國小數學教科書中提供學生幾何推理證明機會之分析

Analysis of Geometric Reasoning-and-proving in Elementary School Mathematics Textbooks

鄭芳妮(Fang-Ni Jheng)

指導教授 ： 陳正忠 ； 蔡文煥

國立清華大學/竹師教育學院/數理教育研究所/碩士(2021年)

摘要

本研究針對國小數學教科書中幾何單元提供學生推理證明機會之分析比較，主要探討K、Ｈ、Ｎ三版本教科書中提供給學生推理證明機會之多寡。以九年一貫課綱四、五、六年級之國小教科書為研究對象，研究方式採「內容分析法」，研究單位分為示範及學生練習以「數學問題」來分析比較，分別從RP問題的目的、證明類型、證明的目的三方面進行分析。
在RP問題的目的分析結果發現：(1)RP問題的題數以Ｋ版本最高，其次為N版本，最少為Ｈ版本；（2）RP問題的目的以提出主張最高，證明主張次之，最少為評估或發展主張；(3)三版本在學生練習的部分，幾乎沒有相關的RP問題。
在證明類型分析結果發現：（1）三版本提供命題證明的比例相近；(2)三版本提供的證明類型皆以經驗證明為主；（3）在證明類型的四五六年級的安排上，Ｋ版本層次設計較佳，隨著年級降低經驗證明的比例，Ｈ版本三個年級證明層次設計較為平均。
在證明的目的分析結果發現：(1)三版本教科書示範多以形成概念為主要的證明目的，其次為解釋；(2)學生練習多以驗證為主要的證明目的，其次為形成概念；(3)三版本教科書皆未以否證為證明的目的。

關鍵字

國小數學幾何教科書 ； 幾何推理證明 ； 教科書分析

並列摘要

This study was conducted to analyze and compare the geometric units in elementary school mathematics textbooks that provide students with opportunities to prove their reasoning. The study was conducted by using the "content analysis method" and the unit of study was divided into demonstrations and student exercises using "mathematical problems" to analyze and compare the purpose of RP problems, the type of proof, and the purpose of proof.
The purpose of the RP questions was analyzed in three ways: (1) the number of questions in the RP questions was highest in the K version, followed by the N version, and least in the H version; (2) the purpose of the RP questions was highest in the formulation of claims, followed by the proof of claims, and least in the evaluation or development of claims; (3) there were almost no relevant RP questions in the student practice section in the three versions.
In the analysis of the types of proofs, it was found that: (1) the three versions provided similar proportions of propositional proofs; (2) all three versions provided mainly empirical proofs; (3) in the arrangement of the types of proofs for grades 4, 5, and 6, the K version had a better hierarchical design, and the proportion of empirical proofs decreased with the grade level, while the H version had a more even hierarchical design for the three grades.
In the analysis of the purpose of proof, it was found that: (1) the three versions of the textbook demonstrated that the main purpose of proof was to form concepts, followed by explanations; (2) students practiced to verify the main purpose of proof, followed by the formation of concepts; (3) none of the three versions of the textbook used disproof as the purpose of proof.

並列關鍵字

elementary school mathematics textbook ； geometric reasoning-and- proving ； textbook analysis

參考文獻

徐偉民（2013）。國小教師數學教科書使用之初探。科學教育學刊，21(1)，25-48。

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