In this paper, we report how digital resources support engineering students in the early stages of mathematical modelling within a Challenge-Based Education (CBE) course. The study was conducted in a second-year engineering course involving mathematics, physics, and ethics. Through a case study of two student teams, we analyze how a digital curriculum resource—specifically, a dashboard designed for feedback and progress monitoring—helped students identify, define, and begin modelling a real-world problem related to crowd flow on train platforms. Using the instrumental approach, we examined the dual processes of instrumentation (integration of resources) and instrumentalization (adaptation and repurposing of tools). Results show that the Dashboard played a central role in fostering self-regulated learning, interdisciplinary collaboration, and the iterative refinement of guiding questions. Students used data analysis, simulations, and modelling techniques to build and validate mathematical representations in answer to the guiding questions. Our findings contribute to ongoing discussions on how mathematics education in engineering can be enhanced through activity-based learning and targeted use of digital tools. We argue that digital feedback systems like dashboards can bridge the gap between abstract mathematical content and its meaningful application in engineering contexts, thus fostering engagement, autonomy, and authentic learning.

This study investigates how pre-service mathematics teachers (PMTs) develop the capacity to plan mathematics lessons regarding reasoning and proving (R P) at a time of curriculum change in Norway. Lesson planning poses challenges for both pre-service and experienced mathematics teachers. In this EU-funded intervention study, PMTs were led through iterative cycles of learning about different approaches to R P; designing and refining R P tasks from reform-oriented textbooks and other resources; developing lesson plans; implementing lessons in the classroom; reflecting on and revising their plans; engaging in peer discussions. The goal was to develop Grade 8 lesson plans that supported pupil reasoning. Using a case study approach, data were collected through multiple methods, including pre- and post-intervention interviews with PMTs; reflective texts; lesson plan iterations (several versions throughout the intervention); and observation field notes. Results from the Norwegian data showed that providing PMTs with commonly used reform-oriented textbooks or teacher guides is insufficient. Instead, PMTs require additional support in two key areas: (a) Understanding different types of R P across various mathematical domains and tasks, and (b) Developing comprehensive lesson plans that address all key components, such as learning objectives, activities, assessment, pupil thinking and misconceptions, and the teacher’s role. By framing curriculum design as part of teachers’ lifelong professional learning, this study contributes to ongoing research on how PMTs develop curricular expertise with the support of curriculum resources.

ChatGPT is a new technological tool with the potential to impact education. Using Vergnaud’s notion of “use schemes,” we analyzed three interviews with engineering students who discovered ChatGPT and started to develop initial utilization schemes of the tool. Results showed that there were three domains of use of ChatGPT: (a) in mathematics/engineering; (b) for general academic purposes; and (c) in the students’ personal lives. Domain (a), with a focus on mathematical modelling, has a relation to mathematics education. Students used ChatGPT to foster their conceptual understanding, to find alternative modelling strategies, to translate mathematical models to computer code, and to optimize this computer code. The students developed a critical attitude in relation to the limitations of the tool and, according to the interview data, their schemes developed over time. The interview data show some evidence for the emergence of a hybrid form of learning in which ChatGPT became a co-agent of learning, an interactive resource with which the students could discuss their ideas. We consider the case as a positive example of how ChatGPT can contribute to student agency in education and support the development of knowledge and student competencies.

This study presents a scoping survey examining the integration of ChatGPT in mathematics education, highlighting its benefits, challenges, and implications for teaching and learning. The survey identifies key themes, including ChatGPT’s ability to assist in understanding mathematical concepts, lesson planning, assessment design, personalized learning, and fostering collaboration. While the tool demonstrates potential in enhancing self-regulated learning, providing real-time feedback, and supporting critical thinking, challenges such as its occasional inaccuracies, ethical concerns, and the risk of over-reliance on AI are also noted. The review emphasizes the importance of human oversight and ethical considerations in leveraging ChatGPT for inclusive and dynamic mathematics education. It concludes that, with thoughtful integration, ChatGPT can serve as a transformative resource, fostering both individualized and collaborative learning experiences while reshaping the learner–tool relationship in educational contexts.

