-

shiangtungliu@gmail.com (Reinvent the wheel)1. to offer meaningful mathematical problems (),2. to emphasize depth in math thinking rather than exposure to a series of fragmented topics (), and3. to have students invent their own strategies () and approaches () rather than rely on memorized procedure (). (NCTM, 1989)Few of teachers have sufficient experience () with authentic () inquiry based learning to make it a common reality () for gifted students.

Inquiry based learning and teaching () () (PCK) (Shulman, 1987) 1. 2. 3. (PCK) 4.

(Grossman, 1990)(Gifted Childrens Mathematics)()

Gifted students problem solving is characterized by insight and seeing general phenomena through a mathematical lens.

Insight of problem solving (Kruttskii, 1976)Knowing how gifted children think mathematically and how this think differs from other studentscan help design both regular and differentiated math curricula ()? Challenge enough ()?()()

43

2

():

- 1 + 2/7 ?(16/7 24 1 ?)6%35050001010%30

(11, 21, 31?)

25%%( 5/4)

-

1

1

()

Lamon12860121830241072271850()1. ()2. 3.

:1 0.0460.00012 0.1350.00013. 0.50.010.001

()

1. (Polya)2. (Schoenfeld)3. -(Mason) 4. ()

(PCK) Polya

1

( ) (A)11 *( ) (B) ( ) (C) ( ) (D) *

1(1)

( ) (A)112233( ) (B)( ) (C)135( )(D)1 35

(2)

( ) (A)9( ) (B)14( ) (C)18( ) (D)28

(A) 1 (B) 4 (C) 5 (D) 1+3+5

4

(Resource) (Heuristics) (Control) (Believe system)(Schoenfeld,1985)()()()

A(1.2)B(1.3)

()()()45(1.2)(1.3)53

(Inquiring)(Focusing)(Testing)

(Repetition) (Revoicing) (Question) (Challenge)

(Resnick, 1995))