In this cross-national study, we explore the different ways of reasoning-and-proving (RP) presented in three 8th grade textbooks, one from each country: Turkey, Norway, and Slovakia. While the analysis revealed that all three textbooks contain similar numbers of problems involving some form of RP, differences exist in terms of the dominating ways…

Opportunities to learn related to the use of quantitative reasoning to solve higher-order real-world applications that reflect the messy nature of the world are scarce and vary across countries. Those experiences are essential to the development of quantitative literacy. This literacy, like that related to language, is critical for all children.…

The aim of this study is to investigate Norwegian primary school students' multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8-9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as…

We suggest that writing lesson plays can be a valuable approach in learning to teach proving in teacher education. A lesson play is an imagined discussion between a teacher and some students about a particular mathematical content, written verbatim. In this paper, we investigate novice teachers' opportunities to work on teaching practices related…

This article addresses argumentation in middle-school students' group work with conjectures in arithmetic with different epistemic states. Twenty-five episodes were analysed using G. J. Stylianides' framework for reasoning and proving, which comprised a mathematical, psychological, and pedagogical component. The mathematical component was studied…

Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers'…

Although the roles of symbolic numerical magnitude processing (SNMP) and working memory (WM) in mathematics performance are well acknowledged, studies examining their joint effects are few. Here, we investigated the profiles of SNMP (1- and 2-digit comparison) and WM (verbal, visual and central executive) among Norwegian first graders (N = 256),…

This paper aims to give detailed insights of interactional aspects of students' agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student-student…

Proof and proving play a fundamental role in mathematics education and have the potential to serve as a vehicle for developing a deeper conceptual understanding. However, engaging students in proving activities presents challenges, and mathematics teacher educators thus are responsible for supporting preservice teachers, providing opportunities to…

This study investigated which domain-specific and domain-general skills measured at grade 1 predict mathematical learning difficulties (MLD) status at grade 3. We used different cut-off criteria and measures of mathematics performance for defining the MLD status. Norwegian children's (N = 206) numeracy, cognitive, and language skills were measured…

The aim of the study is to examine how toddlers (33 months) with weak mathematical skills differ from their peers, the extent to which those weak skills persist into preschool age (57 months), and how the group with persisting weak skills differs from the group with temporary weak skills. Participants were 692 children (344 girls, 348 boys). The…

This is the third in a series of papers focusing reasoning-and-proving. Participants were in-service teachers enrolled in a continuing university education programme in teaching mathematics for grades 5-10. Data were collected from a course assignment in 2018 and 2019, where the in-service teachers reported about their students' work with a…

The purpose of this qualitative study was to explore in-service teachers' first experiences with imaginary dialogues -- a form of mathematical writing where students are introduced to a written and unfinished dialogue between two imaginary persons discussing a mathematical problem. Students are supposed to continue working with the problem and to…

This article presents an origami activity which can lead to rich tasks in several branches of mathematics. This activity is a good first step for preservice teachers to get to know one another, start talking to one another, and start discussing mathematics. It can also show them how mathematics teaching and learning have changed to a more…

This article aims to identify the mathematical reasoning strategies expressed through gestures and speech used by two groups of sixth-grade pupils when solving a task related to the transition between two semiotic representations: figure and Cartesian diagram. The article also identifies the difficulties the pupils meet in the solution process.…