BackgroundAlthough cutting-edge research contexts can be motivating for students, studies reporting student and teacher experiences using this type of authentic contexts are hard to find.PurposeIn this study, we investigated how students and teachers experienced working with context-based learning materials centered on cutting-edge research that are designed to support teachers in fostering student understanding and motivation.SampleSix chemistry teachers in their 10th grade pre-university classes used learning materials using research on 'Early Cancer Diagnosis' as a context to understand chemical bonding concepts.Design and methodsIn this mixed-methods study, teacher and students experiences were investigated using semi-structured teacher and student group interviews, student pre- and post-tests, learner self-reports, and teacher logbooks.ResultsThe context-based learning materials did help to foster student understanding and motivation. In addition, students experienced working with the learning materials as interesting, relevant, complex, challenging and clear.ConclusionUsing authentic contexts can support teachers and foster student understanding and motivation. Teacher and student experiences were positive, and teachers were reflecting when working with the learning materials and trying to use new teaching strategies. Thus, we cautiously conclude that teachers were learning, while they are working with learning materials that feature cutting-edge research contexts.

There are new educational approaches that are moving towards student-centred teaching and learning. One of them is challenge-based education, where students acquire and develop disciplinary knowledge and competencies by collaborating on solving real-life problems. Hence, in this paper, we report on a study of applied mathematics students' learning experiences in the context of challenge-based education in a higher education mathematics course. Using a case study approach, we investigate how students perceive the role of the different resources to help them solve real-life problems during a one-week challenge-based modelling course. We collected data, from four groups of students (5-7 students each) who worked together and interacted with their mathematics supervisors and problem owners. Results show (1) the crucial importance of using and integrating different resources, such as social resources (e.g. mathematics supervisors and problem owner), for such learning environments to link mathematics to an authentic situation and develop the skills of an 'applied mathematician in the real world'; (2) the relevance of mathematical knowledge in creating models to solve real-life challenges.

In this symposium we investigate students’ agency of selecting and using (digital) resources for developing their own learning paths. For that, we first review the literature related to students’ selection and use of resources in mathematics education in different pedagogical settings (presentation 1). Second, we develop insights from the different studies that participate in this symposium (presentation 2–6), at school as well as at university level. Results show that attempts have been made to provide students opportunities to develop agency of their mathematics learning, in particular with the development and provision of numerous digital tools and learning resources at university level and related to innovative pedagogical approaches. At the same time, it is not obvious how these tools and resources help students to develop deeper conceptual understandings. Certainly, students often ‘demand’ more student-centered and autonomous education approaches (e.g., at university level), also in mathematics education. Further, it seems that authentic problem-based education approaches are more motivating for students. These ‘innovative’ approaches necessitate particular types of structure and support for students. Moreover, they require different ways of providing resources that students can and want to interact with, and that help students to navigate through the curriculum to develop their own learning paths. At the same time, teachers also need support on how to orchestrate student learning with the available resources in such environments, so to be able to attend to students’ individual needs. The symposium comprised altogether six presentations: Birgit Pepin Sebastian Rezat: Students’ agency of selecting and using (digital) resources for developing their own learning paths: An overview Annalisa Cusi Agnese I. Telloni: Learning through digital curriculum resource design: students’ reflections on their role as designers Vilma Mesa, Lelia Burley-Sanford, Xinyi Hao, Carlos Quiroz: Interactive features in university textbooks and their use by teachers and students Sebastian Rezat: Fostering university students’ reading and understanding of mathematical text in a flipped classroom approach with a digital marking tool Birgit Pepin Ulises Salinas: Challenge/problem-based mathematics learning at university level: The case of the modeling week Farzad Radmehr: Problem-posing: An inclusive activity for improving teaching and learning of mathematics at university level

There are new needs and concerns in society and industry that require suitable preparation of engineering students for the challenges of this century (e.g., global warming and sustainability). Consequently, new educational approaches have been developed that are more relevant in contributing to the solution of challenges through collaboration between industry and universities (van Uum Pepin, 2022). One of these approaches is Challenge-Based Education (CBE) (Membrillo-Hernández et al., 2019). In this context, it is important to analyze what occurs in these innovative learning environments at the three levels of the curriculum: intended, enacted, and attained. Our research focuses on observing and analyzing what happens at the boundary between enacted and attained level, considering the point of view of the students themselves. We ask two research questions (RQ): (1) How did students perceive the role of available resources to help them solve their challenge during a one-week challenge-based mathematics course? (2) How did students experience their learning in terms of mathematics and professional skills?

