This article reports a recent case study providing evidence that toddlers explore mathematical concepts in their outdoor play. The play experiences the toddlers engaged in gave rise to seven mathematical categories. In each of these categories examples are given of some of the ways the toddlers displayed their mathematical knowledge and skill.

Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

The purpose of this study was to explore individual patterns of strengths and weaknesses in children's mathematical knowledge about common fractions. Tasks that primarily measure either conceptual or procedural aspects of mathematical knowledge were assessed with the same children in their fourth- and fifth-grade years (N = 181, 56% female and 44%…

Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there are dimensions involved in the emergence of mathematical knowing and the production of mathematical…

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

The current experiments examined the role of scale factor in children's proportional reasoning. Experiment 1 used a choice task and Experiment 2 used a production task to examine the abilities of kindergartners through fourth-graders to match equivalent, visually depicted proportional relations. The findings of both experiments show that accuracy…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

Traditionally, Canadian Inuit have lived in the circumpolar regions of Canada and those who still live in these regions, have their own cultures, which they tend to celebrate in their educational curricula. Inuit culture reflects their traditional lifestyle, when they were nomadic, and hunted and fished to survive in incredibly difficult…

School-based agricultural education programs provide contextualized learning environments for the teaching of core academic subject matter. This study sought to examine the mathematics efficacy and professional development needs of Wyoming agricultural education teachers related to teaching contextualized mathematics. Wyoming agricultural…

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic…

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment…

More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…

In order to improve teaching strategies in a college level remedial mathematics course, this study seeks to investigate student perception while they attempt challenging mathematics tasks. The participants were 72 students enrolled in a mid-western university remedial mathematics course. A qualitative case study methodology was used to investigate…

This study investigates the relationship between eighth grade primary school students' success levels in solving equations and proportional reasoning skills. 344 eighth grade students, who were registered at various primary schools in the central districts of Konya in the 2007-2008 educational year, participated in the research. The study had a…