Homework is an extension of students’ classroom learning and an important form of independent learning activity. Because homework procrastination negatively affects students’ academic achievement, it is important to clarify the factors associated with this behavior. Drawing on social cognitive theory and self-regulated learning, this study examined how external contextual factors and individual motivational factors relate to students’ homework procrastination. A total of 609 students from six schools in Heping District, Jinnan District, and Jizhou District of Tianjin participated in the study. Specifically, the study investigated whether parental autonomy support and teacher autonomy support were associated with students’ self-efficacy, whether self-efficacy and perceived homework value were associated with homework procrastination, and whether self-efficacy played a mediating role in the relationships between parental and teacher autonomy support and homework procrastination. The results showed that both parental autonomy support and teacher autonomy support were positively associated with students’ self-efficacy. In addition, both self-efficacy and perceived homework value were negatively associated with homework procrastination. Further analyses indicated that the results were consistent with an indirect-pathway model in which parental and teacher autonomy support were linked to homework procrastination through students’ self-efficacy. These findings suggest that autonomy-supportive contexts may be associated with lower homework procrastination partly through students’ self-efficacy, while perceived homework value is directly associated with homework procrastination.
There is still much debate surrounding the development of an effective teaching sequence for deductive proofs in geometry, and no consensus has been reached on which competencies need to be developed and in what order. In this paper, we examine students’ performance in deductive proofs in geometry in order to suggest a hypothetical teaching sequence for these proofs. By analysing survey data from 238 Year 8 and 208 Year 9 students, we found that there were still challenges relating to competencies concerning the generality of proofs, the structure of proofs, the definitions of shapes, and spatial reasoning in order to achieve more successful proofs in geometry. We then constructed a hypothetical teaching sequence based on path analysis and structural equation modelling. Our results provide guidance on the order in which geometry should be taught for deductive proving.
This study examines secondary mathematics teachers’ attitudes toward argumentation-based instruction (ABI) and its enactment in classroom practice within a Bedouin Arab secondary-school context. Grounded in Toulmin's model of argumentation, the study adopts a qualitative case-study design combining classroom observations and semi-structured interviews. Data were collected from five mathematics teachers, including repeated observations of one Grade 10 classroom. The findings reveal a discrepancy between teachers’ positive orientations toward ABI and its classroom enactment. Although participants viewed argumentation as valuable for promoting conceptual understanding, motivation, and student engagement, observed argumentative episodes were relatively infrequent and generally characterized by low-level reasoning structures, primarily claims supported by data or warrants. Argumentation tended to emerge as an incidental component of problem solving rather than as a systematically planned instructional strategy. Interview data identified several constraints, including time pressure, curriculum demands, exam-oriented accountability, and limited confidence in facilitating dialogic discourse. The findings highlight the complex relationship between teachers’ pedagogical beliefs and their enacted practices, suggesting that positive attitudes toward argumentation do not necessarily translate into sustained dialogic instruction. The study contributes to the literature by integrating structural and dialogic perspectives on argumentation and by providing a context-sensitive account of how argumentation-based pedagogy is implemented within a culturally specific educational setting. In doing so, it advances understanding of the contextual conditions that shape the enactment of student-centered, reasoning-oriented instruction in mathematics education.
This scoping review maps ethnomathematics research in Philippine mathematics education and identifies similarities and differences of patterns with selected international literature. Guided by JBI methodology and PRISMA Extension for Scoping Reviews, 45 studies were analyzed to examine how ethnomathematics is represented and characterized using the lenses of ethnomathematical activities and curriculum typology. The mapped studies show an increase in publications over time, with a shift from ethnographic documentation toward instructional design and classroom applications. Four recurring themes in the reported educational contributions of ethnomathematics were identified: contextualization through Indigenous Knowledge Systems and Practices, teacher agency in lesson co-design, reported student engagement, and conceptual or reflective work. Designing and measuring are the most frequently represented activities, while integration and insertion are the most common at the curriculum level. In relation to selected international literature, the Philippine corpus shows a similar emphasis on mathematical domains and educational levels, particularly geometry and the secondary level. Cultural practices emphasize weaving, fishing, and farming, in contrast to the focus on architecture in some international studies. The review identifies gaps in coverage and highlights the need for broader representation and stronger links between research and curriculum development.
