Search Results (542)

The concepts of variable and parameter are fundamental for mathematical activity but are also challenging to rigorously introduce at a didactic level. In this paper, we discuss findings from an 11th-grade class interdisciplinary project involving mathematics and linguistics, promoting a conceptual approach to the learning of variables and parameters through narratives. We analyze the written productions of 22 Italian students across two tasks: the first aimed at exploring differences in the meaning of variables and parameters while employing a logico–scientific or narrative mode of thinking; the second involved a meta-reflection on the methodological tools used in the disciplines involved. Students’ productions were qualitatively analyzed using content analysis and thematic analysis, respectively. The analysis enables an elaboration on students’ understanding of the different roles of variables and parameters and of their epistemic features. Students’ conceptualizations of variables and parameters went beyond formal description, drawing on a variety of real-world situations. Moreover, the meta-reflection on the methodological tools shows new awareness of students’ understanding of disciplinary concepts. These findings suggest that interdisciplinary approaches involving mathematics and linguistics can effectively support the conceptual understanding of algebraic notions in secondary school. We therefore recommend further research exploring the integration of narrative contexts and cross-disciplinary collaborations in mathematics teaching. Full article

This study examines how student–faculty partnerships are experienced within undergraduate mathematics coursework at a majority Hispanic Serving Institution (HSI). Drawing on the Student as Partners (SaP) theoretical framework and using an interpretive phenomenological research design, we examined the lived experiences of student and faculty partners who participated in a series of professional development sessions on student-faculty partnerships and equitable teaching and learning practices in mathematics courses. Findings indicate that student partners’ lived experiences in the partnership program contributed to the development of sense of belonging, self-efficacy, and awareness of the need to link real-world and culturally responsive applications to mathematics learning. On the part of the faculty partners, findings indicate that their lived experiences in the student-faculty partnership program contributed to enhanced self-efficacy through professional growth, development of new perspectives on teaching, and awareness of fostering culturally responsive teaching and learning experiences. The study highlights the transformative potential of student-faculty partnerships in bridging traditional mathematics instruction with students’ lived learning experiences and perspectives on fostering real-world, reflective, and student-centered learning environments for all students. Specifically, the study showcases the promise of partnership models in mathematics settings and points to the need for future research on scalable approaches that support the success of culturally and linguistically diverse students in STEM. Full article

Tertiary mathematics teaching is predominantly face-to-face, yet large, diverse cohorts and limited contact hours constrain opportunities for individually paced practice and timely feedback. We developed three bespoke, self-paced online numeracy modules, each targeting a specific mathematical concept and disciplinary context. Module design was informed by learning theory (constructivist, active learning, Universal Design for Learning, inclusive learning practices). We ran a qualitative pilot study to gain insight into user perceptions of modules in terms of engagement and perceived learning support, conducting semi-structured interviews with undergraduate science students (n = 11) and educators (n = 7). We applied thematic analysis to interview data, which generated the following insights. Students—many reporting high mathematics anxiety—responded positively, valuing low-stakes iterative practice, clear stepwise scaffolding, multimodal presentation, contextualized examples aligned to their course, and a supportive instructor voice. These features were described as reducing anxiety, reframing errors as part of learning, and supporting inclusion, despite prevalent math avoidance in the cohort. Staff feedback was more cautious, recognizing similar strengths but focusing on areas for improvement. We argue that bespoke, contextualized modules can augment face-to-face instruction by delivering individualized pacing and immediate feedback at scale, while contributing to the creation of an accessible, inclusive, supportive learning environment. Future work should quantify learning outcomes, track affective changes longitudinally, and isolate contributions of specific design features across diverse cohorts and disciplines. Full article

