As part of the project titled "Hands-On Heads-On: The Effective Use of Manipulatives Both Virtual and Physical" being undertaken at Edith Cowan University, there was an investigation into the use of virtual manipulatives and the interactive whiteboard (IWB). Virtual manipulatives may be defined as a virtual representation of a physical…

In the middle years of primary schooling, the teaching of common fractions frequently involves written activities that use abstract representations of numbers, symbols, and images. Many students, however, still need the benefit of concrete materials and sensory motor experiences to enhance their understanding of the concepts associated with common…

This article tells the story of one student who chooses her personal interest in pigeons and their lifestyle to demonstrate her understanding of measurement concepts. The student's work is used to consider the possibilities for assessment afforded by tasks designed within reform-based curricula. Anita (pseudonym) was a Grade 6 student who was part…

When asked to calculate the area of a particular shape, one student responded by asking, "Is that the outside or the inside?" while another student replied, "I think it's the one where you put a little 2 next to it." Both of these responses indicate a lack of conceptual understanding of area and reinforce the research findings…

It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on…

Young students often struggle with abstract concepts in mathematics, causing primary teachers to continue to search for ways to help teach such concepts. "Principles and Standards for School Mathematics" (NCTM, 2000) recommends using concrete models and physical materials before moving on to more abstract ideas. However, some children…

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and…

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…

Citing that the concept of fractions is not a single idea, and that students may be proficient in one area of fractions while also holding contradictory beliefs, the writer reviews some common problems areas in teaching and learning about fractions, and maintains that the fraction concept does not respond to simple remediation methods. The author…

Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990)…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

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…

In 2001, with funding of $7 million, the Australian Government implemented the "Numeracy Research and Development Initiative"--one of several initiatives introduced by the Australian Government to support literacy and numeracy improvement. Other initiatives included the "National Indigenous English Literacy and Numeracy…

Although some bright students in primary school are able to organise numerical data into classes, most attend to the characteristics of individuals rather than the group, and "see the trees rather than the forest". How can teachers in upper primary and early high school teach students to organise large sets of data with widely varying…