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This paper is devoted to the design, description and validation of the Android application TEAtreves, which focuses on structured arithmetic problem-solving for students with autism spectrum disorder (ASD). The application contains multiple adaptations to make it suitable for users with ASD. Validation was carried out with five students with ASD, obtaining positive results which confirm the strength of TEAtreves app for users with ASD. Results and future lines of work are discussed. [ABSTRACT FROM AUTHOR]

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students' reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students' reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures. [ABSTRACT FROM AUTHOR]

This study investigates the impact of a Realistic Mathematics Education (RME) intervention on students’ mathematical problem-solving skills. A comparative evaluation study with a follow-up was conducted in a secondary school in Greece. The intervention engaged students in collaborative problem-solving. Overall, 124 10th-grade students participated in the study (74 in the intervention and 50 in the comparison group). A selection of items from the Programme for International Student Assessment (PISA) was used for the assessments. The post-test results showed that students in the intervention group developed more their problem-solving skills than those in the comparison group. The effect size was d = 0.31, CI 95% [0.11, 0.51]. The intervention group also performed better in the follow-up assessment. This study shows the positive impact of the RME intervention on students’ problem-solving skills and discusses how even a short-term intervention can affect students’ performance in large-scale international assessments. [ABSTRACT FROM AUTHOR]

In the study reported on here we used a qualitative case study design to examine the self-control and self-monitoring behaviour of gifted learners in problem-solving processes. We selected 3 gifted secondary learners using the purposeful sampling method. For the study, each learner completed 10 individual problem-solving sessions. A think-aloud protocol as well as observations and interviews were used in each problem-solving session. The gifted learners displayed various and intertwined self-control and self-monitoring behaviour to read, understand, and solve the problems, and to find and verify the answer. They also displayed this behaviour much more frequently in problems that required using visual drawings and/or had long texts. The gifted learners left or adapted self-control behaviour when the behaviour did not work for solving mathematical problems. They made decisions regarding self-control behaviour by means of the self-monitoring process. The participants presented insistent, quick, flexible, and fluent actions for both self-control and self-monitoring processes. Based on our findings, we propose a portrait of gifted learners' self-regulative behaviour in the mathematical problem-solving process. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic compelled higher education institutions to adopt an alternative approach to learning. For mathematics education, supporting students through blended learning has become increasingly important as it will ensure students' learning is sustained in such a situation. This practical change has illuminated how cloud technology can be employed in mathematics education to improve the instruction process. Using a cloud classroom blended learning-instructional framework for integrating educational cloud tools into mathematics teaching, this study analysed students' metacognitive ability in mathematical problem-solving. A pre-experimental research using a one group pre-test-post-test design was conducted. The sample comprised sixty undergraduate mathematics students enrolled on a Numerical Analysis course. Sample selection was carried out using a simple random sampling technique. Data were analysed using a descriptive analysis, parametric tests, and n-gain. The results revealed that, firstly, the majority of students (90%) achieved a post-test score of metacognitive ability in mathematical problem-solving - this exceeded the 60% threshold. Secondly, students' post-test score of metacognitive ability in mathematical problem-solving (mean score of 82.14, S.D. = 8.29) increased significantly compared to the pre-test score (mean score of 73.54, S.D. = 8.38). Further, the effect size was large. Thirdly, there was an enhancement of metacognitive ability in the mathematical problem-solving of students with a mean n-gain of 0.34, which is in the moderate category. Thus, cloud classroom blended learning significantly improved metacognitive ability in mathematical problem-solving among undergraduate students. Educators can apply the results to assess mathematics learning in order to improve the quality of metacognitive ability in mathematical problem-solving. [ABSTRACT FROM AUTHOR]

Students’ problem-solving abilities are influenced by their self-confidence in learning mathematics. This study intends to investigate junior high school students' mathematics problem-solving abilities in terms of their self-confidence in the set content. Descriptive qualitative research methodology is employed. This research involved 32 students in 7th grade at SMP Negeri 2 Sukodadi, Lamongan. To focus on data analysis, 3 students were selected representing different levels of self-confidence, namely high, medium and low. Subject taking is based on the results of the scores on the self-confidence questionnaire that has been given. Questionnaires on self-confidence, tests of mathematical problem-solving abilities, and interview guidelines were the instruments employed. Based on the data analysis, it was found that there is a close relationship between self-confidence and mathematical problem-solving ability, that is, the higher the level of student self-confidence, the better the ability to solve mathematical problems. Conversely, if students’ self-confidence is lower, their mathematical problem-solving abilities will also be lower. This study emphasizes the importance of students' self-confidence to be grown in learning to support their mathematical problem-solving abilities.

