As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

This paper reports on a combined research-development project conducted in collaboration between researchers and preschool teachers in three Swedish preschools. The aim is to investigate how ongoing preschool activities may become the starting point for mathematics teaching in which toddlers are given the opportunity to distinguish necessary…

Playing board games and other math activities can provide young children with opportunities to develop their math skills. However, it is critical to understand for whom these activities may be most beneficial. In two studies, we examine the extent to which foundational cognitive skills moderate the effects of playing math games on math skills. In…

The authors discuss the use of "real life" activities that are interesting to children in the teaching of measurement and number concepts. In this article, they present a series of lessons targeting volume and capacity that seamlessly incorporate genuine "real-life" experiences with practical mathematical applications. In…

On the lookout for and with a vested interest in Canadian mathematics education matters, this article is dedicated to hockey cards. More specifically, the statistics found on the back of hockey cards. The combination of taking a trip down memory lane, thrifting in British Columbia, traipsing around Toronto, and having coffee (one cream) at Tim…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they…

Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

This study analysed how preschool teachers differently enacted the same mathematical activity for preschool children to discern numbers, and how this affected the children's learning opportunities during the activity. The analysis was based on variation theory and Chi's taxonomy of learning activities. Two Swedish preschool teachers' enactment of…

Recent work has stressed the importance of considering child-level propensities and environmental opportunities when studying early math achievement; however, few studies investigate the interaction between these factors. This study examined whether children's inhibitory control moderates the association between parental math input and children's…

Explore young children's remarkable everyday math that can lay the groundwork for formal math education in kindergarten and beyond. Readers will learn how math is embedded in children's everyday lives, how daily routines contribute to the development of important math concepts, and what adults can do to foster the joy of early math learning.…

We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal makerspace. In particular, we connect research at different grain sizes to illustrate and explain how mathematics plays a crucial, if often implicit, role in this activity. We begin with describing the Approximate Number System and the Ratio-Processing…