Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…

Many beginning university students struggle with the new approaches to mathematics that they find in their courses due to a shift in presentation of mathematical ideas, from a procedural approach to concept definitions and deductive derivations, and ideas building upon each other in quick succession. This paper highlights this struggle by…

Competence in many domains rests on children developing conceptual and procedural knowledge, as well as procedural flexibility. However, research on the developmental relations between these different types of knowledge has yielded unclear results, in part because little attention has been paid to the validity of the measures or to the effects of…

In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

The 2012 U.S. presidential election is the perfect opportunity to present a timely civics lesson on how a U.S. president is elected. More important, it offers opportunities for students to reason mathematically about election issues--for example, about how much time and resources the candidates should invest in particular states. The results of…

Many studies argue that dynamic features of the artefact Cabri may function as instruments of semiotic mediation. Our study is situated in this perspective and aims to observe the impact of the use of the technological artefact Cabri in a teaching experiment that introduces the notion of a trigonometry function, through the articulation of the…

The purpose of this study was to explore teaching styles and how frequently teachers with a variety of teaching styles incorporate multiple representations, such as manipulatives, drawings, counters, etc., in the middle school mathematics classroom. Through this explanatory mixed methods study it was possible to collect the quantitative data in…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

This paper focuses on meaning making as a process that can transform English learners' participation in mathematics. Using selected video transcripts from a one year long project in a fourth grade bilingual classroom, the paper documents the development of participation along a continuum of meaning making, from preparing students to transform…

This paper reports on initial data from teachers at an Australian Year 9-12 secondary school which is attempting to implement a project-based learning model across the entire curriculum. The eight teachers had diverse prior teaching experiences, including work in primary schools, special education, Year 7-10 secondary schools, and technical and…

This paper reports on the different gesture types employed by twenty-three Year 10 students as they endeavoured to explain their understanding of rate of change associated with the functions resulting from two different computer simulations. These gestures also have application to revealing students' understanding of functions. However,…

Portfolios have been regarded as a means of personal self-expression. This study reports on student real-life experiences with portfolio assessment. The focus group comprised 150 freshmen (100 females) from a small campus of a tertiary educational institution. For two semesters (approximately 30 weeks), students engaged in numerous activities…