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24 SES 05.5 A: General Poster Session
General Poster Session | ||
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24. Mathematics Education Research
Poster Mathematical Modelling in Pre-service Teacher Education: A Scoping Review University of Alberta, Canada Presenting Author:This scoping literature review characterizes research on mathematical modelling in pre-service teacher education. In recent years, mathematical modelling has been increasingly recognized as an important competency and included in curricula throughout the world, such as in Germany, Norway, Singapore, the United States, and Canada. However, despite a robust and growing literature on modelling in mathematics education, no single framework or set of competencies defines the process or product of mathematical modelling. There is, however, a general consensus that it entails a connection to real-world phenomena, distinct phases (e.g., real world situations, mathematical representations, etc.), and certain processes or sub-competencies (e.g., mathematizing, validating, etc.) (see Borromeo Ferri, 2006). As described by Niss & Blum (2015), these phases and sub-competencies comprise what is called the modelling cycle, which can be executed in part or whole, and can be enacted by learners in varied ways. One characteristic common to nearly all interpretations of mathematical modelling is the need for recursion between a real-world situation and the domain of mathematics. Unlike a traditional word problem, in which all of the necessary information is provided and the objective is often procedural application, a modelling problem requires assumptions to be made, models to be developed based on those assumptions, and the results of those models to be interpreted in real contexts. In this scoping review, we contribute alongside existing reviews in this research area (Cevikbas, 2022; Krawitz et al., 2025) to a robust characterization of the field by focusing specifically on research on mathematical modelling conducted with pre-service teachers (PSTs). Our interest in PSTs lies in the notion that their dual roles as learners of both mathematics and pedagogy distinguish them from other groups, such as children or in-service teachers. A scoping review of this sub-field of modelling research represents a gap in the existing literature. Speaking to this need, in identifying a limitation of their recent review, Krawitz et al. (2025) noted that by focusing on early years up to secondary education, they “emphasized the learning of mathematical modelling rather than the teaching of it” and suggested that “future research should explore whether perspectives on modelling differ between learning and teaching contexts” (p. 206). We argue that PSTs, especially those learning to teach in primary classrooms, are in fact a unique group, especially with respect to modelling. Given the importance of learning and teaching modelling, and the unique characteristics of PSTs as learners and teachers of modelling, we intend this review to describe the relevant research literature and to support further research on modelling in the context of teacher education. The overarching research question guiding this scoping review is: What characterizes the research on mathematical modelling in pre-service teacher education? Specifically, we address the following sub-questions: i. What are some general characteristics (e.g., geographic, study size, etc.) of the research on mathematical modelling in pre-service teacher education? ii. Which modelling perspectives (goals and task characteristics) are represented in the research? iii. Which competencies for teaching mathematical modelling are taken up in the research? iv. How is the literature on mathematical modelling in preservice teacher education conceptually organized? To answer these questions, we analyzed data generated through a scoping review (Tricco et al., 2018) of empirical research on mathematical modelling in pre-service teacher education. In our poster, we describe the conceptual framework we used to orient our analysis of 87 research studies published in peer-reviewed scholarly journals. Modelling has a long, rich, and varied tradition in mathematics education research, especially in Europe, and in articulating our conceptual orientation, we elaborate on some of the different perspectives that comprise the field and guide our review. Methodology, Methods, Research Instruments or Sources Used We adhered to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) to conduct our literature search (Tricco et al., 2018). We identified pre-service teachers as the relevant population, mathematical modelling as the relevant concept, and teacher training as the relevant context. We conducted our search on five databases, including Education Resources Information Center (ERIC), Education Research Complete, British Education Index, Australian Education Index, and Education Database. Searches on all five databases were conducted on March 27, 2025. Our searches generated a total of 1670 studies and 374 duplicate studies were removed prior to screening, leaving 1296 studies. The authors and one research assistant used pre-defined inclusion and exclusion criteria (described in the poster) and the protocol developed by Polanin (2020) for systematic reviews to screen the abstracts and titles of the remaining 1296 studies. After eliminating 