Mathematical Ability Research Articles

Metaphorical Thinking Intervention in Learning and Its Impact on Mathematical Reasoning Ability

Dalam beberapa tahun terakhir, penelitian tentang intervensi Metaphorical Thinking (MT) dalam pendidikan matematika semakin mendapat perhatian. Namun, penelitian terbatas telah meneliti bagaimana intervensi MT, ketika diintegrasikan dengan model pembelajaran yang menantang, dapat meningkatkan Kemampuan Penalaran Matematis (MRA) siswa. Untuk mengatasi kesenjangan ini, penelitian kuasi-eksperimental dengan menggunakan desain kelompok kontrol posttest-only dilakukan terhadap 50 siswa di SMP Widya Bhakti Ruteng, NTT, Indonesia. Penelitian ini bertujuan untuk menganalisis pengaruh intervensi MT dalam lingkungan Pembelajaran Berbasis Masalah (PBL) terhadap MRA. Data dikumpulkan melalui tes PMA yang terdiri dari lima soal, dan hasilnya dianalisis menggunakan uji t setelah melakukan analisis prasyarat. Temuannya menunjukkan bahwa siswa yang menerima intervensi MT dikombinasikan dengan PBL menunjukkan MRA yang jauh lebih tinggi dibandingkan dengan mereka yang tidak menerima intervensi MT. Hasil ini menggarisbawahi potensi manfaat dari mengintegrasikan intervensi MT dengan pendekatan pedagogi menantang lainnya. In recent years, research on Metaphorical Thinking (MT) interventions in mathematics education has gained increasing attention. However, limited studies have examined how MT interventions, when integrated with challenging instructional models, can enhance students' Mathematical Reasoning Ability (MRA). To address this gap, a quasi-experimental study utilizing a posttest-only control group design was conducted with 50 students at SMP Widya Bhakti Ruteng, NTT, Indonesia. The study aimed to analyze the effects of MT interventions in a Problem-Based Learning (PBL) environment on MRA. Data were collected through a PMA test consisting of five questions, and the results were analyzed using a t-test after performing a prerequisite analysis. The findings revealed that students who received MT interventions combined with PBL demonstrated significantly higher MRA compared to those who did not receive MT interventions. These results underscore the potential benefits of integrating MT interventions with other challenging pedagogical approaches.

Enhancing mathematical problem-solving ability through project-based learning: A study of vocational high school student

This study aims to improve the mathematical problem-solving ability of students at Vocational High School (VHS) through implementing Project Based Learning (PjBL). The research method used was a quasi-experiment with a matching-only pretest-posttest control group design, with a sample of 64 students divided into two classes, namely experimental and control classes, each consisting of 32 students. The sampling technique used was purposive sampling, where the sample was selected based on specific criteria relevant to the research objectives. Data were collected using tests of mathematical problem-solving ability administered before (pre-test) and after (post-test) the treatment. Data were analyzed using an independent sample t-test and a two-way ANOVA test with univariate general linear model (GLM) analysis. The results showed a difference between the experimental and control groups before the treatment. However, after the treatment, the experimental group had higher mathematical problem-solving ability than the control group, including the improvement and interaction between PjBL implementation and the Early Mathematics Skills (EMS) category.

Dimensional versus Categorical Approach: A Comparative Study of Mathematical Cognition

BackgroundResearchers have employed two distinct methods to understand the cognitive underpinnings of mathematical ability: categorical and dimensional. These two methods have different underlying assumptions. However, to the best of our knowledge, research to date has not empirically tested which method can better predict variance in mathematical ability. Method104 children from Indian public schools in the 3rd and 4th grades completed a mathematical ability test. For the categorical approach, participants were categorized into two groups: mathematical learning difficulty and high math achieving. For the dimensional approach, the data of all participants were considered. The cognitive abilities measured included approximate number system, working memory, inhibitory control, and spatial ability. ResultsMixed factorial ANOVA and hierarchical regressions revealed that the dimensional approach demonstrated better predictive power for mathematical ability than the categorical approach. ConclusionsThe dimensional approach offers a more comprehensive insight into mathematical cognition, enabling greater control over the predictors.

