Journal directory listing - Volume 58 (2013) - Journal of Research in Education Sciences【58(1)】March

Application of Generalization Schemas to Solve Figural Pattern Problems on Sixth Graders Author: Chia-Huang Chen(Department of Mathematics Education, National Taichung University of Education)

Vol.&No.:Vol. 58, No. 1
Date:March 2013
Pages:59-90
DOI:10.3966/2073753X2013035801003

Abstract:

The purpose of this study is to enhance our understanding of the generalization process by examining the generalization schemas of figural pattern problems and capturing the cognitive structure of generalization, and by examining the ways in which to improve the generalization schema transformation to construct models for solving generalization problems and promote the effects of algebraic thinking. Three Grade six students in a teaching activity setting completed 32 tasks related to figural pattern problems, and the worksheets and interviews data were collected. The data were analyzed qualitatively, and three stages were considered: (1) Students used both the “relationship of whole figure” and “elements of part structure” concept schemas for problem-solving planning in the abductive stage; (2) both schemas were applied during the connection stage on the “figural characterizes contrast with figural terms” and “objects count contrast with figural terms” to combine the relationship between figures and terms; (3) students used both the “unit combined” and “figural structure” concept schemas to solve the figural pattern problems during the generalized stage. Students used “addition,” “multiplication,” and “practical” operation schemas to integrate the rules and expressions for resolving the figural pattern problems. The change and transformation of the schemas during generalization were influenced by student knowledge, experiences, and characteristics of the figural structure. Researchers constructed both the “utilize the figural structure” and “utilize the number alley” models for problem-solving generalization learning based on students’ generalization schema operation and development. The findings such as the models of problem-solving generalization support teachers’ instruction, engaging students in algebraic thinking and implementing algebraic teaching with figural pattern problem solving.

Keywords:generalization, algebraic thinking, schema, figural pattern problem

《Full Text》 檔名

References:
  1. 吳昭容、徐千惠(2010)。兒童如何在重複中找到規律?重複樣式的程序性與概念性知識。教育科學研究期刊,55(1),1-25。【Wu, C.-J., & Hsu, C.-H. (2010). How do children find patterns in reiteration? Procedural knowledge and conceptual knowledge in identifying repeating patterns. Journal of Research in Education Sciences, 55(1), 1-25.】
  2. 馬秀蘭(2008)。國小高年級學童解樣式題之代數思考:以線性圖形樣式題為例。科學教育研究與發展季刊,50,35-52。【Ma, H.-.L. (2008). The algebraic thinking of upper-grade students to solve linear patterns with pictorial contents. Research and Development in Science Education Quarterly, 50, 35-52.】
  3. 教育部(2003)。國民中小學九年一貫課程綱要:數學學習領域。臺北市:作者。【Ministry of Education. (2003). Grade 1-9 curriculum guidelines: Learning areas of mathematics. Taipei, Taiwan: Author.】
  4. 陳嘉皇(2006)。國小五年級學童代數推理策略應用之研究:以「圖卡覆蓋」解題情境歸納算式關係為例。屏東教育大學學報,25,381-412。【Chen, C.-H. (2006). A study of apply strategies on algebraic reasoning: An example from cover and arrange grids to generalize mathematical equation. Journal of National Pingtung University of Education, 25, 381-412.】
  5. 陳嘉皇(2007)。學童「圖卡覆蓋」代數推理歷程之研究-以三個個案為例。國民教育研究學報,19,79-107。【Chen, C.-H. (2007). A study on the development process analysis of algebraic reasoning: Three examples from student’s cardboard covering. Journal of Research on Elementary and Secondary Education, 19, 79-107.】
» More
APA FormatChen, C.-H. (2013). Application of Generalization Schemas to Solve Figural Pattern Problems on Sixth Graders. Journal of Research in Education Sciences, 58(1), 59-90. doi:10.3966/2073753X2013035801003