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

Journal Articles and Book Chapters
  1. Harel, G. (1987). Variations in linear algebra content presentation, For the Learning of Mathematics, 7, 29-32. Download
  2. Harel, G., & Martin, G. (1988). A pedagogical approach to forming generalizations, International Journal for Mathematics Education in Science and Technology, 19, 101-107.
  3. Harel, G., & Behr, M. (1989). Structure and hierarchy of missing value proportion problems and their representations, Journal of Mathematical Behavior, 8, 77-119.
  4. 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.
  5. Martin, G., & Harel, G. (1989). Proof frame of preservice elementary teachers, Journal for Research in Mathematics Education, 20, 41-51. Download
  6. 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
  7. 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.
  8. Hoz, R., & