國家教育研究院

　　本研究旨在探討數位科技於國中數學教學之應用情形，以及教師對數學科數位教科 書的想像與期待，做為後續發展數位教科書之依據。本研究採立意取樣，選擇任教經驗 10 年以上的國中數學科教師、以及熟悉數學教育或科技教育之學者，總受訪對象共10 人。研究結果發現，第一，抽象的概念定義與多重概念的複雜連結，是學生學習較為困 難部分。第二，教師們多半接觸過教學光碟，但使用情形因人而異。部分教師曾運用動 態幾何軟體、平板及短焦投影機等工具教學；數位教學可幫助學生學習，但也可能因設 備不穩定影響教學流暢。第三，教師期待數位教科書運用動態表徵進行抽象概念的講 解、能強化作業提示與回饋的功能、能依據學生程度給予適當的練習題、能提供教用版 幫助備課與資源連結。最後，教師建議可先由幾何單元，如：相似形，或函數單元著手 發展數位教科書。

　　本研究對於教育政策提出以下建議：

（一）立即可行性建議

1. 建立課程地圖。

　　本研究發現，教師們期待數位教科書能依據學生程度連結先備知識，因此，建議可 先行檢視現行國中數學教科書內容，建立課程地圖，確認抽象概念單元教學前，學生已 具備所需的先備知識與能力。

2. 調查國中數學教師數位教學意願、經驗與能力。

　　本研究受訪的國中教師雖僅6 位，然其教學風貌多樣：倚賴傳統講述者有之、結合傳統講述與動態幾何軟體者有之、搭配廠商製作的教學光碟或軟體輔助講述者有之，未來課堂上的教學風貌可能更為多元。因此，在發展數位教科書的同時，應能掌握教師在理解、應用數位媒材的意願、能力與經驗，作為後續發展教材、教師進修研習課程規劃之依據。

3. 建構數學科教師成長社群。

　　本研究發現，部分教師其校內數學領域教師的合作性強大，在方案的實施、教材發展、教學方法各方面均能互相支持與分享，形成良好的教學氛圍。因此，建議可成立校 內或跨校間的教師成長社群，不論在軟體的使用、教學方法的討論、共同備課、或共同 組成題庫各方面，均能提供教師實質且即時的協助。

（二）中長期建議：

1. 建構足量的、具階層性的題庫。

　　教學成效良窳多由學生表現評定，學生表現最直接者即為測驗分數。教師依賴測驗 結果調整教學，同時，也依賴細緻的評量系統診斷學生的學習困難。因此，多位受訪教 師提及題庫的建立。然而，依據能力指標建構足量的題庫，是一龐大工程，並非個別教 師或單一教師小組得以完成。優質的題庫亦將有助於發揮數位教科書即時回饋以協助學 習之功能。

2. 針對教學與學習較困難的內容嘗試發展數位教科書，以協助學生從具體運思過 渡到形式運思，有助於概念理解。

　　The purposes of this study were to explore the applications of the digital technologies on the mathematics education of secondary education, and to understand teachers’ imagination and expectation of mathematics digital textbooks. The purposive sampling was adopted and those who has at least ten years experience as well as the experts of mathematics education and technology education were chosen to be the participants. The findings were as followings: First, the contents which students felt difficulty included the abstract concept definitions, and the complex linkage between multi-concepts. Secondly, some teachers have been using dynamic geometry software, tablet and interactive whiteboards for teaching. Digital teaching could help students learn, but also might destroy teaching fluency because of the unstable equipments. Thirdly, teachers hope that the digital textbooks could explain the abstract concepts by dynamic representations, could strengthen the functions of prompt and feedback about homework, could provide appropriate exercises according to students' level, and could provide teacher's version to help teaching and connect teaching resources. Finally, teachers suggested that the development of a digital textbook could start from geometry such as similar figures, or from the unit of function.

　　This research presents some recommendations to policy-makers:

1. To establish the course map

　　According to the findings, teachers claimed that the digital textbook should remedy the prior knowledge which students need for new learning. I suggest that we can examine the contents of mathematics textbook of junior high schools and establish the course map, in order to confirm that students have obtained the prerequisite knowledge and capacities before new learning.

2. To survey the willingness, experiences, and capacities of digital teaching of mathematics teachers

　　There were just 6 junior high school math teachers participated this study, but they exhibited diverse teaching styles: Some adopted the traditional lecture, some combined lecture and dynamic geometry software, and some used the teaching software made by publishers. Maybe in the future, there will be more diverse styles in the classroom. Therefore, we should understand teachers’ willingness, capacities and experiences of digital teaching as the bases of developing teaching materials, planning the curriculum of service and pre-service teacher training when we design digital textbook.

3. To encourage teachers to found professional growth communities

　　According to the findings, some teachers cooperate with other math teachers in their own schools. They supported and shared one another in all dimensions such as the implementation of a project, the development of teaching materials, and the teaching methods, so they formed a good teaching climate. Therefore, I suggest that it can be consider encouraging teachers to found professional growth communities, in a school or between schools, to help teachers about the usage of a software, the discussion of teaching methods, to establish item pool, etc.

4. To construct a sufficient and hierarchy item pool

　　The effectiveness of the teaching rely the assessment of students’ performance, the directest performance is the score of a test. Teachers adjust their teaching according to the test scores, at the same time, diagnostic the learning difficulties. Some participants mentioned to construct an item pool. This is a big project which need many teachers cooperate. A good item pool will be helpful to provide immediate feedback on the exercise of students.

5. To choose the contents which is abstract and difficult to develop digital textbook, and help students transition from concrete to formal operations.