六年級學生線性樣式問題一般化表現之研究

A Study of the Pattern Generalization Performance on Liner Problems among the Sixth Graders

陳嘉皇(Chia-Huang Chen)

《高雄師大學報：自然科學與科技類》 29期 (2010/12) Pp. 63-85

https://doi.org/10.7060/KNUJST.201012.0063

摘要

本研究旨在探討六年級學生對線性問題一般化表現與策略應用的情形，藉由不同表徵問題顯示之正確與錯誤者策略之比較，探索影響學生一般化表現的因素，作為改善數學一般化教學的依據。樣本為997位小學六年級學生，參與「代數推理一般化測驗」，測驗完後，從中選取一班30位學童進行訪談。資料分成兩部分處理：有關學生一般化測驗表現部分，以百分比、成對平均數t檢定，考驗學生在不同性質問題的一般化表現是否有顯著差異存在；另依據學生訪談資料，以質性方式加以轉譯分析，理解學生在一般化歷程影響其一般化策略運用的因素為何。研究發現：
（一）學生在一般化測驗上以線性遞增問題之一般化表現較佳。
（二）學生能利用計數、差異、線性等有效多元之一般化策略進行轉化與解題。
（三）常數與變項意義的混淆，影響學生一般化策略的運用與正確表現，可設計能縮減計數關係的作業，協助推理與解題。
研究建議：以線性遞增方式呈現的作業、配合學生推理歷程省思監控的認知能力，輔導對樣式問題一般化使用之計數、差異與線性等多元策略的認識與應用，掌握常數與變項之間的結構關係，持續注意正確算式的完成，可以促進學生一般化的學習成效。

關鍵字

樣式 ； 一般化 ； 策略 ； 代數推理

並列摘要

The research aim was to explore how students adopted the generalization strategies of pattern to solve different questions of characterization. It examined the factors influencing students' effective use of generalization strategies based on their reasoning and question-solving processes. Study sample includes 997 students in 36 sixth-grade class of 12 public primary school in southern Taiwan. They took the ”Test on Pattern Generalization in Algebra Reasoning” designed by the researcher. After the test, an interview was conducted to 30 students to make sure their understanding about the test questions and generalization strategies. Students' performance in solving questions through pattern generalization was scored to indicate their understanding in solving questions of different representations. Each student's strategies used on the test were carefully analyzed. Data were collected and analyzed by three scorers, and all formats questions were checked to see the scorer's reliability coefficient. In addition, a comparison was made between 6 students who obtained all correct answers and the other students who obtained all incorrect answers in the same class. The researcher findings from this study can be summarized as follows:
1. Students' pattern generalization performances in liner increasing question were higher.
2. According to the different features of representation questions, students leared to adopt effective strategies of pattern generalization in solving questions.
3. The factors influence students’ choice and application of pattern generalization strategies and performance in solving questions include misused the meanings of variables and constants, could design the task to reduce the numbers counted to assist students' individual cognitive ability, features and relations of the questions presented.
This researcher made some recommendations for reference on future design for the teaching of pattern generalization in algebraic reasoning.

並列關鍵字

Pattern ； generalization ； strategy ； algebraic reasoning