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The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.

Mathematical reasoning, which plays a critical role in students’ capacity to make sense of mathematics, is now emphasised more strongly in various curricula internationally. However, reasoning is sometimes difficult for teachers to recognise, let alone teach. This case study considers video of one teacher’s implementation of a problem-solving lesson in a year 1 primary school class in Australia. It examines the opportunities this teacher provided to leverage reasoning and contributes to the body of knowledge on ways reasoning may be elicited during problem solving. The new Eliciting Mathematical Reasoning Framework arising from the analysis of the data in this study builds on and extends previous research. It provides a tool to support researchers, teacher educators, professional learning providers, and teachers in recognising and eliciting reasoning.

This research paper aims to characterize Mathematical Reasoning (MR) in teaching and learning of mathematics in high-school education. To achieve this goal and reveal the status of Mathematical Reasoning as a concept, we analyze the content of curricula and official textbooks of the initial and second year of high school in Morocco. Our analytical framework focuses on the commognitive perspective, exploiting the different components of MR presented in literature. The results obtained from this study using a quantitative approach show that MR occupies a central place in mathematics education at Moroccan high school, but the use of some structural and procedural aspects is still too limited.

Improved pedagogical practice does not happen in a silo; it requires impetus. External influences and pressures and internal motivations are drivers for pedagogical change. Professional learning (PL) programs, in their multitude of forms, are key tools for affecting teacher change. In response to an increased focus on fostering students’ reasoning in curriculum documents, our team developed the Mathematical Reasoning Professional Learning Research Program (MRPLRP) to support teacher change. This two-phased project aimed to build teachers’ knowledge of the critical aspects of reasoning pedagogical approaches that foster students’ development of reasoning. Phase One involved researchers’ planning and demonstrating a lesson with a focus on reasoning. In Phase Two, a peer learning team (PLT) is formed to plan a lesson to elicit reasoning and to observe each other teach the lesson. This article reports on Phases One and Two of the MRPLRP from the perspective of one teacher who participated in both phases. The findings provide insights into the aspects of PL that were critical in shifting this teacher’s understanding of reasoning and approaches to teaching reasoning. Whilst the results of a single case cannot be extrapolated to a larger population, we present and discuss the factors of this PL program in raising the awareness of critical aspects of reasoning, and thus this paper has the potential to impact future PL design.

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was carried out with 118 fifth-grade students (11-12-year-olds). As data collection tool, \"mathematical reasoning test\" and \"mental computation test\" were developed and used. In analyzing the data, Pearson's correlation coefficient (r) between participants' scores of each test was computed. Some sample student responses to some questions in both tests were also presented directly. Evidence was found that there is a significant positive correlation between mental computation and mathematical reasoning. It is noteworthy that rather than exposing students to familiar classical problems, students need to be enabled to deal with exceptional/non-routine problems, and especially young children should be encouraged to do mental computing in order for developing both skills. On the other hand, students must be asked to write the strategies they use and on which grounds they preferred them while solving the problems.

Over the past decades, numerical and mathematical cognition has transformed from a niche research area into a thriving global field, with contributions spanning diverse populations, methodologies, and theoretical approaches. The 13 articles in this special issue highlight the breadth and depth of contemporary research, addressing topics such as the development of early numeracy skills, the interplay between mathematical and reading processes, the cognitive mechanisms supporting arithmetic and algebra, and the role of visuospatial thinking in expert mathematical reasoning. The contributions exemplify methodological innovation, from longitudinal studies and psychometric evaluations to interdisciplinary theoretical models that integrate numerical and linguistic frameworks. Together, they collectively advance theoretical, applied, and interdisciplinary perspectives. This introduction synthesizes the contributions, demonstrating how they collectively inspire future directions for research on numerical and mathematical cognition. We discuss the broader implications of the work while also contextualizing its development within its historical ties to Canadian experimental psychology and the foundational work of pioneers such as the late Jamie I. D. Campbell, in memory of whom this special issue was conceived. Au cours des dernières décennies, la cognition numérique et mathématique est passée d'un domaine de recherche de niche à un domaine mondial florissant, avec des contributions couvrant diverses populations, méthodologies et approches théoriques. Les 13 articles de ce numéro spécial mettent en lumière l'étendue et la profondeur de la recherche contemporaine, abordant des sujets tels que le développement des premières compétences en calcul, l'interaction entre les processus mathématiques et de lecture, les mécanismes cognitifs soutenant l'arithmétique et l'algèbre, et le rôle de la pensée visuospatiale dans le raisonnement mathématique expert. Les contributions illustrent l'innovation méthodologique, depuis les études longitudinales et les évaluations psychométriques jusqu'aux modèles théoriques interdisciplinaires qui intègrent des cadres numériques et linguistiques. Ensemble, elles font progresser les perspectives théoriques, appliquées et interdisciplinaires. Cette introduction synthétise les contributions, en montrant comment elles inspirent collectivement les orientations futures de la recherche sur la cognition numérique et mathématique. Nous discutons des implications plus larges de ces travaux tout en contextualisant leur développement dans le cadre de leurs liens historiques avec la psychologie expérimentale canadienne et les travaux fondamentaux de pionniers, tels que le regretté Jamie I. D. Campbell, en mémoire duquel ce numéro spécial a été conçu. Public Significance Statement This special issue brings together a diverse collection of studies examining numerical and mathematical cognition across various populations, methodologies, and theoretical frameworks. The 13 articles showcase both foundational and innovative approaches to understanding how numerical competencies develop, how they connect with other cognitive domains, and the cognitive processes and tools that support mathematical thinking. By bridging these perspectives, the issue not only honors the pioneering work of Jamie I. D. Campbell but also paves the way for future research that will continue to unravel the complexity and relevance of numerical cognition.

A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students' mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students' mathematical reasoning processes such as generalization and justification.

This study aimed to investigate the effect of a training program based on the trends in international mathematics and science study (TIMSS) on developing the habits of mind and mathematical reasoning skills among pre-service math teachers in Oman. The study sample consisted of 24 female pre-service math teachers divided into two equal groups: experimental and control. The study data was collected by sued the mathematical reasoning test and questionnaire that measured the level of habits of mind after appropriate validity and reliability. The study results showed statistically significant differences between the two study groups in favor of the experimental group in the mathematical reasoning test and the habits of mind scale. The study recommended that the need for pre-service math teachers to use programs based on international studies such as TIMSS, PISA, PIRLS, and TAILS; this was done to prove their effectiveness in developing the levels of habits of mind and mathematical reasoning skills by subjecting them to training programs, courses, and workshops with the aim of training teachers to implement the training programs effectively.

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in the philosophy of mathematics and in mathematics education research in general, it is argued that it is necessary to give a relativist account of mathematical reasoning. Hacking’s framework of styles of reasoning is introduced as a possible solution. This framework distinguished between at least six different styles of reasoning, many of which are closely connected to mathematics, and argues that these frameworks define what we accept as decidable assertions, as justifications for such assertions, and as possible objects of such assertions. The article ends with a discussion of the implications of the framework for chosen fields of mathematics education research, which may motivate more focussed studies in the future.