BackgroundIn responding to the global problems facing humankind, there is great value in equipping science and engineering students with skills to function well in multidisciplinary teams. Little attention has been paid into the factors that influence multidisciplinary collaboration and teamwork of science and engineering students.PurposeThis research describes multidisciplinary teamwork of applied physics and mechanical engineering students in a challenge-based learning (CBL) course. The study aimed to: a) identify the facilitators and barriers to multidisciplinary teamwork and b) explore learning outcomes connected to working in multidisciplinary teams.Sample30 students registered to the course, two teachers, and three tutors participated in this research.Design and MethodsAn instrumental case study was conducted in the context of a pilot CBL course. Data included interviews, reflection reports, observations, and design posters. Transcribed video recordings were searched in an attempt to demonstrate the codes revealed with the qualitative content analysis of interview transcripts and reflection reports.ResultsThe results indicated knowledge acquisition, application, and an awareness of other disciplinary approaches as the learning outcomes with some differences for engineering and physics students. The findings also yielded individual (e.g. knowledge of control theory), team (e.g. disciplinary perspectives), and course factors (e.g. disciplinary connections to the challenge) that influenced multidisciplinary teamwork.ConclusionMultidisciplinary teamwork is supported by the unique ways of thinking and approaching problems of the two disciplines. Implications contribute to future research and thinking for similar learning environments while improving student learning in multidisciplinary teams.

Development of teacher pedagogical content knowledge (PCK) is a crucial aspect of teacher learning that can be supported by high-quality materials. In this study, 16 chemistry teachers in The Netherlands used teaching and learning materials situated in the context of research on tumor detection. Teachers' encounters with these learning materials and the development of teacher PCK were investigated using teacher logbooks, card-sorting activities, content representation (CoRe) tasks, and semistructured teacher interviews. Analysis of the results showed that most teachers used strategies that were new to them and made few adaptations to the teaching sequence and activities proposed in the teacher guide. Moreover, growth in teacher PCK for chemical bonding was observed, primarily related to instructional strategies and representations, and to a lesser extent related to three other PCK components (knowledge of curriculum, student understanding, and assessment). The data suggest that the materials facilitate teacher learning by enabling positive classroom experiences and by supporting teachers to expand their instructional repertoire for the topic of chemical bonding, in particular hydrogen bonding.

Abstract We report on the design and construction of a worksheet to develop upper secondary school students’ understanding of the particle-in-a-box model. We designed a worksheet that guided students’ structured-inquiry learning through peer discussion using the PhET simulation ‘Quantum Bound States’. The worksheet was improved in three iterative cycles of (re)designing, testing and evaluating, leading to a validated design and tentative design principles. Students’ discourse was recorded whilst they were using the worksheet and the PhET simulation in the test phase of each cycle. Analyses of students’ discourse informed the redesign of the worksheet for each subsequent cycle, until the design was finalised. The results showed the potential of the simulation to introduce upper secondary school students to the particle-in-a-box model, provided care is taken to accompany student inquiry with a well-developed worksheet as learning support during the lesson.

One way of triggering students' interest in chemistry is making chemistry education more meaningful. Four characteristics of meaningful chemistry education (MCE) were identified in projects that involved a redesign of curriculum materials: daily life context, the need-to-know principle, students' input, and the macro-micro connection. Chemistry education has struggled with the implementation of meaningful learning. A possible solution might be the use of immersive virtual reality (IVR) in chemistry classrooms, a promising tool to support students' meaningful learning. IVR can be described as a computer simulation that provides an interactive simulated virtual environment, while the user wears a head mounted display and can experience immersion and presence in a virtual environment. The aim of this study was to explore features of IVR to support MCE at a secondary school level. A systematic literature search was done, experts were consulted, and animation-and 360 degrees-IVR lessons were designed and tested in classrooms. Features that could support MCE found in both animation-IVR and 360 degrees-IVR were: the application of the characteristics of MCE, the necessity of a storyboard, difficulties in realizing interactive visualization, and positive student experiences. These features can be used to design future IVR lessons to support MCE. Features needing careful consideration since they are different for 360 degrees-IVR and animation-IVR are the need for a professional designer, the degree of interactivity, and classroom use with all students at the same time.

