Journal on Mathematics Education

Bridging geometry and cultures for junior high school level: Rumoh Aceh design from a computational thinking perspective

2025-03-04T04:48:23+00:00

Recent discourse in mathematics education emphasizes the need for culturally relevant pedagogy and the integration of higher-order thinking skills, yet limited research explores the intersection of ethnomathematics and computational thinking within school curricula. This study addresses this gap by proposing a novel instructional framework that incorporates computational thinking into the ethnomathematical exploration of Rumoh Aceh—a traditional Acehnese house—within the context of junior high school geometry education in Indonesia. The research aims to enhance students’ understanding of geometric concepts such as lines, angles, shapes, and spatial structures through culturally grounded learning experiences. Using the four core components of computational thinking—decomposition, abstraction, pattern recognition, and algorithmic thinking—the geometric design of Rumoh Aceh is analyzed to reveal its mathematical significance. Data collection was conducted through ethnographic methods, including observation, interviews with local experts, and documentation analysis. The findings demonstrate that applying computational thinking to cultural artifacts fosters students’ ability to recognize geometric patterns, simplify complex problems, and develop structured problem-solving strategies. Furthermore, the integration of cultural context enriches students’ appreciation of their heritage while cultivating critical thinking and mathematical reasoning. This study provides empirical evidence supporting the pedagogical value of merging ethnomathematics with computational thinking, offering a meaningful and culturally responsive approach to mathematics education.

The influence of gender stereotypes on self-efficacy and mathematical anxiety in Peruvian students aspiring to STEM careers

2025-03-04T04:14:40+00:00

Despite increasing global efforts to promote gender equity in education, gender stereotypes continue to pose significant barriers to female students’ engagement and achievement in mathematics, particularly within pathways leading to STEM careers. Prior studies have established the detrimental effects of such stereotypes, yet there remains a limited understanding of the mediating role these beliefs play in the relationship between mathematical self-efficacy and mathematics anxiety, especially among pre-university students in developing countries. Addressing this gap, the present study investigates the mediating influence of gender stereotypes on the link between self-efficacy and mathematics anxiety among Peruvian pre-university students pursuing STEM-related fields. A total of 304 participants (116 males and 188 females), aged 16 to 35, were drawn from science (n = 38), technology (n = 26), engineering (n = 142), and mathematics (n = 98) disciplines. Quantitative analyses revealed that female students reported significantly higher levels of perceived gender stereotype threat, lower mathematical self-efficacy, and elevated mathematics anxiety compared to their male counterparts. Mediation analysis further demonstrated that stereotype-induced identity threat undermines self-efficacy, thereby intensifying anxiety related to mathematics. However, the study acknowledges limitations, including gender and field imbalances within the sample and the limited scope of variables examined. These findings underscore the urgent need for educational interventions that address stereotype threats and foster equitable learning environments. The results contribute to the broader discourse on gender equity in mathematics education and inform strategies to support female students' sustained participation in STEM trajectories.

How computational thinking can be integrated in statistical learning: A cuboid framework

2025-02-04T09:29:41+00:00

In the context of an increasingly data-intensive society, the integration of Computational Thinking (CT) into statistics education is essential to prepare students with the analytical and problem-solving competencies required for navigating complex data environments. Despite growing recognition of its importance, existing pedagogical practices frequently lack systematic didactical frameworks that effectively embed CT within statistical learning, particularly in higher education. Addressing this gap, the present study introduces a novel hypothetical didactical design—termed the Cuboid Framework—which systematically integrates CT components into the learning of descriptive statistics using the R programming language in a Google Colab environment. This research employed the Didactical Design Research (DDR) methodology, emphasizing the prospective and metapedadidactic stages to construct and evaluate the framework. Targeted at third-semester undergraduate students enrolled in an introductory statistics course, the Cuboid Framework aligns with learners’ developmental levels in both statistical reasoning and CT proficiency. The model is organized as a 5 × 4 × 4 structure, comprising five core statistical tasks, four structured didactical situations (action, formulation, validation, and institutionalization), and four CT elements (decomposition, pattern recognition, abstraction, and algorithmic thinking). Validation procedures included expert review through focus group discussions (FGDs) and an initial classroom implementation followed by metapedadidactic analysis. Findings reveal that the Cuboid Framework fosters a coherent learning progression, enhances students’ engagement in statistical inquiry, and supports the development of CT competencies. Classroom observations confirmed that the intentional design of didactical situations facilitates students’ cognitive adaptation to computational tasks. While preliminary analyses indicate strong theoretical and practical coherence, further retrospective studies and quantitative evaluations are necessary to ascertain the long-term effects on student learning outcomes. This study contributes a structured and theoretically grounded model for CT integration in statistics education, with implications for improving curriculum design and instructional practice in mathematics education. Future research should aim to test the scalability and efficacy of the Cuboid Framework across diverse educational settings.

