This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

This study examined discussions centered on precise mathematical language use in two fifth grade classrooms. Drawing on episodes from lessons in which teachers focused on encouraging mathematics reasoning, our analysis examines the relationship between precise language use and mathematical justifying. We present three classroom episodes that…

The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…

Both additive and proportional reasoning are types of quantitative analogical (QA) reasoning. We investigated the development and nature of primary school children's QA reasoning by offering two missing-value word problems to 3rd to 6th graders. In one problem, ratios between given numbers were integer, in the other ratios were non-integer. These…

This paper looks at 21 fifth grade students as they discuss a linear graph in the Cartesian plane. The problem presented to students depicted a graph showing distance as a function of elapsed time for a person walking at a constant rate of 5 miles/h. The question asked students to consider how many more hours, after having already walked 4 h,…