國立中山大學學位論文典藏.pdf

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4 Polya

5 2-1 Polya Schoenfeld Mayer

6 ~

8 Kilpatrick, 1987 Krulik Rudnick, 1993 Silver Cai, Brown Walter,

9 2000 National Council of Teachers of Mathematics NCTM NCTM, NCTM a 2004a 4

10 2004a -- 5

11 6

12 Mayer 1992 Mayer 7

13 Polya 1945 Schoenfeld 1985 Mayer 1992 Polya. Polya. Schoenfeld. Mayer.. 8

14 . Polya Polya 1945 How to solve it Understand 2. Plan 3. Carry out 4. Look back 2-1 Polya

15 heuristic Polya Polya 2-1 Polya 80 Polya 1999 Polya Polya Polya Polya Polya 2-1 Polya Polya,

16 11

17 . Schoenfeld Schoenfeld Schoenfeld 1985 resources heuristics control belief system heuristics strategies 12

18 Schoenfeld reading 2. analysis 3. exploration well structured 4. planning 5. implement 13

19 6. verify 2-2 Schoenfeld PI1 PI2 PI3 PI4 PI5 PI6 2-2 transition Schoenfeld 2-2 Schoenfeld Schoenfeld, reading R1 R2 R3 analysis A1 A2 A3 A4 A5 A1-A4 14

20 exploration E1 E2 E3 E4 -- planning-implementation PI1 PI2 PI3 PI4 PI5 PI6 verification V1 V2 V3 transition T1 T2 T3 T4 15

21 Schoenfeld Polya Schoenfeld Schoenfeld Schoenfeld metacognition Schoenfeld Polya Schoenfeld thinking aloud 1996 protocol 16

22 . Mayer Mayer 1992 Mayer 1987, Mayer 17

23 Mayer Schoenfeld Polya Mayer Schoenfeld 18

24 2000 Mayer 2-3 Mayer Mayer,

25 . Polya Schoenfeld Mayer Polya 1945 Schoenfeld 1985 Mayer 1992 Schoenfeld Mayer Polya Schoenfeld Mayer

26 Mayer

27 b

30 .... ( ) ( ) ( ) ( ) 1. Dillon Silver Stoyanova and Ellerton

31 ( ) idiosyncratic 2 plausible reasoning 3 before during and after problem solving primitive incomplete inplausible insufficient English

32 2002 Leung Silver, 1997 ( ) 1. Brown and Walter Choosing a starting point 1 Listing attributes 0 2 What-if-not 1 3 Question asking or problem posing 27

33 4 Analyzing the problem A. B. C. D. E. F. G. 3. Moses, Bjork and Goldenberg

34 Moses A. B. C. D. 4. Stoyanova and Ellerton 1996 A. structured B. semi-structured C. free 5. Cudmore and English 1998 A. B. C. 29

35 D. E. F. G. H. I A. B. C. D. E. F. G. H. I. J. K. L

36 31

37 . ( ) NCTM, 1989 Keil Stover 1982 Brown and Walter 1983 The art of problem posing 32

38 What-if-not Silver 1993 open approach teaching Nohda, 1984 Hashimoto, Australian Education Council Stovanova & Ellerton, 1996 Skinner What s your problem Skinner,

39 Winograd 1990 Winograd Winograd Borba

40 Schloemer 1994 What-if-not Silver Mamona-domwns Leung Kenney IP Initial Posing PS Problem Posing AP Additional Posing Leung Silver 1997 TAPP Test Arithmetic Problem Posing 63 English

41 English English Cai ( )

42 /

45 4. 40

46 Polya 1945 How to solve it Understand Plan Carry out Look back 1994 Polya Pose Understand 2-3 Look back Pose Carry out Plan

47 Polya

48 English 1997 NCTM, Brown & Walter, 1983 Stoyanova & Ellerton, 1996 English

49 ( ) 44

50 ( )

51 Mayer

52 N N N N N

53 A N N A A N N N A A-2-2 N N N N N N N-2-17

54 1999 Mayer ordinal interval ratio

55 2-5 50

57 . 2-2 Mayer Mayer Mayer 52

58 ( ) ( ) ( ) ( ) 53

62 ( ) ( ) ( ) ( ) ( ) ( ) 8 35 ( )

63 B 7. A 10 B 14 8 A ? 58

65 .. 60

66 S

68 ~ ~

69 ~ ~

70 36 18 p p s m p-s p-p

71 . ( ) 36 5 p-p-5 ( )

72 p-p p-p p-p p-p

73 p-p p-p-27. ( )

74 30 83% % % ( ) p-s

75 ( ) p-p ( ) p-m-15 70

76 p-m-13 ( ) 5 p-m-18 p-m-25 5 p-m-28 ( ) p-m-1 p-m-3 p-m-9 answer p-m-26 p-m-27 p-m-34 71

77 . ( ) ( ) ( ) 72

78 s p m 3-p s % 73

79 ( ) 4 4-p-35 ( ) 7 7-p-4 ( ) 8 8-p-30 74

80 (1.1%) 1 (0.4%) 273 (98.5%) 75

82 7 ( ) p-3 1-p-12 77

83 p-28 2-p p

84 8 8-p ( ) p-21 79

85 p p-14 80

86 p

87 ( ) p p

88 p A 10 B 14 8 A B p-12 83

89 7 7-p P

90 .. ( ) ( ) ( ). 85

91 ( ) ( ) ( ) ( )

92 ( ) ( )

93 4-3 ( ) 34 (97%) (94%) (86%) (89%) (94%) (91%) (97%) (85%) (80%) (80%) (57%) (69%) (63%) (74%) (46%) (69%)

