Fifth Graders’ Algebraic Thinking and Its Developmental Process under the Context of Mathematical Modeling Activity

• Main Authors: Kuan-Jou Chen, 陳冠州
• Other Authors: Hsiao-Lin Tuan
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/85805989927523323157

博士 === 國立彰化師範大學 === 科學教育研究所 === 97 === This doctoral dissertation aims at investigating the fifth graders’ algebraic thinking and its developmental process through Tall’s E-S-F (Embodiment, Symbolism, and Formalism) cognitive model under the context of mathematical modeling activity. The research subjects are thirty-two fifth graders. The implementation of modeling activity includes article reading, preparation activities, problem description, and strategy sharing, which allow children to discuss and solve visualization pattern and textual algebraic problems in the modeling-eliciting, modeling-exploring, and modeling- adapting stages. The whole modeling activity consists of eight units which have been implemented for a semester. Including the video recording of all the classroom teaching, the other collected data are worksheets, task-reports, students’ journals, and classroom observation records. These qualitative data are triangulated with the video analysis of the classroom teaching records. It can be observed from children’s performances in solving algebraic problems, they can not only use words or symbols to represent algebraic problems and solve the algebraic equations by representing the unknowns with symbols, but also successfully propose a model and solve the problem by detecting the critical elements in the problem context and discovering the rules and relationships within the basic patterns in the modeling activity. The results of this study show that children’s performances in solving algebraic problems can be divided into three stages: comprehending the components of basic patterns to generalized arithmetic, transition from generalized arithmetic to generalized algebra, and from generalized algebra to appreciation of the equivalence of algebraic structures. From the viewpoint of the E-S-F cognitive model, the fifth graders’ algebraic thinking seems to be active in the embodiment phrase through article reading, oral communication and manipulation activity; then, it might be shifted from embodiment phrase to symbolism phrase by way of mental compression of pictures, words, arithmetic and symbols. In addition, under the basis of the former two phrases, it might reach the formal phrase through visuo-spatial, arithmetic, algebraic modes. According to these results, the researcher proposes a hypothetical development trajectory of children’s algebraic thinking from Tall’s E-S-F viewpoint. Finally, some relevant implications and suggestions of instruction, curriculum, leaning and research methodology are addressed.