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1994 Book DidacticsOfMathematicsAsAScien
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Level Two: Level Three: Level Four: Level Five: Yes. Sides are straight at a right angle. Yes, as long as all of the sides are the same length. No, because all sides must be equal. (a) No, because there must be one side of the triangle (hypotenuse) that is longer in a right triangle and equilateral has all sides the same. (b) No, all the angles have to be the same and all three have to equal 180 degrees. (a) No, you can't have 3 right angles because the sum of the an- gles would be 270 degrees and it must equal 180. The angle mea- sure are all the same in an equilateral triangle. (b) No, because an equilateral triangle has all the same angles. If you had a triangle with 3 right angles, you would have 3/4 of a square of the sides would not connect. SCIENCE AND TEACHER EDUCATION REFERENCES Ball, D. L. (1988, April). Prospective teachers' understanding of mathematics: What do they bring with them to teacher education? Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA. Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In D. Grouws, T. Cooney, & D. Jones (Eds.), Perspectives on research on effective mathematics teaching (pp. 27-46). Reston, VA: National Council of Teachers of Mathematics. Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics class- room. Educational Studies in Mathematics, 11, 23-41. Begle, E. G. (1968). Curriculum research in mathematics. In H. J. Klausmeier & G. T. O'Hearn (Eds.), Research and development toward the improvement of education (pp. 44-48). Madison, WI: Dembar Educational Research Services. Brophy, J. E. (1975, November). Reflections on research in elementary schools. Paper pre- sented at the conference on research on teacher effects: An examination by decision- makers and researchers, University of Texas, Austin, TX. Brown, C. A. (1985). A study of the socialization to teaching of beginning secondary math- ematics teachers. Unpublished doctoral dissertation, University of Georgia, Athens, GA. Brown, S. I., Cooney, T. J., & Jones, D. (1990). Mathematics teacher education. In W. R. Houston, M. Haberman, & J. Sikula (Eds.), Handbook of research on teacher education (pp. 639-656). New York: Macmillan. Brownell, W. A. (1945). When is arithmetic meaningful. Journal of Educational Research, 38, 481-498. Bush, W. (1983). Preservice secondary mathematics teachers’ knowledge about teaching mathematics and decision-making during teacher training (Doctoral dissertation, University of Georgia, 1982). Dissertation Abstracts International, 43, 2264A. Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the learning of mathematics. 6(2), 2-9. Cooney, T. (in press) Teacher education as an exercise in adaptation. In D. Aichele (Ed.), NCTM yearbook on teacher education. Reston, VA: National Council of Teachers of Mathematics. Cooney, T. (1992). A survey of secondary teachers’ evaluation practices in Georgia. Athens, GA: University of Georgia. Davis, R. B. (1967). The changing curriculum: Mathematics. Washington, DC: Association for Supervision and Curriculum Development, NEA. Eisenberg, T. A. (1977). Begle revisited: Teacher knowledge and students achievement in algebra. Journal for Research in Mathematics Education, 8, 216-222. Feyerabend, P. (1988). Against method. New York: Verso. Fisher, L. C. (1988). Strategies used by secondary mathematics teachers to solve proportion problems. Journal for Research in Mathematics Education, 19, 157-168. Gage, N. (1972). Teacher effectiveness and teacher education: The search for a scientific basis. Palo Alto, CA: Pacific Books. Gallagher, J. J. (1970). Three studies of the classroom. In J. J. Gallagher, G. A. Nuthall, & B. Rosenshine (Eds.), Classroom obsservation. American Educational Research Association Monogaraph Series on Curriculum Evaluation, Monograph No. 6. Chicago: Rand McNally. Glasersfeld, E. von (1987). The construction of knowledge. Seaside, CA: Intersystems Publications. 114 deeper understanding of the process by which teachers learn to teach so that we can have a better basis for developing teacher education programs. Appropriately defined and applied, science can enable us to develop this understanding and allow us to impact on the practical art of teaching and teacher education in a way not foreseen by Highet and many of our profes- sional forefathers who ascribed to an analytical view of science. THOMAS J. COONEY Glasersfeld, E. von (1989). Constructivism in education. In T. Husen & N. Postlethwaite (Eds.), International encyclopedia of education (pp. 162-163). (Supplementary Vol.). Oxford: Pergamon. Graeber, A., Tirosh, D., & Glover, R. (1986). Preservice teachers’ beliefs and performance on measurement and partitive division problems. In G. Lappan & R. Even (Eds.), Download 5.72 Mb. Do'stlaringiz bilan baham: |
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