A string number line lesson sequence to promote students' relative thinking and understanding of scale, key elements of proportional reasoning

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Journal Article
Australian Primary Mathematics Classroom, 2018, 23 (1), pp. 13 - 18 (6)
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Situations involving scale, rate, ratio, and proportion all require proportional reasoning (Ben-Chaim, Keret, & Ilany, 2007). Proportional reasoners can use multiplicative and relative thinking (in contrast to additive or absolute thinking), have a sense of co-variation, and can recognise situations of comparison requiring multiplicative reasoning (Fielding-Wells, Dole, & Makar, 2014). Not only is proportional reasoning essential for students to succeed in many mathematical contexts, it is also necessary in many other subject areas including art, geography, history, and science (Akatugba & Wallace, 2009). Proportional reasoning is also recognised as one of the most commonly used forms of mental computation in our daily lives and yet a large number of adults cannot reason proportionally (Lamon, 2012). Despite its recognition as a key element of numeracy, research shows that more focus is needed on helping students and teachers to develop the various aspects of proportional reasoning and the foundational concepts that underpin it (Kastberg, D’Ambrosio, & Lynch-Davis, 2012). This article describes research on using a string number line intervention to support children’s development of relative thinking and understanding of linear scale. The intervention proved effective for developing students’ understanding of concepts related to scale and relative thinking as well as their mathematical language. It also proved useful for teachers as a means of assessing and monitoring their students’ understanding and progress.
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