The Developmental Progression of Early Algebraic Thinking of Elementary School Students

• Published in: Journal of intelligence Vol. 11; no. 12; p. 222
• Main Authors: Sun, Siyu, Sun, Dandan, Xu, Tianshu
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 01.12.2023
• Subjects: Algebra; algebraic thinking; Asian students; Child development; Cognition & reasoning; Cognitive development; Curricula; early algebra; elementary school student; Elementary school students; functional thinking; generalized arithmetic; latent class analysis; Learning; Mathematics education; Problem solving; Surveys; Teaching; New York; China; functional thinking; elementary school student; generalized arithmetic; latent class analysis; algebraic thinking; early algebra; quantitative reasoning
• ISSN: 2079-3200; 2079-3200
• DOI: 10.3390/jintelligence11120222

Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist teachers and curriculum developers in implementing instruction that aligns with students' cognitive development. This study adopted a cross-sectional survey approach, involving 526 students from grades three to five in Shanghai, who were tested using a 12-item assessment that measured three aspects: "generalized arithmetic", "functional thinking", and "quantitative reasoning". Latent class analysis was used to analyze students' response strategies, and, in conjunction with individual interviews, this study identified potential developmental pathways in students' early algebraic thinking, progressing from "arithmetic thinking" to "concrete algebraic thinking", "generalized algebraic thinking", and finally to "symbolic algebraic thinking". As thinking levels advanced, significant differences in students' response strategies emerged, with notable improvements in "generalization abilities" and "symbolization abilities". This study suggests that educational practices should encompass content in elementary arithmetic curricula that fosters generalization abilities. Additionally, providing students with opportunities for diverse representations can effectively stimulate the development of early algebraic thinking.