Using a Concept Cartoon to Gain Insight into Children's Calculation Strategies: Matthew Sexton, Ann Gervasoni and Robyn Brandenburg Use a Concept Cartoon as an Effective Way to Encourage Students to Communicate Their Preferred Strategies for Solving Addition Calculations

By Sexton, Matthew; Gervasoni, Ann et al. | Australian Primary Mathematics Classroom, Winter 2009 | Go to article overview

Using a Concept Cartoon to Gain Insight into Children's Calculation Strategies: Matthew Sexton, Ann Gervasoni and Robyn Brandenburg Use a Concept Cartoon as an Effective Way to Encourage Students to Communicate Their Preferred Strategies for Solving Addition Calculations


Sexton, Matthew, Gervasoni, Ann, Brandenburg, Robyn, Australian Primary Mathematics Classroom


Introduction

Life in the twenty-first century requires an unprecedented level of mathematical knowledge, visualisation and skill for full participation in community life, and for access to opportunities in education and employment. It is therefore concerning that some Australian students under-perform in mathematics despite consistent attempts to improve mathematics learning and teaching. For example, Gervasoni, Hadden and Turkenburg (2007) found that 30% of students beginning their final year of primary school in regional Victoria have underdeveloped arithmetic reasoning strategies, a key indicator of mathematical competence. This highlights the importance of children developing reasoning strategies for calculating as opposed to using rote procedures (algorithms) or counting-based strategies.

Curriculum reform aimed at improving students' reasoning strategies for calculating was the focus of a research project in which we participated along with two school communities in regional Victoria. The research involved trialling a curriculum in which the teaching of algorithms for Grade 3 and Grade 4 students was withheld in favour of emphasising mental computation, with students' reasoning strategies recorded on empty number lines to enable monitoring of strategy choice (Gervasoni, Brandenburg, Turkenburg, & Hadden, 2009). Another focus of the research was assisting teachers to gain insight into how their students approached calculations.

This article explores one aspect of the research in which concept cartoons (Sexton, 2008) were introduced as an innovative way for gaining insight into children's strategies for addition calculations in a situation that begs for the use of mental strategies (24+99=n). We examine some of the responses of the 101 Grade 3 and Grade 4 students who participated in the research to find out about their calculation strategies, and then consider the implications for subsequent learning and teaching.

Concept cartoons

A concept cartoon is a learning and teaching tool used primarily in science education to explore scientific concepts. However, we believe they also have great potential in mathematics education. The cartoons share some common traits with those used in comic strips, but rather than being designed to arouse hilarity, they aim to present students with the opportunity to interpret and to understand concepts (Naylor & Keogh, 1999).

Concept cartoons involve the pictorial representation of characters in settings familiar to students along with the use of written language or speech bubbles (Naylor & Keogh, 1999). The familiar settings and characters give relevance to the ideas that are being presented. It is important that alternative conceptions, statements or questions pertaining to a central idea are presented within the cartoon (Kabapinar, 2005; Naylor & Keogh, 1999). In most cases, alternative viewpoints are presented through the use of a group of characters engaging in a dialogue through the use of speech bubbles with minimal use of written language. Due to the characters' dialogue, students have the freedom to make judgements that agree or disagree with the views expressed by the characters without feeling threatened by needing to express their own opinions publicly (Kinchin, 2004). Concept cartoons are primarily intended to act as a teaching and learning tool but they can also be used to assess student cognition (Naylor & Keogh, 1999). In some cases they have been used to assess the affective domain (Kinchin, 2004; Sexton, 2008). Indeed, Sexton (2008) explored the use of concept cartoons in mathematics and found that they were a successful tool for gaining insight into children's and teachers' perceptions of effective mathematics learning environments. In June 2008 the students were shown the Concept Cartoon in Figure 1. The cartoon depicts four characters and dialogue that explains each character's strategy for solving 24 + 99 = n. …

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Using a Concept Cartoon to Gain Insight into Children's Calculation Strategies: Matthew Sexton, Ann Gervasoni and Robyn Brandenburg Use a Concept Cartoon as an Effective Way to Encourage Students to Communicate Their Preferred Strategies for Solving Addition Calculations
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