Kejenuhan Belajar dan Prokrastinasi Akademik terhadap Kemampuan Pemecahan Masalah Matematika

This study used multiple linear regression data analysis techniques to determine the effect of learning burnout and academic procrastination of students, both individually and together, on mathematical problem-solving abilities. The study was conducted on 88 students of class X of SMA Muhammadiyah 1 Palangka Raya, who were selected by simple random sampling. Data collection used a test for problem-solving abilities and a questionnaire for each learning burnout and academic procrastination. Before conducting multiple linear regression, prerequisite tests were carried out, namely: normality test, heteroscedasticity test, linearity test, autocorrelation test, and multicollinearity test. After meeting the prerequisite tests, the analysis was carried out and the results obtained were that there was an effect of learning burnout on students' mathematical problem-solving abilities, there was an effect of academic procrastination on students' mathematical problem-solving abilities, and there was an effect of learning burnout and academic procrastination together on the mathematical problem-solving abilities of class X students of SMA Muhammadiyah 1 Palangka Raya.

Analysis Mathematical Resilience Relationship With Mathematical Problem Solving Ability in Functions Derivative Material

This study is a correlational research aimed at exploring the relationship between mathematical resilience and problem-solving skills in mathematics. Conducted at a senior high school in Karawang, the research involved a sample of 36 students. The method employed was ex post facto, with purposive sampling to select participants based on specific criteria. The instruments used included a test on mathematical problem-solving abilities focused on derivative functions and a scale measuring mathematical resilience. Findings revealed a significant correlation of 0.819 between mathematical resilience and problem-solving abilities, while a correlation of 0.181 was attributed to other factors like conceptual understanding. Students with strong resilience and a solid grasp of concepts typically find it easier to tackle mathematical problems. Conversely, those with weaker resilience and limited understanding of the concepts struggle to comprehend the questions and develop effective strategies, leading to lower problem-solving capabilities. In conclusion, a notable relationship exists between mathematical resilience and students' ability to solve mathematical problems.

Development of Interactive Learning Video Media to Improve Mathematical Representation Ability on Data Presentation Material

One of the main challenges in learning mathematics is overcoming students' difficulties in understanding abstract mathematical material and the lack of engaging and interactive teaching methods. The aim of this research is to develop interactive learning videos that are valid, effective, and practical. This Research and Development (R&D) study uses the ADDIE model. The research subjects were 15 students of class VII A MTsS Ash-Shalihin.. The results of the study show that the interactive learning video is highly valid with a score of 3.7 from expert evaluations. Teacher responses received a score of 3.67, which is categorized as very practical, while student responses received a score of 3.34, indicating that the video is very effective. The t-test and N-Gain test showed a value of 0.67, indicating an improvement in students' mathematical representation abilities in the moderate category. Thus, the learning video has proven to be effective.

Structural and transcriptional signatures of arithmetic abilities in children

Arithmetic ability is critical for daily life, academic achievement, career development, and future economic success. Individual differences in arithmetic skills among children and adolescents are related to variations in brain structures. Most existing studies have used hypothesis-driven region of interest analysis. To identify distributed brain regions related to arithmetic ability, we used data-driven cross-validated predictive models to analyze cross-sectional behavioral and structural MRI data in children and adolescents. The gray matter volume (GMV) of widespread brain regions reliably predicted arithmetic abilities measured by the Comprehensive Mathematical Abilities Test. Furthermore, we applied neuroimaging-transcriptome association analysis to explore transcriptional signatures associated with structural patterns of arithmetic ability. Structural patterns of arithmetic ability primarily correlated with transcriptional profiles enriched for genes involved in transmembrane transport and synaptic signaling. Our findings enhance our understanding of the neural and genetic mechanisms underlying children’s arithmetic ability and offer a practical predictor for arithmetic skills during development.

Finger Configurations and Kindergarteners’ Mathematical Abilities

ABSTRACT Previous research has demonstrated a link between children’s ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved. Five-year-old children in Spain (N = 143) were assessed on their ability to name canonical finger configurations and analogous representations (buildings on a hill), alongside a range of mathematical skills (counting, knowledge of the verbal count sequence, single-digit arithmetic, and subitizing). Findings indicated that five-year-olds only recognize single-hand canonical finger configurations as summary symbols, processing them holistically. However, no direct association was found between the ability to recognize these configurations and the assessed mathematical skills. Notably, only the ability to name finger configurations corresponding to larger numbers (requiring enumeration) was associated with children’s arithmetic skills, suggesting that these configurations elicit combinatorial processes that are handshape specific. The implications of these findings for cognitive development and mathematical assessment are discussed, highlighting the potential for finger configurations as a tool for fostering mathematical understanding and the need for further exploration of their cognitive underpinnings.