1155 studies, the two authors conducted full text reviews of the remaining 141 studies and excluded an additional 54, resulting in a total of 87 studies to be included in the scoping review. Conclusions, Expected Outcomes or Findings Our findings reveal a field that has expanded rapidly in scope, scale, and diversity over the past decade. This growth suggests that mathematical modelling has increasingly become a priority in pre-service teacher education. A predominance of small-scale qualitative studies focused on university coursework indicates that the field remains largely exploratory and practice-oriented, emphasizing the process of learning to teach modelling rather than large-scale program evaluation. Moreover, the limited number of studies involving children, in-service teachers, or practicum contexts highlights a persistent gap between preservice coursework and authentic classroom implementation. With respect to modelling perspectives, which we use as an analytical framework for interpreting our results, we note that the emergence of mathematical modelling with PST’s likely grew out of foundational work on the competencies for teaching mathematical modelling (Borromeo Ferri & Blum, 2010; Borromeo Ferri, 2013; 2018). Within this body of work, new trends have emerged. For example, while most studies still align with educational and pedagogical modelling perspectives, research situated in a sociocritical perspective has recently emerged. We see this is as an important development for several reasons. One is that sociocritical issues, such as those that focus on equity, power dynamics, sustainability, and so on, compound the demands of learning to teach mathematical modelling. We argue modelling can be used to educate and empower students to act on important real-world phenomena. However, Steffensen & Kasari (2023) noted that “when there are additional expectations to address socio–political issues, more pedagogical challenges may emerge as teaching becomes more uncertain” (p. 2). We suggest that as a sociocritical perspective continues to become more prominent, researchers should consider explicitly positioning PSTs as teachers of both modelling and appropriate sociocritical competences (e.g., Bulut & Borromeo Ferri, 2025). References Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM - Mathematics Education, 38(2), 86–95. https://doi.org/10.1007/BF02655883 Borromeo Ferri, R. & Blum, W. (2010). Mathematical modelling in teacher education – Experiences from a modelling seminar. In V. Durand-Guerrier, V., Soury-Lavergne, S., & Arzarello, F. (Eds.), European Society for Research in Mathematics Education – Proceedings of CERME 6 (pp. 2046–2055). Bulut, N. & Borromeo Ferri, Rita. (2025). Bridging mathematical modelling and education for sustainable development in pre-service primary teacher education. Education Sciences, 15(2), 248. Education Database. https://doi.org/10.3390/educsci15020248 Cevikbas, M. (2022). Fostering mathematical modelling competencies: A systematic literature review. In Buchholtz, N., Schwarz, B., & Vorhölter, K. (Eds.), Initiationen mathematikdidaktischer Forschung: Festschrift zum 70. Geburtstag von Gabriele Kaiser (pp. 51–73). Springer. Greefrath, G., Siller, H.-S., Klock, H., & Wess, R. (2022). Pre-service secondary teachers’ pedagogical content knowledge for the teaching of mathematical modelling. Educational Studies in Mathematics, 109(2), 383–407. Kaiser, G. & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM - Mathematics Education, 38(3), 302–310. https://doi.org/10.1007/%20BF02652813 Krawitz, J., Schukajlow, S., Yang, X., & Geiger, V. (2025). A systematic review of international perspectives on mathematical modelling: Modelling goals and task characteristics. ZDM - Mathematics Education, 57, 193–212. https://doi.org/10.1007/s11858-025-01683-2 Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge. Polanin, J. R. (2020). Best practice guidelines for abstract screening large‐evidence systematic reviews and meta‐analyses. Res Syn Meth., 10, 330–342. Schukajlow, S., Kaiser, G., & Stillman, G. (n.d.). Empirical research on teaching and learning of mathematical modelling: A survey on the current state-of-the-art. ZDM - Mathematics Education, 50, 5–13. https://doi.org/10.1007/s11858-018-0933-5 Steffensen, L., & Kasari, G. (2023). Integrating Societal Issues with Mathematical Modelling in Pre-Service Teacher Education. Education Sciences, 13(7), 721. https://doi.org/10.3390/educsci13070721 Tricco, A. C., Lillie, E., Zarin, W., O’Brien, K. K., Colquhoun, H., Levac, D., Moher, D., Peters, M. D. J., Horsley, T., Weeks, L., Hempel, S., Akl, E. A., Chang, C., McGowan, J., Stewart, L., Hartling, L., Aldcroft, A., Wilson, M. G., Garritty, C., … Straus, S. E. (2018). PRISMA extension for scoping reviews (PRISMA-ScR): Checklist and explanation. Ann Intern Med, 169, 467–473. Wiegand, S., & Borromeo Ferri, R. (2023). Promoting pre-service teachers’ professionalism in steam education and education for sustainable development through mathematical modelling activities. ZDM – Mathematics Education, 55(7), 1269–1282. Education Database. https://doi.org/10.1007/s11858-023-01500-8 24. Mathematics Education Research
