國中數學領域教科書之認知需求與數學建模歷程之內容分析：以七年級代數為例

本研究旨在探討不同版本之國中數學教科書之數學建模歷程和數學問題之認知需求在代數教材中的分布情形及異同之處。本研究以109學年度國民中學數學領域審定本課本為研究對象，綜合左台益等人（2018）、PISA（OECD，2018）、Zhu和Fan（2006）歸納發展數學建模歷程分析類目以及Henningsen和Stein（1997）建立之認知需求分析類目，採用內容分析法進行數學教科書之內容探討。本研究結果如下：一、康軒版、翰林版、南一版在數學建模歷程中的各項歷程分布差異性小，在不同單元中也因各出版商著重的內容不同，而給予不同的問題數量及比例。二、生活情境脈絡問題約占各版本代數單元的20%~25%，也代表記憶與程序性問題占多數，而其中虛構應用問題的比例為真實情境問題9至11倍，亦顯示教科書仍重視記憶和程序性的計算，未能從真實情境問題讓學生經歷完整的數學建模歷程。三、數學工具和科技工具的使用機會不足，未能讓學生利用數學工具解決數學問題。四、三個版本數學教科書僅在該單元的最後一節的應用問題讓學習者經歷完整的數學建模歷程，應用問題之前的小節則以訓練數學建模歷程的列式及解決策略為主。五、代數題目偏重於低認知需求，並以程序性計算和概念性的記憶為主，表示數學教科書仍以精熟練習為主要教學目標。

關鍵字

數學建模歷程；認知需求；內容分析；數學教科書；代數

並列摘要

The purpose of this study was to investigate the distribution, similarities, and differences in algebraic material, focusing on the mathematical modeling process and mathematical problems of cognitive needs in different editions of current secondary school mathematics textbooks. In this study, the secondary school mathematic textbooks of the 2020 academic year were used as the research target. The development as well as induction of the framework of mathematical modeling process from Tso, Tai-Yih et al. (2018), PISA (OECD, 2018), Zhu and Fan (2006), and the framework of cognitive needs established by Henningsen and Stein (1997) were introduced. The content analysis method was also used to investigate the content of mathematics textbooks. The results of this study are as follows. 1. The number and proportion of questions in different units differ depending on each publisher's content regarding the distribution of the mathematical modeling process in the Kang-Hsien, Han-Lin, and Nan-Yi editions deviated little. 2. Life situation questions account for approximately 20% to 25% of the algebraic units in each version, representing the preponderance of memorial and procedural questions. The proportion of fictional application problems is 9 to 11 times higher than that of real situation problems, indicating the textbooks still emphasize memorial and procedural computation and do not allow students to experience the complete mathematical modeling experience from actual situation problems. 3. The use of mathematical and technological tools is insufficient to enable students to use mathematical tools to solve problems. 4. Both three editions of the mathematics textbook allow learners to go through the complete mathematical modeling process only in the last section of the unit with some application problems, while the subsections before the application problems focus on training the formulation and solving strategies of the mathematical modeling process. 5. Algebra questions tend to focus on low cognitive needs, based on procedural calculations and conceptual memory, indicating that mathematics textbooks still aim to provide sophisticated practices as their main instructional goal.