Optimalisasi Kemampuan Penalaran Matematis melalui Metode Mind Mapping

Increasingly rapid global developments raise complex problems that require effective and innovative solutions. Mathematical reasoning is the key to solving the problem. But on the other hand, learning in schools is still a lot of conventional learning and the development of the students' mathematical reasoning skills is not optimal. The aim of this study was to explore the effectiveness of using mind map-based learning methods that were judged to be effective in developing mathematical reasoning skills. With a qualitative approach to literature studies, research results were obtained which showed that the method of mind mapping had a significant influence on the mathematical reasoning ability of the students. Library study sources are derived from previous research that had the same focus of study. Library reviews are used to analyze several studies related to the use of mind mapping-based learning methods and their influence on mathematical reasoning capabilities. This research is expected to provide an understanding of the importance of developing mathematical reasoning skills to form intelligent and critical generations

Triangular Fuzzy Cognitive Maps Method for Modelling Interrelation between Causal and Trigger Factors Towards Students' Mathematics Problem-Solving Ability

The purpose of this study is to model the interrelation between causal and trigger factors towards students' mathematics problem-solving ability by using the triangular fuzzy cognitive maps (TrFCM) method. Selection weaknesses and limitations in the method of relational analysis cause the interrelation and influence between variables not to be visualised and do not reveal the characteristics of the actual interaction. As a result, this study demonstrates TrFCM as a more effective way of analysing the relationship between variables based on the complexity that happens in analysing causal factors and triggers for students' problem-solving abilities in mathematics. The results of the influential relations map (IRM) demonstrate that emotion and metacognition are the triggers for problem-solving ability. While executive function is the main cause of success in completing mathematics problems, it is also influenced by additional factors such as motivation, attention, and working memory. These causal and triggering factors also mobilise parts of students' cognitive and behavioural performance to improve the process of solving mathematics problems. Based on the outcomes of this study, computational intelligence methods like fuzzy systems give useful procedures for analysing data from expert surveys. The TrFCM method offers a more accurate relational analysis procedure in modelling interrelation between human factors.

The Effectiveness of Differentiated Learning Strategies on Elementary Students' Mathematical Critical Thinking Ability

This study explores the effectiveness of differentiated learning strategies in improving elementary students' mathematical critical thinking skills. The independent variable is the application of differentiated learning strategies, while the dependent variable is the students' mathematical critical thinking ability. A quantitative approach was used, utilizing a quasi-experimental design with a non-equivalent control group. The sample included 30 fourth-grade students from Al-Falaah Islamic Elementary School and 30 from Jombang 01 Ciputat Elementary School, selected through purposive sampling. Data collection involved tests, questionnaires, observation sheets, and interview guides, and the analysis was conducted using independent sample t-tests and N-Gain tests with the help of SPSS IBM 22.0 software. The statistical analysis showed a significant effect of differentiated learning strategies on critical thinking skills, with a p-value of 0.000 and an N-Gain score of 74.56%. This indicates a notable improvement in students’ abilities in interpretation, analysis, evaluation, and inference. Differentiated learning strategies accounted for 58% of the variation in outcomes, with the remaining 42% influenced by other factors. In conclusion, differentiated learning strategies significantly enhance elementary students' mathematical critical thinking, and educators are encouraged to adopt these methods to foster deeper cognitive engagement.

ANALYSIS OF STUDENTS' ABILITY TO SOLVE MATHEMATICAL PROBLEMS ON CONTEXTUAL PROBLEMS INVOLVING ALGEBRAIC FORMS

This research is motivated by the fact that problem solving is a basic ability that every student must have. However, observations in the field show that students' mathematical problem-solving skills, especially in the material of algebraic form operations, are still relatively low. This study aims to describe students' mathematical problem-solving skills based on Polya's theory, which consists of four stages: (1) understanding the problem, (2) planning problem solving, (3) implementing the plan, and (4) re-examining the results. This study involved 26 ninth grade students as subjects. The method used was descriptive qualitative with data collection techniques including tests, interviews, and documentation, data analysis conducted based on four levels of problem-solving ability: excellent, good, sufficient, and deficient. The results showed that students' mathematical problem-solving ability on algebraic form operation material obtained as a whole was still relatively low with a scale of 42%. The implications of these findings indicate the need for the alication of more varied and contextualized teaching strategies to improve students' problem-solving skills. This research can be the basis for teachers in providing further assistance to students who are experiencing difficulties, focusing on improving skills in understanding and solving mathematical problems as a whole.

