Experts organize and generalize knowledge in different ways than novices, and conceptual development is often characterized by a surface-to-structure shift in attention and categorization. We explored a surface-to-structure shift in rational number arithmetic. Children and adults sorted arithmetic equations with fractions and whole numbers in three separate studies. In all studies, children were more likely to sort by number type, conceptualizing fraction problems as distinct from whole number problems. In two studies, adults were more likely to sort equations by operation, suggesting integrated rational number categories. Across studies, some older children and adults sorted into highly differentiated categories. Evidence for a surface-to-structure shift in arithmetic categories suggests changes in knowledge organization in addition to content with increasing expertise.

专家以与新手不同的方式组织和概括知识，概念发展的特点通常是注意力和分类从表面到结构的转变。我们探索了有理数算术中从表面到结构的转变。在三项独立的研究中，儿童和成人用分数和整数对算术方程进行排序。在所有研究中，儿童更有可能按数字类型进行排序，将分数问题概念化为与整数问题不同的概念。在两项研究中，成年人更有可能通过运算对方程进行排序，这表明综合有理数类别。在研究中，一些年龄较大的儿童和成人被分为高度分化的类别。算术类别从表面到结构转变的证据表明，除了专业知识不断增加的内容之外，知识组织也发生了变化。