-
[email protected] (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))
