Starting points: understanding children's pre-instructional intuitions about function tables

被引:3
作者
Xolocotzin, Ulises [1 ]
Medrano-Moya, Ana M. [1 ]
Rojano, Teresa [1 ]
机构
[1] Natl Polytech Inst, Ctr Res & Adv Studies, Math Educ Dept, Av Inst Politecn Nacl 2508, Mexico City 07360, DF, Mexico
来源
ZDM-MATHEMATICS EDUCATION | 2022年 / 54卷 / 06期
关键词
Early algebra; Functional thinking; Intuitions; Conceptual change; Generalisation; Symbolic notation; EARLY ALGEBRA; THINKING; VARIABLES;
D O I
10.1007/s11858-022-01424-9
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed methods. The sample included 20 grade 3 students and 24 grade 5 students. First, we assessed children's arithmetic skills and intuitive responses to generalisation tasks involving variation tables. The quantitative analysis showed that students' arithmetic skills correlated with functional aspects such as the following: identifying, and expressing function rules with words but not with the symbolic expression of function rules. The qualitative analysis revealed that students constructed framework theories that generated different intuitive conceptions of the algebraic ideas involved in noticing and expressing generalisation. Students' conflicts were concentrated in areas that determine key differences between arithmetic and algebra, such as generalisation, indeterminate quantities, and variable notation. We discuss how these results contribute to explaining the construction of algebra concepts.
引用
收藏
页码:1363 / 1376
页数:14
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