國小六年級學童數感解題之錯誤類型分析

Analysis of the error patterns made by 6th Graders using number sense to solve math problems

本研究主要目的在探究國小六年級學童在數感能力的表現概況，並加以歸納及分析學童的錯誤類型， 探討其可能形成的原因以了解六年級學童對數感學習的迷思與錯誤，進而提供教師教學改善與未來相關研究者的參考。本研究採質量混合設計，以研究者自編「國小六年級學童數感能力分析問卷」進行測驗。研究者選取臺南市東區某國民小學，兩個班共 49 名學童為研究樣本，進行數感能力問卷的施測。再依照學童意願與答題反應，選取部分學童進行晤談。研究者再以 SPSS 21.0 中文視窗版、Microsoft Office Excel 2016 分析量化資料，並比對晤談內容，整理出錯誤類型與可能形成錯誤的原因， 分析研究結果如下： 一、國小六年級學童於數感能力的整體表現偏低， 其中以瞭解運算對數字的意義及其影響的能力為表現最佳的向度。 二、國小六年級學童答題錯誤類型分為以下八項錯誤類型: (一) 整數概念迷思錯誤類型。 (二) 分數的概念迷思錯誤類型。 (三) 小數概念迷思錯誤類型。 (四) 先備知識缺乏錯誤類型。 (五) 刻板精算迷思類型。 (六) 粗心錯誤類型。 (七) 猜答案錯誤類型。 (八) 推理表述能力薄弱錯誤類型。 三、國小六年級學童於數感上的錯誤形成原因，歸納為以下五大可能錯誤原因: (一) 數感概念迷思:包含數感概念錯誤與數感策略誤用。 (二) 習慣列式精算學習。 (三) 消極猜測。 (四) 缺乏數學推理的能力。 黃建中 國立臺南大學應用數學系 (五) 缺乏檢核錯誤的能力。

 

The purposes of this study were to investigate the performance of the ability of number sense for sixth graders, to summarize and analyze the patterns of errors made by school students, and explore the possible reasons for their formation, in order to understand the myths and mistakes of sixth-grade students’ learning number sense. The study results are references for teaching improving and furthering study. Both qualitative and quantitative design were employed in the study, and the number sense questionnaire designed by researcher was used to test 49 subjects who participated in the study from 2 classes of a specific elementary school in the East district of Tainan city. Based on the willingness and responses of subjects, some students were picked and then interviewed. SPSS21 and Microsoft Office Excel 2016 were used to analyze the quantitative data. By comparing the contents of the interviews, the researcher sorted the pattern of error and the cause of the error. The research results are as followings： First, the overall average performance of the sixth-grade elementary school students is low. Among them, ""the ability to understand the meaning of an operation toward a number and the operation’s influence"" is the best indication. Second, the sixth grader’s answer are divided into the following eight patterns of errors: (1) The error pattern of integer concept. (2) The error pattern of the fractional concept. (3) The error pattern of the decimals concept. (4) The error pattern of the lack of prior knowledge. (5) The patterns of stereotyped actuarial concepts. (6) Careless error pattern. (7) The error pattern of guessing. (8) The error pattern of the weak reasoning ability. Third, the reasons for the mistakes made by the sixth grade students in the school are summarized as the following five possible causes: (1) The myth concept of number sense: contains the concept of number sense and the misuse of the number sense strategy. (2) Habitual column computing learning. (3) Negative guesswork. (4) Lack of mathematical reasoning ability. (5) Lack of ability to check errors.