國家教育研究院

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　　臺灣即將實施的十二年國教改革以素養為導向；依照我國學校環境的現實狀況，教科書的提供，是事前必須要規劃的配套措施之一。德、美這兩個國家都比我國早推行素養導向教學，他們的教科書或許有我國可借鏡之處。
本研究擬採內容分析法，以小學的加減法運算教材為研究範圍，選定德、美兩國各一個版本的教科書為對象，先邀請學者就加減法運算教材，劃定分析單位、建構分析類目及次類目的界定，做成檢核表，以找出該兩國素養導向教科書的長處。
本研究以小學的加減法運算教材為研究範圍，其理由如下：
　　現代生活中電算器非常普及，學會運算並非學習數學的主要目的。然而小學的加減法運算教材，是最基本的數學知識，是多數國家數學課程的必要學習課題，更是數學素養的基本要素，用以教導學生如何用「數」進行溝通並體會數的運算是如何形成。
　　加減法運算教材的內容包括數概念、數的應用、十進制位值記數系統、以及直式加減運算；其中「數」概念的形成，是數學抽象思惟的第一座里程碑，學生透過「做數學」的過程將真實世界裡具體物的量，轉化成可思考的數概念，並賦予符號，使之成為心智中的具象。而加減運算規則是來自古印度文化的社會性規約，學生須理解並接受。在加減法直式運算的學習過程中，學生建立數概念，理解並接受既有規約，這些都是培養學生數學素養的起點。

　　The Grades 1-12 Curriculum Reform in Taiwan to be implemented is oriented by competence. In accordance with the reality of Taiwan's school environment, the relevant supporting programs of textbooks providing should be well planned in advance. Germany and the United States have implemented competence in School for years. The textbooks used in these two countries may have some advantage worthy of reference. In this study, the content analysis method will be used to study the instructional material of the addition and subtraction of the primary school, and the textbooks of Germany and the United States are selected as the object. First, the scholars are invited to define the analysis unit, construct the categories and sub-categories and then make a checklist to find out the strengths of these textbooks. This study focus on the instructional materials of addition and subtraction of primary school for the reasons are as follows: In modern life, the calculator is very popular; getting the skills of the operation is not the main purpose of learning mathematics. The instructional materials for addition and subtraction of primary school are the most basic mathematical knowledge. They are also necessary subjects for many countries math courses and are essential elements of math competence. They are used to teach students how to communicate with numbers and to make students understand how the operation rules of number are formed. The instructional materials for the addition and subtraction include the number concepts, the applications of numbers, the place value system based on powers of ten, and the rules of column addition and subtraction. The formation of the number concepts is the first milestone in mathematical abstract thinking; by “doing mathematics” students experiencing the transform process of the amount of real objects in the real world into a number- a thinkable concept and giving the number concept a symbol then making numbers being embodiments in mental. The rules of column addition and subtraction are agreements of ancient Indian social, which students should understand and accept. During the learning of column addition and subtraction, students building their number concept, understanding and accepting the established agreement are all in the first step of cultivating students' mathematical competence.