問題基模與基模圖示表徵解題課程對國小三年級學童數學解題表現之影響

The Effects of Teaching Schematic Drawing on Mathematical Problem-Solving Performance of Third Grade Students

李金雀(Chin-Chueh Li)

指導教授 ： 陳李綢博士

國立臺灣師範大學/教育學院/教育心理與輔導學系/碩士(2005年)

摘要

本研究主要目的在設計一套問題基模圖示表徵解題課程，探討該課程對國小三年級學生在改變與比較題型之加減應用題解題表現的立即及追蹤效果，以及分析學生形成問題基模和自行產生問題基模表徵圖示的情形。以國小三年級六十名學生為研究對象，實驗組、控制組學生各三十名，實驗組接受實驗課程處理，控制組則無。本研究以「加減應用題成就測驗」為量化資料的評量工具，於課程結束二週後再進行追蹤後測，將所得資料以前測成績為共變數，使用獨立樣本單因子共變數分析統計方法進行資料處理，並分析「問題基模分類作業」、「問題基模圖示表徵作業單」、「問題基模圖示表徵學習心得問卷」及「教師省思札記」為輔佐資料，以瞭解本研究課程方案介入的效果。研究結果主要發現如下：
一、問題基模與基模圖示表徵解題課程對加減應用題解題表現具有提升效果
（一）實驗課程對加減應用題解題表現具有立即提升效果
（二）實驗課程對加減應用題解題表現具有追蹤提升效果
二、實驗組學生能形成加減應用題問題基模並據以分類加減應用問題
三、實驗組學童在加減應用題上能自行產生適當的問題基模圖示表徵
四、實驗組學童對問題基模圖示表徵具有正向的意見看法
最後，根據本研究結果加以討論，對未來數學解題教育及未來研究提出具體建議，以做為後續數學教育及未來研究的參考。

關鍵字

問題基模 ； 基模圖示 ； 表徵

並列摘要

The purpose of this study is to design a schematic drawing training program for 3th grade students and to investigate its immediate and tracking effects on students’ problem-solving performance on “changed and compared” word problems. Also, it focuses on the situation of student’s generating problem schema and representation. 60 students from an elementary school were as subjects, 30 students for experimental group and control group. Students in the experimental group went through schematic drawing training program, while those in the control group didn’t. The quantitative instrument utilized to examine the effcts of the training is“Addition and Subtraction Word Problem Achievement Test”, which was administered at the end of the training and 2 weeks later for tracking. The collected data were analyzed with one-way ANCOVA. The other data including “problem schema sorting tasks”, “schematic drawing tasks”, “learning questionnaire of schematic drawing”, and “teacher’s reflective journals” were also analyzed to examine the effects of the training. The findings were presented as follows: 1.Schematic drawing training program could improve the performance of problem-solving for addition and subtraction word problems.for example, (1) The experimental program could immediately improve the performance of problem-solving for addition and subtraction word problems. (2) The experimental program could maintain the improvement in problem-solving for addition and subtraction word problems.2.Experimental group could generate problem schema of addition and subtraction word problems and classify the problems according to the schema.3.Experimental group could generate suitable schematic drawing of addition and subtraction word problems.4.Experimental group have positive opinions on schematic drawing.
Finally, based on the experimental results, we propose suggestions for education of mathematical problem-solving and future research.

並列關鍵字

problem schema ； schematic drawing ； representation