PUBLICATIONS

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Journal Articles and Book Chapters

  1. Harel, G. (2014). Common Core State Standards for Geometry: An Alternative Approach. Notices of the AMS, 61 (1), 24-35. Download
  2. Harel, G. (2013). Intellectual Need. In Vital Direction for Mathematics Education
    Research
    , Leatham, K. Ed., Springer. Download
  3. Harel, G. (2013). DNR-based curricula: The case of complex numbers. Journal of Humanistic Mathematics, 3 (2), 2-61. Download
  4. Watson, A., & Harel, G. (2013). The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two Cases. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 154–168. Download
  5. Harel, G. (2013). Classroom-based interventions in mathematics education: Relevance, significance, and applicability. ZDM Mathematics Education (2013) 45, 483–489. Download
  6. Harel, G., Fuller, E. (2013). Reid, D.A. and Knipping, C.: Proof in mathematics education: Research, learning, and teaching. ZDM Mathematics Education (2013) 45,497–499. Download
  7. Harel, G., & Wilson, S. (2011). The state of high school textbooks. Notices of the AMS, 58, 823-826. Download1 Download2
  8. Harel, G., & Koichu, B. (2010). An operational definition of learning. Journal of Mathematical Behavior. 29, 3, 115-124. Download
  9. Harel, G. (2012). Dueductive reasoning in mathematics education. Encyclopedia of Mathematics Education, Springer. Download
  10. Harel, G., Fuller, E., & Rabin, J. (2008). Attention to meaning. Journal of Mathematical Behavior, 27, 116-127. Download
  11. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction, Part II. Zentralblatt fuer Didaktik der Mathematik.Download
  12. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction: Focus on Proving, Part I. Zentralblatt fuer Didaktik der Mathematik, 40, 487--500. Download
  13. Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. Simons (Eds.), Proof and other dilemmas: Mathematics and philosophy (pp. 265–290). Washington, DC: Mathematical Association of America. Download
  14. Koichu, B. & Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65(3), 349-365. Download
  15. Harel, G., & Sowder, L (2007). Toward a comprehensive perspective on proof, In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, National Council of Teachers of Mathematics. Download
  16. Harel, G. (2007). The DNR System as a Conceptual Framework for Curriculum Development and Instruction, In R. Lesh, J. Kaput, E. Hamilton (Eds.), Foundations for the Future in Mathematics Education, Erlbaum. Download
  17. Harel, G. (2006). Mathematics Education Research, Its Nature, and Its Purpose: A Discussion of Lester's Paper, Zentralblatt fuer Didaktik der Mathematik, 38, 58-62. Download
  18. Harel, G., & Sowder, L. (2005). Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development, Mathematical Thinking and Learning, 7, 27-50. Download
  19. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. International Journal of Mathematics Thinking and Learning, 5, 157-189. Download
  20. Sowder, L., & Harel, G., (2003). Case Studies of Mathematics Majors' Proof Understanding, Production, and Appreciation. Canadian Journal of Science, Mathematics and Technology Education. 3, 251-267. Download
  21. Harel, G. (2001). The Development of Mathematical Induction as a Proof Scheme: A Model for DNR-Based Instruction. In S. Campbell & R. Zaskis (Eds.). Learning and Teaching Number Theory. In C. Maher (Ed.). Journal of Mathematical Behavior. New Jersey, Ablex Publishing Corporation, 185-212. Download
  22. Harel, G. (1999). Students' understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra, Linear Algebra and Its Applications , 302-303, 601-613. Download
  23. Harel, G., & Sowder, L. (1998). Students' proof schemes. Research on Collegiate Mathematics Education, Vol. III. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), AMS, 234-283. Download
  24. Harel, G. (1998). Two Dual Assertions: The First on Learning and the Second on Teaching (Or Vice Versa). The American Mathematical Monthly, 105, 497-507. Download
  25. Greer, B., & Harel, G. (1998). The role of analogy in the learning of mathematics, Journal of Mathematical Behavior, 17, 5-24. Download
  26. Harel, G. (1997). The linear algebra curriculum study group recommendations: Moving beyond concept definition. In Carlson D., Johnson, C, Lay, D., Porter, D., Watkins, A, \& Watkins, W. (Eds.). Resources for Teaching Linear Algebra,. MAA Notes, Vol. 42, 107-126. Download
  27. Behr, M., Khoury, H., Harel, G., Post, T., & Lesh, R. (1997). Conceptual units analysis of preservice elementary school teachers' strategies on a rational-number-as-operator task, Journal for Research in Mathematics Education, 28, 48-69. Download
  28. Harel, G. (1995). From naive interpretist to operation conserver. In J. Sowder & B. Schappelle (Eds.). Providing a Foundation for Teaching Mathematics in the Middle, New York : SUNY Press, 143-165. Download
  29. Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of the number type on the solution of multiplication and division problems: Further considerations. In G. Harel and J. Confrey (Ed). The Development of Multiplicative Reasoning in the Learning of Mathematics. Albany , New York : SUNY Press, 363-384. Download
  30. Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children's anticipatory scheme of constancy of taste, Journal for Research in Mathematics Education, 25, 324-345. Download
  31. Harel, G., & Behr, M. (1992). The blocks task on proportionality: Expert solution models, Journal of Structural Learning, 11, 173-188. Download
  32. Dubinsky, E., & Harel, G. (1992). The process conception of function. In G. Harel & E. Dubinsky. The Concept of Function: Aspects of epistemology and pedagogy, MAA Notes, No. 28, 85-106 Download
  33. Post, T., Harel, G., Behr, M. & Lesh, R. (1991). Intermediate teachers' knowledge of rational number concepts. In E. Fennema , T. P. Carpenter, and S. J. Lamon (Eds.) Integrating Research on Teaching and Learning Mathematics. Albany , New York : SUNY Press, 177-198. Download
  34. Harel, G., & Kaput, J. (1991). The role of conceptual entities in building advanced mathematical concepts and their symbols. In D. Tall (Ed), Advanced Mathematical Thinking. Kluwer Academic Publishers, 82-94. Download
  35. Harel, G., & Behr, M. (1991). Ed's Strategy for solving division problems, Arithmetic Teacher, 39, 38-40. Download
  36. Harel, G., & Tall, D. (1991). The general, the abstract, and the generic, For the Learning of Mathematics, 11, 38-42. Download
  37. Harel, G. (1989). Applying the principle of multiple embodiments in teaching linear algebra: Aspects of familiarity and mode of representation, School Science and Mathematics, 89, 49-57. Download
  38. Martin, G., & Harel, G. (1989). Proof frame of preservice elementary teachers, Journal for Research in Mathematics Education, 20, 41-51. Download
  39. Harel, G. (1987). Variations in linear algebra content presentation, For the Learning of Mathematics, 7, 29-32. Download

© 2012 Guershon Harel