In math classes, teachers often focus instruction on the formulas and processes needed to solve different types of problems, but neglect to teach the concepts on which these tools are based. In this article, the author argues that before they can do this, teachers themselves need to understand "understanding math." Teaching mathematics with…

All teachers are aware of the wide range of abilities that exist within most standard Australian primary school classrooms. Many of these schools implement structures such as ability grouping and/or streaming to help meet the needs of this diverse group of learners; but does ability grouping meet these needs? The number of studies that have looked…

About fifteen years ago, the author discovered an interesting activity in some materials that Malcolm Swan from the Shell Centre (University of Nottingham, UK) had developed for the English National Curriculum Council in 1991. The activity, one which has been used by several presenters in professional development workshops in Australia in recent…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

It is believed by some that most tests are multidimensional, meaning that they measure more than one underlying construct. The primary objective of this study is to illustrate how variations in the secondary ability distribution affect the statistical detection of dimensionality and to demonstrate the difference between substantive and statistical…

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical…

In this article, the author discusses how he incorporates children's literature into the exploration and investigation of various math topics. After doing some activities, he has found that integrating different mathematical topics after discussing books can help children make the connection to mathematics in their daily lives.

Some "drag-to-fit" solutions given by student teachers to three geometric construction problems in a dynamic geometry environment (DGE) are analysed. The responses of a group of experienced mathematics teachers to the question whether or not such solutions can be considered "legitimate" are then discussed. This raises fundamental questions…

Research is described concerning the effectiveness of inquiry-based laboratory environments created in US mathematics/science education programme courses. Laboratory projects were conducted using a framework that allowed pre-service teachers to explore, analyse, and communicate "investigable" realms of physical phenomena. Goals were for…

The aim of this longitudinal study was to investigate cross-lagged relationships between mathematical performance and reading comprehension during the first and second years of primary school. 114 Finnish-speaking children were examined six times on mathematics and reading comprehension during Years 1 and 2. At the beginning of Year 1, they were…

In this study we explored the effectiveness of individualizing instruction using a system that diagnosed students' knowledge gaps in pre-algebra and provided individualized instruction and practice. One hundred middle school students participated, and received either no instruction or individualized computer-based instruction. Diagnosis of…

A correlated science lesson is characterized as an integrated science lesson in that it may incorporate traditionally integrated activities and use math as a tool. However, a correlated math-science lesson also: (1) has the pertinent math and science objectives aligned with state standards; and (2) teaches parallel science and math ideas equally.…

This paper focuses on blended learning in mathematics I module in elementary calculus, at a University of Technology. A computer laboratory was used to create a learning environment that promoted interactive learning together with traditional teaching. The interactive learning was performed using projects to optimize the discovery and error…

This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

This article describes a joint effort between a mathematics educator and a middle school art teacher who wanted their students to experience first hand how construction works in the real world. It starts with students designing and building scale models for a large inflatable item in which they display their art and extends to building the…