The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students…

According to the National Council of Teachers of Mathematics, geometry and spatial sense are fundamental components of mathematics learning. However, learning disabilities (LD) research has shown that many K-12 students encounter particular geometry difficulties (GD). This study examined the effect of an integrated object representation (IOR)…

This article describes a follow-up analysis of findings from a randomized study that tested the efficacy of a blended version of Enhanced Anchored Instruction (EAI) designed to improve both the computation and problem-solving performances of middle school students with disabilities. The goals of the secondary analysis were to track overall error…

The aim of this study was to determine the salient beliefs of pre-service primary school teachers (PPSTs) about why they like or dislike physics and to explore whether these beliefs predict their teaching beliefs about physics. A total of 267 PPSTs (Male = 137, Female = 130) participated in the study. Qualitative data analyses were used and the…

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study…

Of all teaching methods, one-to-one human tutoring is the most powerful method for promoting learning. To achieve this aim and reduce teaching load, researchers developed intelligent tutoring systems (ITSs) to employ one-to-one tutoring (Aleven, McLaren, & Sewall, 2009; Aleven, McLaren, Sewall, & Koedinger, 2009; Anderson, Corbett,…

The National Council of Teachers of Mathematics (2012) and the Council for Exceptional Children (CEC; 2012) have stressed the importance of all students learning algebra. CEC stated that there was a crucial need for algebra instruction and intervention that can help students with disabilities in the general education classroom. Algebra is…

This paper challenges the way in which we are inclined to treat theory and suggests that our tendency to privilege it over method is counterproductive. Some consequences of privileging theory are pointed out and a remedy is proposed. The remedy entails a number of "reversals" in the way we treat theory and method in maths education research, the…

Research on toddlers' mathematical knowledge is sparse. Studies on children's mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

Gesturing is ubiquitous in communication and serves an important function for listeners, who are able to glean meaningful information from the gestures they see. But gesturing also functions for speakers, whose own gestures reduce demands on their working memory. Here we ask whether gesture's beneficial effects on working memory stem from its…

This study was designed to investigate whether and how upper elementary grade teachers who use a reform-based mathematics curriculum adjust instruction for their lower achieving (LA) compared to higher achieving (HA) students during a one-on-one mathematics problem-solving lesson. Little is known about the individualized support teachers provide…

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

A square can be divided into two equal parts with any cut through the center. The first question that arises is, Would any cut through the center of a regular polygon divide it into two equal parts? If not, the second question is, What kind of lines through the center of the polygon would cut it into two halves? However, many objects are not…