( 網 上 版 ) 數 學 教 育 學 習 領 域 數 學 科 課 程 及 評 估 指 引 ( 中 四 至 中 六 ) 課 程 發 展 議 會 與 香 港 考 試 及 評 核 局 聯 合 編 訂 香 港 特 別 行 政 區 政 府 教 育 統 籌 局 建 議 學 校 採 用 二 零 零 七 年
( )
1 1.1 1 1.2 1 1.3 2 1.4 2 5 2.1 5 2.2 6 2.3 9 2.4 9 2.5 11 2.6 34 69 3.1 69 3.2 70 3.3 72 3.4 78 81 4.1 81 4.2 81 4.3 83 4.4 88 4.5 90 4.6 91 4.7 91 93 5.1 93 5.2 93 5.3 94 5.4 95 5.5 98 i 103 6.1 103
6.2 103 6.3 104 6.4 107 6.5 107 109 1. 109 2. 118 127 131
( ) 2005 1 2009 9 2000 (2002) (2007) ( ) 405 4 ( ) 3426 9265 ccdoma@emb.gov.hk 1 334 i
( ) ii
1.1-2005 5 334 1.2 1
1.3 (a) (b) (c) (d) (e) 1.4 1.4.1 2
1.4.2 ( ) / ( ) ( ) 3
( ) 4
2.1 (a) (b) ( ) ( ) (c) ( ) ( ) 5
(d) (e) (f) (g) 2.2 6
( ) ( ) ( ) ( ( ) ) 7
2.2.1 2.2.2 2.2.3 8
2.3 (a) (b) (c) (d) (e) (f) (g) 2.4 9
(1) (2) (3) (4) 10
(5) 15% 405 ( ) 2.5 10% - 12.5% 270-338 15% 405 2.5.1 11
2.5.2 12
2.5.3 13
2.5.4 10% 12.5% 270 338 14
1. 2. 3. 4. 5. 6. 338 12.5% 15 1. 1.1 19 1.2 1.3 y = ax 2 + bx + c x ax 2 + bx + c = 0
1.4 a ± bi 2 ± 48 1.5 1.8 < 0 16 1.6 6 6 + = 5 x x 1 5.4 1.7 α + β = b α β = a c a α β ax 2 + bx + c = 0 a 0
1.8 1.9 a ± bi 2. 2.1 10 17 2.2 1 2 2.3
2.4 3. 3.1 16 n a a 1 n n m a 3 8 18 3.2 a p a q = a p+q a a p q = a p q (a p ) q = a pq a p b p = (ab) p a b p p = a b p 3.3 log a 1 = 0 log a a = 1 log a MN = log a M + log a N
log a M N log a M k = k log a M log b N = = log a M log a N log log a a N b 19 3.4 a >1 0 < a < 1 x f (x) = a x y = a x y = log a x y = x log(x + 26) = 2 3.5 4 x 3 2 x 4 = 0 log(x 22) + 5.3 3.6
3.7 ( ) 4. 4.1 14 4.2 4.3 4.4 H.C.F. gcd 20 4.5 5. 5.1 10 y = ax 2 + bx + c 5.2 5.3 0 360
5.4 6. 6.1 9 6.2 6.3 21 7. 7.1 17 T n = ½ ( T n 1 + T n+1 ) T 1, T 2, T 3, k T 1 + a, k T 2 + a, k T 3 + a, 7.2 7.3 7.4 T n 2 = T n 1 T n+1 T 1, T 2, T 3, k T 1, k T 2, k T 3,
7.5 7.6 7.7 8. 8.1 16 22 8.2 8.3 8.4 8.5 8.6 9. 9.1 11 9.2 y = f (x) f (x) = k
9.3 y = f (x) f (x) > k f (x) < k f (x) k f (x) k 9.4 f (x) f (x) + k f (x + k) k f (x) f (kx) 23 10. 10.1 23
10.2 24 10.3 10.4 A D BC BAC = BDC A B C D
10.5 25 10.6
11. 11.1 7 11.2 26 11.3 y = ax 2 + bx + c 12. 12.1 14 y
27 12.2 12.3
12.4 13. 13.1 21 θ 90 ± θ 180 ± θ 13.2 a sin θ = b a cos θ = b a tan θ = b 0 360 5.3 0 360 13.3 ½ absin C 28 13.4 13.5 13.6 13.3 13.5
14. 14.1 11 14.2 P n r n P r n P r 14.3 29 14.4 C n r n C r n n C r r 14.5 15. 15.1 10 15.2 P(A B) = P(A) + P(B) P(A B) 15.3 P(A B) = P(A) P(B) A B
15.4 P(A B) = P(A) P(B A) 15.5 16. 16.1 14 16.2 30 16.3 16.4 σ = 2 ( x µ ) + K + ( xn µ N 2 1 ) 16.5 16.6
16.7 (i) (ii) (iii) (iv) 31 17. 17.1 8 17.2 17.3
32 18. 20 (a) (b) y = m x + c y = k a x
19. 20 270 33
2.6 2.6.1 2.6.2 ( ) ( ) 34
( ) 35
e 2.6.3 15% ( 405 ) ) 36
1. 2. 3. 4. 37 1. 1.1 ( a + b) n n 3 ( ) 2 3 2. 2.1 e x x e x = 1+ x + + +... 2! 3! 7
2.2 x y = e y = ln x 2.3 38 n x 2.4 y = kx y = ka a n k a > 0 a 1 x y 10 3. 3.1 6
3.2 x α 2 + x 1 39 3.3 dy ' y f '( x) dx 3.4 ) y = f (x x = x0 dy f '( x0 ) dx x= x 0 4. 4.1 10 d ( u + v) = dx d ( uv) = dx du dx dv u dx + + v dv dx du dx
d ( dx dy = dx u v ) = dy du dx 1 = dy dy dx du v u dx 2 v du dx dv dx 40 4.2 ( C)' = 0 C ( x n )' = nx n 1 x ( e )' = e ( ln x)' = x 1 x ( log )' = a x x 1 ln a x ( a )' = a ln a x
5. 5.1 2 2 d y " y f "( x) 2 dx 5.2 6. 6.1 9 27 41 7. 7.1 10 7.2 ( f x) dx kf( xdx ) = k f( x) dx k [ f( x) ± gx ( )] dx= f( x) dx ± gxdx ( )
C kdx= kx+ C k n+ 1 n x x dx= + C 1 n n + 1 1 dx= ln x + C x x x e dx= e + C 42 7.3 7.4 7.5
8. 8.1 15 b ( f x) dx a a b f( x) dx= f() t dt a b 8.2 43 b f( x) dx= Fb ( ) Fa ( ) a d F( x) = f ( x) dx b f( x) dx = f( x) dx a a f( x) dx = 0 a b c b f() x dx= f() x dx+ f() x dx a a c b a b b kf( x) dx= k f( x) dx a k a
8.3 8.4 8.5 8.6 b [ f( x) ± gx ( )] dx a = b b a a f( x) dx± gx ( ) dx 44 9. 9.1 4 29 10. 10.1 3 10.2 P A B = P A P B A P (D C = P D C D
