Creativity is not only for gifted students, but also for regular ones. This case study was aimed to analyze the appropriateness of tasks and the elaboration of multiple solutions to occasion fourth-graders' mathematical creative thinking through a documentary multiple-solution counting task in a figurative setting. The data came from the written…

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…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…

This paper investigated the intuitive development of the concept of integers among primary school students. In order to reveal if primary school students had an intuitive sense of integers, an assessment consisting of five questions was prepared and applied to a total 100 4th grade students. A variety of integer concepts were utilized in the…

Background: Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. Aim: This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It…

Purpose: The purpose of this paper is to examine how lesson study can lead to teacher learning and improvement of instruction by developing teachers' mathematical-task knowledge and by supporting teachers' selection, modification, and implementation of mathematical tasks. Mathematical-task knowledge includes knowledge needed to use tasks that…

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

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…

Although the Curriculum Principle in "Principles and Standards for School Mathematics" states, "A school mathematics curriculum is a strong determinant of what students have an opportunity to learn and what they do learn," this article seeks to help teachers enhance tasks found in commonly used textbooks to create additional opportunities for…

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students'…