乘除擬題能力測驗編製及其實證研究

The Test Design of Multiplication-Division Problem-Posing and Its Empirical Study

林原宏(Yuan-Horng Lin) ； 許淑萍(Hsu-Ping Shu)

《測驗統計年刊》 10期 (2002/12) Pp. 135-171

https://doi.org/10.6773/JRMS.200212.0135

摘要

本研究旨在編製國小高年級學生適用之「乘除擬題能力測驗」，擬題測驗為「算式表徵轉換為文字表徵」的擬題型式，並進行實證研究。
實證對象為國民小學六年級學生，有效樣本總計274位。研究工具為自編「乘除擬題能力測驗」，施測後分析學生所擬出之數學題目的擬題結果、擬題背景、錯誤類型與後設認知。經統計分析後，實證研究結果顯示：
一、自編「乘除擬題能力測驗」工具具有良好試題品質，難易度適中且鑑別度、內部一致性信度、評分者信度與效度相當高。
二、單步驟題型的擬題能力優於多步驟題型的擬題能力。
三、單步驟題型擬題過程的後設忍知能力較在多步驟題型為高。後設認知能力愈高的學生，其在擬題表現上也愈好。就擬題結果乘除類型多寡而言，在單步驟題型中依次為量數同構型、比較型及叉積型；多步驟題型中依次為多重比例型、量數同構型、比較型、叉積型。以整體試題而言，依次為量數同構型、多重比例型、比較型、叉積型。
四、擬題背景分析結果，依序為「自己想出來的」、「曾在某處看過」、「曾在課本上看過」、「老師曾經講過」。
五、單步驟題型擬題錯誤類型主要為：1.擬出加減之題目； 2.「×」將未知數當作已知數加以擬題。多步驟題型捉題之錯誤類型可歸納為：1.隱含元素的單位量轉換錯誤；2.將「×」直接表徵為某一單位數；3.將「二」直接表徵為平分。
本研究結果與發現，可提供有關國小學生學習乘除概念之教學與教材編製之參考，根據研究結果，本文亦提出未來進一步研究之建議。

關鍵字

表徵 ； 後設認知 ； 乘除類型 ； 擬題

並列摘要

The purpose of this study was to design the testing of ”multiplication-division problem-posing”. By this testing, the researchers also proceeded the empirical study.
There were good two hundred seventy-four six-graders from two different elementary schools located in both Taichung city and Taichung county were selected to do this test.
The results of this research were as follows:
1. The characteristics of the test items were showed in this paper. According to the real data analysis, the difficulty, discrimination, internal reliability, scoring reliability, and validity were proper.
2. The result of problem-posing showed the students had higher performance on one-step than multi-step word problems.
3. The meta-cognition ability in one-step word problems was better than multi-step word problems. The students who got higher score in meta-cognition ability had higher performance in problem-posing.
4. The order in motivation research in posing problems was 'one's own idea”, ”saw it before”, ”read it before”, and ”learned it before”.
5. The main error patterns in one-step word problems were ”posing the adder and subtract problems” and ”Posing unknown number as known number”. In multi-step word problems, they were 'Incorrectly translating unity number of the latent component quantity”, ”Misunderstanding the multiply signs as unity number”, and ”Misunderstanding division signs as a equal sign”.
Finally, the researcher also gave some suggessions for elementary teaching methods, material designed and advanced study.

並列關鍵字

meta-cognition ； multiplication and division ； problem-posing ； representation

參考文獻

蔣治邦(1994)。中年級學童解決加減文字題能力之探討：多餘資訊與兩步驟問題。科學教育研究與發展季刊。1(2)，189-212。

馬秀蘭(2001)。透過電腦網路來發展數學加減法問題之研究。科學教育學刊。9(4)，375-399。

Ballard, J.W.(2000).Students` use of multiple representations in mathematical problem solving.Montana State University.

Bruner, J.S.(1966).Toward a theory of instruction.New York:Mcgraw-Hill.

Dought, K.(2000).Problem solving by writing word problems.Dominguez Hills:California State University.