94 . ( ) ( ) ( ) ( ) p-33 89

95 p ( ) 1. 7 A 10 B 14 8 A B

96 p ( ) p-33 91

98 . 4-4 ( ) 1-p ( ) s

99 ( ) 2-p ( ) 4-p

100 95

101 (63%) 5(10%) 9(19%) 4(8%) 48 96

102 . 3-m-16 4-m-7 3-m-27 8-m-11 97

103 . 1-m-23 2-m-20 5-m m-29 2-m-11 6-m-10 98

104 . 1-t 4-T 20 3-t t 99

105 12 1-t 15 7-t. 6 4-t 5-t t 100

106 . 98.5%. 101

107 .. 102

108

109

110 NSC C S NSC C H

111 NSC S NSC NSC S a b

112 NSC S Polya 1945/1993 How to Solve It : a new aspect of mathematics method 107

113 Borba M. C. (1994). High School Students' Mathematical Problem Posing: An Exploratory Study in the Classroom. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA. Brown, S. I. & Walter, M. I. (1983). The Art of Problem Posing. Philadelphia, PA: The Franklin Press. Brown,S. I. & Walter, M. I. (1993). Problem posing: Reflection and application. Hillsdale, NJ: Lawrence Erlbaum Associates. Cai, J. (1998). An investigation of U. S. and Chinese students mathmatical problem posing and problem solving. Mathematics Education Research Journal, 10(1), Cudmore, D. H. & English, L. D. (1998). Using Intranets to Foster Statistical Problem Posing and Critiquing in Secondary Mathematics Classrooms. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA. Dillon, J. T. (1982). Problem finding and solving. Journal of Creative Behavior, 16, English, L. D. (1997). Promoting a problem-posing classroom. Teaching children Mathematics, 4(3), 172. English, L. D. (1998). Children s problem posing within formal and in formal context. Journal for Research in Mathematics Education, 29(1), Hashimoto, Y. (1987). Classroom practices of problem solving in Japanese elementary school. Proceedings of the U.S. Japan Seminar on Mathematical Problem solving. Keil, G. E. (1965). Writing and solving original problems as a means of improving verbal arithmetic problem solving ability. Doctoral dissertation. 108

114 Kilpatrick,J. (1987). Problem formulation: Where do good problems come from? In A. H. Shoenfeld (Ed.), Cognition science and mathematics (pp ). Hillsdale, NJ: Lawrence Erlbaum Associates. Krulik, S., Rudnick, J.A.(1993). Reasoning and problem solving: A handbook for elementary school teachers. Boston: Allyn and Bason. Leung, S. S. & Silver, E. A. (1997). The role of task format, mathematics knowledge, and Creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9 (1), 5-24 Mayer, R. E. (1987). Education psychology: A cognitive approach. Toronto: Little, Brown and company. Mayer, R. E. (1992). Thinking, problem solving, cognition. New York: W. H. Freeman and Company Press. Moses, B., Bjork, E., Goldenberg, E. P. (1993). Beyond peoblem solving: problem posing. In S.I. Brown M. I. Walter (Eds), Problem posing: Reflections and applications (pp ). Hillsdale, NJ: Lawrence Erlbaum Associates. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author. Nohada, N. (1984). The heart of open approach in mathematics teaching. In T. Kawaguchi (Ed.), Proceddings of ICIM-JSME regional conference on mathematics education (pp ). Tokyo: Japan society of Mathematics Education. Polya, G. (1945). How to solve it. (2nd ed.). New York: Doubleday. 109

115 Schloemer, C. G. (1994). Integrating problem posing into instruction in advanced algebra: Feasibility and outcome. Doctoral Dissertation, University of Pittsburgh. Schoenfeld, A. H. (1985). Mathematics problem solving. New York: Academic Press. Silver, E. A. & Cai, J. (1993). Mathematics problem posing and problem solving by middle school students. Paper presented at AERA. Atlanta, GA. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), Silver, E. A., Mamona-Downs, J., Leung,S.S. & Kenney P.A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in mathematics Education, 27(3), Skinner, P. (1990). What s your problem: Posing and solving mathematical problem, K-2. Portsmouth, NH: Heinemann. Stover, G. B. (1982). Structural variables affecting mathematical word problem difficulty in sixth graders. Dissertation Abstracts International, 42, 5050A. Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into student s problem posing in school mathematics. In Corwin, R. B. (Ed.), Talking Mathematics: Supporting Children s Voices. Portsmouth, NH. Winograd, K. (1990). Writing, solving and sharing original math story problem: Case studies of fifth grade children s cognitive behavior. Doctoral Dissertation, University of Northern Colorado. 110

116 1-s-23 1-s-7 111

117 2-s-17 2-s

118 3-s-22 3-s-3 113

119 4-s-35 4-s

120 5-s-31 5-s

121 6-s-11 6-s

122 7-s-12 7-s-7 117

123 8-s-1 8-s

124 5 1-p p

125 5 2-p p

126 5 3-p p-4 121

127 5 4-p p

128 5 5-p p

129 5 6-p p

130 5 7-p p

131 5 8-p p

132 p-m-15 1-m-16 2-m

133 3-m-14 4-m-11 5-m

134 6-m-32 7-m-29 8-m

國立中山大學學位論文典藏.PDF

國立中山大學學位論文典藏.PDF 82 1. 2. 3. 1. 2. 3. The development and reflections of elementary school grade three number and operation problem-posing curriculum and instruction Abstract This study focuses on the result of problem-posing