Domain Of Mathematics Research Articles

Supplementary mathematics among adolescents in Timor-Leste

Abstract Students in Timor-Leste schools have been grappling with mathematics acquisition since the nation’s independence in 2002. Schools encounter scarcity of resources necessary to effect significant change and few other organisations have formally assumed this responsibility. Despite the recognition of the importance of mathematics in Timor-Leste, research in this area remains limited. This paper aims to examine the mathematics proficiency of 10- to 15-year-olds and evaluate the effectiveness of a supplementary tutoring programme designed to address learning gaps. Our findings reveal disparities in students’ proficiency across various mathematical domains. Students demonstrate higher achievement in counting, arithmetic, and number patterns and less so in statistics, angles, and shape recognition. Proficiency in three-quarters of curriculum strands pertaining to cycle 1 (grades 1 to 4) is below 40%. In response to these challenges, a supplementary tutoring initiative for this age group conducted in Tetum language was evaluated. The programme utilised tailored worksheets and small group sessions and took place thrice weekly. Results demonstrated statistically significant improvements over a seven-month period. Students in the intervention group on average gained proficiency in 7.5 new content areas compared to a comparison group value of 1.7. Feedback from participating students underscored the value of incorporating worksheets alongside traditional teaching methods. This study highlights the pressing need to address mathematics education in Timor-Leste and underscores the potential role of supplementary programmes. Importantly, it underscores that solutions can arise from low-resource community-driven interventions.

Recruiting spatial-numerical representations to increase arithmetic fluency in low-income students.

This study examined the effects of training involving spatial versus nonspatial representations of numerical magnitude for promoting arithmetic fluency. The key goal was to advance theoretical understanding of the relation between spatial and math learning, while simultaneously laying the groundwork for the development of future educational interventions. Toward this goal, the study tested the hypothesis that the use of spatial representations during training facilitates arithmetic fluency via improvements in numerical magnitude knowledge. Participants (first graders from low-income racially/ethnically diverse backgrounds, N = 205) were randomly assigned to one of four experimental conditions: spatial-continuous, spatial-discrete, nonspatial-verbal cues, and nonspatial-no verbal cues. All conditions involved eight 30-min training sessions, in which children received instruction on addition/subtraction problems with totals within 10. The key difference between conditions was the type of materials utilized during training-specifically, the type of magnitude cues they contained. The results showed that children's arithmetic skills increased from pre- to posttest in all conditions and that the increase was significantly larger in the spatial, compared to nonspatial, conditions. However, there was no effect of condition on numerical magnitude knowledge, which leaves open the question about the underlying mechanism. The findings demonstrating a causal relation between spatial and mathematical domains have both theoretical significance and practical implications for the choice of instructional materials. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

STEM in chemistry

The development of students' problem-solving skills is vital for cultivating a future-ready workforce, particularly in the domains of Science, Technology, Engineering, and Mathematics (STEM) education. Despite its importance, many students face difficulties in connecting classroom learning to real-world contexts, a challenge that is particularly pronounced in chemistry due to the abstract nature of concepts such as the three levels of chemistry representation (macroscopic, microscopic, and symbolic). The integration of STEM principles into teaching approaches, such as the blended problem-based learning (BPBL) approach, which combines face-to-face and online learning, has shown promise in bridging this gap. By incorporating elements of STEM into the BPBL approach, this study explores how these disciplines can enhance problem-solving skills and facilitate deeper understanding. Specifically, this research investigates the effect of the BPBL_S Module—a module that integrates BPBL with the Socratic method—on students' problem-solving abilities in the three representation levels of chemistry concept. Employing a design and development research approach, the study involved 25 students and one teacher, selected through clustered random sampling. Data were collected through observations, student documents, and interviews, and were analysed thematically. The findings suggest that the BPBL_S Module significantly improves students' problem-solving skills by enabling them to apply STEM concepts to chemistry, thus enhancing their ability to justify solutions comprehensively across macroscopic, microscopic, and symbolic levels. This study underscores the potential of the BPBL_S Module as an effective STEM-based teaching aid to better prepare students for the problem-solving demands of the future workforce.