11. 11.1 4 7 12. 12.1 1 13. 13.1 5 45 13.2 E(X ) Var( X ) 13.3 E ( ax + b) = a E( X ) + b 2 Var( ax + b) = a Var( X ) 14. 14.1 5 ( ) 14.2 15. 15.1 4 ( ) 15.2
16. 16.1 4 ( ) 16.2 17. 17.1 5 24 46 18. 18.1 3 13.3 18.2 σ 1
19. 19.1 2 20. 20.1 x 1, x 2, µ σ 7 P ( X > x1) P ( X < x2 ) P ( x1 < X < x2 ) X ~ N(µ,σ 2 ) 20.2 PX ( > x) ( PX < x) ( Pa< X < x) Px ( < X < b) x X ~ N(µ,σ 2 ) 47 20.3 12 21. 21.1 7 21.2 n µ σ 2 µ 2 σ n
48 21.3 µ N σ N 2 i= = 1 ( x µ) i N 2 x n 21.4 s 2 = n i= 1 ( x i x) n 1 2 22. 22.1 6 22.2 (a) 2 σ µ 100( 1 α )% σ σ ( x z α, x + z α ) 2 2 n n
(b) n µ 100( 1 α )% s s ( x z α, x + z α ) 2 2 n n s 49 23. 23.1 3 ( n ) p 100( 1 α )% 16 pˆ(1 pˆ) pˆ(1 pˆ) ( pˆ zα, pˆ + zα ) 2 2 n n ˆp
24. 10 10 135 50
1. 2. 3. 4. 51 1. k 1.1 a ± b 1.5 2. 2.1 5
3. 3.1 3 4. 4.1 11 Σ 52 4.2 4.3 4.4 1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = cosec 2 θ 4.5 sin(a ± B) = sin A cos B ± cos A sin B cos(a ± B) = cos A cos B m sin A sin B tan(a ± B) = tan A ± tan B 1m tan A tan B sin 2A = 2 sin A cos A
cos 2A = cos 2 A sin 2 A = 1 2 sin 2 A = 2 cos 2 A 1 tan 2A = 2 tan A 1 tan 2 A sin 2 A = 2 1 (1 cos 2A) cos 2 A = 2 1 (1 + cos 2A) 2 sin A cos B = sin(a + B) + sin(a B) 2 cos A cos B = cos(a + B) + cos(a B) 53 2 sin A sin B = cos(a B) cos(a + B) A + B A B sin A + sin B = 2 sin cos 2 2 A + B A B sin A sin B = 2 cos sin 2 2 A + B A B cos A + cos B = 2 cos cos 2 2 A + B A B cos A cos B = 2 sin sin 2 2
sin = 1 cos2 2 2 1 A ( A ) cos 1 cos2 2 2 1 A= ( + A ) 5. e 5.1 e 1.5 e 1 e = lim (1 + ) n n n 54 2 3 x x e x = 1+ x + + + L 2! 3! 6.1 22 6. 6.1 5 x sgn(x)
x x 55 6.2 sin lim θ 0 e x θ θ 1 lim x 0 x = 1 = 1 7. 7.1 14 C x n n x sin x cos x e x ln x dy y' f '(x) dx 7.2 d du dv ( u + v) = + dx dx dx
d ( uv) = dx d ( dx dy = dx u v ) = dy du dv u dx + v du dx du v u dx 2 v du dx dv dx 56 7.3 (C)' = 0 (x n )' = n x n 1 (sin x)' = cos x (cos x)' = sin x (tan x)' = sec 2 x (cot x)' = cosec 2 x (sec x)' = sec x tan x (cosec x)' = cosec x cot x (e x )' = e x (ln x)' = 1 x
x α x 2 + 1 7.4 57 7.5 2 d y y" f "(x) 2 dx 8. 8.1 14 8.2 8.3 x y
8.4 33 58 9. 9.1 16 9.2 kdx= kx+ C n+ 1 n x x dx= + C n + 1 n 1 1 dx= ln x + C x
x x e dx= e + C sinxdx= cos x+ C cosxdx= sin x+ C 2 sec xdx= tan x+ C 2 cosec xdx= cot x+ C secxtanxdx= sec x+ C 59 cosecxcotxdx= cosec x+ C 9.4 9.6 9.3 9.4
9.5 ln xdx 2 2 2 2 9.6 a x, x a 2 2 a + x sin 1 x cos 1 x tan 1 x 60 10. 10.1 11 a b b f( x) dx= f() t dt a 10.2 b f( x) dx = f( x) dx a a f( x) dx = 0 a b c b fxdx () = fxdx () + fxdx () a a c b a
b kf( x) dx= k f( x) dx a b [ f( x) ± gx ( )] dx a = b b a a f( x) dx± gx ( ) dx 10.3 b f( x) dx= Fb ( ) Fa ( ) a d F(x) = f (x) dx a b 61 10.4 10.5 10.6 f a f( x) dx = 0 a f a a f( x) dx= 2 f( x) dx 0 a f (x + T ) = f (x) f
11. 11.1 7 nt f( x) dx= n f( x) dx 0 0 11.2 34 T 62 12. 12.1 3 a b c 1 1 1 a b c 2 2 2 a b c 3 3 3 a b c 1 1 1 a b c 2 2 2 a b c 3 3 3 a a a 1 2 3 = b b b 1 2 3 c c c 1 2 3 c b a 1 1 1 = c b a 2 2 2 c b a 3 3 3 a a a b 1 1 b 2 2 b 3 3 0 0 = 0 0 a kb c 1 1 1 a kb c 2 2 2 a kb c 3 3 3 a b c 1 1 1 = k a b c 2 2 2 a b c 3 3 3
a 1 a2 a 3 b b b 1 2 3 kb kb kb 1 2 3 = 0 + a a b c ' 1 1 1 1 a + a ' b c 2 2 2 2 a + a ' b c 3 3 3 3 a b c 1 1 1 = a b c + a ' b c 2 2 2 a b c 3 3 3 a ' b c 1 1 1 2 2 2 a ' b c 3 3 3 1 a2 a + kb 3 1 + kb 2 a + kb 3 b b b 1 2 3 c c c 1 2 3 a a 1 = a 2 3 b b b 1 2 3 c c c 1 2 3 63 a 1 a2 a 3 b b b 1 2 3 c c c 1 2 3 b = a1 b 2 3 c c 2 3 a 2 b b 1 3 c1 b1 + a3 c b 3 2 c c 1 2 A det(a) 13. 13.1 9 A + B = B + A A + (B + C) = (A + B) + C (λ + µ)a = λa + µa λ(a + B) = λa + λb A(BC) = (AB)C
A(B + C) = AB + AC (A + B)C = AC + BC (λa)(µb) = (λµ)ab AB = A B 64 13.2 A (A 1 ) 1 = A (λa) 1 = λ 1 A 1 (A n ) 1 = (A 1 ) n (A t ) 1 = (A 1 ) t A 1 = A 1 (AB) 1 = B 1 A 1 A B λ 14. 14.1 6 18
15. 15.1 5 a AB a r AB a a a r 65 15.2 a + b = b + a a + (b + c) = (a + b) + c a + 0 = a 0 a = 0 λ(µa) = (λµ)a (λ + µ)a = λa + µa λ(a + b) = λa + λb