This study examines how integrating Minecraft into science, technology, engineering, and mathematics (STEM) education impacts seventh-grade students’ STEM motivation and spatial abilities. The research was conducted with 46 students during the 2021–2022 academic year and employed an explanatory sequential mixed-methods design. Over approximately 2 months, the experimental group ( n = 24) participated in weekly Minecraft-based STEM activities, while the control group ( n = 22) continued with standard instruction aligned with the national curriculum. STEM motivation and spatial ability were measured in both groups before and after the intervention using a motivation scale and a spatial ability test. Qualitative data were obtained through semistructured interviews with students in the experimental group. The results indicate that Minecraft-based STEM activities significantly enhanced students’ STEM motivation and spatial abilities. These findings suggest that actively integrating digital games into STEM education can effectively increase students’ interest in STEM fields and improve their spatial skills.
Meeting the varied academic needs of a diverse student body is not a new problem, and the realization of a need for personalized learning has been developing rapidly amongst all students—moving away from the one-size-fits-all approach that came with standardized curricula and assessment for students of the same age. In this article, I give a narrative overview of the need for personalization in learning mathematics, providing a summary of different interpretations of the construct of personalized learning and a touch on its theoretical and historical background. I discuss how personalized learning fits within social constructivist theories of learning, and how it is consistent with the process of developing students into independent learners. The main objective of the article is to find out how technology—artificial intelligence in particular—can be utilized to facilitate the process of personalizing mathematics learning. Mathematics educators look to respond to the needs and preferences of contemporary students and take advantage of the educational affordances that artificial intelligence platforms offer. The use of learning management systems, interactive learning systems, intelligent tutoring systems and social media in the personalization process is reviewed, and also the use of artificial intelligence systems in the process of gathering student data. Adaptive hyper-media are used in the process of hyper-personalization —adapting automatically to students’ learning needs and learning preferences. Some recommendations are given on how to move to a personalized classroom and concerns, challenges and recommendations are raised, speculating about the future role of personalized learning in mathematics education.
Junior secondary plane geometry requires students to coordinate diagrams, properties, and reasoning, yet classroom assessments often provide limited diagnostic information beyond total scores. Cognitive diagnostic assessment (CDA) can provide fine-grained evidence about students’ mastery, but its classroom-based application to plane geometry remains limited. This study used the sequential generalized deterministic inputs, noisy “and” gate (seq-GDINA) model to analyze responses to a school-based midterm examination in plane geometry completed by 534 grade 8 students at a junior secondary school in China. It examined students’ mastery of five cognitive attributes and inferred possible learning paths from the diagnosed knowledge states of 207 students in four focal classes. Diagnostic interpretation was supported by evidence of test quality, model fit, and attribute-level classification accuracy. The results indicated uneven mastery across the five attributes. The students showed stronger mastery of triangle concepts and axial symmetry but weaker mastery of congruent triangles, polygons and their interior angles, and especially angle-bisector properties. Subgroup and individual analyses showed that students with similar total scores could differ markedly in their geometric profiles. In the four focal classes, the diagnosed knowledge states suggested a dominant inferred path from no stable mastery, through triangle concepts and axial symmetry, then polygons and congruent triangles, and finally to full mastery of all five attributes. This path can be interpreted as a classroom-level inference. The study shows how CDA can help interpret students’ knowledge mastery and guide remedial instruction in plane geometry.
The development of mathematical understanding is widely recognized as a critical goal of mathematics education. Mathematical understanding can be both a product and a process. However, there are varied perspectives on what mathematical understanding is and how it may be fostered. This paper describes a framework that organizes and explains the ways that mathematics educators conceive of research and practice regarding mathematical understanding. Specifically, the framework describes five aspects of mathematical understanding (factual, procedural, conceptual, metacognitive, and affective) and five lenses (mathematical, cognitive, social, diagnostic, and instructional) that mathematics educators use when focusing on fostering students’ mathematical understanding. We illustrate the framework with examples drawn from work published in leading mathematics education research journals. We hope that researchers and practitioners can use this framework to shape their perspectives of different aspects and different lenses of understanding. The paper concludes with a discussion of future directions for research and practice on fostering mathematical understanding.