Shaping mathematics identity: An exploratory study on specifications grading in Calculus I at a Hispanic-Serving institution

2025-04-10T03:35:02+00:00

Calculus I courses play a pivotal role in shaping students' STEM pathways, making it essential to adopt pedagogies that foster both achievement and mathematics identity development, particularly among underserved groups such as Hispanic students. This study explores the impact of Specifications Grading, an alternative assessment method where students meet specific course learning objectives through multiple attempts, on students’ mathematics identity development. Through a comparative case study of two Calculus I students at a Hispanic-Serving Institution, one enrolled in a specification graded course and the other in a traditionally-graded course, we examine shifts in their self-perceptions of competence, interest, recognition in mathematics, and overall mathematics identity. Our findings suggest that specifications grading can enhance students' mathematics identity by encouraging perseverance and a sense of competence. This study contributes to the field of mathematics education by providing empirical evidence that alternative assessment structures, like specifications grading, can serve as powerful tools for creating more equitable and identity-affirming learning environments in foundational STEM courses.

Epistemic actions in proving two-triangle problems by considering mathematical reading and writing ability

2025-04-14T09:48:13+00:00

Mathematical abstraction is essential in constructing mathematical concepts, particularly in proof. The RBC+C epistemic actions—recognizing, building-with, constructing, and consolidating—are key cognitive processes in proof construction. However, the impact of mathematical reading and writing abilities on these processes remains unexplored. This study investigates how students’ mathematical reading and writing abilities affect their epistemic actions when proving the congruence of two triangles. This qualitative research adopts a case study design involving three undergraduate students who have completed a geometry course. The participants were selected based on their reading and writing proficiency levels: high, moderate, and low. Data were collected through reading and writing assessments, proof-solving tasks, and semi-structured interviews. The analysis follows the RBC+C framework to identify patterns in students’ cognitive process during proof construction. Findings reveal that students with high mathematical reading and writing abilities demonstrate a more structured proof strategy, effectively recognizing key properties, building logical connections, and constructing valid arguments. High-proficiency students also exhibit flexibility in using both geometric and algebraic approaches in proving. In contrast, students with lower reading and writing abilities struggle with symbolic representation, logical coherence, and notation consistency, leading to incomplete or incorrect proofs. Moreover, consolidation of mathematical ideas, such as reusing known theorems and revisiting proof steps, occurs more frequently in high-achieving students, enabling deeper conceptual understanding. This study highlights the critical role of mathematical literacy in the proof process. It suggests that strengthening reading and writing instruction in mathematics education can enhance students’ ability to construct rigorous proofs. The findings contribute to the development of instructional strategies that integrate mathematical literacy into proof-based learning, ultimately fostering students’ reasoning and problem-solving skills in mathematics.

In-service teachers’ seeing mathematical creativity: Unravelling and launching mathematical creativity tasks

2025-04-10T03:30:59+00:00

The development of mathematical creativity—typically characterized by fluency, flexibility, originality, and elaboration—has garnered growing attention within mathematics education due to its cognitive value and potential to enhance problem-solving competence. Despite this increasing interest, existing research highlights a critical gap: in-service primary school teachers often exhibit a limited understanding of mathematical creativity and face significant challenges in recognizing and assessing its manifestations in classroom settings. While prior studies have explored the influence of creativity-focused coursework on prospective teachers, investigations involving in-service educators remain sparse. Addressing this gap, the present qualitative study introduces a structured educational program designed to enhance the conceptual understanding and pedagogical practices of seven Greek in-service primary school teachers regarding mathematical creativity. The program integrates theoretical frameworks with creativity-enhancing tasks sourced from established literature, encouraging participants to analyze, solve, and adapt these tasks. Data were collected through pre- and post-program interviews and questionnaires and analyzed using thematic analysis to capture shifts in perception. The findings reveal that although participants exhibited modest enrichment in their understanding—particularly concerning the value of open-ended and non-routine tasks in fostering fluency and flexibility—they continued to struggle with promoting originality and elaboration. These results underscore the necessity for sustained, targeted professional development initiatives that support teachers in identifying and implementing strategies to nurture all dimensions of mathematical creativity. This study contributes to the field by offering empirical evidence on how thoughtfully designed programs can incrementally refine in-service teachers’ perceptions and instructional approaches toward creativity in mathematics education.

