# 初中數學課題的學與教

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## 學與教的銜接」研討會

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Liebeck (1984)

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### 一般的舊中一教科書（85 課程）

Ch 1 (N) Fundamental Arithmetic

Ch 2 (A) Numbers and Counting

Ch 3 (A) Introduction to Algebra

Ch 4 (G) Fundamental Geometry

Ch 5 (N) Percentages

Ch 6 (N+G) Simple Areas and Volumes

Ch 7 (G) Congruence and Similarity

Ch 8 (G) More About Geometrical Constructions

Ch 9 (A) Directed Numbers

Ch10 (G) Introduction to Coordinates

Ch11 (A) Algebraic Expressions

課題內容 分佈平均，

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ii) 分式運算

3 2 2

1

3

2 21 

iii) 指數運算

5 4

3

4 3

5 26 1

a a

a

a a a

##  

22 53

157

3

1110

2

i) 解方程

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### 3 Habits of thinking critical to the developing power in algebraic thinking

1. Doing-undoing (the capacity not only able to use a process to get to a goal, but also to understand the process well enough to work backward from the answer to the starting point)

2. Building rules to represent functions (the capacity to

recognize patterns and organize data to represent situations in which input is related to output by well-defined functional

rules)

3. Abstracting from computations (the capacity to think about computations independently of particular numbers that are used)

Mark Driscoll (1999) Fostering Algebraic Thinking

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### 二、教學內容上的銜接

ab = a × b 但 23 = 2 × 10 + 3

2 (3+4)=2 3+2 4 而且 a (b + c) = ab + ac 但是 f (a + b)  f (a) + f (b) a (b+c) = ab + ac 但是 (b+c)a ba + ca

x 由一未知數變得更廣的意義

2 2

2

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2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

m

n

(m+n)

m

n

mn

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2

=

x x

x 1

1 1

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### - 繪畫立體圖形的 橫切面

立 體 平 面 圖 像 摺 紙 圖 樣

立 方 體

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## References

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