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 problemsolving 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’ problemsolving skills. [ABSTRACT FROM AUTHOR]

Although previous studies have found general cognitive factors provided pillars for basic mathematical performance, relatively fewer studies examined the cognitive mechanisms underlying children's advanced mathematical performance. Guided by cognitive loading theory and dual-coding theory, this study tested longitudinal pathways to investigate the role of working memory, inhibition, phonological awareness, and visual perception in mathematical reasoning and problem-solving in primary school children. The participants were 81 primary school students (32 boys; mean age were 8.54 ± 0.64 years old) whom were first tested in third grade (T1) regarding working memory, inhibition, phonological awareness, visual perception, and mathematical reasoning. Mathematical reasoning and problem-solving were assessed 6 months later (T2). The results indicated that T1 working memory predicted T2 mathematical reasoning. T1 working memory, inhibition, and phonological awareness predicted T2 mathematical problem-solving. The findings highlighted the importance of working memory, inhibition and phonological awareness in children's advanced mathematical performance. [ABSTRACT FROM AUTHOR]

This study aims to examine the effect of problem posing-based active learning activities on students' problem-posing skills and problem-solving achievement. To this aim, an experimental design with pre-test post-test control group was employed. The participants consisted of two groups of sixth graders, one experimental group (N=23) and one control group (N=25). Students in the experimental group were exposed to seven problem-based active learning activities over the course of six weeks. The study used problem-solving and problem-posing tests to collect data. The results revealed that eventhough the intervention was not statistically significant, the increase in the problem-solving mean score of the experimental groups was higher than that of the control group. Problem posing pre- and post-test scores of the experimental group differed statistically significantly with a high level of effect size (η2=0.80 ). Finally, educational implications are discussed, and recommendations are made for future research.

This study intended to investigate the creative thinking dispositions of students who can perform truth-seeking in solving mathematical problems. Truth-seeking behavior tends to show students' thinking disposition when they need to solve math problems. This behavior is very much needed by students in solving math problems, especially HOTS-type questions. This study is qualitative and employs a phenomenological approach. Three students from the Integrated Islamic Junior High School in Manokwari who sought the truth served as research subjects. Their answers on the answer sheets encouraged the determination of the subjects’ tendencies in truth-seeking and creative thinking. The results of thought-based and task-based interviews were then incorporated into the analysis to determine the creative thinking dispositions of truth-seeking students and the relationship between truth-seeking and creative thinking dispositions. The findings of this study indicate that all research subjects have diverse creative thinking dispositions; the more truth-seeker indicators that are met, the more creative thinking dispositions they possess. When solving mathematical problems, students tend to show how they think by how hard they try to find the truth. This result implies that it needs more research on the level of creative thinking disposition and how to increase students' true search.

The general objective to be achieved in this study is to determine the effect of using Blended Learning in terms of Intrapersonal Intelligence on Problem Solving Ability. This research is a quasi-experimental research with a two × three factorial design. Documentation, questionnaires, and tests were carried out in the data collection method. The instruments used to collect the data were the learning achievement test instrument and the student's intrapersonal intelligence questionnaire instrument. The data analysis used was ANOVA with a two-way analysis of variance 2 x 3. The prerequisite test for Variance Analysis used the Lillifors method for the normality test and the Barlett method for the homogeneity test. The results showed (1) that the implementation of blended learning geometry material resulted in better learning achievement and problem-solving abilities than conventional learning. As evidenced by student learning achievement in the experimental class is categorized as high with an average score of 70,935. At the same time, the control class is lower, with an average score of 53,792. (2)There is an interaction between the Blended Learning model and students' intrapersonal intelligence on mathematics learning achievement and problem-solving abilities. (3) There are differences in student learning achievement with blended Learning and conventional Learning seen from intrapersonal intelligence. [ABSTRACT FROM AUTHOR]

