We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children's reliance on these neural…

This study aimed to investigate how the semantic structures of problems posed by sixth-grade middle school students for the addition of fractions affect their problem-posing performance. The students were presented with symbolic operations involving the addition of fractions and asked to pose two different problems related to daily-life situations…

The study reported in this paper is part of a larger study on the roles of examples in learning to prove. We focus here on manifestations of students' productive use of examples for proving in the course of exploring conjectures and proving or disproving them. In this context, we define productive use of examples for proving as students'…

This study explored the connections between teacher leadership and a professional development model focused on problem-solving, Math Teachers' Circles (MTC). Surveys were completed by 213 MTC participants resulting in three years of data across multiple sites. A mathematics education leadership framework provided a data analysis tool. Findings…

Both writing and math require purposeful teaching. This article describes how one teacher discovered that she could teach math in a way that paralleled how she taught writing by researching what students know and then nudging them ahead to the next level of understanding. Just as effective writers employ creativity, perseverance, and revising,…

Gender differences in the strategies elementary school children use to solve multidigit addition and subtraction story problems that require regrouping are investigated in two studies. Study 1 replicates the Fennema and colleagues (1998) study by reexamining previously published data on 72 children's addition and subtraction solution strategies.…

The purpose of the study was to meta-synthesize research findings on the effectiveness of problem posing and to investigate the factors that might affect the incorporation of problem posing in the teaching and learning of mathematics. The eligibility criteria for inclusion of literature in the meta-analysis was: published between 1989 and 2011,…

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…

Chocolate chip cookies are used to illustrate the importance and effectiveness of control charts in Statistical Process Control. By counting the number of chocolate chips, creating the spreadsheet, calculating the control limits and graphing the control charts, the student becomes actively engaged in the learning process. In addition, examining…

Dodgson's method of computing determinants is attractive, but fails if an interior entry of an intermediate matrix is zero. This paper reviews Dodgson's method and introduces a generalization, the double-crossing method, that provides a workaround for many interesting cases.

In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. We determine Fay's optimal path minimizing segment length, and thus maximizing the number of times they meet…

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between…