This study explored how mathematics teachers in Chinese special schools provide instructional support to primary-aged students with intellectual and developmental disabilities (IDD). The types, characteristics, and classroom implementation processes of such support were identified to address a gap in the literature regarding subject-specific instructional practices in special education settings. A qualitative research design using interpretative phenomenological analysis (IPA) was employed. Five mathematics teachers from special schools in Shanghai participated in the study. Data were collected through 15 video-recorded classroom observations and five semi-structured interviews. Thematic analysis was conducted to identify key patterns of instructional support. The analysis revealed five core domains of instructional support for students with IDD: (1) comprehension facilitation through simplified explanations, real-life connections, and visual scaffolding; (2) responding to tasks involving prompts, modeling, and hand-over-hand support; (3) maintaining attention using individual and collective cues; (4) sustaining motivation through praise, encouragement, and second-chance opportunities; and (5) regulating behavior such as verbal restraint, physical proximity, and attention redirection. The findings contribute to a deeper understanding of effective instructional support tailored to students with IDD. Full article

This paper aims to understand the teaching and learning practices and perceptions regarding the subject of Differential and Integral Calculus 1 (DIC1) based on the current French model, as implemented at Université Claude Bernard Lyon 1 (LYON 1), and the Brazilian model, as observed at the Federal University of Technology—Paraná (UTFPR). Five tutorial groups were studied at LYON 1. At UTFPR, four classes of DIC1 were analyzed. Teaching activities were observed, and teachers responded to a questionnaire regarding the frequency with which they implemented certain activities and their beliefs about which activities contribute most to student learning. Students responded to the same questionnaire, reflecting on how often their instructors employed these activities and which ones they believed were most beneficial for learning. There was general agreement between teachers and students about the instructional methodologies used in class; however, discrepancies emerged between observed practices, stated methodologies, and the activities considered essential for learning. In engineering programs, the time allocated to problem-solving—individually or on the board—emerged as a key aspect that may inspire changes and improvements in the Brazilian model. In contrast, group work and mathematical software may serve as avenues for improvement in the French model. Full article

This article introduces a framework for scientific and professional language training tailored for STEM (Science, Technology, Engineering and Mathematics) specialists, emphasising the integration of digital technologies and artificial intelligence (AI) in language education. The framework aims to develop students’ research communication skills and digital competencies, which are essential for effective participation in both national and international scientific discourse. The article discusses contemporary trends in STEM education, emphasising the importance of interdisciplinary approaches, project-based learning, and the utilisation of digital tools to boost language skills and scientific literacy. The article outlines the development and deployment of a digital platform aimed at supporting personalised and adaptive learning experiences, integrating various educational technologies and approaches. Empirical research conducted through a pedagogical experiment demonstrates the effectiveness of the framework, showing significant improvements in students’ academic and linguistic competencies across multiple modules. The findings highlight the importance of combining language training with STEM education to equip future engineers for the challenges of a globalised and digitalised professional world. This work reports on the “Enhancing Scientific and Professional Language Learning for Engineering Students in Kazakhstan through Digital Technologies” project conducted at Saginov Technical University (STU) in Kazakhstan and funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP19678460). The research contributes to the ongoing discussion on improving language teaching in STEM fields, offering a framework that aligns with current educational demands and technological progress. Full article

Short-form video platforms increasingly shape students’ media practices, yet little is known about the pedagogical value of student-generated videos in university mathematics. This study examined an intervention in a first-year mathematics course at a European university in which students produced 1–2 min explanatory videos solving integration problems and subsequently engaged in peer evaluation of selected exemplars. A mixed-methods design was employed, combining coursework and final examination scores with interview data. No statistically significant performance gains were observed; however, strong positive correlations between coursework, final examination and overall grade indicated stable achievement patterns across assessment points. Qualitative analysis suggested that the process of producing short instructional videos encouraged students to reflect on explanatory clarity, peer perspectives, and the communication of mathematical reasoning, despite linguistic and technical challenges. Overall, the findings provide exploratory insights into how student-generated videos can be integrated into undergraduate mathematics courses as a low-stakes instructional activity supporting reflective engagement and peer-oriented explanation. This study contributes to the scholarship of teaching and learning (SoTL) in STEM education by offering an empirically grounded account of a media-based, peer-oriented learning activity in a university mathematics context. Full article

