實體教具融入國小數學教學設計：以方塊堆疊與計數為例

Integrating Physical Manipulatives Into the Instructional Design of Elementary School Mathematics: Use Counting Stacked Cubes As an Example

長久以來，如何在課程中融入實體教具操作進而發展學生數學概念是一大挑戰。本研究發展出五項教學設計原則，並以方塊堆疊與計數為例進行教學設計，後經三個二年級班級的實踐，調整成最後版本。五項原則如下：一、選擇適合學生學習之現象問題；二、佈題層次依具體活動、表徵活動及抽象運思活動做編排；三、透過心理學佈題促進解題活動層次之提升；四、透過社會學佈題促進群體溝通討論；五、預測學生可能之解題策略及思考後續教學處理。教學實施後，學生不僅發展出多元的方塊計數策略，亦認為教具有助於學習且讓數學課變得有趣好玩。本教學設計與五項原則間之關係在文中多所論述，期供教師未來進行融入實體教具的教學設計參考。

For a long time, how to integrate the operation of physical manipulatives into the curriculum to develop students’ mathematical concepts has been a big challenge. This study developed five design principles, and used counting stacked cubes as an example for instructional design. After the practice of three second-grade classes, the instructional design was adjusted to the final version. The five principles are as follows: (1) Choose phenomenological problems that suit students’ learning. (2) The level of topic layout is arranged according to sensori-motor activity, re-presenting activity and mental activity. (3) Improve the level of problem-solving activities through psychological problems. (4) Promote group communication and discussion through sociological problems. (5) Predict students’ possible problem-solving strategies and think about subsequent teaching treatments. After the implementation of the teaching, students not only developed a variety of stacked cubes counting strategies, but also thinked that physical manipulatives were helpful for learning and made math lessons interesting. The relationship between this instructional design and the five principles is discussed in the article, and it is expected to be a reference for teachers in future instructional design incorporating physical manipulatives.