In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning.…

This paper considers the kind of pedagogical knowledge and principles involved in the operationalisation of knowledge of children's mathematical thinking as a process of dynamic assessment. Using a case study of a particular child, this paper explores planning and instruction for a child determined by a detailed and informed interpretation of the…

The socioeconomic attainment gap in mathematics starts early and increases over time. This study aimed to examine why this gap exists. Four-year-olds from diverse backgrounds were randomly allocated to a brief intervention designed to improve executive functions (N = 87) or to an active control group (N = 88). The study was preregistered and…

The aim of this study is to analyse undergraduate students' understanding of polar coordinates based on two theories, Action, Process, Object and Schema (APOS) and Onto-Semiotic Approach (OSA). These two theories complement each other and each of them separately has been used in many research to explore students' performance of mathematical…

This paper focuses on problem solving and problem posing in mathematics education with 6-year-olds. After working on a problem-solving activity, the young students were asked to pose a "similar" task to a friend. This article explores how the students interpret the notion of "similar." To be able to pose a problem-solving task…

The Standards for Educational and Psychological Testing identify several strands of validity evidence that may be needed as support for particular interpretations and uses of assessments. Yet assessment validation often does not seem guided by these Standards, with validations lacking a particular strand even when it appears relevant to an…

Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims: The present study aimed to explore 4- to 5-year…

Secondary students with persistent mathematics difficulties need the most intensive intervention in order to improve their mathematics outcomes. One approach to intensifying and individualizing intervention is through data-based individualization (DBI). The present study used a single-subject, multiple-baseline-across-participants,…

Physical activity has not only been associated with increased physical and mental health, but also with beneficial effects on various cognitive and brain functions. This study investigated the effects of a motor and coordination oriented exercise intervention on academic achievements, attention/concentration ability, and on different facets of…

This research aimed to describe the levels of feeling of rightness (FOR) of students. This research used a qualitative method with an explorative type. The subjects of this research were 3 students of 5th grade selected from 77 other students in Indonesia. In uncovering FOR subject of this research, instruments were used in the form of problems…

Most of the research examining the relation between instructional quality (INQUA) and mathematics teachers' competence was restricted to a limited set of competence facets. Furthermore, mostly variable-oriented approaches were applied that assume homogeneity of teacher competence. In our study, teacher competence is conceptualized as a…

We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects. We describe a model that incorporates projects at all stages across the undergraduate mathematics…

The spatial ability is defined as the combination of some abilities such as imagining the movements of objects, mental rotation, and spatial transformations. Students' spatial abilities can be enhanced through specific education programs. This study investigated the effects of engineering design-based instruction on spatial abilities of 8th grade…

In this paper we present the results of an investigation related to the developing of mathematical knowledge and skills by first semester university students when solving a Model Eliciting Activity [MEA] which involves quadratic function knowledge. This was a qualitative research. The theoretical framework was Models and Modeling Perspective…