Using a case-study approach, we aim to understand how teachers interact with both analogue and digital resources in the science classroom for formative assessment (FA) purposes and their justifications for such interactions. The study was conducted in the context of a European Union project on FA in science and mathematics education. The case involved two Norwegian primary school teachers teaching their grades 5 and 7 students a series of science lessons on the topic "how to prevent microorganisms from spreading." The data set consisted of lesson plans, classroom observations, pre- and post-interviews conducted with teachers, student tasks, post-interviews with students, and student work. We identified eight analogue and digital resources, which were used to employ five FA strategies. The strategies that were most commonly used related to "engineering effective classroom discussions" that elicited evidence of student understanding and "activating students" as autonomous learners and peer instructors. The teachers' rationales for using the selected resources were mainly connected to their effectiveness, practicality, and relevance. Teacher interactions with the selected resources are described, and educational implications are discussed.

In this chapter we review the recent mathematics education research literature through the "lens of resources," asking (1) what kinds of resources students select and use and (2) which factors influence their selection and use of resources, in order to develop insights into learning environments that may foster student agency (in the selection and use of digital resources). Results from the literature review show that there are four factors that influence students' selection and use of digital resources: (1) the availability and nature of resources; (2) the nature and structure of the course and its associated pedagogical approaches; (3) institutional framework; and (4) student beliefs and goals. From these, we developed the notion of what we referred to as "agentic" environments, and we characterized such "agentic" learning environments. We concluded that "agency" in the kinds of digital learning environments we reviewed was "distributed," in particular the "resource agency" was often underestimated.

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AbstractIn this chapter we investigate the evolution of research in mathematics education related to digital resources as an essential element of the external context for mathematics teachers’ professional activity. In the relevant research literature, we identified different themes and different kinds of evolution. We investigate the evolution of research with respect to educational policies related to digital resources, and to teacher integration of digital resources, including digital assessment. We also analyze the evolution of research concerning the quality of digital curriculum resources, and discuss emerging research questions related to mathematics and programming; to collective dimensions of teachers’ work with digital resources; and about the COVID-19 pandemic consequences. The different kinds of research developments are a result of evolution in the external context, or from more general trends in the research in mathematics education. We finally discuss possible directions for future research.

Background: Quantum physics has found its way into upper secondary school physics curricula worldwide. This trend coincides with increased attention for conceptual understanding in physics education in general and quantum physics education in particular. Students' conceptual difficulties of learning quantum physics are regularly reported. Little systematic attention has been paid to the opportunities and challenges teachers and students experience for teaching and learning quantum physics.Purpose: The opportunities and challenges secondary school teachers and their students experience were examined to gain insights into their perspectives teaching and learning quantum physics. These insights inform improvements in teaching and learning quantum physics at the secondary school level.Sample: Three teachers and five of each teacher's students participated in this study.Design & Methods: A context analysis was conducted to explore the experiences of the teachers and students. Teachers were individually interviewed; students were interviewed in a focus group session. The semi-structured interviews were analysed resulting in three case reports. These case reports were used to conduct a cross-case analysis to find common opportunities and challenges among teachers' and students' experiences.Results: Teachers and students felt that teachers had an important role in supporting students' understanding of quantum physics. Teachers were challenged to enthuse their students for quantum physics as they struggled to convey the relevance of the subject to their students. Freely available digital materials were considered as an opportunity to support students' conceptual understanding as they have the potential to engage students and benefit their conceptual development. Conclusion: Several implications are discussed to improve teaching and learning of quantum physics, such as opportunities for teacher professional development as well as ways to effectively use freely available digital materials.