Analysing the Influence of Students’ Resilience on their Mathematics Academic Performance in Mezam Division, Cameroon

The main objective of the study was to analyse the influence of students’ resilience on their Mathematics academic performance in Mezam Division in Cameroon. The study adopted the causal comparative research design. The study was carried out using seven functional public secondary schools in Mezam Division for the 2023/2024 academic year, with first cycle students (Forms 1 to 5) constituting the population of the study. With the help of the Krejcie and Morgan Table, a sample of 368 students was drawn from an accessible population of 8813 first cycle students. The proportionate stratified random sampling technique was used to select this sample for the collection of data. Data was collected using a structured questionnaire. The questionnaire was vetted by three experts and its test-retest reliability index established as 0.87. The data collected were analysed using frequency counts, means, Pearson product-moment correlation, one sample t-test and regression analysis. The findings of the study revealed that students in Mezam Division exhibit significantly low resilient abilities in Mathematics. The findings also revealed that there is a moderate positive correlation (0.587) between students' resilience and their Mathematics academic performance. Furthermore, the regression analysis indicated that approximately 34.4% of the variations in students' Mathematics academic performance can be accounted for or predicted by their resilience. It was recommended that educators and policymakers need to focus on nurturing, developing and fostering students' resilient abilities through targeted interventions and teaching strategies.

Development of domino media to improve problem solving and mathematical communication for Islamic boarding school students

Mathematical problem solving and communication skills are important factors in learning mathematics. Therefore, it is necessary to develop learning media, especially in Islamic boarding school curricula where the learning load is greater than the regular curriculum. On this basis, the aim of this research is to develop domino card media to improve problem solving and mathematical communication skills of Islamic boarding school students. Development was carried out at Al-Izzah IIBS Batu Middle School, Malang, using the ADDIE model. Data obtained from documents, observations, questionnaires and tests were analyzed using qualitative and quantitative approaches. Based on the results of the validation analysis, the domino card media was declared valid from the aspects of design, material, curriculum, consistency, language, practicality, problem solving development and mathematical communication. Meanwhile, the effectiveness of using domino card media in learning is classified as effective, if seen from the results of the problem solving ability test with an N-Gain score of 76.79%, and the results of the mathematical communication ability test with an N-Gain score of 61.79%. Many factors cause this non-optimality, including a lack of mathematics lesson hours, a busy lesson schedule that is less suited to conditions, many demands on students, and the learning load in the curriculum.

Exploration Mathematical Aesthetics through Logical and Critical Thinking Based on High Mathematical Ability

This study aims to explore the logical and critical thinking process of junior high school students in solving ill-structured problems based on mathematics ability. The research subject consisted of one student with high mathematics ability. The supporting instruments for data collection were: 1) Test of Mathematical Ability (TKM) consisting of 10 items in the form of descriptions to select subjects with high mathematical ability, 2) Ill-structured Problem Task (TMI), 3) Interviewing the subject based on the task (TMI). The data analysed in this study are interview transcript data, document data and field notes. This study used three stages in data analysis, namely data condensation, data display and conclusion drawing and verification. To validate the findings, the author applied method triangulation until consistent data was obtained, i.e. the data was structured and the content was relatively the same. Furthermore, consistent data in this study is categorised as research data. The results showed that the logical and critical thinking process of high mathematics ability students in solving ill-structured problems consisted of: (1) problem representation; (2) Generating Solution; (3) Justification; and (4) Monitoring and Evaluation. Based on the results of research related to the exploration of mathematical aesthetics through logical and critical thinking, it is recommended as material for further research development in terms of other aspects

Developing the Ability to Solve Mathematics Problems ‘Polygons’, Through Open Approach Learning Management for Sixth-Grade Students

This action research aims to develop the ability to solve mathematical problems, particularly in polygons, through open-approach learning management for sixth-grade students, with the goal of achieving an average score exceeding 70% of the total possible score. The target group consisted of eight students in the second semester of the academic year 2023. Data collection tools included lesson plans, mathematics problem-solving ability tests, student behavior observation forms, and student journal logs. The data were analyzed using statistical methods, including percentages, means, and standard deviations. The findings showed that an open approach to learning management can effectively enhance mathematical problem-solving skills. Furthermore, it was observed that the students demonstrated various problem-solving approaches, actively engaged in group and inter-group learning exchanges, displayed confidence in problem-solving, and improved their mathematical problem-solving abilities.