αa + βb = α 1 a + β 1 b a b α = α 1 β = β 1 15.3 R 3 2 2 OP = x + y + z 2 66 R 2 sin θ = cos θ = x 2 x + y 2 x 2 y + y 2 15.2 16. 16.1 5 a b = b a a (λb) = λ(a b) a (b + c) = a b + a c a a = a 2 0 a a = 0 a = 0
a b a b a b 2 = a 2 + b 2 2(a b) 67 16.2 R 3 a a = 0 b a = (a b) (a + b) c = a c + b c a (b + c) = a b + a c (λa) b = a (λb) = λ(a b) a b 2 = a 2 b 2 (a b) 2 (a b) c = a (b c) (a b) c = (b c) a = (c a) b 17. 17.1 8 18
18. 10 10 135 68
3.1 (a) (b) (c) (d) (e) 69
(f) (g) (h) 3.2 3.2.1 (a) (b) (c) (d) (e) (f) (g) 70
3.2.2 71
3.3 72
( ) 73
74
75
76
77
3.4 ( ) (a) (b) 78
(c) 79
( ) 80
(2007) 4.1 4.2 : : 81
: : : : : : : : : 82
: : : 4.3 83
combination lock n C r n r 84
A D B C A B C D AC BD AB CD AB AC * * 85
2 2 ( x 5 = 0 x 2x 5 = 0 2 x 2x c = 0 ) x 2 86
a b 2 = a 2 + b 2 2(a b) a b a b a b = 0 87
a b a b a b x 2 = x x 4.4 88
(a) (b) 89
4.5 90
4.6 x 3 x x 2 3x + 2 4.7 91
92
2006 5.1 5.2 93
2001 5.3 94
5.4 5.4.1 (a) (b) (c) 95
(d) (e) (f) (g) (h) 5.4.2 96
97
5.5 5.5.1 (a) (b) (c) (d) (e) 98
5.5.2 5.1 5.1 55% 30% 15% 2¼ 1¼ 100% 2½ 100% 2½ 85% 15% 5.5.4 5.2 5.5.3 99
5.5.4 100
5.2 2012 100 2013 100 2014 2015 100 100 2016 15 2009 5.5.5 5.1 5.1 U 1 2 3 4 5 / 1 5 5 1 U 101
4 5 A D A D 4 5 ** * 102
6.1 6.2 103
6.3 6.3.1 6.1?????????? 6.2 104
6.2????? 6.3.2???? 6.3.3 Winplot Geometer s Sketchpad 105
Ask Dr Math Ask NRICH http:// www.emb.gov.hk/index.aspx?langno=2& nodeid=2403 6.3.4 http://www.hkame.org.hk/ http://www.hkasme.org/us.htm http://www.math.hkbu.edu.hk/hkms/hkms.html http://www.hkss.org.hk 106
6.4 6.5 / ( ) http://www.emb.gov.hk/cr 107
( ) 108
1 (1) Bernstein, S. ( ) 2002 ( ) (2) Bolt, B. ( 1995 (3) Bolt, B. 1996 (4) Bolt, B. ( ) 1996 (5) Bolt, B. 1995 (6) Bolt, B., & Hobbs, D. ( ) 1996 (7) Dunham, W. 1995 (8) Polya, G. ( ) 1998 (9) Sobel, M.A., & Maletsky, E.M. ( ) 1996 (10) 1986 (11) 2002 (12) 1981 1 4 (13) 2003 (14) 2000 109
(15) 1998 (16) 1997 (17) 2000 (18) 2004 1 (19) 2006 ( ) (20) 2006 ( ) (21) 2006 ( ) (22) ( ) 2001 (23) ( ) 1992 1984 (24) 2003 (25) 2002 (26) ( ) 1999 (27) 2004 (28) 2003 (29) 1996 (30) 1995 (31) 1985 (32) 1993 (33) 1999 (34) 1999 (35) ( ) 1967 (36) ( ) 2002 ( ) 110
(37) 2003 (38) 2003 (39) 2003 (40) 2004 (41) 2004 (42) 2003 (43) 1998 (44) (2005) : (45) 1980 (46) (1998) : (47) 2001 1 I (48) 2001 II (49) 1982 (50) 2000 (51) 2000 (52) 2000 (53) ( ) 1992 1990 (54) (2005) : (55) 1997 (56) 2004 111
(57) 2003 (58) Bolt, B. (1982). Mathematical Activities: A Resource Book for Teachers. New York: Cambridge University Press. (59) Bolt, B. (1985). More Mathematical Activities: A Resource Book for Teachers. New York: Cambridge University Press. (60) Bolt, B. (1987). Even More Mathematical Activities. New York: Cambridge University Press. (61) Bolt, B. (1989). The Mathematical Funfair. New York: Cambridge University Press. (62) Bolt, B., & Hobbs, D. (1989). 101 Mathematical Projects: A Resource Book. New York: Cambridge University Press. (63) Coxeter, H.S.M., & Greitzer, S.L. (1967). Geometry Revisited. Washington, D.C.: The Mathematical Association of America. (64) Curriculum Development Council (1991). An English-Chinese Glossary of Terms Commonly Used in the Teaching of Mathematics in Secondary School. Hong Kong: the Curriculum Development Council, the Education Department. (65) Gamow, G. (1988). One, Two, Three Infinity: Facts and Speculations of Science. New York: Dover Publications. (66) Heath, T.L. (1926). The Thirteen Books of Euclid s Elements, translated from the text of Heiberg, with Introduction and Commentary. University Press, Cambridge. (Dover reprint 1956). (67) Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. (68) Leung, K.T., & Cheung, P.H. (1988). Fundamental Concepts of Mathematics. Hong Kong: Hong Kong University Press. (69) Maxwell, E.A. (1959). Fallacies in Mathematics. New York: Cambridge University Press. (70) Moore, D.S. (2000). The Basic Practice of Statistics. (second edition) New York : W.H. Freeman and Company. (71) Pappas, T. (1989). The Joy of Mathematics: Discovering Mathematics All Around You. San Carlo: Wide World. (72) Polya, G. (1981). Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. New York: Wiley. (73) Polya, G. (1990). Mathematics and Plausible Reasoning. New Jersey: Princeton University Press. 112