The explicit and implicit teaching of values in mathematics education has been explored across many education systems. Currently, researchers and significant education stakeholders argue for the explicit teaching of values in mathematics education. Following this global trend, the current Ghanaian pre-tertiary mathematics curricula emphasize the explicit development of values, unlike previous ones. Therefore, this paper investigates how values are portrayed in mathematics curricula and the valuing pedagogies that account for the portrayal of the identified values. The study utilized qualitative content analysis to identify values and valuing pedagogies in the lower primary, upper primary, and junior high school (JHS) curricula. The analysis revealed varying degrees of portrayal of six explicit values—commitment to achieving excellence, diversity, equity, teamwork/collaboration, truth and integrity, and respect—and three inherent values—problem-solving, innovation, and relevance. Additionally, the curricula strongly prioritize the affective aspect (51.6%) of valuing pedagogies, the cognitive aspect (36.7%), and the social aspect accounting for 11.7% of total valuing references. The study recommends that while the Ghanaian lower primary, upper primary, and JHS mathematics curricula have made strides in integrating key values, there is a need for more attention to the underrepresented values.
Lesson planning in Mathematics is complex and time-consuming for preservice teachers. Artificial intelligence (AI) offers promising support, warranting integration into teacher education. This study examined how 23 preservice mathematics teachers from a Philippine Teacher Education Institution used AI in lesson planning during an AI-assisted workshop. Thematic analysis of prompts and reflections identified two main AI functions: content generation and support tool. Artificial intelligence effectively produced curriculum-aligned objectives, student-centered tasks, and organized lesson formats, but outputs could be verbose, unrealistic, or inaccurate. As a support tool, AI-aided content organization showed weaknesses in formatting, clarity, and content retention. Participants addressed these through refined prompts and manual edits, highlighting AI's potential and limitations, and the need for training in prompt engineering and critical evaluation.
The aim of this study is to examine mastery of the percentage concept among Japanese and Finnish lower secondary school students. This research developed from a long-standing collaboration between Japanese and Finnish researchers, reflecting a shared interest in students’ percentage mastery at this educational level. The primary justification for this comparative study design between Finland and Japan is rooted in the curricular differences between the two countries. The questionnaire of the study comprised six problems, based on a theoretical framework that defines the process descriptions required to solve the problems and the various multimodal approaches that students use to present their solutions. The problems were identical for both Japanese and Finnish students. The main findings indicated that students’ proficiency levels increased from grade 7 to grade 9 in both countries. Conversely, significant differences in the proportion of correct answers were observed, reflecting variations in the curricula and treatment of instructional content between the two countries. The typical errors observed in percentage problems common to both countries were primarily attributable to the incorrect identification of the base quantity. In addition, the multimodal skills essential for solving percentage problems were not necessarily sufficient in either country.
This article presents a study describing the agency of non-human entities within a mathematics education practice involving a teacher and seven high school students from a Brazilian public school. Data collected through observations were analyzed using Actor-Network Theory, mainly drawing on Bruno Latour's sociological insights. The analysis suggested that viewing mathematics education as a complex network of interconnected human and non-human actors allows us to understand how non-human agents contribute to performing a mathematics task. This study provided valuable insights into the role of these agents, revealing whether they act. Elements such as computers, calculators, the task itself, and the computer lab did not operate as mere tools but as active agents that influenced decisions, generated conflicts, and redirected the learning process in mathematics. The analysis also suggests that these non-human and human actors take on different roles, sometimes as intermediaries when their influence goes unnoticed, and sometimes as mediators when they actively intervene and alter the course of action. Furthermore, the study highlights the instability of hybrid association networks, showing how students’ leadership and strategies are constantly reshaped through interactions with various material objects.