Generative artificial intelligence (GenAI) shows transformative potential in mathematics education. However, empirical findings remain inconsistent, and a systematic synthesis of its effects across distinct engagement dimensions is lacking. This preregistered meta-analysis (INPLASY2025110051) systematically reviewed 22 empirical studies (46 independent samples, N = 5232) published between 2023 and 2025. The results indicated that GenAI has a moderate positive impact on students’ mathematics learning outcomes (g = 0.534). Moderation analysis further revealed that the level of GenAI integration in teaching, sample size, and learning content are the primary factors influencing this effect. The study found that the effect was most pronounced under the creative transformation (CT) integration mode, was significant when applied to geometry learning, and was stronger in studies with small samples or small class sizes; collaborative learning approaches also significantly enhance these mathematics learning outcomes. By contrast, educational stage and intervention duration did not show significant moderating effects. The GRADE assessment indicated that while the overall evidence is supportive, the certainty of evidence is stronger for cognitive outcomes than for non-cognitive domains. The findings also offer a reference for future research on constructing a human–machine collaborative learning environment. Full article

Since the introduction of Carol Dweck’s landmark work in mindset, many scholars have studied the impact of a change in mindset on learning, behavior, and health. National and international large-scale studies have validated the consistent correlation between learners developing a growth mindset (knowing that they can learn and improve) and performance on learning outcomes and longer-term learning behaviors. Whilst mindset interventions can have a positive impact on student learning, recent years have shown the need for more than a change in messaging. For widescale and lasting improvements in mathematics learning, messages need to be specific to mathematics, and delivered through a change in teaching approach, with mindset ideas infused through teaching practices and through assessment. This paper shares the evidence on the need for a “mathematical mindset” approach and the wide scale benefits that the approach promises to bring about. Full article

This study explores the potential of educational game design as a pedagogical strategy for teaching Mathematics in lower secondary education, addressing persistent challenges related to students’ motivation and engagement with the subject. The research focuses on the creation and implementation of a game, CriaMat, an ideation tool developed to support students in designing their own mathematical games. A qualitative approach was adopted, structured as a case study conducted in four classes and involving a total of 50 students. Data collection followed a mixed-methods strategy, combining participant observation, document analysis, and questionnaire-based inquiry, each applied during different phases of the intervention. The results indicate a positive reception of the approach, particularly in terms of student engagement, collaboration, and perceived learning. Analysis of the games produced demonstrates students’ ability to create functional games that integrate the knowledge and skills developed throughout the process. The findings also suggest that learning to design games was perceived as a valuable strategy for engaging with and consolidating mathematical content, while simultaneously providing a privileged context for developing essential competencies—such as critical thinking, creativity, and problem-solving—aligned with the national competency framework for compulsory education. The study does not aim to measure learning gains, but rather to explore students’ perceptions and experiences of learning mathematics through the process of game creation. Full article

The most widespread lesson preparation resource used by mathematics teachers is the textbook. Initial teacher training programmes should therefore develop the skill of curricular noticing, i.e., the ability to critically analyse and make decisions concerning an activity sequence from a textbook. This mix-method study focused on the interpretations and decisions adopted by 85 Spanish pre-service primary school teachers (PTs) in relation to a three-dimensional (3D) geometry activity sequence from a textbook. The PTs were assigned two tasks: the first was identifying the limitations of the activity sequence for supporting students’ geometrical understanding regarding three aspects—attributes, geometrical processes, and modes of representation—and the second was completing the sequence. Most PTs interpreted a number of activity sequence limitations. In terms of their decision-making, the PTs prioritised certain characteristics over others, such as introducing further attributes rather than changing representation modes, or adding geometrical processes to their activity sequence designs. Moreover, the analysis allowed determining how PTs completed the activity sequence to address limitations, thereby revealing relationships between their interpretations and decisions. The study findings help teacher educators to design courses aimed at supporting the PTs’ ability to make more informed and effective teaching choices that enhance student learning. Full article

