In this theoretical article, we explore the possibility that instead of a mathematical connection arising "in-between" two (or more) pre-existing ideas or objects, which have presumably been known or understood, that connection is itself the motor of understanding. The standard view of connection, in which two existing ideas or concepts…

Estimating and accounting for statistical uncertainty have become essential in today's information age, and crucial for cultivating a sound decision making citizenry. Engaging with statistical uncertainty early on can support the gradual development of uncertainty-related considerations that are often challenging to foster at any age. Statistical…

This paper presents findings from a study that examined the strategies that children, who had only been taught the part-whole fraction sub-construct at school, used for finding the fraction associated with solving varied partitive quotient problems. A qualitative, microgenetic research design was used involving nine year 5 (aged 9-10) children…

There is a long tradition of teaching science through inquiry, with broad agreement about the form it should take. Students should investigate researchable questions; gather and analyse data; and develop and represent evidence-based claims. Authoritative teacher or textbook representations are generally used to guide this learning (Buckley &…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

Computational thinking (CT) has acquired the status of a necessary 21st-century skill and is currently being introduced in school curricula around the world, despite a lack of consensus about what it entails. The aims of this review are to provide an overview of the existing literature on CT activities in primary mathematics education, and to…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one's own thinking and engaging with others' ideas, can promote students' mathematics learning. However, precisely "how" participating in these ways supports learning has not often been examined in…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

Learning mathematical concepts and procedures typically requires extended cognitive effort, presenting a challenge for many children. People can make tracing actions with the index finger, as well as mimic another's movements, with little or no conscious effort. From the perspective of cognitive load theory, such biologically primary actions may…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The paper addresses concept formation processes of students in the field of geometry. More precisely, the paper deals with the questions of what knowledge do students activate about triangles in different contexts with different (digital) tools and furthermore what content-related meaning do they give to the concept of triangles? Methodologically,…

Coaching is a complex endeavor that blends a myriad of concepts and skills. Practical experience, content knowledge, and coaching knowledge are instrumental to becoming an effective math coach. In order to design a professional development system to best support and build the capacity of coaches, we must identify what specific content and coaching…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…