Academic journal article Australian Primary Mathematics Classroom

Revisiting Mathematics Manipulative Materials: Paul Swan and Linda Marshall Revisit the Use of Manipulatives. They Look at the Different Types and the Ways in Which They Are Used by Teachers

Academic journal article Australian Primary Mathematics Classroom

Revisiting Mathematics Manipulative Materials: Paul Swan and Linda Marshall Revisit the Use of Manipulatives. They Look at the Different Types and the Ways in Which They Are Used by Teachers

Article excerpt

Introduction

It is over 12 years since APMC published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms (Perry & Howard, 1997). Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative materials. In addition, the introduction of national testing (NAPLAN) in 2008, in which pictures of mathematics manipulative materials are included, but no access to them is given, is likely to impact on how mathematics manipulatives are used. It seems timely then to revisit the use of mathematics manipulative materials in primary and, in Western Australia, designated middle schools.

What is a manipulative?

The issue of defining what is meant by the term "manipulative" continues to be problematic. Perry and Howard used Hynes' definition of manipulatives as "concrete models that incorporate mathematical concepts, appeal to several senses and can be touched and moved around by students" (Hynes, 1986, p. 11). The current authors were concerned that the use of mathematics manipulative materials is often justified on the basis that the students are involved in "hands on" learning. This justification is simply not enough, and so it was decided to create a new definition of a mathematics manipulative material that encompassed the idea that students need to engage with the manipulative and that thinking should be stimulated. Our definition is:

A mathematics manipulative material is an object that can be handled by an individual in a sensory manner during which conscious and unconscious mathematical thinking will be fostered.

Consequently, a mathematics manipulative object has the potential to lead to an awareness and development of concepts and ideas linked with mathematics and they would most likely be purpose designed. We do not consider the above definition all-embracing. After careful consideration, we believe that there are also tools (such as calculators), teaching tools (demonstration models) and teaching aids (e.g., fraction charts); but these are somewhat different from mathematics manipulative materials. Within our definition, structured and unstructured mathematics manipulative materials are recognised. Under both Hynes' and our definitions, virtual manipulatives are not included. We believe it best to delay the use of virtual manipulatives until students have had experience of the "real thing". We have noted in observations of classes where physical and virtual manipulatives are used, younger children experience difficulty understanding two-dimensional representations of three-dimensional objects. It was also noted that when virtual manipulatives are used on an interactive whiteboard, student access is somewhat limited. In many cases the interactive whiteboard is used mainly for demonstration (Mildenhall, Swan, Northcote & Marshall, 2008). This may become less of an issue as handheld technologies such as the i-pad become more available. Initially this is more likely to be the case in secondary and upper primary classes.

This study

Perry and Howard (1997) based their findings on responses from 249 primary teachers in New South Wales. To mirror their investigation, a four-page survey was sent to all primary and designated middle schools in Western Australia. Responses were received from over 820 teachers across 250 schools. That is at least one teacher in each of approximately one-third of all Western Australian schools, responded to the survey. In some schools many more teachers, up to a maximum of 15, responded. The responses were from teachers in large metropolitan primary schools, district high schools (Years K-10), and remote Aboriginal community schools. They encompassed many religious and educational philosophies, from Catholic, Anglican, Lutheran and Islamic colleges to Montessori and alternative schools. …

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