This study explores how questioning fosters explorative participation in prospective mathematics teacher (PMT) education, drawing on commognitive and sociocultural perspectives that frame discourse as central to mathematical learning. Situated in a Basic Mathematical Concepts course for senior PMTs at a Turkish university, the study examines classroom interactions related to equations and inequalities. Based on classroom observations of 20 participants, the analysis was conducted in two phases: first, identifying instances of explorative participation, and second, characterizing the forms and functions of both lecturer and student generated questioning. The findings reveal that the lecturer deliberately avoided presenting definitions directly, instead using strategic questioning to elicit analyzing, justifying, and forming-narrative processes from the students. These questioning practices structured students’ engagement by expanding, refining, and stabilizing mathematical meanings. The results further show that explorative participation is not solely a product of dialogic interaction but is systematically mediated through differentiated questioning practices. While lecturer-generated questions orchestrated a broad range of epistemic functions, student-generated questions remained more limited, indicating an asymmetry in the development of mathematical discourse practices. Overall, the study reconceptualizes explorative participation as a multi-layered commognitive process and highlights questioning as a central mechanism for supporting the co-construction of mathematical discourse in teacher education.
This mixed-methods, quasi-experimental one-group pre–post study investigated whether a structured sequence of unplugged computational thinking (CT) activities embedded in regular primary mathematics lessons was associated with measurable changes in pupils’ CT practices and how such changes manifested in classroom interaction. Participants were 150 grade 4–5 pupils in a Vietnamese public primary school who completed eight 45-min, screen-free lessons aligned to five CT practices: decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging. Quantitative analyses revealed statistically significant pre–post improvements across all five CT subscales (all p < .001 ), with large effect sizes (Cohen's d = 2.58 − 3.29 ). Gains were consistent across practices, indicating broad within-cohort growth rather than isolated skill shifts. Qualitative evidence from structured observations, student interviews, and artifact analysis converged with these results, documenting increased representational coordination, more explicit articulation of stepwise procedures, systematic test–revise (debugging) cycles, and distributed collaborative monitoring. Joint analysis linked subscale gains to three mechanism clusters: (i) representational fluency that stabilized invariants for inspection and generalization, (ii) iterative strategic refinement through visible debugging routines, and (iii) collaborative regulation enacted through role rotation and peer verification. Within the bounds of a classroom-based design, the findings provide convergent evidence that low-cost, unplugged tasks can be integrated into routine mathematics instruction and are associated with substantial growth in taxonomy-referenced CT practices in a resource-constrained setting.
The use of dynamic mathematical software as pedagogical tools in mathematics education is widely believed to enrich learning experiences and offer enhanced opportunities for learners to reconceptualize mathematical content. However, there is a dearth of empirically supported literature on how these technological tools facilitate learners’ construction of mathematical knowledge. This study employed the Action–Process–Object–Schema (APOS) theoretical lens to explore the utilization of Autograph technology in deepening learners’ conceptualization of hyperbolic functions at a marginalized rural high school in South Africa. The study adopted a descriptive qualitative case study methodology, where data were collected through diagnostic testing and task-based clinical interviews. Qualitative and textual analysis of data revealed compelling evidence that the representational affordance of Autograph facilitates capacity for logical and reflective thinking, which ultimately promotes adaptive reasoning. The participant learners were able to encapsulate the hyperbolic function concept as an object in totality that could be transformed or manipulated, as demonstrated by their flexibility in switching between the algebraic and graphical representations of the function. The study cogently recommends that Autograph, and other relevant mathematical software, should be made available to mathematics teachers, particularly in marginalized schools in South Africa, and targeted efforts be made to develop the teachers’ technical and pedagogical competency. Further research is recommended to explore the use of Autograph technology in the teaching of other problematic topics, such as geometry, measurement, statistics and probability.
As mathematical modelling problems often allow for a variety of approaches and thus various difficulties can arise, it is particularly important that teachers spontaneously perceive and interpret students’ individual solutions and difficulties and come to a decision about their reaction. In this study, teacher noticing—namely perception, interpretation, and decision-making—is promoted in a modelling seminar. Pre-service teachers’ abilities to notice modelling processes are assessed before and after the seminar using a video-based instrument. The criteria breadth of perception, depth of interpretation and nature of decision-making are used to identify different types of competence profiles, which describe the differences and similarities in the ability to notice mathematical modelling processes. Furthermore, the individual development is evaluated. The analysis reveals tendencies to change in different facets of noticing regarding mathematical modelling processes: Instead of an overall improvement in noticing, the participants mostly develop regarding one facet of noticing (perception, interpretation or decision-making).