Mathematical Error Patterns of Students With Mathematics Difficulty: A Systematic Review

This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the criteria used to identify mathematics difficulties and the coding processes varied; (b) the mathematics topics investigated encompassed fractions (including fraction computation and representation), problem-solving, and general computation; and (c) a variety of common error types were identified across these mathematical domains. Implications for practitioners and researchers were discussed.

Correction: Teacher–child interactions during shared book reading in the domain of early mathematics

Correction: Teacher–child interactions during shared book reading in the domain of early mathematics

Rasch tree 방법을 활용한 PISA 2022 수학 영역 차별기능문항 탐색

The purpose of this study is to detect differential item functioning (DIF) and its underlying causes within the mathematics domain of PISA 2022, employing the Rasch tree method. The two subtests, MTB002 and MTB004, were chosen, focusing on response data from Korean students to identify and examine DIF. The findings revealed that educational context variables, including socioeconomic status, family educational support, and school quality, significantly influenced DIF. Moreover, the observed variations in DIF across common items between the two subtests demonstrated that DIF characteristics can differ depending on item context, content knowledge, and problem-solving processes. This study emphasizes the significance of the Rasch tree method as a robust, data-driven tool for subgroup exploration without the need for predefined classifications, offering practical implications for enhancing the fairness of assessment tools and advancing educational environments.

Comparison of Problem-solving Performance Across Mathematical Domains with Large Language Models

This study investigates problem-solving performance across four mathematical domains, using statistical techniques to analyse domain-specific differences. By leveraging the NuminaMath-TIR dataset, we categorized problems into algebra, geometry, number theory, and combinatorics, selecting 8,000 problems for the analysis. Models including GPT-4o-mini, Mathstral-7B, Qwen2.5-Math-7B, and Llama-3.1-8B-Instruct were applied to assess answer correctness. Significant differences in solution accuracy were identified, with algebra showing the highest correctness rates and combinatorics the lowest. The results highlight the impact of domain on model performance and suggest the potential for tool-integrated reasoning (TIR) techniques to enhance consistency across domains. Future work can explore targeted model training improvements, aiming to optimize educational technologies and adaptive learning systems

Enhancing Students’ Performance in Solving Problems Involving Sides and Angles of Polygon through Polygon Relay Race

This study aimed to enhance grade seven students’ performance in solving problems involving the sides and angles of polygons through the use of the Polygon Relay Race, an innovative teaching strategy. Traditional classroom environments often failed to actively engage students, resulting in a lack of understanding and interest in geometry. This research employed a quantitative approach using a quasi-experimental one-group pretest-posttest design. A sample of 20 grade seven students was selected through purposive sampling from a school identified for its least-learned competency. The data collected were statistically analyzed using the mean, standard deviation, and Wilcoxon signed-rank test to determine significant differences. The pre-test results classified students' performance as Did Not Meet the Expectation, while the post-test results classified their performance as Fairly Satisfactory. Furthermore, the Wilcoxon signed-rank test results rejected the null hypothesis, indicating a significant difference between pre-test and post-test scores. The findings demonstrated that students’ performance in solving problems involving the sides and angles of polygons improved through the implementation of the Polygon Relay Race. The study concluded that the Polygon Relay Race was an effective pedagogical tool for enhancing students' understanding of polygons in geometry. It also recommended adopting similar strategies in mathematics curricula to improve engagement and cognitive learning outcomes. Future research could explore the application of this approach in other mathematical domains.

Early numerical skills and mathematical domains in autistic students in primary school.

