Patterns are a fundamental component of mathematics, and the patterning ability of young children has been well researched; however, this research has largely been conducted with relatively small cohorts (±70) and in an interventionist way (in laboratory settings or with researchers directly intervening in educational contexts). The current study…

Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the…

In this study, we examine students' mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3-5) engaged in a series of fraction-as-measurement tasks…

Backward transfer is defined as the influence that new learning has on individuals' prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students' prior ways of reasoning about linear functions. Two algebra classes and their teachers…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying…

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this…

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the…

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a…

Whole-class discussions in mathematics are envisioned as spaces for the sharing of ideas and making connections among them. We pursue how Palestinian/Arab Israeli teachers consider making use of multiple solutions to a task: which three they indicate that they would select for a whole-class discussion and in what sequence. Under the hypothetical…

This paper studies grade 7 (age 13) students' expressed understanding about the equal sign/notion of equivalence in order to investigate what aspects of the concept that could be seen as an established knowledge at lower secondary school/middle school. Using items from different instruments and combining these to a new one that covered a broad…

Despite the documented influence of motivation on mathematics learning for most students, we understand far less about this relation for students identified with learning disabilities. Based on Rogoff's three planes of analysis (i.e., personal, community, and interpersonal), we gathered survey, interview, and video data to understand the…

Studies have shown that learning mathematics through programming can be complex and that the programming itself might even hamper students' learning. However, few studies have focused on the role of the teacher and the teacher-student interaction that aims to support students' learning when using programming. The present study examines a didactic…

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…

Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a…

Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a…