Mathematical reasoning and communication word problems with mathematical problem-solving orientation: A relation between the skills

2025-03-19T10:46:22+00:00

Developing students’ mathematical reasoning skills (MRS) and mathematical communication skills (MCS) is crucial, as both are fundamental to effective mathematical problem-solving (MPS). Despite their theoretical interconnectedness, limited empirical evidence exists on how MRS and MCS relate to MPS, particularly in problem-based contexts. This study investigates the relationship between MRS and MCS within an MPS-oriented framework using a quantitative, descriptive correlational design. A modified mathematical word problem (MWP) essay test was administered to 117 students across two pilot classes. The test items were designed to elicit reasoning and communication processes associated with MPS. Psychometric analyses, including evidence of content validity (Aiken’s V), consequential validity, reliability (α and ω coefficients), and item-level metrics (discrimination and difficulty indices), confirmed the instrument’s robustness. Factor analysis supported a unidimensional structure aligned with MPS. Correlational analyses revealed significant positive associations between MRS and MCS, meeting bivariate normality assumptions. Pearson’s r was 0.529 (95% CI: 0.261–0.722), Spearman’s ρ was 0.493 (CI: 0.215–0.697), and Kendall’s τ was 0.400 (CI: 0.101–0.632), indicating a strong relationship. These findings underscore the interdependence of reasoning and communication skills in the context of MPS. The study also offers a detailed analysis of student obstacles in solving MWPs, contributing to a nuanced understanding of cognitive and linguistic dimensions in mathematical problem-solving. Implications are discussed for researchers, policymakers, and educators, particularly in designing instructional interventions that strengthen MRS and MCS in support of MPS.

A SOLO Taxonomy-based rubric for assessing conceptual understanding in applied calculus

2025-03-15T22:35:54+00:00

Assessing conceptual understanding in mathematics remains a persistent challenge for educators, as traditional assessment methods often prioritize procedural fluency over the complexity of connections between mathematical ideas. Consequently, these methods frequently fail to capture the depth of students’ conceptual understanding. This paper addresses this gap by developing and applying a novel rubric based on the Structure of Observed Learning Outcomes (SOLO) Taxonomy, designed to classify student responses according to demonstrated knowledge capacity and cognitive complexity. The rubric introduces transitional levels between the main SOLO categories and includes provisions for evaluating unconventional solutions, enabling a more nuanced assessment of student work based on knowledge depth and integration. The rubric was constructed through an analysis of the conceptual knowledge components required to solve each problem, validated by expert review, and guided by criteria aligned with SOLO level classifications. It also incorporates qualitative feedback to justify each SOLO level assignment. Using this rubric, the study analyzed responses from 57 first-year undergraduate students—primarily chemistry and computer science majors at a private university in the Philippines—to test items on linear approximations and the Extreme Value Theorem. Interrater reliability was established through weighted Cohen’s kappa coefficients (0.659 and 0.667 for the two items). The results demonstrate the rubric’s capacity to differentiate levels of conceptual understanding and reveal key patterns in student thinking, including reasoning gaps, reliance on symbolic manipulation, and misconceptions in mathematical logic. These findings underscore the value of the SOLO Taxonomy in evaluating complex and relational thinking and offer insights for enhancing calculus instruction. By emphasizing the interconnectedness of mathematical ideas, the study highlights the potential of conceptually oriented assessments to foster deeper learning and improve educational outcomes. Furthermore, the rubric’s adaptability suggests its applicability beyond calculus, supporting a broader shift toward concept-focused assessment practices in higher education.

Ethnomathematical insights from the tide-forecasting calendar of an Indonesian coastal community into mathematics classroom

2025-05-22T08:58:20+00:00

The integration of cultural knowledge systems into mathematics education remains underexplored, particularly within Indonesian coastal communities, where traditional practices are deeply intertwined with environmental and astronomical phenomena. Although ethnomathematics has received increasing scholarly attention, there is a notable lack of empirical studies that illuminate the mathematical reasoning embedded in indigenous calendar systems—especially those employed by coastal communities for subsistence activities. This study addresses that gap by investigating the ethnomathematical knowledge inherent in the calendrical system used by villagers in the Lungkak community of East Lombok, Indonesia. It highlights a unique integration of the Pupuru (known as the Pleiades star cluster), lunar phases, the Hijri calendar, and the Gregorian calendar to predict seasonal transitions and tidal patterns essential to fishing practices. Adopting an ethnographic approach to comprehensively explore cultural dynamics and social phenomena within the community, data were collected through purposive sampling, in-depth interviews, participant observation, and document analysis, and subsequently analyzed using interactive ethnographic methods. The findings reveal the existence of sophisticated mathematical constructs within the community’s calendrical practices, including trigonometric reasoning (angular positioning of celestial bodies), numerical and arithmetic sequences (patterns of star and lunar visibility), modular arithmetic (cyclical forecasting of astronomical events), and set theory (classification of tidal phases). These results demonstrate the community’s implicit engagement with formal mathematical concepts through culturally embedded knowledge. This study contributes to the advancement of culturally responsive mathematics education by advocating for the integration of ethnomathematical content into classroom instruction. Such integration enhances students’ mathematical literacy, contextual relevance, and engagement with mathematical learning.

