國小六年級生對數學素養導向試題之作答表現探究

108課綱強調將所學的知識、技能運用於生活情境解決問題，但除了PISA外，目前沒有其他正式的數學素養導向評量工具，可以用來了解小學第三學習階段學生的數學素養能力。故本研究利用國家教育研究公告的數學素養導向試題188題及其全國各縣市施測結果，探討國小六年級學生在作答數學素養試題時，選擇題與非選擇題的表現差異、不同情境取材試題的表現差異，以及學生在嘗試作答非選擇題且作答錯誤時，常見的錯誤類型。研究發現，學生在非選擇題的得分率比選擇題低2成。針對不同情境取材的試題，學生在社會與公共、購物與商業活動這二種情境的答題表現較佳，平均得分率大於4成，其餘情境試題的平均得分率皆不到4成。最後，當學生嘗試作答且作答錯誤時，常見的錯誤類型大致可分為：概念迷思的錯誤、直觀推論的錯誤、單位轉換的錯誤、計算過程的錯誤四種類型。

關鍵字

錯誤類型；數學素養；數學素養導向評量

並列摘要

The 108-year syllabus puts emphasis on enhancing students' abilities in solving real-life problems by applying the knowledge and skills learned in school. However, apart from PISA, there is no formal literacy-oriented assessment tools that can be used to assess students' mathematics literacy of in the third learning stage of elementary school. Therefore, in this study we use the 188 items developed by the National Academy for Educational Research and the relevant test results to investigate: (1) the difference in students' performances between the multiple-choice and non-multiple-choice questions, (2) the difference in students' performances of items which are developed with different situations, and (3) the types of mistakes students make when they try to answer. This study found that students' scoring rate of non-multiple-choice questions is 20% less than that of multiple-choice questions. For different situational items, the students' performances in the social and public realm, and in shopping and business activities are better, with the average scoring rates of more than 40%. Beside these two situational items, the average scoring rates in other situations are all less than 40%. Finally, when students try to answer non-multiple-choice questions but cannot get full scores, the common types of errors can be roughly divided into four types: errors in misconceptions, errors in intuitive inferences, errors in unit conversions, and errors in calculation processes.

並列關鍵字

error types ； mathematics literacy ； mathematical literacy-oriented assessment

參考文獻

Bingölbali, E., & Bingölbali, F. (2021). An examination of open-ended mathematics questions' affordances. International Journal of Progressive Education, 17(4), 1–16.

Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive science, 4(4), 379–426.

Fujii, T. (2014). Misconceptions and alternative conceptions in mathematics education. In: S. Lerman (Ed.). Encyclopedia of mathematics education. Dordrecht, Netherlands: Springer.

OECD (2017). PISA 2015 Assessment and analytical framework: Science, reading, mathematic, financial literacy and collaborative problem solving (Revised ed.). Paris, France: OECD Publishing.

Sivan, E. (1986). Motivation in social constructivist theory. Educational Psychologist, 21(3), 209–233.

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