認知學徒制在國小數學解題教學成效之研究

A Study of Teaching Mathematical Problem Solving through Cognitive Apprenticeship at the Primary School Level

方吉正(Ji-Jeng Fang) ； 張新仁(Shin-Jen Chang)

《課程與教學》 3卷4期 (2000/10) Pp. 49-72+171

https://doi.org/10.6384/CIQ.200010.0049

摘要

本研究以高雄市楠梓園小六年級學童為對象，以六上「怎樣解題」三個單元為題材，進行二十節課的教學實驗。本研究採準實驗設計中的不等組前後測設計，隨機抽取三個班級分派為「認知學徒制數學解題教學組」、「一般數學解題教學組」、以及「自行練習解題組」於實驗前、實驗後立即、以及實驗後八週，實施自編之「國小數學解題測驗」、「國小數學解題遷移測驗」。研究結果發現：「認知學徒制數學解題教學」在「數學解題表現」具顯著成效，且具遷移與保留效果。教學組別與程度別的交互作用僅顯現於「數學解題表現」之「了解題意」分項。數學程度與各依變項均大致呈現正向關係。

關鍵字

認知學徒制 ； 數學解題 ； 情境學習 ； 情境認知

並列摘要

The major purpose of this study was to explore the effects of cognitive apprenticeship approach while applied to teaching mathematical problem solving at the elementary school level in Taiwan.Three sixth-grade classrooms at Nantze Elementary School in Kaoshiung were randomly assigned to three different treatments in teaching mathematical problem solving: cognitive apprenticeship group, regular group, and control group. These sample students were tested by Mathematical Problem-Solving Test and Mathematical Problem-Solving Transfer Test. The above tests were implemented three times: pre-treatment, immediate post-treatment, and eight weeks after treatments.Results indicate that the cognitive apprenticeship approach can significantly improve students' problem-solving performance on the curriculum-related problems and transfer problems, and these above teaching effects can last eight weeks. Nearly all interactions between treatments and student's, mathematical levels were not significant except students' performance on understanding problems. There were positive relationships between students' mathematical level and all of the dependent variables.

並列關鍵字

cognitive apprenticeship ； mathematical problem solving ； situated learning ； situated cognition.

參考文獻

Collins, A.,Brown, J. S.,Newman, S. E.(1987).Cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics.Educational Resources Information Center.

Collins, A.,Brown, J. S.,Newman, S. E.(1989).Knowing, learning, and instruction: Essays in honor of Robert Glaser.Hillsdale, NJ:Lawrence Erlbaum.

Johnson, S. D.,Fischbach, R. M.(1992).Teaching problem solving and technical mathematics through cognitive apprenticeship at the community college level.Educational Resources Information Center.

Lampert, M.(1986).Knowing, doing, and teaching multiplication.Cognition and Instruction.3(4),305-342.

Palinscar, A. S.,Brown, A. L.(1984).Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities.Cognition and Instruction.1(2),117-175.