52734 437347 1
2 82 87 re-education re-socialization Patterson & Czajkowski,1979
3
4 88 88 88
5 52734 347437
6
7
8
9
10
11
12
13
14
15 52734 5 2 3 5234 semantic 5 2 ( ) 3
16 assignment sentence I 5 2 7 82 5 2 3 5 2 3 4 7 7 3 4 5234 527 734 52734 52734 52734 52734 5234
52734 527 734 52734 5 2 3 4 4 527 734 7 7 3 4 semantic structure Carpenter, 1985; Riley et al., 1983; Verschaffel, et al., 1992; Lin, 1997 Riley 1983 change combine compare Carpenter1985 equalize Carpenter join separate, 17
18 Compared set referent set Riley 1981 Pauwels 1987 86 Riley 1981 Pauwels 1987 86 Rrilay 1981 Pauwels 1987 86 5 3 100 100 100 97 93 96 5 8 56 100 100 67 81 87 3 8 28 80 95 43 73 88 8 5 100 100 100 88 78 92 8 3 78 100 100 83 78 91 5 3 39 70 80 78 83 89 5 3 100 100 100 83 95 97 8 5 39 70 100 98 68 88 8 5 8 5 28 85 100 79 72 90 8 3 11 65 75 46 73 85 5 3 17 80 100 47 58 79 8 5 22 75 100 78 82 93 8 3 6 35 75 38 66 87 5 3 28 90 95 44 58 72 Pauwels1987 DeCorte & Verschaffel1991 Pauwels1987 Riley 1981 86 Willis & Fuson, 1988 ; Riley, 1981 3 38 835
Lewis & Mayer, 1987; Verschaffel, et al., 1992; Verschaffel, 1994; Lin, 1997 19
1152136 215 21 6 321 15 6 4 136 26 35 1152136 215 21 321 15 41521 6 52115 6 16 25 316 115 21 6 221156 3 1152136 215216 321156 415621 21 1 2 3 15 21 21 1 2 3 4152136 515 6 21 621 6 15 71521 6 82115 6 12115 6 21521 6 4 315 6 21 20
21 1 2 3 4 1 2 3 4 2 3 1 4 2 3 1 4 4 1 1 2 3 4 1 2 3 4 1 2 3 4 1 4 2 3 1 4 2 3 1 2 3 4 1 2 3 2 8 5 3 4 58 1 2 3 4 1 2 853 3 4 5 8 1 4 2 3 1 2 3 4
22 853 5 8 85 1 2 3 4 1 10 1 2, 3 1 8 6 2 1 6 10 6 1 2 3
23 3 3 87 5 4 9 2 3 7 725 927 707 770 725 927 7 437347
24
25 5 2 3 5234 527 7 734 52743
26 347 4 3 7 347437 347437 4 3 7 23 9 2 7 2 347437 347437
1999 NSC88-2511-S134-002 86 355-361 88 1999 87 87 : 82 85 82a, 1 (1),101-108. 82b 34 2 85 M. Donaldson1978. Children s Minds 27
85 83 60-76 87 Bruner, J. S.1966. Toward a Theory of Instruction. Cambridge, MA: Harvard University. Carpenter, T. P.1985. Learning to add and subtract: An exercise in problem solving. In E. A. SilverEd..Teaching and Learning Mathematics Problem Solving: Multiple Research Perspectives (pp.17-40). Hillsdale, NJ: Lawarence Erlbaum. Carpenter, T. P. & Moser, J. M.1984. The acquisition of addition and subtraction concepts in grade one through three. Journal for Research in Mathematics Education, 15, 179-202. Cohen, L. & Manion, L. (1984). Action Research. In Bell, et al. (Eds.), Conducting Small-Scale Investigations in Educational Management London: Open University. De Corte, E., Verschaffel, L.,1991. Some factors influencing the solution of addition and subtraction word problems. In K. Durkin and B. ShrieEds.. Language in Mathematical Education (pp.117-130). London: Open University. Elliott, J. (1993). Professional development in a land of choice and diversity: the future challenge of action research. In D. Bridges & T. Kerry (Eds.) Developing Teachers Professionally, 23-50. London: Routledge. Lesh, R. (1979). Mathematical learning disabilities: consideration for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G. KantowskEds., Applied Mathematical Problem Solving. Columbus, OH: ERIC/SMEAC. Lewis, A., & Mayer, R.1987. Students miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology,79, 363-371. Lin, P. (1997). Children s Cognitive Processes in Solving Two-step Compare Word Problems. Unpublished dissertation, University of Minnesota. Patterson, J. L. & Czajkowski, T. J.1979Implementation: Neglected phase in curriculum change, Educational Leadership, 373, 204206. Riley, M. S.1981. Conceptual and Procedural Knowledge in Development. Unpublished master s thesis, University of Pittsburgh. Riley, M. S., Greeno, J. G., & Heller, J. I.1983. Development of children s problem solving ability in arithmetic. In H. P. GinsbergEds.. The Development of 28
Mathematical Thinking (pp.153-196). San Diego, CA: Academic Press. Verschaffel, L., De Corte, E., & Pauwels, A.1992. Solving compare problems: An eye-movement test of Lewis and Mayer s consistency hypothesis. Journal of Educational Psychology, 84, 85-94. Verschaffel, L.1994. Using retelling data to study elementary school children s representations and solutions of compare problems. Journal for Research in Mathematics Education, 25, 141-166. Webb, R, (1990). Practitioner Research in the Primary school, London: Falmer. Willis, G. B., & Fuson, K. C.1988. Teaching children to use schematic drawing to solve addition and subtraction word problems. Journal of Educational Psychology, 80 192-201. 29
A MODEL OF PROFESSIONAL DEVELOPMENT FOR ELEMENTARY TEACHERS BASED ON CHILDREN S COGNITION OF MATHEAMTICS Pi-Jen Lin Department of Mathematics and Science Education Hsin-Chu Teachers College ABSTRACT The study was to construct a model of school-centered professional development for elementary mathematics teachers. The purpose of the professional development was to help teachers become more aware of children s learning and become more reflective on their mathematics classroom practice. The study taking collaborative action research as an approach set up a co-development group in Ding-Pu elementary school of Shin-Chu city. The major participants of the co-development group are the researcher and six teachers of Ding-Pu elementary school. The regular weekly meeting of the co-development group is the place in which we initiated, discussed and resolved the issues of mathematics teaching. It is also the time that we shared our various experience and knowledge with others. The paper describes that the cognitive activities we engaged in a professional development project and the issues relevant with children s cognition we addressed in the discussions of the team. The theories underpinning the issues resolved are illustrated. The issues that we addressed in the team included: the distinctions among concrete activity, representation, and mathematical expression; grouping; mathematical expression used followed by representation, teaching strategies in order to avoid the use of 52734 expressed two-step word problems. Teachers have better understanding of children s learning; for instance, 437 is not identical with 347 for first graders. Key words: Professional development Collaborative action research Co-development group 30