國小高年級學生在數學素養導向試題解題之錯誤類型分析

An Analysis of the Error Types in Solving Problems of Mathematical Literacy by Upper Elementary Students

本研究旨在探討國小高年級學生在作答數學素養導向試題時，各歷程中常見的錯誤類型及其可能成因。本研究採橫斷式調查法，並以國家教育研究院公告之79個素養導向試題題組（含188道試題）分成20個題本，利用兩階段分層隨機抽樣蒐集3,000多位學生作答進行分析比較，並利用其中26道試題進行學生常見的錯誤類型研究。研究結果顯示，在「形成」歷程中，主要錯誤類型為「訊息擷取錯誤」與「表徵使用錯誤」，其中部分試題的錯誤比例超過30%。在「運用」歷程中，「數據處理錯誤」為最常見的錯誤類型，幾乎出現在所有試題中，且部分試題的錯誤比例亦超過30%，其次為「忽略單位或單位使用錯誤」學生在大部分試題都有出現此錯誤類型。在「詮釋評估」歷程中，「直觀詮釋訊息導致錯誤」和「策略未完整呈現」是最常見的錯誤類型，在部份試題中分別約有20%和50%的學生常犯這些錯誤。針對這些錯誤類型，本研究進一步分析其可能成因，並輔以學生作答範例進行說明。透過建立錯誤類型與其可能成因的對應關係，將可協助教師識別學生的學習困難，迅速察覺學生可能的學習問題，進而提供適切的教學調整與指導。

This study aimed to investigate the common error types and their underlying causes in upper elementary students' responses to mathematical literacy-oriented test items. A cross-sectional survey design was adopted, utilizing 79 item sets (comprising 188 test items) developed by the National Academy for Educational Research. These items were systematically distributed across 20 test booklets, and responses from over 3,000 students were collected through a two-stage stratified random sampling procedure for analysis and comparison. Among these, 26 test items were selected for an in-depth examination of students' most frequent errors. The results indicate that in the formulation process, the predominant error types were ''information extraction errors'' and ''representation usage errors,'' with some items exhibiting error rates exceeding 30%. In the employment process, ''data processing errors'' were the most prevalent, occurring across nearly all test items, with error rates surpassing 30% in some cases. Additionally, ''neglecting units or incorrect unit usage'' emerged as a recurrent issue across a majority of the test items. In the interpretation and evaluation process, the most frequently observed errors were ''intuitive misinterpretation of information'' and ''incomplete strategy presentation,'' with approximately 20% and 50% of students, respectively, exhibiting these errors in certain test items. To provide deeper insights, this study further analyzed the potential causes of these errors and supplemented them with examples of student responses. By establishing a systematic correspondence between error types and their underlying causes, the findings offer valuable implications for educators in diagnosing students’learning difficulties, identifying potential misconceptions, and implementing targeted instructional interventions to enhance mathematical literacy and problem-solving competencies.