(74) Sobel, M.A., & Maletsky, E.M. (1999). Teaching Mathematics: A Sourcebook of Aids, Activities and Strategies. Allyn & Bacon. (75) Stevenson, H. W. (1992). Learning Gap: Why Our Schools Are Failing And What We Can Learn From Japanese And Chinese Education. New York: Summit Books. (76) Stigler, J.W., & Hiebert, J. (1999). The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom. New York: Free Press. (77) Struik, D.J. (1987). A Concise History of Mathematics. New York: Dover Publications. 113
(1) Bernstein, S. ( ) 2002 ( ) (2) Bolt, B., & Hobbs, D. ( ) 1996 (3) Bolt, B. ( ) 1996 (4) Bolt, B. ( ) 1995 (5) Bolt, B. ( ) 1996 (6) Bolt, B. ( ) 1995 (7) Dunham, W. ( ) 1995 (8) Polya, G. ( ) 1998 (9) ( ) 1986 (10) ( ) 2002 (11) ( ) 1981 1 4 (12) 2003 (13) 2000 (14) 1998 (15) 1997 (16) 2000 114
(17) 2004 1 (18) 2006 ( ) (19) 2006 ( ) (20) 2006 ( ) (21) ( ) 2003 (22) 2003 (23) ( ) 1999 (24) 2004 (25) 2003 (26) 1995 (27) 1985 (28) 1993 (29) 1999 (30) 1999 (31) ( ) 1967 (32) ( ) 2002 ( ) (33) 2003 (34) 2003 (35) 2003 (36) 2004 (37) 2004 (38) 2003 (39) 2005 : 115
(40) 1980 (41) 1998 : (42) 2001 1 I (43) 2001 II (44) 1982 (45) ( ) 1992 (46) 2005 : (47) 1997 (48) 2004 (49) 2003 (50) Bolt, B. (1982). Mathematical Activities: A Resource Book for Teachers. New York: Cambridge University Press. (51) Bolt, B. (1985). More Mathematical Activities: A Resource Book for Teachers. New York: Cambridge University Press. (52) Bolt, B. (1987). Even More Mathematical Activities. New York: Cambridge University Press. (53) Bolt, B. (1989). The Mathematical Funfair. New York: Cambridge University Press. (54) Bolt, B., & Hobbs, D. (1989). 101 Mathematical Projects: A Resource Book. New York: Cambridge University Press. (55) Coxeter, H.S.M., & Greitzer, S.L. (1967). Geometry Revisited. Washington, D.C.: The Mathematical Association of America. (56) Curriculum Development Council (1991). An English-Chinese Glossary of Terms Commonly Used in the Teaching of Mathematics in Secondary School. Hong Kong: the Curriculum Development Council, the Education Department. (57) Gamow, G. (1947). One, Two, Three Infinity. New York: Dover Publications. (58) Heath, T.L. (1952). The Thirteen Books of Euclid s Elements. New York: Dover Publications. (59) Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New 116
York: Oxford University Press. (60) Leung, K.T., & Cheung, P.H. (1988). Fundamental Concepts of Mathematics. Hong Kong: Hong Kong University Press. (61) Maxwell, E.A. (1959). Fallacies in Mathematics. New York: Cambridge University Press. (62) Pappas, T. (1989). The Joy of Mathematics: Discovering Mathematics All Around You. San Carlo: Wide World. (63) Polya, G. (1981). Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. New York: Wiley. (64) Polya, G. (1990). Mathematics and Plausible Reasoning. New Jersey: Princeton University Press. (65) Struik, D.J. (1987). A Concise History of Mathematics. New York: Dover Publications. 117
