Institut de Psychologie, Batiment Géopolis, University of Lausanne, Lausanne, Switzerland.
University of Lorraine (2LPN, EA 7489), Nancy Cedex, France.
Br J Educ Psychol. 2023 Sep;93(3):727-741. doi: 10.1111/bjep.12588. Epub 2023 Feb 5.
In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations.
In order to address this question, our goal was to determine the predictive power of previously taught operations on newly taught ones above general cognitive skills and basic numerical skills.
More than one hundred children in each school level from Grades 2 to 5 from various socio-cultural environments (N = 435, 229 girls) were tested.
Children were assessed on their abilities to solve the four basic arithmetic operations. They were also tested on their general cognitive abilities, including working memory, executive functions (i.e., inhibition and flexibility), visual attention and language. Finally, their basic numerical skills were measured through a matching task between symbolic and nonsymbolic numerosity representations. Additions and subtractions were presented to children from Grade 2, multiplications from Grade 3 and divisions from Grade 4.
We show that addition predicts subtraction and multiplication performance in all grades. Moreover, multiplication predicts division performance in both Grades 4 and 5. Finally, addition predicts division in Grade 4 but not in Grade 5 and subtraction and division are not related whatever the school grade. These results are examined considering the existing literature, and their implications in terms of instruction are discussed.
近年来，许多国家儿童的数学技能都在以惊人的速度下降，对于这种令人担忧的情况，有一种解释是儿童在建立算术运算之间的关系方面存在困难。
为了解决这个问题，我们的目标是确定先前教授的运算对新教授的运算的预测能力，而不仅仅是一般认知技能和基本数值技能。
来自不同社会文化环境的各个年级（2 年级至 5 年级）的一百多名儿童（N=435，229 名女孩）参加了测试。
儿童被评估解决四个基本算术运算的能力。他们还接受了一般认知能力的测试，包括工作记忆、执行功能（即抑制和灵活性）、视觉注意力和语言。最后，通过符号和非符号数量表示之间的匹配任务来测量他们的基本数值技能。从 2 年级开始向儿童呈现加法和减法，从 3 年级开始呈现乘法，从 4 年级开始呈现除法。
我们表明，在所有年级中，加法都可以预测减法和乘法的表现。此外，乘法在 4 年级和 5 年级都可以预测除法的表现。最后，加法在 4 年级可以预测除法，但在 5 年级则不能，而减法和除法无论在哪个年级都没有关系。我们根据现有文献来检查这些结果，并讨论了它们在教学方面的意义。