Poster Developing Students’ Analytical Skills in Solving Applied Mathematical Problems through Blended Learning Models 1: NIS Shymkent Abay, Kazakhstan; 2: Nazarbayev University, Kazakhstan; 3: Binom School Lyceum named after Abish Kekilbayev in Astana, Kazakhstan; 4: Secondary school No. 48 named after Turar Ryskulov in Taraz, Kazakhstan Presenting Author:In contemporary education, increasing attention is paid not only to students’ acquisition of subject knowledge but also to their ability to apply this knowledge in real-life and interdisciplinary contexts. In mathematics education, one of the persistent challenges is students’ difficulty in solving text-based applied problems. These difficulties are particularly evident in tasks requiring mathematical modelling, where students must interpret contextual information, translate it into mathematical language, construct an appropriate model, and justify their solution. Observations from external summative assessment indicate that many students struggle at the analysis and modelling stages, resulting in low performance in applied problem-solving sections. Methodology, Methods, Research Instruments or Sources Used This study employed an action research methodology, allowing systematic reflection on teaching practice while implementing and refining instructional strategies in a real classroom context. Action research was chosen due to its focus on practitioner-led inquiry aimed at improving learning outcomes and addressing context-specific challenges. Participants were Grade 12 students studying calculus as part of the school curriculum.The research was conducted over a sequence of lessons focused on solving applied problems involving maximum and minimum values. Data were collected through classroom observations, analysis of students’ written work, online assessment results, and student reflections. The flipped classroom model served as the core blended learning approach. Prior to lessons, students were provided with theoretical materials, instructional videos, and online resources via digital platforms. This allowed students to familiarize themselves with key concepts independently and at their own pace. Classroom time was then dedicated to higher-order learning activities, including problem analysis, modelling, and discussion. Lessons began with problem-based questions linked to physical or geometric contexts to activate prior knowledge and stimulate inquiry. Question-and-answer strategies were used to assess students’ readiness and understanding, employing probing and guiding questions to support analytical thinking. Group work was organised using the case method, where students analysed different applied problems, identified key information, translated conditions into mathematical expressions, and developed solution algorithms collaboratively. Peer assessment and formative assessment strategies were integral to the methodology. Mark schemes were used during pair work to guide self- and peer-evaluation, enabling students to identify errors and reflect on their reasoning. Online assessment tools such as Teacher Made and Microsoft Forms were used to collect individual performance data efficiently and provide immediate feedback. Qualitative data from observations and reflections were analysed to identify patterns in students’ engagement, analytical processes, and problem-solving approaches. Quantitative data from assessments supported the evaluation of learning outcomes. The cyclical nature of action research allowed ongoing refinement of instructional strategies based on observed challenges and successes. Conclusions, Expected Outcomes or Findings The expected outcomes of this research include both pedagogical and learner-related improvements. It is anticipated that the integration of blended learning, particularly the flipped classroom model, will enhance students’ preparedness for lessons and allow more effective use of classroom time for analytical and collaborative activities. In terms of student learning, the study is expected to demonstrate improvement in students’ ability to analyse applied problems, identify key information, and construct appropriate mathematical models. Students are also expected to show increased confidence in solving interdisciplinary tasks involving mathematics, physics, and geometry. Enhanced engagement and motivation are anticipated as a result of interactive learning strategies and the use of digital assessment tools. From a pedagogical perspective, the research is expected to provide evidence that combining problem-based learning, case methods, and formative assessment within a blended learning environment supports the development of higher-order thinking skills. The findings may inform teaching practices beyond the immediate context of the study, offering practical strategies for improving applied mathematics instruction. The results of the study are intended to contribute to professional dialogue among educators by highlighting effective approaches to developing analytical skills. The research outcomes may also support the dissemination of best practices through seminars, professional learning communities, and future collaborative research initiatives. References 1.Bishop, J. L., & Verleger, M. A. (2013). The flipped classroom: A survey of the research. ASEE National Conference Proceedings, 30(9), 1–18. 2.Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. Longman. 3.Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson. 4.Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. 5.Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development. Prentice Hall. 6.Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. 24. Mathematics Education Research
