This article reports on a study which investigated first year university engineering students' construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in…

The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…

Patterns are commonly used in middle years mathematics classrooms to teach students about functions and modelling with tables, graphs, and equations. Grade 6 students are expected to, "continue and create sequences involving whole numbers, fractions and decimals," and "describe the rule used to create the sequence." (Australian…

In this article Leicha Bragg introduces an open-ended assessment task that gives students the opportunity to access skills and knowledge from the Measurement and Geometry strand. Students take on the roles of cartographer and map user to "hide, map and seek."

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

The Common Core math standards promote several important differences in how math concepts are taught and should be talked about. These changes will make it easier for younger students to comprehend and adapt to more complex concepts in the later grades. This guide should help elementary teachers make changes and adaptations that are in line the…

The paper introduces an interpretative framework that contains a characterization of "epistemic schemes" (constructs that are used to explain how class agents themselves are able to gain convincement in or promote convincement of mathematical statements) and "epistemic states" (a person's internal states, such as…

Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs' interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler's rules were used in analyzing PSTs' responses to…

In this article, a classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding. The authors note that mathematics vocabulary may be more difficult to learn than other academic vocabulary for several reasons: (1) definitions are filled with technical vocabulary, symbols, and diagrams;…

A sample of third-, fourth-, and fifth-grade student responses to the question "What is a fraction?" were examined to gain an understanding of how children in upper elementary grades make sense of fractions. Rather than measure children's understanding of fractions relative to mathematically conventional part-whole constructions of…

I present an active learning classroom exercise illustrating essential principles of one-way analysis of variance (ANOVA) methods. The exercise is easily conducted by the instructor and is instructive (as well as enjoyable) for the students. This is conducive for demonstrating many theoretical and practical issues related to ANOVA and lends itself…

In this article, we obtain a genetic decomposition of students' progress in developing an understanding of the decimal 0.9 and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in…

The teaching of Probability Theory constitutes a new trend in mathematics education internationally. The purpose of this research project was to explore the degree to which preschoolers understand key concepts of probabilistic thinking, such as sample space, the probability of an event and probability comparisons. At the same time, we evaluated an…

Calculus instruction is an important topic for high school and college teachers alike. A prime target for attention is integration, which, unfortunately, students too often treat as a rote procedure. Understanding the integral better will support students' application of their mathematical knowledge to science, technology, and engineering…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…