2 www.emb.gov.hk/index.aspx?langno=2&nodeid= 2403 (1) http://home.netvigator.com/~adtalent/index.html (2) http://www.czsx.com.cn/ (3) http://www.cmi.hku.hk/teaching/math.html (4) http://www.pep.com.cn/gzsx/ (5) http://menet.math.ecnu.edu.cn/index.php (6) All Elementary Mathematics- Online Math School http://www.bymath.com/stuff/aboutus.html (7) Ask Dr. Math http://forum.swarthmore.edu/dr.math/dr-math.html (8) Association of Teachers of Mathematics in UK http://www.atm.org.uk/ (9) Centre for Innovation in Mathematics Teaching http://www.ex.ac.uk/cimt/welcome.html (10) Centre for Teaching Mathematics, University of Plymouth http://www.tech.plym.ac.uk/maths/ctmhome/ctm.html (11) Education Department of The Hong Kong Institute of Education http://www.ied.edu.hk/math/ (12) EMB Mathematics Education Website http://www.emb.gov.hk/index.aspx?nodeid=2403&langno=1 (13) ExploreMath http://www.exploremath.com/index.cfm 118
(14) Fun Mathematics Lessons http://math.rice.edu/~lanius/lessons/ (15) HK Association for Mathematics Education http://www.hkame.org.hk/ (16) HK Association for Science and Mathematics Education Ltd http://www.hkasme.org/ (17) Java Applets on Mathematics http://www.walter-fendt.de/m14e/index.html (18) Manipula Math with Java http://www.ies.co.jp/math/java/ (19) Math Forum T2T Elementary Thoughts http://mathforum.org/t2t/faq/gail/index.html (20) Math in Daily Life http://www.learner.org/exhibits/dailymath/ (21) Mathematical Association of America Online http://www.maa.org/ (22) Mathematics LIVE on the Web http://www.aamt.edu.au/archives/livemath/mathview/home.htm (23) MathNet http://mathsnet.net/index.html (24) Maths On-line http://www.univie.ac.at/future.media/moe/galerie.html (25) MSTE Online Resources http://www.mste.uiuc.edu/resources.php (26) National Council of Teachers of Mathematics http://www.nctm.org/ (27) Numeracy Teaching Ideas http://www.teachingideas.co.uk/maths/contents.htm (28) Open-ended Assessment in Mathematics http://www.heinemann.com/math/register.cfm (29) Project Interactivate http://www.shodor.org/interactivate/ 119
(30) Schools of California Online Resources for Education (SCORE) Mathematics http://score.kings.k12.ca.us/ (31) Secondary Mathematics Assessment and Resource Database (SMARD) http://smard.cqu.edu.au/ (32) Shapescape http://www.shapescape.com/ (33) Support Measure for the Exceptionally Gifted Students http://gifted.hkedcity.net/ (34) http://www.math.ied.edu.hk/spkwan/paperfolding/index.htm (35) http://www.plklht.edu.hk/funmaths/fmaths.html (36) Curve Fitting Expert http://curveexpert.webhop.biz/ (37) Interactive Mathematics Miscellany and Puzzles http://www.cut-the-knot.org/ (38) Living Mathematics http://sunsite.ubc.ca/livingmathematics/ (39) Mathematical Excalibur http://www.math.ust.hk/mathematical_excalibur/ (40) Mathematical Stamp Collecting http://www.math.wfu.edu/~kuz/stamps/stamppage.htm (41) Mathpuzzle http://mathpuzzle.com/ (42) Mega Mathematics http://www.cs.uidaho.edu/~casey931/mega-math/index.html (43) NRICH Mathematics Enrichment Club http://nrich.maths.org/ 120
(44) Origami and Mathematics http://www.paperfolding.com/math/ (45) Probability Games http://www.betweenwaters.com/probab/probab.html (46) The Integrator http://integrals.wolfram.com/ (47) The National Math Trail http://www.nationalmathtrail.org/ (48) Agriculture, Fisheries and Conservation Department - Country & Marine Parks Useful Statistics http://www.afcd.gov.hk/tc_chi/country/cou-lea/cou_lea_use/cou_lea_use.html (49) Business-Stat Online http://stat.tdctrade.com/index_c.html (50) Census & Statistics Department http://www.censtatd.gov.hk (51) Economic and Social Commission for Asia and the Pacific (ESCAP) -- Statistics Division http://www.unescap.org/stat/data/index.asp (52) Economic Commission for Europe (ECE) -- Statistical Division http://www.unece.org/stats/data.htm (53) Environmental Protection Department http://www.epd.gov.hk/epd/tc_chi/environmentinhk/waste/data/waste_data.html (54) European Union: Eurostat http://europa.eu.int/comm/eurostat/ (55) Food and Agriculture Organization of the United Nations (FAO) http://www.fao.org/waicent/portal/statistics_en.asp (56) Hong Kong International Airport-International Air Traffic Statistics at HKIA http://www.hongkongairport.com/chi/aboutus/statistics.html (57) Hong Kong Statistical Society http:/www.hkss.org.hk/ 121