Teaching conditional probability in grade 12 using realistic mathematics education theory

2025-06-17T09:35:30+00:00

The perspective on applying mathematics to solve practical problems is clearly expressed in Vietnam's Mathematics General Education Curriculum in 2018. Therefore, Realistic Mathematics Education (RME) is suitable for the goals of mathematics education in Vietnam and can become one of the fundamental theories for designing mathematics teaching models in high schools. This study presents an experimental result of teaching conditional probability based on RME and following a five-step process we develop, including problem setting, experience, rediscovering conditional probability, forming conditional probability, application. Worksheets containing problems were distributed to 42 students to solve, and their work was collected immediately afterwards. The works will be analyzed to identify emergent models constructed by students. The new result of the paper is from the study of De Lange, Jupri and Drijvers, we propose a mathematization process for teaching conditional probability in Vietnam. The data analysis method is a qualitative method, through observing the students' problem-solving process. Experimental results show that students actively participated in the process of reinventing conditional probability through solving learning tasks.

Classification of inductive thinking in mathematical problem solving

2025-06-13T02:56:51+00:00

Inductive thinking is a method of thinking that involves recognizing patterns, understanding relationships, and deconstructing general rules. This method of thinking develops through a variety of factors that support complex problem solving. Using mathematical problems that describe the inductive thinking process within the context of number problems helps investigate students' inductive thinking process. This study, employing a qualitative descriptive research approach, seeks to develop a novel classification framework for students' inductive thinking in the context of mathematical problem solving. The study was conducted in a structured manner on 21 students enrolled in the Department of Mathematics during their fifth semester at a university in Indonesia using number sequence as the problem material. The collection of data was executed through the administration of tests and the observations of problem-solving behaviors. The analysis was conducted using constant comparative procedures (CCP). The instruments used in this study included mathematical problems and recording devices. The findings of this study are presented in the form of three different classifications of inductive thinking: the use of variables, the use of visual, and the use of formulae. The study offers significant theoretical insights for future research and practical implications for the implementation of inductive thinking in improving mathematical problem-solving.

The development of web-based learning environment to enhance students’ numeracy and reasoning

2025-05-27T02:38:00+00:00

Despite the growing emphasis on numeracy as a critical outcome of mathematics education, many instructional approaches fail to connect numeracy learning with students’ reasoning development in meaningful ways. Existing research has not sufficiently explored the integration of technology-supported environments for fostering numeracy through theoretically grounded task design. Addressing this gap, the present study introduces a novel web-based learning environment grounded in numeracy theory and task design principles aimed at enhancing students' numeracy competence and mathematical reasoning. The development and implementation process involved iterative trials with 25 fifth-grade students: a one-to-one trial (n = 2), a small-group trial (n = 5), and a field trial (n = 18). Data were collected from students’ written responses on the web-based platform and their oral explanations. Findings demonstrate that the developed environment meets three key criteria: validity, as it aligns with relevant theoretical and empirical foundations; practicality, based on its usability and feasibility for students; and effectiveness, as evidenced by improved reasoning skills. These results highlight the potential of well-designed web-based learning environments to meaningfully support the development of numeracy competence while simultaneously fostering mathematical reasoning in primary education.

Integrating technology, Javanese ethnomathematics, and realistic mathematics education in supporting prospective mathematics teachers' numeracy skills: A learning trajectory

