Parental engagement in children’s mathematics education has been widely examined, often in contexts where parents report limited mathematical confidence or challenging prior mathematical experiences. Much less is known about parents with advanced disciplinary expertise such as mathematicians. This qualitative study adopts a narrative approach to examine how mathematician parents in two contrasting policy contexts, Slovenia and Ontario (Canada), understand and enact engagement in their children’s mathematics learning. Narrative interviews were conducted with 21 mathematician parents (13 Slovenian; 8 Canadian) and analyzed inductively through thematic analysis. Despite policy differences, a consistent pattern emerged across sites: parents reported limited engagement in school mathematics, especially homework, citing children’s responsibility, respect for teachers’ authority, and the tension of their dual role as parent and mathematician. In contrast, they described abundant, often spontaneous, everyday mathematical activities at home, including games, puzzles, measurement, and discussions that convey the practical, logical, and esthetic aspects of mathematics in daily life. This low-visibility yet pervasive presence, together with the nuanced portrayal of mathematician parental engagement, offers insight into alternative ways families may support children’s mathematical development and into how to balance the cultivation of mathematical appreciation with the promotion of academic independence. This article is part of a special issue titled “Parents, caregivers and community in mathematics education.” To see other articles in this issue, please select https://link.springer.com/collections/cibgdgbdfj .
Artificial intelligence (AI) offers new opportunities to support students’ mathematical argumentation in classrooms. We illustrate how a secondary teacher supports collective argumentation in AI-integrated lessons. This study proposes a networking approach between instrumental orchestration and teacher noticing. We identified four types of whole-class orchestrations—Spot-and-share, Sherpa-at-work, Discuss-the-screen, and Explain-the-screen—to support collective argumentation and various foci of noticing of students’ argumentation within and across the orchestrations. In Spot-and-share, the teacher interpreted AI-generated analyses of student arguments and identified critical events with potential to facilitate collective argumentation. In Sherpa-at-work, she asked students to explain their arguments and interpreted the mathematical ideas and argument components embedded in their responses. She requested further explanation when students presented incorrect warrants and summarized valid warrants while inviting the class to evaluate the warrants. In Discuss-the-screen, the teacher evaluated the influence of students’ prior contributions on the developing argument and invited the class to provide backing or rebuttals. In doing so, she reorganized students’ contributions in relation to the developing argument and extended the argument structure. In Explain-the-screen, she integrated students’ prior contributions into the emerging argument and guided the class toward a shared conclusion. We propose that networking instrumental orchestration and noticing provides a productive approach for analyzing teachers’ practices to facilitate collective argumentation in AI-integrated lessons. Our findings also offer implications for research and practice on teacher expertise in supporting collective argumentation in AI-integrated instruction.
The present research examined the relationship between natural number bias and mathematics state anxiety in two studies with fifth- and sixth-grade students from Belgium and Greece. Previous research by Halme et al. (2024) found that low-performing Finnish students who exhibited systematic natural number bias in fraction arithmetic reported lower state anxiety than low-performing peers who showed no evidence of natural number bias reasoning. Since this was the first study to demonstrate this relationship, the present research aimed to replicate and extend the finding to additional mathematical domains, such as fraction and decimal ordering. Similar methodology was used in two independent samples: 413 fifth-grade students from Belgium in Study 1 and 418 fifth- and sixth-grade students from Greece in Study 2. Participants completed paper-and-pencil tasks, and state anxiety was assessed using a single-item self-report measure after each task. The findings provided partial support for the original result. Significant differences in state anxiety emerged, in some, but not all, rational-number task contexts, between students classified as exhibiting a strong natural number bias profile and those classified as low performers without evidence of natural number bias reasoning. These results suggest that natural number bias-related response profiles may be associated with different levels of self-reported state anxiety, although the mechanisms underlying this relation remain unclear. Overall, this research improves our understanding of the relationship between conceptual biases and emotional responses in mathematics learning and emphasizes the importance of addressing both in mathematics education.
Selecting mathematical problems requires teachers to anticipate students’ learning needs and motivational responses. Understanding how teachers judge students’ motivation across problem types is essential for effective instructional design. However, little is known about the accuracy of such judgments or their relationship to teachers’ own motivational perceptions. This study replicates the work of Böswald and Schukajlow (2023), who investigated how pre-service teachers judge students’ task value and self-efficacy across problems differing in their degree of contextualisation. Extending the original design—which contrasted pre-service teachers’ self-ratings with judgments of hypothetical students—we included a sample of sixth-grade students and revised the mathematical content to focus on area measurement. This three-perspective design enables a comparison of task-related motivation and provides insights into how motivational appraisals vary by problem type. We address four research questions concerning how pre-service teachers (via self-ratings and diagnostic judgments) and students rate task value and self-efficacy for problems differing in their degree of contextualisation, and whether these ratings differ across perspectives. A total of 154 pre-service teachers and 160 sixth-grade students rated their perceived task value and self-efficacy for 12 problems, and 222 pre-service teachers judged these attributes for hypothetical students solving the same problems. Analyses confirm that problem type influences both motivational constructs across perspectives and that pre-service teachers’ perceived motivation relates to their diagnostic judgments. The study contributes to research on diagnostic competence and underscores the importance of replication for confirming and extending findings in mathematics education.
This paper focuses on proving as a rational process, contributing to the field of teaching and learning of proof, with reference to its relationship with argumentation. Within a larger study that investigates how cognitive role-playing in digital storytelling can foster students’ proving processes, in this paper, we use the components of Habermas’ construct of rationality to characterise the roles students play while proving, considering both knowledge and meta-knowledge perspectives. We do moreover exploit this characterisation as a lens to analyse the synchronous discursive digital interactions of students engaged in a proving activity, with a view to illuminate the emergence of rational behaviour activated by cognitive role-playing. The findings suggest a deeper model which highlights some key meta-level elements required for students to be successful in the conjecturing and proving process, in the perspective of their gradual interiorisation. These elements make evident the cognitive roles’ interconnections, giving rise to a preliminary systemic model to observe them. The latter can help students to recognise their own shifts from one role to another, and develop awareness that these roles cannot be fixed as they represent different yet cooperating facets of a single whole.
