Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh- and eighth-grade students learned to solve equations (a)…

This experiment tested a treatment designed to improve choral students' expressiveness regarding keyword emphasis and phrase shaping. The treatment was founded upon the constructivist belief that students actively construct conceptual knowledge through problem solving. Participants were 46 university students randomly selected from a nonauditioned…

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…

In contrast to subjects such as mathematics and the sciences, it has been argued that technology education lacks a clear definition and a clearly defined knowledge base. This discursive article seeks to inform the debate by highlighting the matter of subject definition and in addition to examine the key issue of the knowledge which underpins…

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…

This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

Based on the comments by Lopez-Facal and Jimenez-Aleixandre, we consider that the cultural identities within Europe interfere with the question of the re-introduction of the Slovenian bear, generating a kind of "discrimination." When the SAQs under debate run against the students' systems of value, it seems that the closer the connection…

This article describes a technology-based and hands-on instructional intervention designed to advance middle school students' understandings of fractions. This problem-solving experience is based on the principles of Enhanced Anchored Instruction (EAI) and proved instructionally worthwhile and motivating to teachers and students in both inclusive …

The author was asked to develop a list of actions that teachers could take to build students' mathematics abilities. Too many students fail to graduate and fail to pass state assessments as a result of weak mathematics skills. Even many students who do graduate leave high school lacking sufficient understanding of mathematics to pass college…

Synthesizing a decade of research, the author describes a taxonomy of meaningful learning. The most meaningful learning outcome is problem solving. In this taxonomy, four different kinds of problem solving are arranged in a hierarchical manner. Prerequisite/corequisite with problem-solving outcomes are two fundamental reasoning skills that…

This paper defines correlation, describes the Mix It Up program, discusses the teachers' beliefs about the value of correlating mathematics and science prior to program participation, and identifies problems teachers associated with correlation before and during the program. Teachers' beliefs about the value of correlation and about the problems…

Bodily manipulations, such as juggling, suggest a well-synchronized physical interaction as if the person were a physics expert. The juggler uses "knowledge" that is rooted in bodily experience, to interact with the environment. Such enacted bodily knowledge is powerful, efficient, predictive, and relates to sensory perception of the dynamics of…

In the last column we focused (as a primary goal of instruction) on the importance of teaching so that students learn to think their way into and through content. We stressed the need for well-designed daily structures and tactics for fostering deep learning, offering three strategies as examples. In this column, we provide four additional…