Poster What Is the Impact of Homework Based on Digital Monitoring and Motivation on Students’ Achievement? Nazarbayev Intellectual School in Almaty, Nauryzbay, Kazakhstan Presenting Author:This research was conducted during the 2024–2025 and the first half of the 2025–2026 academic year and examined the impact of mathematics homework and the provision of systematic feedback on students’ academic achievement. It was assumed that homework also implements the hidden curriculum and may lead to changes in learners’ behavior, personal qualities, and habits; therefore, the analysis of results also considered students’ non-academic achievements. Homework is defined as any task that school teachers expect students to complete out of classroom (Cooper, 1989). According to De Jong, Westerhof, and Creemers (2000), homework refers to the completion of school curriculum tasks outside regular classroom lessons. A number of literature reviews indicate that homework has a positive effect on students’ academic achievement. Homework is one of the most widespread practices that teaches children that effort leads to results (Cooper et al., 2006; Epstein & Van Voorhis, 2001; Trautwein et al., 2009). Homework influences not only academic achievement but also personal development. Teachers assign homework to help students develop time management, planning, study skills, and the ability to cope with distractions (Epstein & Van Voorhis, 2001). Similar findings were reported in studies by Fan et al. (2017) and Falch and Rønning (2012), which covered 16 OECD countries. Although differences between countries were observed, the overall trend was similar (Dettmers et al., 2009). Some researchers oppose the practice of assigning homework. According to Galloway et al., homework limits the time students have to develop socially, physically, civically, or spiritually, causes academic stress, and disrupts life balance (Galloway, 2013). Studies by Gökhan Baş, Cihad Şentürk, and Fatih Mehmet Ciğerci show that homework has only a minimal effect on students’ academic achievement (Issues in Educational Research, 27(1), 2017). The main aim of the study is to determine the impact of homework on students’ achievement and to identify how the digitalization of feedback formats affects its efficiency. Research question: Objectives:
The study involved 120 students aged 14–17. During the study, a digital platform was developed to identify the relationship between students’ mathematics achievement and the systematic completion of homework. The platform was designed to regularly record students’ homework completion levels, classroom engagement, and formative assessment results in daily instructional practice. The key feature of the digital tool is its focus on increasing learning motivation by integrating continuous monitoring of students’ learning activities with prompt feedback. On the platform, each lesson’s homework completion is marked using specific visual symbols: a “full heart” indicates that homework was completed fully and correctly, a “half heart” indicates partial completion, and an “empty heart” indicates that the homework was not completed at all. Formative assessment on the platform is provided through textual and visual support. This marking system aims to help students clearly perceive their responsibility and develop consistent daily learning habits. For students who achieve the highest result (10 points), an automatic reward mechanism is activated on the platform. This assessment system is not intended for comparison or punishment, but rather to support students’ progress and enhance their confidence. The results of summative assessment by units showed an increase in task completion levels from 76% to 80%. However, the growth was uneven: initially, results increased to 90%, then declined to 68%. The final indicator reached 80%, which is only a 4% increase compared to the pre-study results. Methodology, Methods, Research Instruments or Sources Used Data are based on document analysis and surveys. In addition to structured closed-ended questions, the survey included open-ended questions that allowed respondents to freely express their opinions and perspectives. As this was a qualitative study, individual and group interviews were conducted. These helped to identify key trends and guided the exploration of ways to improve homework effectiveness. The study analyzed the opinions of 75 teachers and 100 parents from three selective schools and three general education schools. Among the teachers surveyed, 76% assign homework daily. While 48.8% of teachers assign 3–5 tasks, 36.6% reported providing homework feedback in a general manner during lessons. These results prompted the search for more effective feedback strategies. Among the students who participated in the study, 67.5% believed that homework positively affects academic performance, 7.5% believed it has no effect, and 25% expressed a neutral position. The majority of respondents (60%) noted that homework supports independent learning. Another notable finding is that only 20% of students stated that homework contributes to conducting research and solving problems independently. This indicates the need to focus on homework quality to enhance its impact on student achievement. Additionally, 30% of respondents reported that homework causes anxiety, and 55% indicated that it interferes with sports or