The paper presents an analysis of elementary grade mathematics teaching in India focusing on mathematical reasoning. Mathematical reasoning is an important tool to make sense of mathematical ideas, which in turn makes mathematics more accessible to learners and promotes social equality. The paper analyzes 112 lessons from Grades 1 to 8 by 21…

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

In this paper, we examine sixth grade students' degree of conceptualization of fractions. A specially developed test aimed to measure students' understanding of fractions along the three stages proposed by Sfard ("1991") was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test…

How does classroom interaction support students' apprenticeship into the ways of speaking, writing, and diagramming that constitute the practice of mathematics? We address this problem through an interpretative analysis of a whole-group conversation about alternative ways of solving a problem involving percent discounts that occurred in a sixth…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…