Abstract The objective of this study was to identify cognitive apprehensions used by fifth- and sixth-grade students (10–12-year-olds) when answering far generalization questions in two problems of visual pattern generalization. A total of 81 students solved two linear generalizing problems, presented in two different configurations, in a succession of figures (square tables or trapezoid tables). The results showed that students used different types of cognitive apprehensions to solve problems and that these apprehensions sometimes changed according to the configuration of the sequence of figures. This finding indicates that configurations could determine apprehensions used by students, which in some cases led to the emergence of algebraic thinking. In addition, difficulties in modifying apprehension and a lack of coordination between spatial and numerical structures could explain some students’ difficulties in far generalization.

中文翻译：

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视觉模式泛化问题中的认知理解/视觉模式泛化问题中的认知理解

摘要这项研究的目的是确定在回答视觉模式泛化的两个问题中的远泛化问题时，五年级和六年级学生（10至12岁）所使用的认知理解。共有81名学生用一连串的数字（方桌或梯形桌）解决了两种线性概化问题，这些问题以两种不同的配置呈现。结果表明，学生使用不同类型的认知理解来解决问题，并且这些理解有时会根据数字序列的配置而变化。这一发现表明，构型可以决定学生所使用的担心，这在某些情况下导致代数思维的出现。此外，