### Abstract

分數乘法教學的主流方式大都以「程序記憶」的形式出現。例如只要求學生記下分數乘法的公式(ab xcd =axcbxd )。這個公式只是計算過程的總結，或者是基模的表達，知道公式不一定代表理解概念。強記而缺乏深度概念，做成以後更多的學習困難。本文討論如何引入概念教學，以ELPS (Experience, Language, Picture, Symbol) 模式，理解分數乘法的結構(分數比例除乘概念)和分數連加概念。首先學習整數乘單位分數，再引入兩個分數相乘的概念。學習過程以「結構對應概念」和「猜想引證」主導，並在兩個小學試教。學生由不同的表達形式和結構對應計算來加強分數乘法的理解。

The “main stream” approach in teaching multiplication of fractions is “memory and procedural”, for example, students are usually taught to remember the formula of fractions multiplication (a/(b )× c/d = (a×c)/(b×d)). The formula is a procedural result which is only a conclusion of a procedure or a representation of a schema. Knowing the formula does not necessary imply concept understanding. Such memorization approach without sufficient depth in concept formation resulted in further difficulties ahead in learning. This paper discusses a conceptual approach in teaching fractions multiplication, with reference to the ELPS model (Experience, Language, Picture, symbol) and the understanding of the structure of fraction multiplications (ratio using division and multiplication) which connected with repeated fraction additions. The teaching starts with multiplication of a whole number with a unit fraction, before proceeding to multiplication of two fractions. The learning approach involves activities in “concept and structure correspondence” and “conjecturing with verification”. The teachings were conducted in two primary schools, students work with different representations to enhance their understanding of fraction multiplication through correspondence is structure and calculation. Copyright © 2011 Department of Mathematics and Information Technology, The Hong Kong Institute of Education.

The “main stream” approach in teaching multiplication of fractions is “memory and procedural”, for example, students are usually taught to remember the formula of fractions multiplication (a/(b )× c/d = (a×c)/(b×d)). The formula is a procedural result which is only a conclusion of a procedure or a representation of a schema. Knowing the formula does not necessary imply concept understanding. Such memorization approach without sufficient depth in concept formation resulted in further difficulties ahead in learning. This paper discusses a conceptual approach in teaching fractions multiplication, with reference to the ELPS model (Experience, Language, Picture, symbol) and the understanding of the structure of fraction multiplications (ratio using division and multiplication) which connected with repeated fraction additions. The teaching starts with multiplication of a whole number with a unit fraction, before proceeding to multiplication of two fractions. The learning approach involves activities in “concept and structure correspondence” and “conjecturing with verification”. The teachings were conducted in two primary schools, students work with different representations to enhance their understanding of fraction multiplication through correspondence is structure and calculation. Copyright © 2011 Department of Mathematics and Information Technology, The Hong Kong Institute of Education.

Original language | Chinese |
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Pages (from-to) | 55-65 |

Journal | 數學教育期刊 |

Volume | 45 |

Publication status | Published - Jun 2011 |

### Citation

鄭振初(2011)：分數乘法結構教學設計，《數學教育期刊》，45，頁55-65。### Keywords

- 分數乘法教學
- ELPS的教學模式
- Alt. title: Teaching design in structure if fractions multiplication