Science, technology, engineering, and mathematics (STEM) problem-solving is necessary to be infused into the classroom. Nevertheless, the criticism of underrepresented mathematics in STEM problem-solving assessment is an issue. In this study, we develop and investigate the psychometric evidence of an integrated STEM-based mathematical problem-solving test. The product of the test was a mathematical essay test that contains three scientific scenarios related to the environment in every middle school grade. The mathematical contents were integrated into engineering-based design using the technology. Three experts filled an assessment sheet to assess content validity, which was analyzed using a content validity index (CVI) and intraclass correlation coefficient (ICC). The result of content validity revealed that overall items were valid and reliable. The construct validity was examined using the Rasch analysis from the data of Grades 7–9 students in Indonesia (n = 286). The construct of all scenarios and prompting items indicated fit with various difficulty levels and acceptable discrimination value. Nevertheless, four prompting items were reported as misfit based on unweighted mean square value. The recommendation for improvement is emphasized in the language clarity aspect. The inter-rater reliability was also declared good. A further study is suggested to provide a computer-based test.

The introducer of ethnomathematics defined ethnomathematics as mathematics practised among identified cultural groups. Ethnomathematics positively impacts the learning process either as a Moderate or an approach to, for example, problem-solving ability. Previous researchers have carried out several studies on implementing ethnomathematical-based learning to improve students’ problem-solving ability. However, the analysis shown is very varied, so it still raises doubts about the impact of learning using ethnomathematics on mathematical problem-solving abilities. This study aims to determine the correlation between ethnomathematical-based with students’ problem-solving skills. This study uses meta-analysis research, which combines several experimental Studies that collate the effectuality of ethnomathematical-based learning and regular instruction on improving the mathematical problem-solving ability. Relevant studies were searched through e-resources from Perpusnas databases with the specified keywords. There are 106 studies obtained from the search query. Fourteen studies were selected according to the inclusion and exclusion criteria. Meta-Mar was used to determine the joined effect size by analysing the selected studies. This study shows that the joined effect size of applied ethnomathematical-based learning in improving mathematical problem-solving skills is 1,04 and was classified as a strong effect. Therefore, it is deduced that ethnomathematical-based learning relies on mathematical problem-solving abilities. Statistically, the implementation of ethnomathematics-based learning in improving mathematical problem-solving ability is also influenced by the study’s characteristics at the level of education.

Mobile eye-tracking research has provided evidence both on teachers' visual attention in relation to their intentions and on teachers’ student-centred gaze patterns. However, the importance of a teacher’s eye-movements when giving instructions is unexplored. In this study we used mobile eye-tracking to investigate six teachers’ gaze patterns when they are giving task instructions for a geometry problem in four different phases of a mathematical problem-solving lesson. We analysed the teachers’ eye-tracking data, their verbal data, and classroom video recordings. Our paper brings forth a novel interpretative lens for teacher’s pedagogical intentions communicated by gaze during teacher-led moments such as when introducing new tasks, reorganizing the social structures of students for collaboration, and lesson wrap-ups. A change in the students’ task changes teachers’ gaze patterns, which may indicate a change in teacher’s pedagogical intention. We found that teachers gazed at students throughout the lesson, whereas teachers’ focus was at task-related targets during collaborative instruction-giving more than during the introductory and reflective task instructions. Hence, we suggest two previously not detected gaze types: contextualizing gaze for task readiness and collaborative gaze for task focus to contribute to the present discussion on teacher gaze

This study aims to examine the effect of problem posing-based active learning activities on students' problem-posing skills and problem-solving achievement. To this aim, an experimental design with pre-test post-test control group was employed. The participants consisted of two groups of sixth graders, one experimental group (N=23) and one control group (N=25). Students in the experimental group were exposed to seven problem-based active learning activities over the course of six weeks. The study used problem-solving and problem-posing tests to collect data. The results revealed that eventhough the intervention was not statistically significant, the increase in the problem-solving mean score of the experimental groups was higher than that of the control group. Problem posing pre- and post-test scores of the experimental group differed statistically significantly with a high level of effect size (η²= 0.80). Finally, educational implications are discussed, and recommendations are made for future research. [ABSTRACT FROM AUTHOR]

