Over the last years, there is a growing interest in studying students' difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students' understanding of rational numbers. The present study tests the effect of the "whole" or "natural number bias" (i.e., the…

The paper examined the relations among problem solving, automaticity, and working memory load (WML) by changing the difficulty level of task characteristics through two applications. In Study 1, involving 68 engineering students, a 2 (automaticity) x 2 (WML) design was utilized for arithmetic problems. In Study 2, involving 76 engineering…

In the current study, it is aimed to determine the activities that need to be done to eliminate the mistakes made by primary school fourth grade students in multiplication and division operations and to present solution suggestions for eliminating these mistakes. The study employed action research, one of the qualitative research methods. The…

There is a growing body of research that suggests that video-based interventions, such as video modeling and video prompting, are effective tools for teaching academic skills to struggling learners. This study used a single subject, multiple-baseline-across-subjects design to evaluate whether a video-prompting intervention could effectively assist…

Recent multiplication with regrouping research shows that the combination of the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) has been effective in several studies. More evidence is needed to demonstrate CRA-SIM's effectiveness across settings and students. Therefore, the purpose of this study was to…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

Developments in mathematics education tend to emphasize mathematics teaching with the help of activities that will allow the students to create these concepts rather than to make them memorize mathematical rules. The purpose of this study is to analyze the applicability of the application of multiplication with fingers developed by the researcher.…

Recent years have seen a quick expansion of tablet computers in households and schools. One of the educational affordances of tablet computers is using math apps to engage students in mathematics learning. However, given the short history of the mobile devices, little research exists on the effectiveness of math apps, particularly for struggling…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

This study explores the ways in which eleven preservice elementary teachers used a web-based teacher resource to apply a mathematical definition, to correct a procedural error in arithmetic, and to make sense of a story requiring the multiplication of fractions. In our analysis we propose a framework to compare the behaviors and values expressed…