In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This action research study employed a mixed-method design to examine the impact of a number talks intervention on the number sense development and mathematical proficiency of students in one third-grade mathematics class. The number talks strategy was also studied to determine its impact on third-grade students' development of a productive…

In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of…

In education, the use of information, computers, and the Internet as a form of blended technology has been receiving increased attention and consideration. Additionally, increasing attention is being paid toward a scaffolding mechanism that can be integrated into science classrooms in order to solve technological challenges. This work describes a…

We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…

Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results…

Spatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number-space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading…

The purpose of this study is to investigate the number sense performance of secondary school students according to grade level, gender and the components of number sense. A descriptive survey design was used to collect data. A total of 576 secondary school students (291 girls and 285 boys) participated in the study. The results revealed that the…

As outlined in the paper "The 20 Matchstick Triangle Challenge: An Activity to Foster Reasoning and Problem Solving" by Pat Graham and Helen Chick [EJ1093090], an incredibly useful set of information about the mathematical ability of your students will be revealed. You can look at the way your students try to solve the 20 matchsticks…

This study was organized to examine the impact of a field experience for elementary preservice teachers working with young children enrolled in a summer academy focusing on early mathematics. The academy was designed to provide engaging learning experiences to support the development of early number concepts for pre-K students from an elementary…

In this study, a situation-based interactive e-book system was developed for improving children's learning performance of numerical operations. To evaluate the effectiveness of the system, an experiment was conducted in one kindergarten. The results showed that the proposed approach significantly improved the children's learning achievements.…

This report examines which instructional components (e.g., visual representations, use of number lines, teaching and using of mathematical language) and study features (e.g., group size, interventionist training) may have contributed to the effectiveness of intervention. In choosing to focus on instructional components and study features, the…

Previous research suggests that block adding, subtracting and counting direction are early forms of number-space mapping. In this study, an embodiment perspective on these skills was taken. Embodiment theory assumes that cognition emerges through sensory-motor interaction with the environment. In line with this assumption, it was investigated if…

Using a game-based context and concentrating explicitly on language, students in the early years are able to make sense about place value amid the vagaries of the English language in naming numbers. This conceptual approach to understanding place value allows students to further develop number strategies beyond counting by ones.

A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the "complex precalculus" part of the course. In…