(58) Macau - Statistics and Census Service http://www.dsec.gov.mo/c_index.html (59) Narcotics Division, Security Bureau http://www.nd.gov.hk/c_statistics_list.htm (60) Organization for Economic Co-operation and Development (OECD) http://www.oecd.org/statsportal/0,2639,en_2825_293564_1_1_1_1_1,00.html (61) Singapore Department of Statistics http://www.singstat.gov.sg/keystats/mqstats/indicators.html (62) Statistical Glossary http://www.statsoft.com/textbook/glosfra.html (63) The Land Registry http://www.landreg.gov.hk/ch/monthly/monthly.htm (64) The World Bank Group http://devdata.worldbank.org/data-query/ (65) U.S. Census Bureau http://www.census.gov/main/www/access.html (66) United Nations Development Programme (UNDP) http://hdr.undp.org/statistics/data/ (67) United Nations Educational, Scientific and Cultural Organization (UNESCO) http://stats.uis.unesco.org/reportfolders/reportfolders.aspx (68) United Nations Headquarters -- Statistics Division (UNSD) http://unstats.un.org/unsd/databases.htm (69) World Health Organization (WHO) http://www3.who.int/whosis/mort/text/download.cfm?path=whosis,mort,mort_do wnload&language=english (70) http://www.cmi.hku.hk/ref/glossary/mat/k.htm (71) A Dictionary of Measures, Units and Conversions http://www.ex.ac.uk/cimt/dictunit/dictunit.htm#si 122
(72) Eric Weisstein's World of Mathematics http://mathworld.wolfram.com/ (73) Eurostat ISI Glossary of Statistics http://europa.eu.int/en/comm/eurostat/research/isi/alpha/en/en_list.htm (74) Glossary of Mathematical Terms http://www.cut-the-knot.com/glossary/atop.shtml (75) Interactive Mathematics Dictionary http://www.intermath-uga.gatech.edu/dictnary/homepg.asp (76) Math Dictionary http://users.adelphia.net/~mathhomeworkhelp/index.html (77) Mathematical Quotation Server http://math.furman.edu/mqs.html (78) The Encyclopedia of Polyhedra http://www.georgehart.com/virtual-polyhedra/vp.html (79) The Internet Glossary of Statistical Terms http://www.animatedsoftware.com/statglos/statglos.htm (80) Wikipedia - Mathematics http://www.wikipedia.org/wiki/mathematics (81) Xah Visual Dictionary of Special Plane Curves http://www.xahlee.org/specialplanecurves_dir/specialplanecurves.html (82) http://www.chiculture.net/0803/html/index.html (83) Chronological List of Mathematicians http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html (84) MacTutor History of Mathematics http://www-gap.dcs.st-and.ac.uk/~history/ (85) Mathematicians who were born or died today http://www-history.mcs.st-and.ac.uk/~history/day_files/now.html 123
(86) Cabri Geometry http://www.ti.com/calc/docs/cabri.htm (87) Geometer's Sketchpad http://www.keypress.com/pages/x5521.xml (88) Gnuplot http://www.gnuplot.info/ (89) Math WWW Virtual Library Mathematics Software http://www.math.fsu.edu/science/software.html (90) NCTM Illuminations - Tools http://illuminations.nctm.org/tools/index.aspx (91) Peanut Software (Winplot, Wingeom, Winstats,..) http://math.exeter.edu/rparris/winplot.html (92) Poly http://www.peda.com/poly/ (93) QuickMath http://www.quickmath.com/ (94) Scilab http://www.scilab.org/ (95) Hang Lung Mathematics Award http://www.hkedcity.net/article/special/hanglung/news.phtml (96) Hong Kong Mathematics Olympiad (HKMO) http://www.ied.edu.hk/msst/en/index.htm (97) International Mathematical Olympiad http://www.camel.math.ca/imo/ (98) International Mathematics Olympiad Hong Kong Preliminary Selection Contest http://gifted.hkedcity.net 124