It is crucial to provide a quality educational response to the needs of autistic children across various mathematical domains. However, there is no consensus on which of the early skills have the greatest predictive effect in the short and long term within these domains. Therefore, this research aimed to a) compare early numerical skills and mathematics domains, and 2) analyze the predictive value of early numerical skills into mathematics domains. Forty-two children (twenty-one autistic children and twenty-one non-autistic children) aged 6-12 years participated in the study. Three areas were evaluated through different tasks: 1) control tasks: reading, impulse control and manual speed, 2) early numerical skills: counting, verbal subitizing, magnitude comparison and estimation, and 3) mathematical domains: arithmetic calculation and arithmetic word problems. Significant differences were found in subitizing and estimation tasks. Both groups showed similar mathematical skills in arithmetic calculation and arithmetic word problems. For autistic students, several non-symbolic tasks predict performance in mathematical domains, whereas for non-autistic students, symbolic tasks were predictors. Although mathematics does not seem to be an area of concern for autistic children, future studies should explore early numerical and mathematical domains in children with cognitive support needs through longitudinal research.

Mathematical processes for the development of algebraic reasoning in geometrical situations with in-service secondary school teachers

This paper starts from the hypothesis that algebraic reasoning can be used as an axis between different mathematical domains at school. This is relevant given the importance attributed to mathematical connections for curriculum development and the algebraic reasoning makes it possible to articulate it in a coherent manner. A definition of generalized algebraic reasoning is proposed, based on the notion of elementary algebraic reasoning of the onto-semiotic approach, and it is used to highlight the presence of typical algebraic processes in problem solving in geometrical contexts. To develop these ideas, a training course is designed and implemented with in-service secondary school teachers. Based on design-based research, the results obtained are contrasted with the expected answers. In this way, relevant information is obtained on how teachers mobilize different typically algebraic processes, that is, particularization-generalization, representation-signification, decomposition-reification and modelling. Actually, it is clear to affirm that teachers need specific training to improve their skills about how algebraic reasoning can help them to develop mathematical connections with their students.

Existence Analysis of Conformable Fractional Boundary Value Problems

This study examined the fractional boundary value issue at flexible derivatives, focusing on establishing the existence of solutions and uniqueness. We introduce conditions that advance our understanding of this complex mathematical domain by capitalizing on the innovative framework of contraction principles. Moreover, the versatility of the proposed method is emphasized by its effectiveness in dealing with a wide set for compatible fractional differential equations characterized by diverse boundary conditions.

Mathematical Information Retrieval: A Review

Mathematical formulas are commonly used to demonstrate theories and basic fundamentals in the Science, Technology, Engineering, and Mathematics (STEM) domain. The burgeoning research in the STEM domain results in the mass production of scientific documents that contain both textual and mathematical terms. In scientific information, the definition of mathematical formulas is expressed through context and symbolic structure that adheres to strong domain-specific notions. Whereas the retrieval of textual information is well-researched, and numerous text-based search engines are present. However, textual information retrieval systems are inadequate for searching scientific information containing mathematical formulas, including simple symbols to complicated mathematical structures. The retrieval of mathematical information is in its infancy, and it requires the inclusion of new technologies and tools to promote the retrieval of scientific information and the management of digital libraries. This article provides a comprehensive study of mathematical information retrieval and highlights their challenges and future opportunities.

Preparing students for success

With increased demand for skilled professionals in science and technology, universities are broadening entry requirements resulting in students entering these specialised degrees with potential knowledge gaps. This presents an opportunity to uplift student capability through personalised learning journeys, enhancing their university readiness. This report details the Monash College's new maths uplift program, which uses skills analysis tools and self-assessment processes to determine “where students are” on their learning journey, both at entry to the Monash College and through to their first year of university. Mapped to the maths requirements of their chosen degree, this program comprises three key components: (1) a comprehensive Teaching and Learning progression that maps the learning trajectory via six core domains of mathematics, (2) a set of skills analysis tests aimed at different entry and exit points in mathematics, and (3) a large set of self-paced online learning modules recommended to students based on the outcomes of their individual skills analysis tests. The three key components work together to provide a tailored educational experience supporting students towards their destination degrees. This paper reports on the development of this uplift program and presents preliminary findings indicating positive impacts on student preparedness and engagement.

