MATHEMATICAL GIFTEDNESS AS A QUALITY OF PROBLEM-SOLVING ACTS

Creativity in Mathematics and the Education of Gifted Students

Volumn , Issue , 2009, Pages 115-128

  Leikin, Roza ^a   Berman, Abraham ^b   Koichu, Boris ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85142814692     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1163/9789087909352_009     Document Type: Chapter

References (52)

1. Babaeva, J.D. (1999). A dynamic approach to giftedness: Theory and practice. High Ability Studies, 10, 51-68.
2. Babinskaya, I.L. (1975). Problems from mathematics Olympiads. Moscow, Russia: Science. (In Russian)
3. Brown, S.I., & Walter, M.I. (1983). The art of problem posing. Hillsdale, NJ: Lawrence Erlbaum.
4. Cahan, S., & Linchevski, L. (1996). The cumulative effect of ability grouping on mathematical achievement: A longitudinal perspective. Studies in Educational Evaluation, 22, 29-40.
5. Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45-75.
6. Charles, R., & Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, CA: Dale Seymour.
7. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158.
8. Courant, R., & Robbins, H. (1996/1941). What is mathematics? London: Oxford University Press.
9. Davis, G.A., & Rimm, S.B. (2004). Education of the gifted and talented (5th ed.). Boston: Pearson Education Press.
10. Dawson, M.M. (1987). Beyond ability grouping: A review of effectiveness of ability grouping and its alternative. School Psychology Review, 16, 348-369.
11. English, L.D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
12. Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp.42-53). Dordrecht, Netherlands: Kluwer.
13. Gonzales, N.A. (1998). A blueprint for problem posing. School Science and Mathematics, 98 (8), 448-456.
14. Harel, G. (in press). What is mathematics? A pedagogical answer to a philosophical question. In R.B. Gold & R. Simons (Eds.), Current issues in the philosophy of mathematics from the perspective of mathematicians. Mathematical Association of America.
15. Harel, G., Koichu, B., & Manaster, A. (2006, July). Algebra teachers' ways of thinking characterizing the mental act of problem posing. In J.Novotna, H.Moraova, M.Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol.3, pp.241-248). Prague, Czech Republic: Charles University.
16. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A.H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp.123-147). Hillsdale, NJ: Lawrence Erlbaum Associates.
17. Koichu, B. (2003). Junior high school students' heuristic behaviors in mathematical problem solving. Unpublished Doctoral Dissertation, Technion, Haifa.
18. Koichu, B., Berman, A., & Moore, M. (2006). Patterns of middle school students' heuristic behaviors in solving seemingly familiar problems. In J.Novotna, H.Moraova, M.Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp.457-464). Prague: Charles University.
19. Koichu, B., Berman, A., & Moore, M. (2007). Heuristic literacy development and its relation to mathematical achievements of middle school students. Instructional Science, 35, 99-139.
20. Koichu, B. (2008). Multiple solutions to semi-structured problem posing tasks. In R. Leikin (Ed.), Proceedings of the International Research Workshop of the Israel Science Foundation "Multiple Solution Cconnecting Tasks" (pp.45-52). Israel: CET press.
21. Kulik, J.A. (1993). An analysis of the research on ability grouping. Eric Digest, 397, 95.
22. Kulik, J.A. (2003). Grouping and tracking. In N. Colangelo & G. Davis (Eds.), Handbook of gifted education (3rd ed.) (pp.268-281). Boston, MA: Allyn & Bacon.
23. Krutetskii, V.A. (1976). The psychology of mathematical abilities in school children (J.Teller, Trans., J. Kilpatrick & I.Wirszup, Eds.). Chicago: The University of Chicago Press.
24. Leikin, R. (2000). A very isosceles triangle. Empire of mathematics, 2, 18-22. (In Russian).
25. Leikin, R. (2006). About four types of mathematical connections and solving problems in different ways. Aleh- The (Israeli) Senior School Mathematics Journal, 36, 8-14. (in Hebrew).
26. Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. The Fifth Conference of the European Society for Research in Mathematics Education- CERME-5.
27. Leikin, R. (2009). Multiple proof tasks: Teacher practice and teacher education. ICMI Study-19, Taiwan, Taipey.
28. Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In the Proceedings of the 31st International Conference for the Psychology of Mathematics Education.
29. Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66, 349-371.
30. Ma, L. (1999). Knowing and teaching elementary mathematics: Teacher's understanding of fundamental mathematics in China and the United States. Hillsdale, NJ: Erlbaum.
31. Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. London: Addison-Wesley.
32. Mestre, P.J. (2002). Probing adults' conceptual understanding and transfer of learning via problem posing. Applied Developmental Psychology, 23, 9-50.
33. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: The Author.
34. Nevo, B. (Head). (2004, July). Report of the committee for promotion of education of the gifted in Israel (Published online). Retrieved August 14, 2006, from http://www.education.gov.il/gifted/download/doch_kidum_mechonanim. doc (in Hebrew)
35. Piirto, J. (1999). Talented children and adults: Their development and education (2nd ed.). Upper Saddle River, NJ: Merrill.
36. Polya, G. (1945/1973). How to solve it. Princeton, NJ: Princeton University.
37. Renzulli, J. (1978). What makes giftedness? Re-examining a definition. Phi Delta Kappan, 60, 180-184, 261.
38. Renzulli, J. (2002). Expanding the conception of giftedness to include co-cognitive traits and to promote social capital. Phi Delta Kappan, 84(1), 33-58.
39. Renzulli, J.S. (1995). Teachers as talent scouts. Educational Leadership, 52(4), 75-81.
40. Schoenfeld, A.H. (1985). Mathematical problem solving. New York: Academic Press.
41. Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp.334-370). New York: MacMillan.
42. Silver, E.A. (1994). On mathematical problem solving. For the Learning of Mathematics, 14, 19-28.
43. Silver, E.A., Mamona-Downs, J., Leung, S., & Kenny, P.A. (1996). Posing mathematical problems in a complex environment: An exploratory study. Journal for Research in Mathematics Education, 27, 293-309.
44. Silver, E.A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 3, 75-80.
45. Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations. The Journal of Secondary Gifted Education, 14, 151-165.
46. Sternberg, R.J. (Ed.). (2000). Handbook of intelligence. New York: Cambridge University Press.
47. Tirosh, D. (1989). Teaching mathematically gifted children. In R.M. Milgram (Ed.), Teaching gifted and talented learners in regular classrooms (pp.205-222). Springfield, IL: Charles C.Thomas.
48. Torrance, E.P. (1966). The torrance tests of creative thinking- norms-technical manual research edition- verbal tests, forms A and B- figural tests, forms A and B.Princeton, NJ: Personnel Press.
49. Torrance, E.P. (1974). Torrance tests of creative thinking. Bensenville, IL: Scholastic Testing Service.
50. Verschaffel, L. (1999). Realistic mathematical modelling and problem solving. In J.H.M.Hamers, J.E.H. Van Luit, & B. Csapo (Eds.), Teaching and learning thinking skills (pp.215-239). Lisse: Swets & Zeitlinger.
51. Vygotsky, L.S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
52. Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum.