Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative…

Word problems are often used to assess numeracy, despite the growing number of reports on difficulties students encounter with this genre of mathematical problems. These reports contend that a large number of difficulties are influenced by the way the problems are presented, that is, with verbal representations of the problem situations. These…

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach,…

In this "Delving Deeper" article, the author introduces the slip-slide method for solving Algebra 1 mathematics problems. This article compares the traditional method approach of trial and error to the slip-slide method of factoring. Tools that used to be taken for granted now make it possible to investigate relationships visually,…

We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention within the literature: the spatial distributions of TSP and MST-P stimuli. First, we describe a method for quantifying the relative degree of…

The purpose of this study was to investigate the effect of a computer-based story on sixth grade students' mathematics word problem solving achievement. Problems were embedded in a story presented on a computer, and then compared to a paper-based story and to a condition that presented the problems as typical, isolated words problems. One hundred…

This paper presents a comparative analysis of prospective elementary teachers' mathematical problem solving-related beliefs in Cyprus and England. Twenty-four participants, twelve from a well-regarded university in each country, were interviewed qualitatively at the exit point of their undergraduate teacher education studies. Analyses revealed…

The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students. Through analysis of the 32 students' answers it appears that the number…

The present study used a new assessment technique, the story-generation task, to examine students' understanding of subtraction scenes. The students from four grade levels (110 first-, 107 third-, 110 fourth- and 119 sixth-graders) generated stories under the constraints provided by a picture (representing Change, Combine or Compare scene) and a…

Fifteen learning-disabled (LD), 33 attention disordered (AD), and 28 normal adolescents were assessed with 2 performance measures and 3 behavioral measures while working on mathematics problems. Findings support theoretical predictions that LD and AD children have difficulty with repetitive stimuli, contributing to mathematics deficits. (SLD)

Brown's 1933 diagnostic test was used as a screening examination for 79 psychology students to determine their areas of weakness in statistical calculations, and to see whether the difficulties of a previous era have been changed by methods of teaching mathematics today. General similarities were found. (LBH)

Three studies examined strategy flexibility in mathematical problem solving among high school students on Scholastic Assessment Test-Mathematics problems and among college students on Graduate Record Examination-Quantitative items. Results suggested that strategy flexibility was a source of gender differences in mathematics ability as assessed by…