Mapping the Research Landscape of Ordinary Differential Equations through Bibliometric Analysis

Ordinary Differential Equations (ODEs) are a fundamental field used for mathematical modelling in wide-ranging applications. This research visually represents the research landscape of ODEs by utilizing bibliometric analysis and social network analysis. We analysed 1,849 documents related to topic developments, patterns in publications, and collaborative networks spanning the years 2019 to 2024. Consequently, numerous papers have been published by authors from the United States, China, and Russia, where research activity is significantly focused. The analysis identifies the articles with the highest citation rates, as well as the important authors and universities that are at the centre of publishing on ODEs. Furthermore, we display the collaborative network of the research group and countries using the VOSviewer application. In conclusion, the study highlights the current state and progress of ODE research by identifying recent developments and intriguing topics for future exploration. This paper serves as a valuable reference for researchers seeking to understand the impact and progress of ODE investigations within the broader mathematical domain.

Research on the design of gamified classroom teaching mode based on fuzzy conjoint analysis method

Operations research is an applied mathematics discipline aimed at providing optimal solutions for complex systems and decision-making processes. However, the theoretical aspects of operations research can often be abstract, making it challenging and potentially tedious for students with a weaker foundational background. To address this issue, game-based learning has been introduced into operations research education in recent years, demonstrating promising results. In this context, gamified learning is seen as a potential solution to enhance student motivation and classroom engagement. Although gamification has been explored in education, its application in operations research, especially within a complex mathematical domain, remains under-researched. These games transform abstract operations research theories into concrete scenarios and problems, allowing students to learn and apply operations research knowledge through interactive play. This study aims to investigate students’ perceptions and attitudes toward game-based operations research classrooms using fuzzy set joint analysis. By employing fuzzy conjoint analysis, we aim to provide a nuanced understanding of student preferences and optimize gamified teaching strategies. In the investigation process, 83 students from School D were selected as the research subjects, and a questionnaire encompassing 16 items was administered. These items covered various aspects of integrating operations research board games into the classroom, including students’ engagement, cooperation, understanding, and application of operations research knowledge during the game process. By utilizing a Likert seven-point scale to collect students’ responses to each item, the data were subsequently converted into fuzzy sets to assess students’ views on game-based operations research classrooms. The results were used to provide targeted optimization for gamified teaching. Group experimental results involving the 83 students showed that gamified teaching in operations research has a positive impact on students’ learning of the subject. This finding holds significant implications for educators and teaching practices, offering valuable insights for the design and implementation of future operations research teaching methods.

Enhancing AR‐based learning environments for STEM education: A design‐based study on design features, kinematics learning and mathematics self‐efficacy

AbstractThis design‐based research project explored how various design features of AR‐based learning environments (ARLE) influence students' mathematics self‐efficacy and learning of kinematics. Specifically, five ARLEs with different design features were developed and implemented with 136 seventh‐grade students in two rounds. Data were gathered from pre‐ and post‐mathematics self‐efficacy tests, interviews, classroom observation records and reflective journals, to identify which design features promote or hinder students' learning and self‐efficacy. Results revealed that adopting a well‐designed ARLE is a viable way to promote students' learning and mathematics self‐efficacy, and the success of ARLE lies in (1) coherent tasks with proper time for self‐exploration, progressive levels, useful problem contexts and a certain degree of open‐endedness, and (2) sufficient technological affordances with strengthened authenticity, clarity and integrated media presentation, as well as engaging interactions with decent flexibility, embodied actions and feedback. These results validated the applicability of the proposed checklist for ARLE designers and practitioners in their design and implementation of ARLEs, within the domain of mathematics, physics and beyond. Practitioner notesWhat is already known about this topic AR‐based learning environments (ARLEs) have demonstrated substantial advantages in STEM education, but ARLEs can be a drawback if they are not adequately designed. ARLE may facilitate students' mathematics self‐efficacy, and relevant design features are underexplored. Design‐based research sustains interventions combining empirical research and theory‐driven design of innovative learning environments, for example, ARLEs. What this paper adds Demonstrates the potential of ARLEs that can be used in classrooms to support STEM learning. Identifies a collection of effective and ineffective design features of ARLEs that promote or hinder students' STEM learning and mathematics self‐efficacy. Tackles the challenges for the design of ARLEs for classrooms by taking AR technological affordances and the pedagogical perspective together. Implications for practice and/or policy Five ARLEs for STEM topics were developed and implemented in secondary schools. Evidence of positive impacts of ARLEs on students' learning and mathematics self‐efficacy. Our research produces useful guidelines for designers and practitioners in their development and implementation of ARLEs in real classrooms.