(99) Mathematics Challenge for Young Australians http://www.amt.canberra.edu.au/wumcya.html (100) Mathematics Project Competition For Secondary Schools http://cd1.emb.hkedcity.net/cd/maths/en/ref_res/proj_learn/index.html (101) Web Sites with information about Mathematics Competitions http://www.mathpropress.com/competitions.html (102) World Class Tests http://www.worldclassarena.org/ondemand/default.asp?bhcp=1 (109) http://www.edp.ust.hk/previous/default.htm (110) http://www.math.sinica.edu.tw/media/default.jsp (103) American Mathematical Society http://e-math.ams.org/ (104) London Mathematical Society http://www.lms.ac.uk/ (105) Mathematical Database http://eng.mathdb.org/ (106) Mathematics Virtual Library http://www.math.fsu.edu/science/math.html (107) The Math Forum http://mathforum.org/ (108) Wolfram Research http://www.wolfram.com/ 125
( ) 126
( ) 127
128
129
130
(1) 2001 ( ) (2) 2003 ( ) (3) 2001 (4) 2004 ( ) : (5) ( ) 2004 (6) Ad hoc Committee on Holistic Review of the Mathematics Curriculum (2000). Report on Holistic Review of the Mathematics Curriculum. Hong Kong: The Government Printer. (7) Australian Education Council (1991). A National Statement on Mathematics for Australian Schools. Australia : Curriculum Corporation. (8) Baroody, A.J., & Coslick, R.T. (1998). Fostering Children s Mathematical Power An Investigative Approach to K-8 Mathematics Instruction. U.S.A.: Lawrence Erlbaum Associates. (9) Black, P., & William, D. (1998a). Assessment and classroom learning. Assessment in Education, 5 (1), 7-74. (10) Black, P., & William, D. (1998b). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, October, 139-148. (11) Board of Studies NSW (2003). HSC Assessment in a Standards-referenced Framework. Australia : New South Wales Board of Studies. (12) Bransford, J.D., Brown, A.L., & Cocking, R.R. (2001). How People Learn: Brain, Mind, Experience, and School: Expanded Edition. National Research Council. (13) Brumbaugh, D.K., & Rock, D. (2001). Teaching Secondary Mathematics. Second Edition. Lawrence Erlbaum Associates. (14) California State Board of Education (1992). Mathematics Framework for California Public Schools. USA : California Department of Education. (15) CDC (1985). Syllabuses for Secondary Schools Mathematics (Forms I-V). Hong Kong: The Government Printer. (16) CDC (1991). Syllabuses for Secondary Schools Mathematics and Statistics 131
(Advanced Supplementary Level). Hong Kong: The Government Printer. (17) CDC (1992). Syllabuses for Secondary Schools Applied Mathematics (Advanced Level). Hong Kong: The Government Printer. (18) CDC (1998). Syllabuses for Secondary Schools Applied Mathematics (Advanced Supplementary Level). Hong Kong: The Printing Department. (19) CDC (1999). Syllabuses for Secondary Schools Mathematics (Secondary 1 5). Hong Kong: The Printing Department. (20) CDC (2000). Learning to Learn Key Learning Area Mathematics Education Consultation Document. Hong Kong: The Printing Department. (21) CDC (2001). Learning to Learn Life Long Learning and Whole-person Development. Hong Kong: The Printing Department. (22) CDC (2001). Mathematics Education Key Learning Area Additional Mathematics Curriculum Guide (S4-S5). Hong Kong: The Printing Department. (23) CDC (2002). Basic Education Curriculum Guide Building on Strengths. Hong Kong: The Printing Department. (24) CDC (2002). Mathematics Education Key Learning Area Curriculum Guide (Primary 1 Secondary 3). Hong Kong: The Printing Department. (25) CDC (2004). Mathematics Education Key Learning Area Pure Mathematics Curriculum and Assessment Guide (Advanced Level). Hong Kong: The Government Logistics Department. (26) Cooney, T.J. (1990). Teaching and Learning Mathematics in the 1990s. 1990 Year Book. National