ABSTRACT

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1–4) and a group with mathematical difficulties (study 2; N = 61, Grades 4–6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.

摘要

数感和工作记忆有助于整个小学的数学发展。然而，目前还不清楚这些预测因素中的每一个的贡献如何随着发展而变化，以及认知贡献对于有和没有数学困难的儿童是否相同。本文的两项研究旨在阐明这些主题。在横断面设计中，一组发育正常的儿童（研究 1；N = 459，1-4 年级）和一组有数学困难的儿童（研究 2；N = 61，4-6 年级）完成了一组数字感觉和工作记忆测试，以及算术能力的衡量标准。研究 1 的结果表明，数字感在一年级时很重要，而工作记忆在二年级时变得很重要，之后两个预测因子的预测值都下降了。从一年级开始，数感和工作记忆相互独立地支持数学发展。对任务需求的分析表明，通常发育中的儿童依赖于对早期发展中数量与数字关联的理解和可视化。在开发的后期，学生依靠比较更大的数字和工作记忆，直到自动化。有数学困难的孩子在数学运算中不太能够运用数感，因此在算术任务中可能仍然依赖于他们的工作记忆资源。这表明有数学困难的儿童需要帮助，以便从小就使用数学工作记忆，以便能够在以后的发展中自动化数学能力。