Science, technology, engineering, and mathematics (STEM) is a complex problem-solving that depends on the deep structures of domain-specific prior knowledge (DSPK) in mathematics. However, there is a lack of mathematics DSPK tests measuring several mathematics topics in every problem-solving phase in conceptual and procedural knowledge. This study aims to develop a mathematical problem-solving test as a mathematics DSPK test and investigate the content and construct validity. The product of test development is a 30-multiple-choice-item test in six mathematics topics. Every topic underlined all problem-solving phases in conceptual and procedural knowledge in a science or individual context. There were six experts performed the content validity sheets which analyzed using the content validity index (CVI) and intraclass correlation coefficient (ICC). The construct validity was examined using the Rasch model from 175 data of 7th grader students in Indonesia (Mage=12.66, SD=55). The result of content validity revealed overall items were valid (CVI≥83) and reliable (a=863; rxx=513). The construct of all items indicated fit (90≤weigheted MNSQ≤1.16) and were reliable (a=74) with various levels of difficulties and six low discrimination items. The recommendation for improvement is emphasized in language aspects. The absence of knowledge of facts could be an improvement for further study. [ABSTRACT FROM AUTHOR]

This study investigated the mathematical problem-solving ability of 42,644 ninth-grade students who participated in regional education quality health monitoring from Z province in East China and the factors which influence their performance of mathematical problem-solving. The results are as follows: (1) ~96% of the students’ mathematics problem-solving ability meets the basic academic requirements of the mathematics curriculum standards; (2) boys and children without siblings performed better, and urban students performed significantly better than county and rural students; (3) ~28% of students’ mathematical problem-solving performance came from inter-school variability; urban and rural backgrounds had a greater impact on mathematical problem-solving than did teaching factors, while teaching self-efficacy had the least impact among the school-level influencing factors. In contrast, the influence of individual non-intelligence factors was higher than that of student background variables, including a greater positive effect of self-efficacy and a greater negative effect of mathematics anxiety.

Developing students’ skills in solving mathematical problems and supporting creative mathematical thinking have been important topics of Finnish National Core Curricula 2004 and 2014. To foster these skills, students should be provided with rich, meaningful problem-solving tasks already in primary school. Teachers have a crucial role in equipping students with a variety of tools for solving diverse mathematical problems. This can be challenging if the instruction is based solely on tasks presented in mathematics textbooks. The aim of this study was to map whether a teaching approach, which focuses on teaching general heuristics for mathematical problem-solving by providing visual tools called Problem-solving Keys, would improve students’ performance in tasks and skills in justifying their reasoning. To map students' problem-solving skills and strategies, data from 25 fifth graders’ pre-tests and post-tests with non-routine mathematical tasks were analysed. The results indicate that the teaching approach, which emphasized finding different approaches to solve mathematical problems had the potential for improving students’ performance in a problem-solving test and skills, but also in explaining their thinking in tasks. The findings of this research suggest that teachers could support the development of problem-solving strategies by fostering classroom discussions and using for example a visual heuristics tool called Problem-solving Keys.

This study aims to describe mathematical resilience on slow learner students in solving problems. According to the previous research, there is no research focused on the subject of slow learners. The research method is a qualitative descriptive approach. The total population of this study was 71 students with special needs, which consisted of 51 male students and 20 female students. The selection of subjects in this study was reviewed based on three levels of mathematical resilience, namely high, medium, and low. The process of selecting this subject uses the Wright Maps table on Winsteps application version 3.73. Selected subjects were given instruments and interviews to analyze their mathematical problem-solving. The results showed that mathematical resilience on slow learner students was directly proportional to solving mathematical problems for subjects with high mathematical resilience. Meanwhile, subjects with medium and low mathematical resilience were inversely proportional to solving mathematical problems. The stages of solving the problem of the slow learners were incomplete because they have not passed one of the stages formulated by Polya. Therefore, based on the results of this research analysis, teachers can pay more attention to the slow-learners learning strategies in solving problems.

This study examined the impact of a program based on problem-solving in mathematical problem-solving among 10th grade students. The sample of this study consisted of (89) male and female students; Wadi Bani Kharous Basic Education School and Om Hakeem Basic Education School located in AlBatina South Governorate (Oman). The study followed the quasi-experimental research design with experimental group consisted of (48) students, and control group consisted of (41) students. The instructional materials of Polynomial and Algebraic Functions Unit and Trigonometric Functions Unit for Grade 10th were designed according to a program based on problem-solving. The problemsolving test was valid and reliable. The findings indicated that there were significant statistical differences in mathematical problem-solving test between the experimental and control group due to teaching method in favor of experimental group. The findings indicated that there were no significant statistical differences in mathematical problemsolving test between male and female students. The findings also indicated that there were statistical significance differences in mathematical problem-solving test due to the interaction between and teaching method and gender. The study recommended organizing training workshops for mathematics teachers to introduce programs based on problem solving, training them to build educational programs based on problem solving, and urging them to adopt it due to the positive impact it has shown in teaching mathematics.