Efforts to improve undergraduate education in mathematics and other STEM fields often work with instructors to implement research-based instructional practices that emphasize active and collaborative learning. To measure the progress and outcomes of such initiatives, researchers need measurement tools that are versatile, meaningful, and inexpensive to use, to know what teaching practices are occurring. Because students spend a great deal of time observing class conditions, they are well positioned to report the teaching that they experienced. We report results from some 2400 student surveys on the use of active and collaborative learning (ACL) approaches in over 200 recitation sections of gateway courses in tertiary mathematics, physics, and computer science. We developed a set of survey items, TAMI-SS, and a compound measure based on the items, called S-ACL for Student-reported Active and Collaborative Learning, that reflects the extent of active and collaborative learning as reported by students. We find that S-ACL scores compare favorably with instructor surveys and observations, and with students’ reports of their classroom experience using established measures. Moreover, S-ACL reflected departments’ progress in implementing ACL in recitations. When focused on specific, observable classroom behaviors, student surveys of instructional practice can be used to measure the progress of instructional change initiatives in mathematics and similar fields. Full article

Mathematics is a discipline that forms the foundation of many fields and should be learned gradually, starting from early childhood. However, some subjects can be difficult to learn due to their abstract nature, the need for attention and planning, and math anxiety. Therefore, in this study, a system that contributes to mathematics teaching using computer vision approaches has been developed. In the proposed system, users can write operations directly in their own handwriting on the system interface, learn their results, or test the accuracy of their answers. They can also test themselves with random questions generated by the system. In addition, visual graph generation has been added to the system, ensuring that education is supported with visuals and made enjoyable. Besides the character recognition test, which is applied on public datasets, the system was also tested with images obtained from 22 different users, and successful results were observed. The study utilizes CNN networks for handwritten character detection and self-created image processing algorithms to organize the obtained characters into equations. The system can work with equations that include single and multiple unknowns, trigonometric functions, derivatives, integrals, etc. Operations can be performed, and successful results can be achieved even for users who write in italicized handwriting. Furthermore, equations written within each closed figure on the same page are evaluated locally. This allows multiple problems to be solved on the same page, providing a user-friendly approach. The system can be an assistant for improving performance in mathematics education. Full article

Current calls to integrate science and mathematics in PK-16 education build on decades of prior initiatives, yet the United States still lacks consensus on what integration entails and consistent policies to support it. This study systematically reviews current U.S. policies to identify guidance on the preparation of teachers to integrate science and mathematics. Given that teacher preparation is inherently connected to PK-12 policy, we also review PK-12 policy guidance focused on dual or integrated teacher endorsements, school designations, and PK-12 science and mathematics learning standards. Drawing on an established framework that defines meaningful integration as authentic problem solving supported by the use of multiple STEM disciplines, we examine the degree to which current policies enable such practice. Our findings reveal recommendations for integrating science and mathematics, yet policies overwhelmingly reinforce a siloed approach. We argue that misalignment between teacher preparation policy and PK-12 policy creates a circular problem: teachers cannot be expected to implement integrated science and mathematics instruction without adequate preparation, yet preparation programs have little incentive to design coursework for an instructional approach not systematically supported in PK-12 settings. Clarifying and aligning these policies is therefore essential for advancing coherent, scalable integration across the PK-16 system. Full article

In this project, Anishinaabe artists and knowledge carriers worked with non-Indigenous classroom teachers to explore the cultural significance and mathematics of making wiigwaas makakoon (birch bark baskets). The artists spent two weeks in two grade 6 classrooms teaching students the process of basket making. They combined Indigenous pedagogy and intentionally designed inquiry tasks in order to generate mathematically related concepts. To make cultural–mathematical connections, we looked to Battiste’s characteristics of Indigenous pedagogy and explored how the learning that took place was holistic, part of a lifelong process, experiential, rooted in language and culture, spiritual, communal, and an integration of Indigenous and Eurocentric knowledges. Mathematically, students explored measurement with non-standard units, bisected angles without the use of a protractor, and explored the best way to optimize the capacity of their baskets. This work is an example of integrating Indigenous knowledge and heritage into elementary mathematics instruction. Full article