The Impact of Rich Teaching of The Concept on Mathematical Ability and The Survival of The Learning Impact of Basic Seventh Grade Students

The study aims to demonstrate the impact of rich teaching of the concept on mathematical ability and the survival of learning impact. The study relied on the experimental approach. It represents the research community of all seventh grade students in Irbid governorate, and reaches the size of the study sample (44) students distributed to two groups: a pilot group taught by rich conceptual teaching and the other is a control group taught in the traditional way. A mathematical ability test was prepared and re-applied two weeks later to measure the level of survival of the learning impact and the results of the study showed statistically significant differences at the indicative level (0.05) in the average scores of female students of the experimental and control group in the mathematical ability test, and they were in favour of the pilot group studied through the rich teaching of the concept, It also showed that there were no statistically significant differences at the indicative level (0.05) between the average pilot group in the dimensional and deferred application.

A multigroup random-intercept cross-lagged panel model for Finnish secondary school students in frame of situated expectancy-value theory

The aim of this study is to examine both within-person and between-person associations of academic self-concept and task values in literacy and mathematics to identify the most promising motivational construct to prevent motivational decline during school transitions. The sample included 3636 students (average age at the start: 15.73 years, SD: 0.32 years) followed up three times from lower secondary school (T1) to the third year (T3) of upper secondary education, either in vocational or academic tracks. Multi-group random intercept cross-lagged panel models detected several spillover (cross-lagged) effects between self-concept and task values in mathematics but not in literacy. There were also marginal but significant differences between students from different educational tracks in both subjects. Overall, utility value and academic self-concept in mathematics were found to be the most promising motivational constructs in changing motivational beliefs, thus presenting important starting points in motivational interventions. Educational relevance and implications statementThis study highlights that spillover effects are more pronounced in maths than in literacy, emphasising the need for tailored interventions in mathematics education. Moreover, the potential disruption in students' motivational beliefs during school transitions suggests the importance of ensuring continuity in support to help mitigate the impact of these transitions. While our results indicate limited carryover effects, it is possible that school transitions are experienced as breaks in motivational development. The role of utility value in exhibiting spillover effects over school transitions in both maths and literacy suggests the significance of emphasising the practical relevance of academic subjects to sustain students' motivation. Additionally, recognising the superior role of academic self-concept in maths in spillover effects on task values underscores the importance of nurturing students' confidence and beliefs in their own mathematical abilities.

EFEKTIVITAS BLENDED LEARNING TIPE FLIPPED CLASSROOM TERHADAP KEMAMPUAN PEMAHAMAN MATEMATIS SISWA SMP

This study aims to measure the effectiveness of the flipped classroom blended learning model on the mathematical understanding abilities of junior high school students. The research adopts a quantitative approach with a quasi-experimental design involving two classes at SMPN 3 Karawang Barat. Class VIII-B, serving as the experimental group, received instruction using the flipped classroom model, while class VIII-A, serving as the control group, was taught using conventional teaching methods. Data were collected through pretests and posttests that measured the students' mathematical understanding abilities. The results indicated a significant improvement in the mathematical understanding abilities of the students in the flipped classroom model compared to those in the conventional teaching methods. This conclusion was derived from data analysis using the t-test, which showed a significant difference between the students who were taught using the flipped classroom model and those who were taught using conventional methods in terms of their improvement in mathematical understanding abilities. Further analysis using N-gain and effect size tests was conducted, This study concludes that the flipped classroom blended learning model can be an effective alternative to enhance the mathematical understanding abilities of junior high school students.

Analysis of Mathematical Connection Ability and Self-Confidence on Junior High School Students

This research is motivated by the importance of students’ mathematical connection abilities and self-confidence in learning mathematics. Mathematical connection ability is an important factor in understanding mathematical concepts. The aim of this research is to analyze the level of students’ mathematical connection abilities and junior high school students’ self-confidence. The method used in this research is a descriptive-qualitative method. The research subjects were 37 students in class VIII-C of SMPN 3 Margahayu. The instruments used were four items of mathematical connection test material on the System of Two-Variable Linear Equations and non-tests of students’ confidence in learning mathematics. The results of the analysis show that the average score of all mathematical connection ability test questions in indicator 1 using relationships between mathematical topics is 5%, indicator 2 is understanding equivalent representations of the same concept (36%), indicator 3 uses mathematics in everyday life (52%), and indicator 4 uses mathematics in other subjects (27%). So the average is 30%. So the students’ mathematical connection ability is included in the low category. Most students are unable to solve problems with indicators using relationships between mathematical topics. This is shown by the results of the mathematical connection ability test; students did not connect optimally. But in learning mathematics, students already have good self-confidence.