2025-03-03T02:52:09+00:00

In the era of the 21st century and Industrial Revolution 4.0, prospective mathematics teachers (PMTs) are expected not only to possess strong mathematical content knowledge but also to develop pedagogical approaches that promote students’ numeracy skills in meaningful and contextually relevant ways. However, despite growing global attention to numeracy, there remains a gap in instructional models that effectively integrate local cultural contexts and technological tools in the preparation of PMTs. Addressing this gap, this study introduces a novel learning trajectory that embeds technology, Javanese ethnomathematics, and Realistic Mathematics Education into a coherent instructional design framework, namely TE-RME aimed at enhancing PMTs' numeracy competencies. The research employed a design research methodology encompassing three iterative stages: preliminary design, design experiments consisting of a pilot and teaching experiment, and retrospective analysis. The participants were 25 fifth-semester PMTs enrolled at a private university in Semarang, Indonesia. The resulting trajectory comprises five learning activities, such as orientation to cultural contexts, exploration and problem-solving of numeracy tasks, task design involving numeracy elements, communication and interpretation of mathematical solutions, and instructional design involving the integration of numeracy tasks. Findings revealed that the TE-RME approach effectively supported PMTs in making meaningful connections between culturally embedded practices and everyday mathematical reasoning. By engaging with authentic local contexts, students demonstrated increased fluency in solving numeracy problems and designing contextually relevant learning activities. This research contributes a culturally responsive instructional model for mathematics teacher education and underscores the pedagogical potential of integrating local wisdom with contemporary mathematics education approaches. Implications point to further research exploring other ethnomathematical contexts to enrich mathematics instruction and promote equitable and culturally grounded mathematics learning.

How can the mathematics anxiety rating scale be modified for Indonesian elementary students (aged 10-12)? A psychometric analysis

2025-06-23T01:33:37+00:00

Mathematics anxiety is a significant psychological factor affecting students' learning and academic performance. The Mathematics Anxiety Rating Scale (MARS) is widely used to assess this anxiety, but its original version is designed for adolescents and adults. A modified version is necessary to effectively measure mathematics anxiety among younger students. This study aims to modify and validate the MARS for Indonesian elementary school students aged 10-12 years, ensuring its reliability and validity through psychometric analysis. This study employed a quantitative psychometric approach with a cross-sectional survey design, involving 324 Indonesian elementary school students aged 10-12 years. The MARS-30 was adapted by simplifying language and adjusting contextual items to suit younger students. Data were collected through an online questionnaire distributed via social media. Exploratory Factor Analysis (EFA) was conducted to determine the factor structure, while Confirmatory Factor Analysis (CFA) assessed model fit. Cronbach’s Alpha measured the scale’s internal consistency and reliability. EFA revealed a two-factor structure consisting of Mathematics Test Anxiety and Numerical Anxiety, explaining 57.62% of the total variance. CFA confirmed a good model fit with CFI = 0.94, TLI = 0.92, RMSEA = 0.06, and SRMR = 0.05. The modified MARS demonstrated excellent internal consistency (α = 0.87), with both subscales showing high reliability (Mathematics Test Anxiety: α = 0.85, Numerical Anxiety: α = 0.84). These findings confirm that mathematics anxiety in young students consists of distinct dimensions, rather than being a single construct. In conclusion, the modified MARS for Indonesian elementary students is a valid and reliable tool for assessing mathematics anxiety in children aged 10-12 years. The study confirms that mathematics anxiety consists of two distinct dimensions and highlights the importance of early identification and intervention. Future research should explore longitudinal trends and strategies to help students manage mathematics anxiety effectively.

Investigation of the impact online single and multiple representation scaffolding on mathematical concept mastery and mathematical problem-solving skill

2025-06-30T11:26:19+00:00

Representation plays a central role in mathematical problem solving, serving as a cognitive bridge between abstract concepts and concrete understanding. However, while prior studies have examined the effects of scaffolding in mathematics learning, limited attention has been given to the comparative impact of single versus multiple online representations, particularly in relation to students’ cognitive processes such as eye movement behavior. This study addresses this gap by investigating the effectiveness of online single and multiple representation scaffolding in enhancing students’ mathematical concept mastery, problem-solving performance, and eye movement patterns during problem-solving tasks. A quasi-experimental design was employed involving 300 high school students, randomly assigned to either a multiple representation scaffolding group (n = 150) or a single representation scaffolding group (n = 150). Data were analyzed using one-way MANCOVA, ANCOVA, MANOVA, and ANOVA tests. The results revealed that students who received multiple representation scaffolding outperformed their peers in mastering mathematical concepts, solving complex problems—including advanced-level tasks—and demonstrating more efficient visual processing, indicated by shorter fixation durations and rereading times. Furthermore, these students exhibited more adaptive strategies across varying question types (basic, combination, and advanced). The findings highlight the pedagogical advantage of using multiple representation scaffolding in online mathematics instruction, suggesting that it offers more comprehensive cognitive support and promotes deeper conceptual understanding. This study contributes to the growing body of research on digital scaffolding by evidencing the cognitive and performance-related benefits of multimodal representation and underscores its potential to inform the design of technology-enhanced mathematics learning environments.