PUBLICATIONS

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Books Edited

  1. Selden, A. Hitt, F., Harel, G., &  Hauk, S. (Eds.). (2006). Research in Collegiate Mathematics Education. VI, AMS | MAA, 248 pp.
  2. Selden, A. Dubinsky, E, Harel, G., & Hitt, F. (Eds.). (2003). Research in Collegiate Mathematics Education. VI, AMS | MAA, 206 pp.
  3. Harel, G., & Confrey, J. (Eds.). (1994). The development of multiplicative reasoning in the learning of mathematics. SUNY Press.
  4. Harel, G., & Dubinsky, E. (Eds.). (1992). The concept of function; aspects of epistemology and pedagogy. MAA Notes No. 28.

Journal Articles and Book Chapters

  1. Hanna, G., Harel, G., Kidron, I., Selden, A. Selden, J., & Keith, W. (in press). Justification and proof in mathematics and mathematics education, In Mathematics and Mathematics Education: Searching for Common Ground, (Fried, M., & Dreyfus, T., Eds.), Springer - Advances in Mathematics Education series.
  2. Harel, G., Fuller, E., & Soto, O., (in press), Determinants of a DNR expert's teaching, In Transforming Mathematics Instruction: Multiple approaches and practices, (Li, Y., Ed.), Springer.
  3. Harel, G. (2014). Common Core State Standarts for Geometry: An Alternative Approach. Notices of the AMS, 61 (1), 24-35. Download
  4. Harel, G. (2013). Intellectual Need. In Vital Direction for Mathematics Education
    Research
    , Leatham, K. Ed., Springer.
  5. Harel, G. (2013). DNR-based curricula: The case of complex numbers. Journal of Humanistic Mathematics, 3 (2), 2-61.
  6. 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.
  7. Harel, G. (2013). Classroom-based interventions in mathematics education: Relevance, significance, and applicability. ZDM Mathematics Education (2013) 45, 483–489.
  8. 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.
  9. Harel, G. (2013). The Kaputian program and its relation to DNR-based instruction: A common commitment to the developmnent of mathematics with meaning, In The SimCalc Vision and Contribution, (Fried, M., & Dreyfus, T., Eds.), Springer, 438-448.
  10. Harel, G. (2012). Deductive reasoning in mathematics education. Encyclopedia of Mathematics Education, Springer.
  11. Koichu, B., Harel, G., & Manaster, A. (2012). Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions, Instructional Science, 40, 4,
  12. Harel, G., & Wilson, S. (2011). The state of high school textbooks. Notices of the AMS, 58, 823-826. Download
  13. Harel, G., & Koichu, B. (2010). An operational definition of learning. Journal of Mathematical Behavior. 29, 3, 115-124.
  14. Fuller, E., Rabin, J., & Harel, G. (2011). Intellectual need and problem-free activity in the classroom, International Journal for Studies in Mathematics Education 4(1), 80-114.
  15. Harel, G., & Rabin, J. (2010). Teaching practices that can promote the authoritative proof scheme. Canadian Journal of Science, Mathematics and Technology Education, 10, 139-159.
  16. Harel, G., & Rabin, J. (2010). Teaching practices sssociated with the authoritative proof scheme. Journal for Research in Mathematics Education, 41, 14-19.
  17. Harel, G. (2010). Commentary on the Theoretical, conceptual, and philosophical foundations for research in mathematics education. In Theories of Mathematics Education, Barath, S., & English, L., Eds., Springer, 87-94.
  18. Harel, G. (2010). DNR-Based Instruction in Mathematics as a Conceptual Framework. Theories of Mathematics Education. Barath, S., & English, L., Eds., Springer, 343-367.
  19. Harel, G. & Fuller, E. (2009). Current contributions toward comprehensive perspectives on the learning and teaching of proof. Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge/Taylor & Francis, 275-289.
  20. Harel, G. & Sowder, L. (2009). College instructors' views of students vis-a-vi proof. Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge/Taylor & Francis, 275-289.
  21. Harel, G., Fuller, E., & Rabin, J. (2008). Attention to meaning by algebra teachers. Journal of Mathematical Behavior, 27, 116-127. Download
  22. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction: Focus on Proving, Part I, ZDM—The International Journal on Mathematics Education, 40, 487-500. Download
  23. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction, Part II, ZDM—The International Journal on Mathematics Education. Download
  24. Harel, G., & Brown, S. (2008).  Mathematical Induction: Cognitive and Instructional Considerations.  In M. Carlson, & C. Rasmussen (Eds.), Making the Connection: Research and Practice in Undergraduate Mathematics, Mathematical American Association, 111-123.
  25. 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
  26. Harel, G. (2008). Maintaining the mathematical integrity of school curricula: The challenge, For the Learning of Mathematics, 28, 10.
  27. Koichu, B. & Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65(3), 349-365. Download
  28. 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
  29. 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
  30. Hitt, F., Harel, G., & Selden, A. (2006). Preface , Research in Collegiate Mathematics Education, 6.
  31. 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
  32. Harel, G., & Sowder, L. (2005). Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development, Mathematical Thinking and Learning, 7, 27-50. Download
  33. Harel, G. (2004). A Perspective on "Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity." In T. Carpenter, J. Dossey, & L. Koehler (Eds.), Classics in Mathematics Education Research, 98.
  34. Harel, G., & Rabin, J. (2003). Polygons whose vertex triangles have equal area. The American Mathematical Monthly, 110, 606--610.
  35. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. International Journal of Mathematics Thinking and Learning, 5, 157-189. Download
  36. 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
  37. Harel, G. (in press). Students' proof schemes revisited: Historical and epistemological considerations. In P. Boero (Ed.), Theorems in School, Kluwer.
