from a two-year research project involving a total of 288 teachers from primary and secondary school on teacher’s problem-solving were presented as the manifestation of teacher quality regarding mathematical problem-solving. More specifically, the teachers participating in such a research project were indicated to have beliefs about nature of mathematics, mathematics teaching and mathematics learning ranging from Instrumentalist view to problem-solving view. Also, it was found that teacher problem-solving content knowledge such as knowledge of mathematics problem and problem-solving strategies was insufficient to hold a problem-solving instruction. Furthermore, the teacher’s teaching practice, assessed by observing how the teacher participants guide their students to solve a mathematics problem following Polya’s four stages of problem-solving, range from directive to consultative teaching. In sum, beliefs, knowledge, and teaching practice are discussed as three interdependent factors which determine the quality of teacher’s mathematical problem-solving.

The main target of the current study is to explain the metacognition of junior high school students with Field Independent (FI) and Field Dependent (FD) cognitive styles in mathematics problem-solving. It should be noted that the statistical population of this study was all junior high school students in the Sragen regency in the 2018/2019 academic year. To reach the research purpose, different instruments such as the cognitive style tests, the problem-solving exercises, and the interview guidance were used. Data analysis was carried out by data collection, data reduction, data presentation, and conclusion. The results indicated that the students who have field-independent cognitive style had high self-confidence that they were able to solve the problem correctly, able to do planning steps, able to make important decisions for themselves, so they can solve the problem properly. Students with FD cognitive style are completely confident that their answer is correct, but they have not yet clarified the steps they need to solve their problems and have not yet focused on their shortcomings in mathematics problem solving, so their task results in mathematics problem-solving incorrectness answer.
 
 Keywords: Cognitive style; Mathematics problem solving; Metacognition

The semantic system is involved in mathematical problem solving