Academic journal article Australian Primary Mathematics Classroom

Kitchen Gardens: Contexts for Developing Proportional Reasoning

Academic journal article Australian Primary Mathematics Classroom

Kitchen Gardens: Contexts for Developing Proportional Reasoning

Article excerpt

Introduction

Across Australia, many schools have kitchen gardens. Some of these schools have been developed through the Stephanie Alexander Foundation while others, including the school described here, have chosen to create their own kitchen garden with the help of the school community. Lyon and Bragg (2011) described ways to integrate mathematics with other curriculum areas through the creation of a kitchen garden. This article focuses on activities used to engage students in a variety of mathematical situations involving proportional reasoning through a series of lessons in their school's kitchen garden. It also identifies the proportional reasoning problem types that arose through the activities.

Proportional reasoning is a key component of numeracy. It involves the ability to understand and use multiplicative relationships in situations of comparison (Behr, Harel, Post & Lesh, 1992). The importance of proportional reasoning in primary school children's mathematics education has long been recognised. Lesh, Post and Behr (1988) described it as the capstone of elementary school arithmetic and the cornerstone of the mathematics learning that follows. Being such a pivotal aspect of numeracy, the development of proportional reasoning skills is critical if children are to be well placed to succeed in mathematics beyond primary and indeed middle schooling. Failure to develop proportional reasoning ability by adolescence can also preclude students from participation in subjects beyond the middle years, including science, mathematics, and technology (Lanius & Williams, 2003).

Generally speaking, situations of proportion require some application of multiplicative or relative thinking. A variety of proportional reasoning problem types are identified in the literature. For example, Lamon (1993) identified the following types of proportion problems:

* rate problems (involving both commonly used rates, such as speed, and rate situations in which the relationship between quantities is defined within the question);

* part--part-whole (e.g., ratio problems in which two complementary parts are compared with each other or the whole); and

* stretchers and shrinkers (growth or scale problems).

In addition, according to Lesh et al. (1988), certain problem types are often neglected in textbooks and classroom instruction. These include problems that require transformation of representational types or modes. While providing students with opportunities to engage in a variety of proportional reasoning situations is important, it is equally important to expose students to situations that are non-proportional in nature (Bright, Joyner & Wallis, 2003) because students often rely on proportional reasoning in circumstances that do not require it--e.g., constant, linear and additive situations (Van Dooren, De Bock, Hessels, Janssens & Verschaffel, 2005).

Proportional reasoning is very often used in real-life mathematics; for example, comparing costs at the supermarket or estimating the travel time required to reach a destination on time. In schools, there exist many opportunities to develop students' proportional reasoning skills in authentic contexts. The focus of this article is the rich context of the kitchen garden.

Enhancing proportional reasoning in context

The authors are leading a project involving 28 schools in Queensland and South Australia. The project aims to enhance proportional reasoning education through a series of workshops with teachers within six school clusters over a period of two years. Each school cluster includes three to five primary schools with at least one of their local secondary schools. The research team works within clusters and individual schools to support teachers to develop activities that promote proportional reasoning across subject areas and within contexts relevant to each school or cluster. The schools in one of the participating clusters have a long history of collaboration and several of them have developed kitchen garden programs, either through the Stephanie Alexander Foundation or independently. …

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