Final Program of ICMT5

Annalisa Cusi  Sapienza (University of Rome, Italy)

The use of digital resources for learning and metacognition: exploring students’ perspective

Belongs to Conference Theme 4 - Studies of the use of (including interaction with) curriculum resources by students and/or teachers (including student teachers and teacher educators) 

This talk focuses on students' use of digital resources and their reflections on the role of these resources as tools to support mathematics learning and metacognition. Through the lens provided by the instrumental genesis framework (Rabardel, 2002) and interpreting the students’ interaction with digital resources and environments in terms of co-action (Hegedus & Moreno-Armella, 2009), I will discuss the main findings of some studies conducted at upper secondary and university levels, which aimed at investigating both the utilisation schemes that students develop when interacting with digital resources, including digital resources using generative artificial intelligence, and their perspectives on this interaction. Based on these results, I will propose some reflections on how the instrumental genesis framework could be extended to take into account the interactions between human users and digital environments in the new context that the advent of generative artificial intelligence has brought to the research scene.

Contel, F., & Cusi, A. (under revision). Investigating the role of ChatGPT in supporting metacognitive processes during problem solving activities. Digital Experiences in Mathematics Education.

Cusi, A., Telloni, A. I., & Visconti, K. (2022). Students’ reflections on the design of digital resources to scaffold metacognitive activities. In C. Fernàndez, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of PME, Vol. 2 (pp. 203–210). PME.

Hegedus, S.J., & Moreno-Armella, L. (2010). Accomodating the instrumental genesis framework within dynamic technological environments. For the Learning of Mathematics, 30(1), 26–31.

Rabardel, P. (2002). People and technology – a cognitive approach to contemporary instruments. https://hal.archives-ouvertes.fr/hal-01020705

Alden Jack Edson (Michigan State University, East Lansing, Michigan, USA)

The Evolution in Curriculum Design of a Problem-Based Mathematics Curriculum: New Directions for the AI World

Belongs to Conference Theme 1 - Theoretical and/or methodological issues in the design of curriculum resources 

This session explores the evolution of curriculum design within the Connected Mathematics Project (CMP), highlighting its efforts to provide a problem-based mathematics curriculum, Connected Mathematics. For over 40 years, CMP has developed student and teacher materials through iterative design, extensive field-testing, evaluation, and dissemination, adapting to emerging educational - 6 - needs and technological advancements. Over four iterations, the curriculum evolved to meet diverse needs, contexts, and populations. Each iteration reflects a commitment to helping students and teachers develop mathematical knowledge, understanding, and skill along with an awareness of and appreciation for the rich connections among mathematical strands and between mathematics and other disciplines. As educational needs and technological advancements have evolved, CMP has embraced these changes to further enhance its curriculum. The design of a mathematics curriculum involves setting clear learning objectives, engaging students with meaningful problems, employing sound pedagogical strategies, providing robust assessment and feedback mechanisms, and supporting teacher planning and reflection. Recent advances in digital technologies have prompted CMP to develop a digital collaborative platform that integrates artificial intelligence for teaching and learning. Artificial intelligence in education often focuses on personalized learning, support for students with special needs and multi-language learners, online and blended learning, and teacher feedback on classroom dynamics and student engagement. This session will discuss how CMP’s platform integrates artificial intelligence to assess, support, and track students’ proportional reasoning, potentially transforming the teaching and learning of mathematics. Understanding these developments is crucial for advancing student engagement, improving teaching practices, supporting teacher growth, and informing future educational policies.

Lianghuo Fan (University of Macau, Macao SAR, China)

Digitalizing mathematics textbooks in the age of AI: What have we learned from a large research project (EZSMP) in Chinese education settings?

Belongs to Conference Theme 5 - Studies of the production, selection, acquisition and distribution of curriculum resources within educational systems and institutions 

The fast development of information and communication technology, particularly in the area of Artificial Intelligence (AI), has transformed in a sense every aspect of education, including the development and designing of modern mathematics textbooks. Nevertheless, research in this area, particularly about what and how AI can be integrated into the development of mathematics textbooks, is still relatively at an early stage (Fan et al., 2013). This presentation is based on a large research project entitled “A study of developing digital mathematics textbooks and its effect on mathematics teaching and learning”, or called EZSMP for short, of which I served as the PI. Starting from 2019, the project team has developed a comprehensive digital mathematics curricular resource platform for mathematics teaching and learning, with a core part being the digitalization of a complete series of mathematics textbooks at the junior secondary level. The digital resources developed have been used in more than 10 schools in the East China region including Shanghai, Zhejiang, and Jiangsu. In the presentation, I will introduce the rationale and research focus, illustrate the conceptual framework, and report the relevant findings of the project. I will also discuss the problems and challenges encountered in the designing, developing and use of the digital mathematics textbooks, and share my views on issues in relation to the development, use and research concerning digital mathematics textbooks.