  38. Harel, G., & Lesh, R. (2003).  Local conceptual development of proof schemes in a cooperative learning setting.  In R. Lesh & H. M. Doerr (Eds.).  Beyond constructivism:  A models and modeling perspective on mathematics teaching, learning, and problem solving. Mahwah , NJ : Lawrence Erlbaum Associates, 359-382.
  39. 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
  40. Harel, G. (2000). Three principles of learning and teaching mathematics: Particular reference to linear algebra--Old and new observations. In Jean-Luc Dorier (Ed.), On the Teaching of Linear Algebra, Kluwer Academic Publishers , 177-190.
  41. 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
  42. Sowder, L., & Harel, G. (1998). Types of students' justifications. Mathematics Teacher, 91, 670-675.
  43. 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
  44. 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
  45. Greer, B., & Harel, G. (1998). The role of analogy in the learning of mathematics, Journal of Mathematical Behavior, 17, 5-24. Download
  46. Hoz, R., Harel, G., & Tedeski, J. (1997). The role of structural and semantic factors in the solution of algebra speed problems. International Journal for Mathematics Education in Science and Technology, 28, 397-409.
  47. Harel, G., & A. Trgalova (1997). Higher Mathematics Education. In A. Bishop (Ed.), International Handbook in Mathematics Education, Kluwer Academic Publishers, 675-700.
  48. Harel, G. (1997). Three Principles of Learning and Teaching, With Particular Reference to the Learning and Teaching of Linear Algebra. In Jean-Luc Dorier (Ed.), Recherches en Didactique des Mathematiques, La Pensee sauvage, editions.
  49. 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
  50. 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
  51. Harel, G., Behr, M. (1995). Teachers' solutions for multiplicative problems, Hiroshima Journal for Research in Mathematics Education, 31-51.
  52. 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
  53. Behr, M., Harel, G., Post, T., & Lesh, R. (1994). Units of quantity: A conceptual basis common to additive and multiplicative structures. In G. Harel and J. Confrey (Eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics. Albany , New York : SUNY Press, 123-180.
  54. 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
  55. 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
  56. Harel, G. (1993). On teacher education programs in mathematics, International Journal for Mathematics Education in Science and Technology, 25, 113-119.
  57. Post, T., Cramer, K., Lesh, R., Behr, M., & Harel, G. (1992). Curriculum implications. In T. Carpenter, L. Fennema, & T. Romberg (Eds.), Learning, Teaching, and Assessing Rational Number Concepts: Multiple Research Perspectives. Hillsdale , New Jersey : Erlbaum, 327-362.
  58. Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational numbers: An integration of research. In T. Carpenter, L. Fennema, & T. Romberg (Eds.), Learning, Teaching, and Assessing Rational Number Concepts: Multiple Research Perspectives. Hillsdale , New Jersey : Erlbaum, 13-48.
  59. Harel, G., Behr, M., Post, T., & Lesh, R. (1992). The blocks task; comparative analyses with other proportion tasks, and qualitative reasoning skills among 7th grade children in solving the task, Cognition and Instruction, 9, 45-96.
  60. Harel, G., & Behr, M. (1992). The blocks task on proportionality: Expert solution models, Journal of Structural Learning, 11, 173-188. Download
  61. 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
  62. Behr, M., Harel, G., Post, T, & Lesh, R. (1992). Rational number, ratio, and proportion. In D. Grouws (Ed.). Handbook for Research on Mathematics Teaching and Learning. New York : Macmillan, 296-333.
  63. 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
  64. 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
  65. Harel, G., & Behr, M. (1991). Ed's Strategy for solving division problems, Arithmetic Teacher, 39, 38-40. Download
  66. Harel, G., & Tall, D. (1991). The general, the abstract, and the generic, For the Learning of Mathematics, 11, 38-42. Download
  67. Behr, M., & Harel, G. (1990). Students' errors, misconception, and cognitive conflict in application of procedures, Focus on Learning Problems in Mathematics, 12, 75-84.
  68. McKenna, N., & Harel, G. (1990). The effect of order and coordination of the problem quantities on difficulty of missing value proportion problems, International Journal for Mathematics Education in Science and Technology, 21, 589-593.
  69. Harel, G. (1990). Using geometric models and vector arithmetic to teach high-school students basic notions in linear algebra, International Journal for Mathematics Education in Science and Technology, 21, 387-392.
  70. Hoz, R., & Harel, G. (1990). Higher order knowledge involved in the solution of algebra speed word problems, Journal of Structural Learning, 10, 305-328.
  71. Harel, G., & Hoz, R. (1990). The structure of speed problems and its relation to problem complexity and isomorphism, Journal of Structural Learning, 10, 177-196.
  72. 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
  73. Martin, G., & Harel, G. (1989). Proof frame of preservice elementary teachers, Journal for Research in Mathematics Education, 20, 41-51. Download
  74. Harel, G. (1989). Learning and teaching linear algebra: Difficulties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11, 139-148.
  75. Harel, G., & Behr, M. (1989). Structure and hierarchy of missing value proportion problems and their representations, Journal of Mathematical Behavior, 8, 77-119.
  76. Harel, G., & Martin, G. (1988). A pedagogical approach to forming generalizations, International Journal for Mathematics Education in Science and Technology, 19, 101-107.
  77. Harel, G. (1987). Variations in linear algebra content presentation, For the Learning of Mathematics, 7, 29-32. Download

© 2012 Guershon Harel