不同類型加減法文字題對低年級解題表現之研究

Different Kinds of Word Problems on First and Second Graders’ Problem-solving Performance

施慧君(Hui-Chun Shih)

指導教授 ： 許慧玉

國立清華大學/竹師教育學院/數理教育研究所/碩士(2020年)

摘要

本研究將加減法文字題分成三大類型與八種形式題型進行研究，研究目的在探討低年級學生在不同類型加減法文字題的解題情形與差異，並了解「圖像表徵」在不同類型文字題的影響。研究者蒐集新竹縣市三所國小低年級學生共436份問卷，以獨立樣本t檢定與二因子變異數分析圖像表徵對學生在不同類型加減法文字題解題表現的影響。研究結果顯示：
（一）低年級學生的解題表現不會因圖像表徵的輔助而有所差異，但不同類型的布題，是影響低年級學生解題表現的重要因素。低年級學生在「改變類」及「合併類」的解題表現均顯著優於「比較類」題型。
（二）二年級學生解不同形式題型時，解題表現會因圖形表徵的輔助而有差異，在「比較類—參照量未知」與「合併類—子集合未知」兩題型，「圖像表徵」有助於學生的解題表現，但在其他六類的題型下，「圖像表徵」則無顯著影響。
（三）「圖像表徵」需在難度較高的題型下，才能有助於學生解題；若題目的難度較低，圖像表徵對解題便無助益，甚至可能會造成解題的干擾。
（四）學生需掌握「圖像表徵」的意義，方能對學生解題有助益，反之，則圖像表徵可能會造成解題的困難。本研究中發現二年級學生對圖像表徵的理解能力優於一年級學生，可能是因為一年級學生對圖像表徵的應用尚未熟悉；而二年級學生對其較熟悉且已有概念，因此圖像表徵有助於二年級學生解題。

關鍵字

圖像表徵 ； t檢定 ； 二因子變異數分析

並列摘要

The research divides the word problems into different types of questions. The purpose of the research is to explore the problem-solving situation and differences of lower graders in different types of addition and subtraction word problems, and to understand the impact of "diagram representation" on different types of word problems. The researcher collected 436 questionnaires from students in three elementary schools in Hsinchu County and analyzed the effect of diagram representation on the performance of students in different types of addition and subtraction word problems with independent sample t test and two-way ANOVA.The research shows:
(1)The problem-solving performance of lower graders will not be different due to the help of diagram representation. However, different types of problems is an important factor that affects the performance of lower graders in solving problems. The performance of the lower graders in Change type and Merger type of problems is significantly better than in Comparative type.
(2) When the second graders solve different types of problems, with or without the aid of diagram representation will be different. Diagram representation is helpful to solve Comparative type and Merged type problems.
(3) Diagram representation can only help students to solve difficult problems. If the problem is simple, diagram representation may even become interference.
(4) Students must understand the meaning of diagram representation in order to help solve problems. Otherwise, diagram representation may cause difficulty in solving problems. In this study, it was found that the second graders had better understanding of diagram representation than the first graders. It may be that the first graders are not proficient in the application of diagram representation, but the second graders have already understood. Therefore, diagram representation is helpful for second graders to solve problems.

並列關鍵字

image representation ； t test ； two-way ANOVA

參考文獻

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