Word problem-solving is one major area in mathematics that has been identified as being particularly challenging for students, specifically for those with learning disabilities (LDs) and emotional and behavioral disorders (EBD). This study aims at evaluating the effects of a strategic math intervention with concept maps on the ability to solve word problems (addition and subtraction problems, number range of thousand) among students with LDs and EBD from the eighth grade. A multiple-baseline design across participants (N = 9) was applied to evaluate the intervention, which was held three times a week over a 6-week period. Overall, the results demonstrated a functional relation between the amount of correctly solved word problem tasks and the intervention. All nine students improved in word problem-solving, as evidenced by the fact that more tasks were solved, with a higher score in the intervention phase compared with the baseline (between-case standardized mean difference was 1.84; 95% confidence interval [1.24, 2.44]). The social validity data display that all students found the intervention helpful but also partly exhausting. The limitations and implications of this study are discussed. [ABSTRACT FROM AUTHOR]

Are humans intuitive Bayesians? It depends. People seem to be Bayesians when updating probabilities from experience but not when acquiring probabilities from descriptions (i.e., Bayesian textbook problems). Decades of research on textbook problems have focused on how the format of the statistical information (e.g., the natural frequency effect) affects such reasoning. However, it pays much less attention to the wording of these problems. Mathematical problem-solving literature indicates that wording is critical for performance. Wording effects (the wording varied across the problems and manipulations) can also have far-reaching consequences. These may have confounded between-format comparisons and moderated within-format variability in prior research. Therefore, across seven experiments (N = 4909), we investigated the impact of the wording of medical screening problems and statistical formats on Bayesian reasoning in a general adult population. Participants generated more Bayesian answers with natural frequencies than with single-event probabilities, but only with the improved wording. The improved wording of the natural frequencies consistently led to more Bayesian answers than the natural frequencies with standard wording. The improved wording effect occurred mainly due to a more efficient description of the statistical information—cueing required mathematical operations, an unambiguous association of numbers with their reference class and verbal simplification. The wording effect extends the current theoretical explanations of Bayesian reasoning and bears methodological and practical implications. Ultimately, even intuitive Bayesians must be good readers when solving Bayesian textbook problems. [ABSTRACT FROM AUTHOR]

Many studies have been conducted on problem-solving but only a small number of studies emphasized the strategies of teaching problem-solving. This paper explores the teaching strategies for mathematical problem-solving in a secondary school in Johor, Malaysia. It involves a qualitative study in which a semi-structured interview was conducted with mathematics teachers. Data were analyzed using a sixstep thematic analysis. The results can be viewed from three contexts of findings, namely the teaching strategies, the problems faced by teachers, and the solutions to overcome the problems. The findings revealed that there are teachers who have implemented personal teaching strategies, namely the Easy-Maths Model and the Cut-Stop-Solve Model to effectively teach mathematical problem-solving. The findings also explained some problems in teaching mathematical problem-solving, whereby students’ weaknesses in basic mathematics emerged as the main drawback. This study provides useful information to teachers on the different strategies for teaching mathematical problem-solving.

The present study aimed at investigating the effect of a training program based on mathematical problem-solving strategies on critical thinking skills among seventh-grade students in King Abdullah II schools of Excellence. The study adopted the quasi-experimental research approach. The participants of the study comprised of 29 male seventh graders. The participants were randomly distributed into a control group (n = 14) and an interventional group (n = 15). The study adopted the critical thinking skills test (75 items). The tests consisted of five subtests (identifying assumptions, deduction, conclusion, interpretation, and discussion). The interventional training program was a group of training situations complementary to the official curriculum. These situations were based on the strategy of building an organized list or a table, the strategy of finding a pattern, trial and error strategy, the strategy of using an equation or a law, the strategy of building a model or a diagram, the strategy of solving an easier problem, deletion strategy, go backward strategy, and logical justification strategy. The results showed that there were significant statistical differences in the critical thinking post-test scores between the control group (M = 26.5714, SD = 3.95580) and the interventional group (M = 43.6667, SD = 4.68534, t = 10.640, p = 0.000). The study concluded that the training program based on solving mathematical problems is an effective interventional tool to improve the seventh graders’ critical thinking skills. The study recommends reviewing the content of the curricula designed for the elementary stage in Jordan and including drills related to solving mathematical problems that aim to improve critical thinking skills of the elementary stage students.

