國小三年級學童代數推理教學與解題表現研究

The Algebraic Reasoning Teaching and Problem Solving Performances of Third Graders

10.7060/KNUJST.200712.0125

陳嘉皇(Jia-Huang Chen)

課程設計 ； 代數推理 ； 解題 ； curriculum design ； algebraic reasoning ； problem solving

高雄師大學報：自然科學與科技類

23期（2007 / 12 / 01）

125 - 150

繁體中文

本研究旨在了解國小三年級學童代數推理解題表現情形及教學實驗效果，樣本為公立國小三年級學童30名。研究分三階段進行，首先，參考文獻資料和《九年一貫課程綱要》能力指標，先行設計代數推理解題評量工具，檢測學童解題表現，並透過觀察訪談，瞭解學童在代數推理歷程產生之困難、錯誤觀念或欠缺的能力技巧，做為第二階段課程活動設計及教學的依據，俟教學完後，再進行解題後測，並伴隨觀察訪談蒐集資料，藉以比較教學前、後學童代數推理解題表現情形。根據結果發現，大多數小學三年級學童在代數推理解題前測的表現不盡理想，對代數推理各項活動產生困難，透過課程設計與教學實施後，學童能表現出更為優異的推理解題能力。 從學童作業結果分析，發現本研究設計之課程，可以誘發學生根據其學習經驗與認知發展，進行代數推理解題，符應所謂的從描述進步到符號化的學習歷程。最後，根據研究結果，作者提出相關建議，以作為未來代數融入國小數學教學的參考。

The purpose of this study is to investigate the third graders' performances on algebraic reasoning and the effects on the curriculum design and teaching effects of algebraic reasoning. The subjects were 30 students from a southern Taiwan elementary school. For the purpose, there are three stages on trails for the students, including a pilot test, and then four periods of teaching, and after three months, the students took the post test. However, to understand whether the process of algebraic reasoning of students is necessary, the researcher observed how students used strategies to their thinking patterns. After that, the researcher interviewed students. Researcher summarized some main findings and offered some suggestions of learning algebra for young children and teachers.

1. Blanton M. L.,Kaput, J.,R. Nemirovsky.,A. S. Rosebery.,J. Solomon.,B. Warren (Eds.)(2005).Everyday matters in science and mathematics: Studies of complex classroom events.Mahwah, NJ:Lawrence Erlbaum Associates.
2. Bodanskii, F.,V. Davydov (Ed.)(1991).Soviet studies in mathematics education. Psychological abilities of primary school children in learning mathematics.Reston, VA:The National Council of Teachers of Mathematics.
3. Edwards, E. L. Jr.(Ed.)(1990).Algebra for everyone.Reston, VA:National Council of Teachers of Mathematics.
4. Kaput, J.,E. Fennema,T. Romberg (Eds.)(1999).Mathematics classrooms that promote understanding.Mahwah, NJ:Lawrence Erlbaum Associates.
5. National Council of Teachers of Mathematics(2000).Principles and standards for school mathematics.Reston, VA:Author.
6. Schliemann, A. D.,Carraher, D. W. Brizuela, B. M.(2007).Bringing out the algebraic character of arithmetic: From children`s ideas to classroom practice.Mahwah, NJ:Lawrence Erlbaum Associates.
7. Silver, E. A.,Kilpatrick, J.(1987).Paper from Dialogue on Alternative Modes of Assessment for the Future.Mathematical Science Education Board.
8. Usiskin, Z.,B. Moses(Ed.)(1999).Algebraic thinking grades K-12.Reston, Virginia:National Council of Teachers of Mathematics.
9. 呂玉琴(1989)。在國小實施代數教學的可能性研究。台北師院學報，2，263-283。
10. 教育部(2003)。國民教育九年一貫課程綱要：數學學習領域。台北教育部。
11. 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。
12. 陳維民(1998)。碩士論文(碩士論文)。高雄市，國立高雄師範大學數學系。
13. 黃寶彰(2002)。碩士論文(碩士論文)。屏東市，國立屏東師範學院數理教育研究所。

1. 陳佩秀(2018)。資訊科技與提問教學策略對數學學習困難學童在數量關係單元解題表現之成效。臺北市立大學學報：教育類，49(2)，53-78。
2. 孫慧茹、洪碧霞(2013)。國民小學代數動態評量的發展與應用。數位學習科技期刊，5(2)，59-82。
3. (2012)。國小數學教科書研究之回顧與前瞻。教育研究月刊，217，74-87。
4. (2019)。由認知負荷觀點探討國中代數試題難度。教育研究學報，53(1)，45-70。