Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the…

Despite decades of research on the close link between eye movements and human cognitive processes, the exact nature of the link between eye movements and deliberative thinking in problem-solving remains unknown. Thus, this study explored the critical eye-movement indicators of deliberative thinking and investigated whether visual behaviors could…

The goal of this paper is to present a succinct consolidation of the why, what and how of the 'Model' method as there is a lack of such documentation for researchers, practitioners and policy makers thus far. The 'Model' method is a tool for representing and visualising relationships when solving whole number arithmetic (WNA) word problems. The…

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

Having a deeper understanding of division derived from multiple models is of great importance for teachers and students. For example, students will benefit from a greater understanding of division contexts as they study long division, fractions, and division of fractions. The purpose of this article is to build on teachers' and students'…

During the semester break, 36 second-grade students accessed a set of resources and completed a series of online math activities focused on the application of the model method for arithmetic in two contexts 1) addition/subtraction and 2) multiplication/division. The learning environment first modeled and then supported the use of a scripted series…

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better…

Two experiments, one measuring eye fixations of 38 undergraduates and the other assessing memory of 37 undergraduates, provide evidence that unsuccessful problem solvers are more likely to comprehend by direct translation and that successful word problem solvers are more likely to build a problem model. (SLD)

Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

Simple arithmetic word problems are often featured in elementary school education. One type of problem, "compare with unknown reference set," ranks among the most difficult to solve. Differences in item difficulty for compare problems with unknown reference set are observed depending on the direction of the relational statement (more than vs. less…

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…

Ongoing work toward developing a learning environment that will perform real-time diagnoses of students' difficulties in solving mathematical word problems is described. The learning environment designed consists of a microworld and expert modules. The microworld (or toolbox) is a collection of mouse-driven interfaces that facilitate a transition…

This document contains the fourth volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 64 research report papers: (1) Situated or Abstract: The Effect of…