臺灣與中國大陸七至九年級數學教科書代數內容分析之研究

本研究旨在探討臺灣與中國大陸七至九年級數學教科書代數教材內容之異同。研究對象為臺灣康軒版數學教科書及中國大陸北師大版數學教科書。本研究採用內容分析法，以「數學問題」為分析單位，數學問題類型以Stein el at.(2000）對學生解題時所需的「認知需求」能力的定義、數學問題呈現方式以Lesh & Lamon(1992)對真實情境的定義、數學問題表徵形式以Zhu & Fan(2006)問題表徵型式的定義，分析兩套教科書代數教材的數學問題類型、問題呈現方式、數學表徵形式的特色與異同。歸納本研究之結論如下：壹、兩套教科書代數主題內容教材之異同一、兩套教科書皆重視代數教材，在六冊數學教材中比例大致相同，所重視的單元主題亦相同，但教材編排與版面呈現設計不同二、數學史、數學家的故事以及數學趣味問題為兩套教科書所重視三、數學概念的建構有差異：康軒版採取較傳統方式的鋪陳數學概念，康北師大版則以問答式的詰問鋪陳數學概念貳、兩套教科書代數主題問題認知需求方面一、皆以低認知需求能力中的無連結程序型為主；記憶類型佈題康軒版多於北師大北，具連結程序型佈題北師大版多於康軒版；康軒版無作數學題型，北師大版則有2題二、運算的熟練度與推演的技巧，兩套教科書一致的強調練習角色的重要性，以精熟學習獲得解題的正確性與效能。參、代數主題問題表徵形式一、代數主題問題呈現方式，兩套教科書都是以「純數學形式」為主要的問題呈現方式。二、兩套教科書在問題表徵形式的使用上並不均勻，純數學形式較多，視覺形式較少肆、代數主題的問題呈現方式一、兩套教科書都是以「無情境佈題」為主要的問題呈現方式，均以「方程式」類別為最高二、兩套教科書在問題呈現的兩種方式中，比例皆相差懸殊，仍有改善空間三、問題呈現方式應與時俱進與國家接軌，應多使用情境式佈題及開放性問題，以發展思考、推理與歸納的能力最後，依據研究結論提出數項具提建議，以供未來編修教科書之相關人員與教學設計者及未來研究者參考。

關鍵字

內容分析；代數教材；數學教科書

並列摘要

The purpose of this study was to compare and analyze the similarities and differences on algebra of the junior high school’s mathematics textbooks between Taiwan and China. The objects of the study are Kang-Hsuan version of Taiwan and the Beijing Normal University version of China. Content analysis was used as method and mathematics problem was as unit to analyze, they were based on classification of Stein’s taxonomy of Educational Objectives (2000) employed as the analytic tool, Lesh and Lamon’s definition (1992) to real situation and Zhu and Fan’s representational forms from problems (2006). The results are concluded as follows: 1.The classification of the mathematics problem on Algebra (1)Both of the textbooks are emphasized on algebra. The distribution ratio, and unit title are the same, but edit ways and teaching materials. (2)Both of the textbooks are emphasized on the history of mathematics, the story of mathematicians, and interesting math problems. (3)The mathematical concept and construction are different: Kang-Hsuan version used a more traditional way to arrange the mathematical concept and construction, but Beijing Normal University version used questions & answers and interrogation method. 2.Cognitive demand of the mathematics problem on Algebra (1)Both of the textbooks are mainly focus on the “procedures without connections” which belongs to “low-level task”; “memorization task” is more in Kan-Hsuan version; “procedures with connections task” is more in the Beijing Normal University version; there is no “doing mathematics task” in Kan-Hsuan version, but there are two task in the Beijing Normal University version. (2)Both of the textbooks are equally emphasized on the importance of practice. Getting corrective and efficacy by mastery learning. 3.Representational forms from problems on Algebra (1)“Problems in a purely mathematical form” is the main topic form from problems on both textbooks. (2)The distribution ratio is not balance in presenting the form from problems on both textbooks. “problems in a purely mathematical form” is the most, but “problems in a visual form” is the least. 4.Forms from problems on Algebra (1)“Non-situational problem” is the main topic form from problems on both textbooks. The form of “equation” is the most. (2)The distribution ratio is not balance in presenting the form from problems on both textbooks. There is much space to be improved. (3)The forms from problems should be advancing with the time. Using much more situational problems and open questions to develop the abilities of learning, inference, and induction. According to the research results mentions above, the researcher several suggestions for the related mathematics education units and personnel revising the textbooks or doing future research.