Abstract
In this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10. Our aim is to reveal what is to be learnt and how it might be learnt by means of discerning particular aspects of numbers. The Variation theory of learning informs the analysis of 2184 observations of 4- to 7-year-olds solving arithmetic tasks, placing the focus on what constitutes the ways of experiencing numbers that were observed among these children. The aspects found to be necessary to discern in order to develop powerful arithmetic skills were as follows: modes of number representations, ordinality, cardinality, and part-whole relation (the latter has four subcategories: differentiating parts and whole, decomposing numbers, commutativity, and inverse relationship between addition and subtraction). In the paper, we discuss particularly how the discernment of the aspects opens up for more powerful ways of perceiving numbers. Our way of describing arithmetic skills, in terms of discerned aspects of numbers, makes it possible to explain why children cannot use certain strategies and how they learn to solve tasks they could not previously solve, which has significant implications for the teaching of elementary arithmetic.
Highlights
In this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10
We present a way of describing variation in learning, and apply this to the study of young children’s learning of elementary arithmetic within the number range 1–10
Our approach may contribute to the field of research by taking a pedagogical perspective on the learning of arithmetic skills founded in Variation theory of learning, in our quest to describe observed variations in learning, and in particular to conceptualise how the learning of numbers’ meaning proceed in terms of what is to be learnt and how this might be learnt
Summary
Our aim is to reveal what is to be learnt as well as how it might be learnt To fulfil this aim, we observed 103 children’s attempts to solve eight arithmetic tasks on three occasions and analysed what constitutes their ways of experiencing numbers. Earlier research on arithmetic skills among young students has presented thorough observations of what children do when encountering arithmetic tasks, resulting in descriptions of trajectories in the development of arithmetic skills (e.g., Fuson, 1982, 1992) Other scholars, such as Steffe (2004) have made efforts to describe the processes of constructing schemes that open the ability to solve tasks that are more advanced. It is our goal with the present study to further explore how these positive outcomes can be explained, on a theoretical basis
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