The new normal period makes ICT-based education the spearhead of the implementation of learning. This becomes an obstacle and a challenge for students, especially in the mathematical problem-solving ability (MPSA), which is very important for students because it is a prior mathematical ability and is included in HOTS. Self-regulated learning in mathematics (SRL) also has a significant role in adapting to learning in the new normal and influences students' mathematical learning outcomes. However, the facts on the ground show that these two abilities are still low. To solve this problem, the researchers developed VBA Microsoft Word-based teaching materials on the relevant polyhedron materials for use so that learning would be more optimal. The method used in this research is an experimental method with a pretest-posttest control group design. The population is all the students in Cimahi City, while the sample is two classes randomly selected. This study indicates that VBA Microsoft Word-based teaching materials are appropriate to be applied in the new normal period, as indicated by the results of the achievement and improvement of MPSA and SRL of students is better than ordinary learning. There is an association between MPSA and SRL and positive response even though they still have difficulty making mathematical models on MPSA questions. Students are more enthusiastic in learning and don't get bored quickly; in line with the challenges of the new normal, the industrial revolution 4.0, and the learning curriculum, learning is more structured, interactive, effective, and efficient.

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

This research was motivated by the fact that the mathematical problem-solving ability of junior high school students during the Covid-19 pandemic in Indonesia was low. The strategy and approach used in learning mathematics are success factors in the mathematics learning process. One of the objectives of this research is to analyze the mathematical problem-solving ability of junior high school students using mobile learning with the Microsoft Kaizala application. The method used in this research is an experiment with a Pre-Experimental Design Research and One-Group Pretest-Posttest Design Research Design. The research was conducted at SMPN 50 Satap Oku, Ogan Komering Ulu Regency, South Sumatra Province. The results showed that the final mathematical problemsolving ability of students who received learning using mobile learning with the Microsoft Kaizala application was better than the students' initial mathematical problem-solving ability and the average percentage of students' mathematical problem-solving ability achievement after using the Microsoft Kaizala application was 85.16% (excellent). It means that the students' problem-solving ability is getting better after using mobile learning with Microsoft Kaizala application. [ABSTRACT FROM AUTHOR]

This study aims to find out: (1) the influence of the use of the Problem-Based Learning (PBL) model on the mathematical communication skill; (2) the influence of the use of the Problem-Based Learning (PBL) model on the mathematical problem-solving skill. This study was conducted on class VIII. The research design is pre-post quasi experimental design. Samples were selected using the cluster random sampling technique. The employed instrument in this study was an essay test. The obtained data were then analyzed using independent samples t-test and simple linear regression. The results indicated that (1) the average score of students' mathematical communication skills taught by problem-based learning models was higher than those taught by conventional methods; (2) the average score of students' mathematical problem-solving abilities taught by problem-based learning models is higher than students taught by conventional methods

Background: During their university studies, student teachers are equipped for the teaching profession in various domains of knowledge and practice. In addition to learning pedagogic skills for practice purposes, they also expand their knowledge of the subjects that they will teach. In mathematics teacher education, one important principle is that the content of the subject must, somehow, be fused with the pedagogy in what has become known as mathematical knowledge for teaching (MKT). Although several studies have been conducted about students’ performance of MKT, there is little research in South Africa about how students routinely experience the coursework itself. In this study, I argue that mathematics knowledge and skills should ideally precede the teaching of pedagogy, for reasons of communicating the concepts clearly and for building a foundation of mathematical thinking prior to practising teaching skills. Aim: To find out what the student teachers’ self-reported experience of one component of a mathematics content course are, namely their engagement with problem-solving tasks. Methods: A qualitative case study of student teachers’ learning, with the primary source of data, the student teachers’ reflective journal entries. Data were analysed through coding, categorising and thematised mindful of the MPSKT framework. Results: The findings indicated that, whilst the students’ understanding of the processes of problem-solving was deepened during the course, matters of pedagogy arose spontaneously.

Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students’ mathematical problem-solving in heterogeneous classrooms in grade five, in which students with special needs are educated alongside with their peers. The intervention combined a cooperative learning approach with instruction in problem-solving strategies including mathematical models of multiplication/division, proportionality, and geometry. The teachers in the experimental group received training in cooperative learning and mathematical problem-solving, and implemented the intervention for 15 weeks. The teachers in the control group received training in mathematical problem-solving and provided instruction as they would usually. Students (269 in the intervention and 312 in the control group) participated in tests of mathematical problem-solving in the areas of multiplication/division, proportionality, and geometry before and after the intervention. The results revealed significant effects of the intervention on student performance in overall problem-solving and problem-solving in geometry. The students who received higher scores on social acceptance and friendships for the pre-test also received higher scores on the selected tests of mathematical problem-solving. Thus, the cooperative learning approach may lead to gains in mathematical problem-solving in heterogeneous classrooms, but social acceptance and friendships may also greatly impact students’ results.

Developing students' skills in solving mathematical problems and supporting creative mathematical thinking have been important topics of Finnish National Core Curricula 2004 and 2014. To foster these skills, students should be provided with rich, meaningful problem-solving tasks already in primary school. Teachers have a crucial role in equipping students with a variety of tools for solving diverse mathematical problems. This can be challenging if the instruction is based solely on tasks presented in mathematics textbooks. The aim of this study was to map whether a teaching approach, which focuses on teaching general heuristics for mathematical problem-solving by providing visual tools called Problem-solving Keys, would improve students' performance in tasks and skills in justifying their reasoning. To map students' problem-solving skills and strategies, data from 25 fifth graders' pre-tests and post-tests with non-routine mathematical tasks were analysed. The results indicate that the teaching approach, which emphasized finding different approaches to solve mathematical problems had the potential for improving students' performance in a problem-solving test and skills, but also in explaining their thinking in tasks. The findings of this research suggest that teachers could support the development of problem-solving strategies by fostering classroom discussions and using for example a visual heuristics tool called Problemsolving Keys. [ABSTRACT FROM AUTHOR]

This qualitative descriptive study aimed to analyze student errors to solve mathematical problems in gender. The subject in this research were Mathematics Education students in the Linear Program subject. The sample selection used purposive sampling by looking at the results of student tests on linear program material categorized by gender. The analysis data using observation methods, test methods and interview methods, meanwhile to validity test of the data using triangulation of data source and triangulation method. Based on the results of the study obtained results: 1) Errors experienced by male and female students are almost similar, but the mistakes experienced by female students are fewer than male students, 2) Female and male students with high ability categories possess different types of errors, namely female students only experience process errors and results of errors, while male experience transformation errors, process errors, results in errors, 3) Female and male students with low ability categories have the same type of errors, namely misunderstanding, transformation errors, process errors, results errors. In this study also none of the subjects experienced reading errors.

The main purpose of this study was to compare and examine the effectiveness of problem-posing and think-pair-share cooperatives' learning models on mathematical problem-solving skills and mathematical communication skills. This study was experimental research with a quasi-experimental design. The samples of the study were 41 students for classroom experiments and 40 students for classroom control. The instruments employed in this study were pre-test and post-test. The instruments were made in essay forms which design to measure students’ mathematical problem-solving skills. The result of the study showed that problem-posing and think-pair-share are very effective to improve students’ mathematical achievements. However, between the problem-posing and think-pair-share, the think-pair-share is more effective than problem-posing, view from the standards of mathematical problem-solving skills and mathematical communication skills of Junior High School students.

