In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

The student's criterion for being diagnosed with MLD (Mathematics Learning Disabilities) can be classified as low arithmetic skills and poor working memory. The goal of this research is to understand students' process of thinking through the Polya stages when tackling arithmetic problems, as it has been expounded by Dr. Polya For students who have…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

The classic Chickens and Pigs problem is considered to be an algebraic problem with two equations and two unknowns. In this article, the authors describe how third-grade teacher Maria is using it to develop a problem-based lesson because she is looking to her students' future needs. As Maria plans, she considers how a series of problems with the…

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…

The period from adolescence through young adulthood is one of great promise and vulnerability. As teenagers approach maturity, they must develop and apply the skills and habits necessary to navigate adulthood and compete in an ever more technological and globalized world. But as parents and researchers have long known, there is a crucial dichotomy…

This paper describes an approach to task analysis which seeks to identify potential sources of difficulty in the self-discovery of improved procedures by students who have been taught simpler procedures. The approach considers novices' procedures in terms of the changes needed to produce an expert procedure; the knowledge required to make those…

Approaches to helping students remember concepts in secondary mathematics are presented. The eleven points listed are: 1) distinguishing between natural and whole numbers; 2) remembering isosceles triangles have two equal sides; 3) finding all possible pairs of integral factors of a given number; 4) recalling the meaning of reflexive, symmetric,…

Presents two teaching ideas for mathematics instruction. The first employs "mind maps" as a method to help students learn, record, and recall mathematical information. Provides examples for solving quadratic equations and complex numbers. The second discusses two ways to find the average speed during a trip employing differing constant…

To determine whether children's knowledge of arithmetic facts becomes increasingly "automatic" with age, 7-year-olds, 11-year-olds, and adults were given a number-matching task for which mental arithmetic should have been irrelevant. Specifically, students were required to verify the presence of a probe number in a previously presented pair (e.g.,…

Contemporary trends in education reflect a shift from traditional teacher-centered approaches to more student-centered approaches to learning. Empowering students in their own learning is facilitated by teaching them effective meaning-making strategies that support active participation in their own learning. Making this happen requires using…

Recent research points to the inborn abilities of infants and shows how early experiences influence cognitive skills. This book presents activities for parents and their infants--building on activities babies instinctively love--to develop their unique abilities. The book is organized around six intellectual skills: (1) problem solving; (2)…

This document contains the third volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Ead and Kou:…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…