2015．第43卷第1期（Vol. 43 No. 1）．pp. 103–127
Study of Gestures, Verbal Presentation and Algebraic Thinking
陳嘉皇、梁淑坤（Chia-Huang CHEN & Shuk-Kwan S. LEUNG）
This study investigated how students generalize graphic patterns, aiming to understand how they utilize words and gestures at each phase of generalization, how they identify links between problems and recognize the equivalence of generalized equations, and how their understanding of algebra evolves. We conducted a case study of two sixth-grade students from a public elementary school in southern Taiwan, using video recordings, interviews and writing to collect data, which was then analyzed qualitatively. The study found that: (a) In the concept phase, students form rules by using visual graphics to compare changes in objects and item numbers, in accordance with the common elements of iconic, deictic and metaphoric gestures and perceptions. (b) In the linking phase, most students use deictic and metaphoric gestures and semantics, along with numbers and equations, to identify relationships in the problem structure. (c) Students employ strategies such as verifying metaphoric and computational outcomes, and comparing equation structure and object relationships, to comprehend the equivalence of different equations. (d) Students continue to develop their understanding of algebraic concepts based on item numbers, numbering of symbols, and the unknowns of relationship diagrams. Recommendations on diverse permeation and the relationship between development of algebraic concepts and symbol indication were provided. They can serve as references in advancing algebraic thinking.
Keywords: generalization; algebraic thinking; gesture; graphic pattern