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2. T 3. 2010ISBN : 978-9963-0-9115-7ISBN: 978-9963-0-9130-0 4. 5. 1 2 5 5 9 15 119 230 346 463 577 689 797 8 105 1 109 2 124 3 143 4 163 5 176 6 183 7 190 8 197 6. 1202 2214 3227 4241 5252 6268 7277 8286 1296 2304 3313 4323 5333 6343 7358 8378 - 1393 2402 3413 4424 5432 6440 7452 8461 7. , , . , , . , , , . (National Council of Teachers of Mathematics, 2000). , (National Council on Education and the Disciplines,2001). (Behm & Lloyd, 2009). . (Clements, 2007: Mullis, Martin, & Foy, 2007: OECD, 2006) 1 8. , (Sdrolias & Triandafilidis, 2007). ( ,2009). , , . , . . , , . , . : 1: . , . , , . , 2 9. (Baroody,2003). 2: (Schoenfeld, 1994). , . , . , / /. , . . : , .3 10. 3: . , ( Dienes, , , .) (Berry, Graham & Smith,2005). . , . , . , (Jackiw & Sinclair, 2009: Ruthven,Deaney, Hennessy, 2009:). , , (Christou, Mousoulides, Pittalis,Pitta-Pantazi, 2004), . 4: / / , . .4 11. , , : , : . . , . . . . , . , , (-12). , , 5 12. . , , , -. . , , . , . , . : : . , . .6 13. . . . , . . , . , , . . , 7 14. . , . . . . , , . , . - , . . , .8 15. . . , , , . / / ., , . 1 , , . , 1 . 1 . . , / . 9 16. / / . : / . /. , . / , . / , . 1: - 10 17. . , . . . , . , . ., , . , , (NCTM, 2000,Connecticut State Department of Education, 2006). , , , (Weiss, Knapp, Hollweg, & Burrill, 2001). , , (Stein & Kim, 2009: Grant, Kline, Crumbaugh, Kim & Cengiz, 2009). 11 18. , , , , , . 2 , . 2 ( ) : : 12 19. , , . . . . , . 13 20. - . , . , . . (, , ). , , , , ., . . . , , . , 14 21. , ., . , , . , , . 1-8 . ,, - ., . , , . , . , . . . ., ., ., ., ., ,, , ,15 22. . -12, 12 . 1 , 2 ... 3.4 , 3 4. . (, , , - ) , .16 23. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A.J.Baroody & A.Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1-33). Mahwah, NJ: Erlbaum.Behm, S., & Lloyd, G. (2009). Factors influencing student teachers use of mathematics curriculum materials. In J. Remillard, B. Herbel-Eisenmann, ., & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction. New York: Routledge, Taylor and Francis.Berry J., Graham E. & Smith A. (2005) Classifying Students Calculator Strategies. The International Journal for Technology in Mathematics Education, 12(1), 15-31.Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339-352.Clement, D. (2007). Curriculum research: Towards a framework for Research-based Curricula. Journal for Research in Mathematics Education, 38(1), 35-70.Connecticut State Department of Education (2006). A Guide to Curriculum Development: Purposes, Practices, Procedures. http://www.sde.ct.gov/sde/cwp/view.asp?a=2618&q=321162Grant, T., Kline, K., Crumbaugh, C., Kim, O., & Cengiz, N. (2009). How can curriculum materials support teachers in pursuing student thinking during whole group discussions? In J. Remillard, B. Herbel-Eisenmann, ., & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction. New York: Routledge, Taylor and17 24. Francis.Jackiw, N. & Sinclair, N. (2009). Sounds and pictures: dynamism and dualityin Dynamic Geometry. ZDM, 41(4), 413-426.Mullis, I.V.S., Martin, M.O., & Foy, P. (with Olson, J.F., Preuschoff, C.,Erberber, E., Arora, A., & Galia, J.). (2008).TIMSS 2007 InternationalMathematics Report: Findings form IEAS Trends in InternationalMathematics and Science Study at the Fourth and Eight Grades. ChestnutHill, MA: TIMSS & PIRLS International Study Center, Boston College.National Council of Teachers of Mathematics (2000). Principles and standardsfor school mathematics. Reston: Va, NCTM.National Council on Education and the Disciplines (2001). Mathematics andDemocracy: The case for quantitative literacy. The Woodrow WilsonNational Fellowship Foundation.OECD Education (2006). Assessing scientific, reading and mathematicalliteracy: A framework for PISA 2006. OECD.Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software toteach about algebraic forms: A study of technology-supported practice insecondary-school mathematics. Educational Studies in Mathematics,71(3), 279-297.Schoenfeld, A. (1994). What do we know about mathematics curricula?Journal of Mathematical Behavior, 13, 55-80.Sdrolias, K.A., & Triandafillidis, T.A. (2007). The transition to secondary schoolgeometry: can there be a chain of school mathematics? EducationalStudies in Mathematics, 67(2), 159-169.Stein, M., & Kim G. (2009). The role of mathematics curriculum materials in 18 25. large scale urban reform: An analysis of demands and opportunities forteacher learning. In J. Remillard, B. Herbel-Eisenmann, ., & G. Lloyd(Eds.), Mathematics teachers at work: Connecting curriculum materialsand classroom instruction. New York: Routledge, Taylor and Francis.Weiss, I.R., Knapp, M.S., Hollweg, K.S., & Burrill, G. (2001). Investigating theInfluence of Standards: A Framework for Research in Mathematics,Science, and Technology Education. Center for Education, NationalResearch Council. (2009). 12 2009 ( 2020). , V, 28.5.2009, 2009/C 119/02. 19 26. - 1 1 : 1, , 100.2 100.3 ( 6) .4 100 , , , , unifix/Dienes .5 1-1, 2-2, 5-5 10-10 100.6 100 , , , .7 1 1 1 1 1 ( , , , , ) 2 3 4 6 8 , , .8 . 9 ( 20).10 , unifix/Dienes, .11 20. 19 27. - 112 100.13 .14 :() () () 15 .16 . .. :1 , : 1.1 . .2 , : 1.1 .20 21 22 23 2410 12 14 15 16 1820 28. - 13 1.2, : . - . - . - 3 5 . - .4 , :1.3 .________ ____ ____ ____ ____5 , Dienes, :A1.4 22, Dienes.(http://nlvm.usu.edu/en/nav/frames_asid_152_g_4_t_2.html) 21 29. - 16 1-1, 2-2, 5-5: 1.5 , -.7 , :1.6 , .() 12 = ___ + __ = __() __= 2 + 12 = __ 8 , : 1.71 2 1 . , 4 .( , http://www.oswego.org/ocsd-web/games/fractionflags/fractionflags.html)9 1.8 , : 1 50 . ;22 30. - 1 .. :1 , : A1.9 ;()---------- ()---------- ()---------- 2 , Dienes,1.10: Dienes, : 4 + 7.(http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html) 23 31. - 13 1.11, : , . ()() .4 1.12, : . ;() 50+2=70() 60-10=595 , : 1.13 .() 9 + 5 =() 7 + 6 =24 32. - 16 1.14, : , 3, 4 7.7 , :1.15 5 . .( Kids and Cookies (...))8 , :1.16 . , 18 24 ; 108 10 5 4 6 25 33. - 1 :..1 , .1.1 :4445 4630692 , 7, 8, 6, 1.1.2() 7 ________() 18 _____() 80 82 ______3 1.3 . 1.4 ________________________ _________ _______________4 . 1.4 .1.6 26 34. - 15 10 . -