personal interests. This highlights the importance of considering approaches to homework that do not hinder students’ personal development. For 80% of students, homework is important for reviewing and reinforcing classroom learning, while 15% believe that homework is unnecessary because classroom instruction is sufficient. According to the survey results, 44% of students spend approximately of an hour on mathematics homework, and 16.7% spend less than one hour. According to 79.2% of parents, homework is assigned in appropriate amounts. The majority of parents (58.3%) stated that homework does not negatively affect their child’s personal development or health. Correspondingly, 87.5% and 62.5% of parents reported that homework contributes to knowledge consolidation and increased responsibility. In addition, the performance data of students registered on the specially developed digital platform and were analyzed as a research instrument. Comparisons were made between students’ homework completion levels and their classroom achievement. Observations conducted during lessons and extracurricular activities examined changes in students’ personal qualities, competencies, and skills. Of the 37 students who participated in individual interviews, 22 students (59.4%) stated that tracking achievements through the digital platform increased their responsibility toward homework completion and their accountability for actions, decisions, and outcomes. Conclusions, Expected Outcomes or Findings The majority of mathematics teachers assign homework every lesson and believe that homework influences students’ achievement. Teachers pay attention to assigning homework in moderation. For students, homework is a natural part of the learning process and is necessary for reinforcing classroom knowledge. Moreover, students’ academic achievement is closely linked to the timeliness, consistency, and constructiveness of feedback on homework. Systematic homework assignment also supports the implementation of the hidden curriculum, such as effective time use, responsibility, and self-regulation. Students who invested more effort in homework demonstrated more positive development of qualities such as neatness and sustained attention. The study showed that assigning a smaller number of tasks that encourage research and inquiry is more effective than giving multiple repetitive tasks. Compared to traditional homework practices, diversifying the formats of homework checking and feedback has a strong impact on increasing productivity and responsibility. Viewing homework completion not as a one-time result but as a cumulative indicator over time that reflects students’ consistency and continuous development yielded positive outcomes. Animated congratulatory messages and peer support elements fostered a positive emotional climate among students and socially reinforced academic achievement. Such visual elements allow students to immediately see the results of their efforts and motivate them to complete tasks fully. Creating a digital environment can enhance the effectiveness of homework by clearly demonstrating the relationship between homework completion and classroom engagement, thereby supporting students in achieving stable and high academic performance in mathematics. References Guidelines for Organization of Educational Progress in Nazarbayev Intellectual Schools in 2024- 2025 Academic Year, https://ustaz.nis.edu.kz/kk/categories/6 K. Shamshidinova., (2025). The best. How to help a chaild? Mentor Baspasy Barbara Flunger., Ulrich Trautwein. (2016). A Person-Centered Approach to Homework Behavior: Students’ Characteristics Predict Their Homework Learning Type. Contemporary Educational Psychology 48. DOI:10.1016/j.cedpsych.2016.07.002 Gökhan Baş Ömer Halisdemir., Cihad Şentürk ., Fatih Mehmet Ciğerci Bilecik Şeyh Edebali. Homework and academic achievement: A meta-analytic review of research. Issues in Educational Research, 27(1), 2017, from https://www.iier.org.au/iier27/bas.pdf Joyce L. Erstein., Frances L. Van Voorhis. (2001). More Than Minutes: Teachers' Roles in Designing Homework. Educational Psychologist, September 2001, 36(3):181-193. DOI:10.1207/S15326985EP3603_4 José Carlos Núñez., Sara Pascual., Natalia Suárez y Pedro Rosário. Perceived parental involvement and children’s homework engagement at the end of Primary Education: A cluster analysis. Revista de Psicología: y Educación / Journal of Psychology and Education, 2021, https://doi.org/10.23923/rpye2021.01.204 R Joyce L., Epstein., Frances L., Van Voorhis., More Than Minutes: Teachers' Roles in Designing Homework. Educational Psychologist, 2001, DOI:10.1207/S15326985EP3603_4 Molie Galloway., Jerusha Conner., Denise Pope. Nonacademic Effects of Homework in Privileged, High-Performing High Schools. The Journal of Experimental Education, 2013, https://doi.org/10.1080/00220973.2012.745469 Muhammad Nisar UI Haq., Anila Fatima Shakil., Muhammad Naseer Ud Din. (2020). Impact of Homework on the Student Academic Performance at Secondary School Level. Global Social Sciences Review V(I):586-595.DOI:10.31703/gssr.2020(V-I).59 Cooper, H. (1989). Homework. Longman. https://doi.org/10.1037/11578-000 R. de Jong., Westerhof K. J. ,Creemers B.P.M. Homework and Student Math Achievement in Junior High Schools. Educational Research and Evaluation, 2000, from https://research.rug.nl/en/publications/homework-and-student-math-achievement-in-junior-high-schools/ | ||