國小六年級學童在比與比值單元錯誤類型之研究

A Study on the Error Patterns of Sixth-Grade Elementary School Students in the Unit of Ratio and Proportion

本研究旨在探討國小六年級學生在比與比值單元中的解題表現，並深入研究學生在該單元中常見的錯誤類型。研究採用紙筆測驗收集量化資料，對臺南市8所小學13個班級的237名學童進行施測，利用研究者自編的「比與比值成就測驗」。接著，對學生在比與比值單元中的錯誤類型進行分析，並探討可能形成這些錯誤的原因。研究結果如下：一、國小六年級學童在比與比值單元的整體表現以及各向度表現各有不同，其中在相等的比向度表現最佳，而在比的應用向度表現最差。二、國小六年級學生在比與比值單元常見的錯誤類型分為十七種，包括誤解題意、錯置前後項、前後項概念不清、比值概念不清、比與比值概念混淆、相等的比概念不清、最簡整數比概念不清、最簡單整數比認知不足未化至最簡、以一(多)步驟的方式解題、忽略題意資訊、列式錯誤或未完整、計算式錯誤、單位換算錯誤、單位錯誤、無計算過程、應用問題未寫出答案、計算錯誤。三、國小六年級學生在比與比值單元出現的錯誤類型可能形成的原因包括整體量或分量的概念不清、比與比值概念混淆、誤解題意、比的相關算則不清、比的概念不清、閱讀理解題目能力不足、基本運算能力不足、書寫粗心等八種原因。

 

The purpose of this study was to explore the problem-solving performance of sixth-grade elementary school students in the unit of ratio and proportion, explored the error patterns that students often made in this unit. This study adopted paper-and-pencil tests to collect quantitative data. The sample consisted of 237 students from thirteen classes of eight elementary schools in Tainan City. The students were tested by the researcher’s self-edited "Ratio and Proportion Achievement Test."Subsequently, organized the error patterns made by students in the ratio and proportion unit, and found out the possible reasons of the error patterns. The research results are as follows: 1.The performance of sixth-grade elementary school students in the ratio and proportion unit from the entirety and different dimensions was different. All of the students had the higest grade in the equivalent ratio dimension, and had the lowest grade in the application of the ratio dimension. 2..There were seventeen error patterns that commonly made by sixth-grade elementary school students in the unit of ratio and proportion: Misunderstanding the question, misplacing antecedent or consequent of the ratio, unclear concept of antecedent and consequent of the ratio, unclear concept of proportion, confusing concept of ratio with concept of proportion, unclear concept of equivalent ratio, unclear concept of irreducible ratio, not converting ratios into the lowest term by insufficient knowledge of irreducible ratio, solving the problem by using one or multiple steps, ignoring the meaning of the question, the wrong or incomplete of the equation, the incorrect formula of calculation, transferring the unit incorrectly, the incorrect unit, not calculating process, not writting the answer of the application questions, and the incorrect calculation. 6.There were eight possible reasons for the error patterns made by sixth-grade elementary school students in the unit of ratio and ratio: Unclear concept of the whole quantity or part quantity, confusing concept of ratio with concept of proportion, misunderstanding the question, unclear the calculation rules of the ratio, unclear concept of ratio, insufficient knowledge of reading comprehension, insufficient of basic arithmetic ability, and writing carelessly.