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.

在本文中，我们提出了一种描述幼儿在1到10范围内的初等算术学习中的变化的方法。我们的目的是通过辨别数字的特定方面，揭示要学习的知识以及如何学习。学习的变异理论为4到7岁儿童解决算术任务的2184个观察结果提供了分析依据，重点放在构成这些孩子中观察到的数字的方式的构成上。为了发展强大的算术技能，发现需要辨别的方面如下：数字表示模式，序数，基数和部分整体关系（后者有四个子类别：区分部分和整体，分解数字，可交换性，以及加减法之间的反比关系）。在本文中，我们特别讨论如何识别方面以提供更强大的数字感知方式。我们用数字的辨别方面来描述算术技能的方式，可以解释为什么孩子不能使用某些策略，以及他们如何学习解决以前无法解决的任务，这对基础算术的教学具有重要意义。