Second-Order Neutral Differential Equations with a Sublinear Neutral Term: Examining the Oscillatory Behavior

This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations under study. By employing the Riccati technique in various ways, we derive results that expand the scope of previous research and enhance the cognitive understanding of this mathematical domain. Additionally, we provide three illustrative examples to demonstrate the validity and applicability of our findings.

Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain

Creating and sharing linear algebra metaphors as an assessment for engaging students beyond the cognitive domain

Performance on curriculum-based mathematics assessments in developmental dyscalculia: the effect of content domain and question format

Developmental Dyscalculia (DD) is characterised by persistent difficulties in learning mathematical skills, which usually becomes apparent in the early years of schooling. Traditionally, DD is known to affect children’s arithmetic processing, whilst other domains of mathematics receive much less research attention. Nevertheless, contemporary diagnostic guidelines suggest that DD is linked to widespread and diverse difficulties, both within and outside of the domain of numbers. This study examined the performance (i.e., accuracy and number of questions attempted) of children on a curriculum-based mathematics assessment, considering the effect of content domains, question format (i.e., multiple-choice questions vs. constructed response questions) and test half. Participants were forty children aged 8 to 11 years old with DD (n = 20) and a carefully matched control group of typically developing children (n = 20) from primary schools in Northern Ireland. Results revealed that the DD group achieved significantly lower scores than the control group across all areas of the curriculum, and the magnitude of group differences was similar across all content domains. These findings indicate that performance in content domains other than in arithmetic may be equally informative in supporting the identification of children with DD. In addition, we found that using multiple-choice questions may support learners with DD in achieving the best outcome, and, thus, could be useful for assessing mathematics skills in dyscalculic children in classroom contexts. Nevertheless, constructed response questions may show the greatest sensitivity to identifying learners at risk, and could be the most useful in diagnostic settings.

Computational thinking in primary mathematics classroom activities

The integration of computational thinking (CT) into primary education is often facilitated using one or more CT tools, such as block-based programming environments and educational robotics. A major concern is that these CT tools often are used to design mathematics classroom activities that focus on CT at the expense of mathematics. Hence, there is a need to investigate more closely how CT tools can be used in primary mathematics classroom activities in ways that enable a stronger focus on the learning of mathematics. Using information ecology as a theoretical lens, this study aims to understand how and why CT tools are integrated into primary mathematics classrooms, and how teachers value the possible contributions of such tools. We draw on multiple interviews with two primary teachers, recordings of planning sessions where classroom activities that include CT were designed, the classroom implementations themselves, and reflective conversations with the teachers after the CT tools were integrated in their mathematics classrooms. A deductive analytical approach to our data revealed that (1) CT tools, to varying degrees, facilitate the learning of mathematics; (2) some CT tools were valued by teachers as a better ‘fit’ than others; and (3) CT tools are primarily used to support the learning of geometry, excluding other mathematical domains. Based on these findings, we suggest that there is a need for more research on the use of different CT tools and their role in the learning of primary mathematics. Moreover, more research is needed to understand how CT tools can be used in topics other than geometry.