Textbook-centred mathematics teaching rarely allows teachers to draw on their valuable learning experiences. This narrative study explored how novice mathematics teachers draw on their learning experiences in their current teaching practice. The participants include three mathematics teachers – two from private schools and one from a public school in the Kathmandu Valley, Nepal. They participated in at least two in-depth qualitative interviews that collected information about their experiences as mathematics learners and how those experiences shaped their teaching. The findings indicate that novice teachers often draw on their prior learning experiences as a form of hidden curriculum that implicitly guides their classroom practices. The underprepared and unconfident novice teachers tend to reproduce the inherited, traditional approaches to mathematics teaching. Nevertheless, once novice teachers gradually collect some experiences and merge these experiences with their emerging knowledge, they gradually emulate their role model mathematics teachers and replicate the practices that they appreciated as learners. These results suggest that recognizing and critically engaging novice and in-service teachers with their own learning experiences can support student-centred teaching.
Over the past decade, the integration of ethnomathematics based technology has grown in mathematics education. This systematic review explores digital cultural-based media integration into mathematics education in Indonesia. A systematic review was conducted following PRISMA guidelines to gather research that meets the inclusion criteria. Articles from 2013 to 2023 were searched using Google Scholar. Screening yielded 23 relevant articles. Thematic analysis was used to categorize research patterns and data from the 23 articles. The analysis reveals a surge in articles from 2016 to 2023, peaking in 2022, underscoring a heightened interest in enhancing mathematics education with digital cultural media. However, a gap from 2013 to 2015 suggests a need for more research during that period. Geometry emerges as the dominant topic, with limited representation of numbers, indicating potential for expansion. High school and primary school students were the primary participants, highlighting the significance of integrating digital cultural media at both levels. Various instructional design models, such as ADDIE, Borg and Gall, and Four-D (4D) were employed. At the same time, evaluation methods ranged from questionnaires to performance tests, providing insights into digital resource efficacy and usability. Overall, the review underscores the potential of integrating digital cultural media in Indonesian mathematics education. By utilizing innovative pedagogical approaches and technology, educators can create engaging, culturally relevant learning experiences, fostering a deeper understanding and appreciation of mathematics among students.
For problem posing to play a more central role in mathematics classrooms, teachers must have access to resources for problem-posing activities. The integration of problem posing into school mathematics can be evaluated through the lens of three levels of curriculum: the planned curriculum, the intended curriculum, and the implemented curriculum. This article discusses how different countries are trying to integrate problem posing into school mathematics at the three different levels. This article provides recommendations to integrate problem posing into school mathematics to present a low barrier to entry for teachers and students, which can then serve as a springboard to solve the problem of problem posing in school mathematics.
One typical challenge in learning multiplication is that students apply multiplication algorithms without understanding why they work. To better enable students to develop a conceptual understanding of multiplication, the distributive property of multiplication over addition can be introduced, allowing students to comprehend and justify computational processes by emphasizing the underlying structure of multiplication algorithms. As a strategic contribution to understanding the distributive property, this study adopts representational reasoning, where mathematical concepts and principles are developed through engaging with and connecting various representations. Cuisenaire rods and arrays were employed to help students grasp the idea of the distributive property, and a qualitative analysis was conducted to investigate students’ representational reasoning. Results indicated that Cuisenaire rods and arrays were effective in helping students understand the decomposition of multiplication factors and in applying partial products to solve problems. However, students often modeled multiplication by interpreting it additively or struggled to connect the Cuisenaire rods and arrays with numerical equations. These findings suggest that while representational reasoning with Cuisenaire rods and arrays can enhance students’ conceptual understanding of multiplication, it does not necessarily ensure proficiency in transitioning between different representations. The study offers pedagogical implications for using representations to support students’ understanding of multiplication.