Council of Teachers of Mathematics. (27) Education Commission (1999). Education Blueprint for the 21 st Century: Review of Academic System Aims of Education Consultation Document. Hong Kong: The Printing Department. (28) Education Commission (2000). Reform Proposals for the Education System in Hong Kong. Hong Kong: The Printing Department. (29) Education Commission (2003). Review of the Academic Structure of Senior Secondary Education. Hong Kong: Education Commission. (30) Fan, L., Wong, N.Y., Cai, J., & Li, S. (2004). Series on Mathematics Education Vol. 1: How Chinese Learn Mathematics Perspectives from Insiders. (31) Fung, C.I., & Wong N.Y. (1997). Mathematics Curriculum for Hong Kong. Hong Kong: Hong Kong Association for Mathematics Education. (32) Grinstein, L.S., & Lipsey, S.I. (2001). Encyclopedia of Mathematics Education. RoutledgeFalmer. 132
(33) International Baccalaureate Organization (2001). Diploma Programme Group 5 Mathematics. International Baccalaureate Organization. (34) Jan de Lange Jzn (1987). Mathematics Insight and Meaning. Vakgroep Onderzock Wiskundeonderwijs en Onderwijscomputercentrum. (35) Kodaira, K. (1996). Algebra and Geometry: Japanese grade 11. USA: American Mathematical Society. (36) Kodaira, K. (1996). Basic analysis: Japanese grade 11. USA: American Mathematical Society. (37) Kodaira, K. (1996). Mathematics 1: Japanese grade 10. USA: American Mathematical Society. (38) Kodaira, K. (1997). Mathematics 2s: Japanese grade 11. USA: American Mathematical Society. (39) Leung, F.K.S., Lam, C.C., Mok, I.A.C., Wong, P.K.M. & Wong, N.Y. (1999). Comparative Study of the Mathematics Curricula of Major Asian and Western Countries. Hong Kong : Hong Kong Education Department. (40) National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. (41) National Council of Teachers of Mathematics (1998). Exploring Classroom Assessment in Mathematics A Guide for Professional Development. Reston, VA: National Council of Teachers of Mathematics. (42) National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. (43) National Council of Teachers of Mathematics (2002). Mathematics Assessment Myths, Models, Good Questions and Practical Suggestions. Reston, VA: National Council of Teachers of Mathematics. (44) Orton, A., & Wain, G. (1994). Issues in Teaching Mathematics. Cassell. (45) Orton, A., (1987). Learning Mathematics: Issues, Theory and Classroom Practice. Second Edition. Cassell. (46) Smith, A. (2004). Making Mathematics Count. London: DfES. (47) Stiggins, R. (2004). New assessment beliefs for a new school mission. Phi Delta Kappan, 86 (1), 22-27. (48) Sue J.W., Peter J.W., Pimm, D., & Westwell, J. (1999). Learning to Teach Mathematics in the Secondary School: A Companion to School Experience. RoutledgeFalmer. (49) Tomlinson, M. (2004). Working Group on 14-19 Reform Interim Report. London: 133
Working Group on 14-19 Reform. (50) Wang, J., & Xu, B. (2004). Trends and Challenges in Mathematics Education. Shanghai: East China Normal University Press. (51) Watkins, C. (2005). Classrooms as Learning communities: What s in it for schools? Routledge. (52) Willoughby, S. (1990). Mathematics Education for a Challenging World. Association for Supervision and Curriculum Development. (53) Wong, N.Y., Lam, C.C., Leung, F.K.S., Mok, I.A.C. & Wong, P.K.M. (1999). An Analysis of the Views of Various Sectors on the Mathematics Curriculum. Hong Kong: Hong Kong: Education Department. 134
( 2003 12 ) : : 2004 1 2004 1 2004 1 2004 1 2005 8 2004 1 2004 1 : 2006 3 2006 4 :
( 2005 2 ) : : 2006 8 2006 9 2005 8 2005 9 : 2005 8 2005 9
( 2005 2 ) : : 2006 8 : 2005 8 2005 9 2006 8 2006 9
( 2005 2 ) : : 2005 9 2005 8 : 2005 8 2005 9 2006 8 2006 9
( 2005 2 ) : : 2006 9 : 2005 2 2005 8 2005 9 2006 8 2006 9