應用電腦化類比解題策略輔助國小學生數學學習

The Use of Computerized Analogical Problem Solving Strategy to Facilitate Elementary School Students Learning Mathematics Word Problems

林國賓(Kuo-Pin Lin)

指導教授 ： 吳正己

國立臺灣師範大學/教育學院/資訊教育學系/碩士(2004年)

摘要

摘要

應用電腦化類比解題策略輔助國小學生數學學習

林國賓

本研究嘗試以電腦化類比解題策略輔助國小學生學習數學文字題。研究首先發展應用類比解題策略的數學輔助學習系統，接著由國小學生實際使用以評估其成效。學習系統的內容包括國小六年級的「公因數、公倍數」、「分數的除法」、「以符號代表數」、「等式與數量關係」及「速率」等單元。
學習系統是以類比策略循序漸近的協助學生解題，類比策略的使用依序分為表徵、回想、映對、及應用等階段。「表徵階段」要求學生指出已知數及未知數以確認題意，「回想階段」提示學生以問題表徵（已知數及未知數）為線索回想類似題，「映對一階段」提供學生已做過的類似題題目幫助學生思考解法，「映對二階段」進一步提供欲解問題與類似題問題表徵的比對，最後的「應用階段」則直接給予學生類似題解法。希望學生經由系統逐步的協助後終能解題，並能習得類比解題技巧。
系統實際使用評估是以33位國小六年級學生為對象，學生共使用系統進行六週十二次的解題練習。綜合分析學生解題記錄、學生問卷、教師問卷、與課堂觀察紀錄得到以下結論：（1）系統在提供類似題題目（映對一）階段對學生的學習最有幫助，（2）學生對系統的使用持正面的態度，（3）系統在使用介面、回想策略、及類似題庫建立等方面仍待改善。

關鍵詞：類比解題、數學文字題、電腦輔助學習

關鍵字

類比解題 ； 數學文字題 ； 電腦輔助學習

並列摘要

Abstract
The Use of Computerized Analogical Problem Solving Strategy
to Facilitate Elementary School Students Learning Mathematics Word Problems
By
Kuo-Pin Lin
This study tried to use computerized analogical problem solving strategy to help elementary school students learn mathematics word problems. The study began with developing a computer-assisted instruction system, then a field-test was implemented to assess the effect of this system. The contents of the learning system include: ‘common factor and common multiple’, ‘division of fractional number’, ‘representing the number by symbol’, ‘equation and number relation’, and ‘speed’.
This learning system uses analogical strategy to gradually help students solve problems. The strategy in sequence is representation, retrieval, mapping and using stage. ‘The representation stage’ requires students to point out known numbers and unknown numbers in order to confirm the meaning of the question. ‘The retrieval stage’ reminds students to recall the similar problem by the clue of the question representation (known numbers and unknown numbers). ‘The mapping I stage’ offers the similar question that students had done before to help students to ponder over the solution. ‘The mapping II stage’ compares the representation of the question to be solved with the representation of the similar question. ‘The using stage’ offers the solution to the similar problem directly. We hope students can solve problems and learn the skill of analogical problems solving through the progressive aid of the system.
Thirty-three sixth-grade elementary school students participated in the 12 problems solving exercises during six weeks. We get the following conclusions by synthetical analysis of students’ solving problems records, students’ questionnaire, teacher’s questionnaire, and the classroom observation: (1) ‘The mapping I stage’ offers the similar question that students had done before is the most helpful to students’ learning, (2) students showed positive attitude toward the use of computer-assisted system, and (3) the interface, retrieval strategy, and the analogical questions database of the system need to be improved in the future.

Keywords: analogical problem solving, mathematics word problems, computer-assisted instruction.

並列關鍵字

analogical problem solving ； mathematics word problems ； computer-assisted instruction