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 teaching, covering units on number and operation on third grade elementary school students. The problem-posing teaching method incorporates: teacher formulating problem, discussion and debate, problem-solving activities, and problem-posing activities. This researcher was also the one who carried out teaching. The teachers guide was adapted from the teaching goals of textbook published by KNSH in 1993 and the researcher selected the units on number and operation from the fifth and sixth volumes. We used the teacher s math diaries, videotapes of actual teaching sessions, observation notes on teaching records, students feedback surveys, and interviews of students. The objectives of this study are: 1. developing and integrating problem-posing into mathematics curriculum; 2. promoting students ability in communication; and, 3. reflecting upon practice on problem-posing instruction through action research. There results are three results. First, when comparing performances of experimental class to control group, 5 out of 9 units were having statistical significance and 4 were not. Second, students ability in communication improved after problem-posing instruction. Third, two challenges were identified when teachers implemented the problem-posing activities. Keywords: Elementary school grade three, Number and operation, Problem-posing teaching, Development of teaching materials, Reflections
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1996 1997 1997 2000 - (NCTM 1989) (NCTM1991)- 2
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Stovanova Ellerton1986 Stovanova Ellerton Silver1994 Silver1994 1994 7
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Reitman Stovanova & Ellerton Skinner1990 What s your problem 15
Tsubota1987 Tsubota 1997 Test of General Mathematical Problem PosingTGPP Leung & Wu1999 16
17 Leung & Wu2000 Van den Brink1987 1997 2002 14
2003 24 English1998 54 18
2000 2004 Winograd1990 19
Winograd 1996 104 40 2002 20
21 1996 English1997 Cohen Stover1982 1999 Cai1998 181 223
2002 Keil1965 2005 22
2006 Brown Walter1983 The art of problem posing what-if-not Ellerton1986 English1997 23
1997 1999 2003 Borba1994 24
Van den Brink1995 1993 18-1994 1995 25
65 127 Silver Mamona-downsLeung Kenney1996 53 28 IP PS AP Leung Silver 1997 TAPPTest Arithmetic Problem Posing 63 26
Schloemer 1994Brown Walter 1983 what-if-not 2002 2000 2004 27
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29 2-3-1 Polya1945 1995 1995 Polya 2-3-2 2-3-2 1994p.159 Look Back Plan Carry out Pose
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7 RT Kitty 6 42 75
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7 7 6612 12618 18624 24630 30636 36642 7 6 6 12 6 18 7 42 7 6 530 423012 1266 660 527 7 5 6 530 30 42 12 2 12 7 42 67 7 42 6 7 77
RT S RT S RT S15 6 RT S15 78
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4-3-3 91.10.21 91.10.23 91.10.28 91.10.30 91.12.17 91.12.18 91.12.23 91.12.25 91.02.18 92.02.19 92.03.20 92.03.21 92.04.09 92.04.10 92.05.04 92.05.05 92.05.28 16 22 20 12 14 20 22 14 14 18 20 18 10 12 22 26 10 10 25 25 12 08 20 30 10 12 18 30 06 08 10 38 06 09 11 44 06 13 12 39 06 05 13 46 04 09 09 48 04 04 11 51 04 03 09 54 02 02 08 54 02 02 10 56 02 02 08 58 108
92.05.30 0 02 06 62 4-3-4 4-3-4 91.10.21 12 10 2 8 4 2 10 91.10.23 91.10.28 91.10.30 91.12.17 91.12.18 91.12.23 91.12.25 91.02.18 14 13 1 9 5 3 11 18 17 1 14 4 3 15 26 24 2 19 7 4 22 25 25 0 22 3 9 16 30 28 2 16 14 11 19 30 27 3 20 10 0 30 38 36 2 32 6 0 38 44 44 0 42 2 37 7 109
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S15 S3 5 2 7 S15 S3 27 RT 27 27 S34 29 8 37 37 6 6 1 RT S RT S RT 15 S15 29 6 4 5 8 6 1 2 415 RT S15 527 115
RT S15 6 7 61 1 1 1 5 6 RT 15 29 64 529 6 4 5 8 61 2 8 6 1 2 415 415 527 7 61 1 1 1 516 6 1 116
Kitty 6 24 3 22 2 Kitty 6 24 372 72 612 22 244 44 67 2 12719 19 2 S29 RT 2! 5 S RT5 S5 24 3 24 372 72 6 12 22 244 RT S5 22 2 RT 2 S 3 117
RT S12 22 366 66 RT 5 22 244 S5 2 2 RT 24 372 72 612 22 366 66 66 2132 132 132 622 6 122234 Kitty 6 34 1 118
12 6 2 12 672 72 236 RT S 36 RT S RT S8 6 S16 2 2 S RT 12 672 72 236 S 119
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RT S ------ RT S ------ RT S 12 RT S1/12 S0.1 S28 0.1 RT28 0.1 S28 10 0.1 RT28 1/12 S28 12 1/12 RT S15 10 S32 10 1293 1091 1/10 121
RT 10 1/100.1 10 10 - - 10 122
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124
125
126
127
128
129
130
1996 2002 1995 2005 ~ 1996 1997 2004-1999 131
NSC-88-2815-C-023-001-S 1987 2002 1997 NSC-86-2815-C-023-005-H 1988 1996 1993 1994 pp.152~167 1995 NSC-83-0111-S-023-007 NSC-84-2511-S-023-001 132
1996 1997 NSC84-2511-S-023-006 1999 184~220 1996 2002-2003 1995 1998 2005-2003 133
1993 2003-2002 3 2003 3 2002 3 2003 3 1993-11101-108 1996 1994 2000 134
1996 2000 AEP 2003 2006 ~ 2002-2000 - 1996 1998 2000 135
1996 2002-2002 - 1996 2002 136
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dissertation. Kilpatrick, J. (1987). Problem formulating: Were do good problems come from? In A.H.Schoenfeld (Ed), Cognitive science and mathematics education (pp.123-147). Hillsdale,NJ: Lawrence Erlbaum Associate. 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. Leung, S. S. & Wu, R. X. (1999). Problem posing with middle grades mathematics: Two real classroom example. Mathematics teaching in the middle school, Reston,VA: National Council of Teachers of Mathematics, USA. Leung, S. S. & Wu, R. X. (2000). Sharing problem posing and problem solving at home through diary writing. Australian Primary Mathematics Classroom, 5(1), 28-32. Lindquist, M. (Ed.), (1989). Results of the 4th NAEP. Reston, VA: NCTM. National Council of Teacher of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council of Teacher of Mathematics (1991). Professional standards for teaching mathematics. Reston,VA:Author. Polya, G.(1945). How to solve it.(2nd ed.). New York:Doubleday. Schloemer, C. G. (1994). Integrating problem posing into instruction in advanced algebra: Feasibility and outcome.doctoral Dissertation, University of Pittsburgh. Silver, E. A., & Adams, V. M. (1987). Problem solving tips for teachers: 138
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