This research aims to build students’ abilities in mathematical problem-solving and to explain the uniqueness of the steps of realistic mathematic education in building the problem-solving abilities of a grade 11 (social science track) class in the study of probability at one of the schools in Kupang. The observation results found that every student was having difficulties to solving the mathematical problems, particularly the narrative questions. The research method is Kemmis and Taggart model of Classroom Action Research which was conducted in three cycles, from October 4 to November 3 with twenty-four students. Triangulation had been done to every instrument of variable. The data of mathematical problem-solving was obtained from the students by using test sheets, questionnaires, and student’s discussion sheets. Meanwhile, the data of realistic mathematic education’s variable was obtained from three sources: mentors, two colleagues, and students that were using test sheets, questionnaires, and student’s discussion sheets. The results showed that the fourteen-steps of Realistic Mathematic Education that had been done were able to build mathematical problem-solving abilities of the students. This was evidenced through the increase of three indicators of mathematical problem-solving in every cycle. The average increase of indicators of mathematical problem-solving of the grade 11 students from the first to the third cycle was 10%. Therefore, it can be concluded that the Realistic Mathematics Approach can build the ability of problem-solving of grade 11 students in a social science track studying probability at one of the schools in Kupang. BAHASA INDONESIA ABSTRACT: Penelitian ini bertujuan untuk membangun kemampuan pemecahan masalah matematis siswa dan menjelaskan kekhasan langkah-langkah pendekatan matematika realistik untuk membangun kemampuan tersebut di salah satu sekolah di Kupang kelas XI IPS pada materi peluang topik kaidah pencacahan. Pada hasil pengamatan ditemukan bahwa setiap siswa kesulitan dalam memecahkan masalah matematis khususnya soal berbentuk cerita. Metode penelitian yang digunakan adalah Penelitian Tindakan Kelas model Kemmis dan Taggart yang berlangsung selama tiga siklus, yaitu 04 Oktober – 03 November kepada 24 orang siswa. Triangulasi dilakukan pada setiap instrumen variabel. Data variabel kemampuan pemecahan masalah matematis diperoleh dari siswa menggunakan lembar tes, lembar angket, dan lembar diskusi siswa. Sedangkan data variabel tingkat pelaksanaan pendekatan matematika realistik diperoleh dari tiga sumber, yaitu mentor, dua orang rekan sejawat, dan siswa menggunakan lembar observasi, lembar angket, dan lembar wawancara. Hasil penelitian menunjukkan bahwa keempat belas langkah-langkah pendekatan matematika realistik yang terlaksana dengan baik sekali mampu membangun kemampuan pemecahan masalah matematis setiap siswa kelas XI IPS di salah satu sekolah di Kupang. Hal ini dinyatakan melalui peningkatan ketiga indikator pemecahan masalah matematis di setiap siklus. Peningkatan rata-rata indikator pemecahan masalah matematis siswa kelas XI IPS dari siklus pertama sampai ketiga adalah sebesar 10%. Oleh karena itu, dapat disimpulkan bahwa pendekatan matematika realistik dapat membangun kemampuan pemecahan masalah matematis siswa kelas XI IPS di salah satu sekolah di Kupang pada materi peluang topik kaidah pencacahan.

Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality. We took advantage of this recreational aspect of video games when investigating whether there are similarities between the procedures used to pass a video game level and those used to solve a mathematical problem. Moreover, we also questioned whether the use of video games can reduce the negative emotions generated by mathematical problems and logical–mathematical knowledge in general. To verify this, we used the Portal 2 video game as a research method or tool. This video game features concepts from the spatial–geometric field that the students must identify and relate in order to carry out the procedures required to solve challenges in each level. The procedures were recorded in a questionnaire that was separated into two blocks of content in order to compare them with the procedures used to solve mathematical problems. The first block pertains to the procedures employed and the second block to the emotions that the students experienced when playing the video game and when solving a mathematical problem. The results reveal that the recreational aspect of video games is more important than the educational aspect. However, the students were not aware of using the problem-solving procedures they learned at school to solve different challenges in the video games. Furthermore, overcoming video game challenges stimulates positive emotions as opposed to the negative emotions generated when solving mathematical problems.

Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality. We took advantage of this recreational aspect of video games when investigating whether there are similarities between the procedures used to pass a video game level and those used to solve a mathematical problem. Moreover, we also questioned whether the use of video games can reduce the negative emotions generated by mathematical problems and logical–mathematical knowledge in general. To verify this, we used the Portal 2 video game as a research method or tool. This video game features concepts from the spatial–geometric field that the students must identify and relate in order to carry out the procedures required to solve challenges in each level. The procedures were recorded in a questionnaire that was separated into two blocks of content in order to compare them with the procedures used to solve mathematical problems. The first block pertains to the procedures employed and the second block to the emotions that the students experienced when playing the video game and when solving a mathematical problem. The results reveal that the recreational aspect of video games is more important than the educational aspect. However, the students were not aware of using the problem-solving procedures they learned at school to solve different challenges in the video games. Furthermore, overcoming video game challenges stimulates positive emotions as opposed to the negative emotions generated when solving mathematical problems. [ABSTRACT FROM AUTHOR]