Fan, L., Zhu, Y. & Miao, Z. (2013). Textbook research in mathematics education: development status and directions. ZDM-International Journal on Mathematics Education, 45(5), 633-646. https://doi.org/10.1007/s11858-013-0539-x

Jana Trgalová (Haute Ecole Pédagogique, Lausanne, Switzerland)

Evaluation of digital curricular resources: an issue for research and teacher education

Belongs to Conference Theme 3 - Theoretical and/or methodological issues in evaluation of curriculum resources 

Recent research on the use of digital tools and resources in mathematics education acknowledges the fact that being aware of a tool / resource affordances and limitations is necessary to make relevant choices when planning and enacting digitally enhanced mathematics teaching. Hence, being able to evaluate digital tools and resources appears as a key component of mathematics teachers’ digital competency.  In this talk, we will compare and contrast diverse approaches to the evaluation of digital resources, highlighting the complexity when it comes to define evaluation criteria. We will conclude by drawing implications for mathematics teacher education and by outlining avenues for further research on this issue.

Jana Višňovská (University of Queensland, Brisbane, Australia)

Mathematics as (an invisible) theory in the world of curriculum resources

Belongs to Conference Theme 7 - Comparative studies of curriculum resources (including, but not restricted to, international or transcultural studies) 

In this presentation I draw on the history of mathematics and mathematics education to show that at the time when mathematics as an academic discipline was reconceptualised, the proposals for propagating the changes to school mathematics were highly contested, and accepted only tentatively, as conjectures to be revisited. Using analyses of current national curriculum documents from Australia and Mexico, I demonstrate that these once tentative changes act as the unquestionable truths about mathematics in schools today. They affect what mathematics can and cannot be—and thus how it can and cannot be encountered by students. In addition, they render certain phenomena invisible (and thus not attended to and unachievable) in both mathematics teaching and mathematics education research. As conceptualised in the primary curricula of these two countries, mathematics is not a practice developed in response to the human need for understanding of quantitative phenomena, and quantitative phenomena are currently not part of the mathematics-to-be-taught. These omissions have severe consequences in that they introduce mathematical incoherencies into classrooms. While it is possible to envision textbooks that correct the omissions introduced by curricular frames to some extent, the cause I raise is that of adopting mathematically coherent conceptualisations to underpin mathematics in curricular frameworks, so that these frameworks could provide sound guidance to textbook designers and teachers. I give two historical examples, from France and China, in which such conceptualisations—theories of school mathematics—underpinned mathematics curricula. I propose some directions for what a construction of a mathematically coherent theory of school mathematics might involve today.

Carl Winslow (University of Copenhagen, Denmark)

Panel on recent research about digital curriculum resources

Panelists:

• professor Gilbert Greefrath (University of Münster, Germany)
• associate professor Shuhui Li (East China Normal University,
• China)
• professor Farzad Radmehr (Norwegian University of Science and Technology, Norway)
• associate professor Osama Swidan (Ben-Gurion University of the Negev, Israel)

The use of digital tools has been common in schools for around 50 years, and it has affected many aspects of mathematics teaching and learning. The development and use of digital textbooks and similar forms of digital material is more recent. As the tools, digital curriculum resources (cf. Pepin & Gueudet, 2018) come in many forms, for instance, text and tool may be integrated. Theorizing is needed for research to capture, with precision, the essential features of digital text for mathematics education, as well as their impact on teaching and learning.

The present panel sets out to address the following question:

According to current research, what are the new potentials of digital curriculum resources for mathematics teaching and learning? How can such potentials be theorized?

First, panelists will provide their initial answers, based on personal perspectives and research. Then we invite reactions, questions and further answers from the audience, interspersed with comments from the panel where called for. A round of brief, final remarks by panelists will conclude the session.

Reference

Pepin, B., & Gueudet, G. (2018). Curriculum resources and textbooks in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 172–176). Springer.

Symposium: The Quality of Print and Digital Mathematics Curriculum Resources

Organizers:

• Sebastian Rezat (Paderborn University, Germany)
• Dubravka Glasnović Gracin (University of Zagreb, Croatia)
• Hendrik Van Steenbrugge (Stockholm University, Sweden)
• Henning Sievert (University of Hildesheim, Germany)

Abstract:

Due to the special role of curriculum resources (CR) in the educational system, their content, structure, use, effects, and nature—particularly the transition from print to digital—have long been the subject of research (Fan et al., 2013; Rezat, 2024). This research has resulted in a highly differentiated view of CR and the factors influencing their use. However, there appears to be no clear, shared vision regarding the quality of print and digital CR. In the case of textbooks, this is reflected in the multitude of catalogs with varying textbook evaluation criteria.

This symposium aims to establish a clearer vision of the quality of print and digital CR, the factors that influence and contribute to it, and how the quality of CR can be examined by addressing the following questions:

1. How can the quality of print and digital CR be conceptualized, operationalized, and measured? This also includes the relationship between quality features and the use of these resources.
2. What factors and features relate to the quality of print and digital CR?
3. What does “the quality of digital CR” mean, and how does it differ from the notion of “quality of printed CR”?
4. What quality features are more generic, and which seem to be more context-specific?

Contributions:

1. S. Rezat, D. Glasnović Gracin, & H. Van Steenbrugge:
   • The quality of digital curriculum resources identified in mathematics education research
2. S. Olsher, M. Yerushalmy, & A. Weizman:
   • Curriculum resources‘ descriptive structure: Difference as a measure of quality
3. A. Wunsch, R. von Hering, & H. Sievert:
   • Determining textbook quality in primary school’s topic data and chance
4. J. Remillard, T. Koljonen, H. Krzywacki, L. Condon, & R. Sayuj:
   • Curriculum material quality from the perspective of teacher enactment

Program of Oral Communications (PDF)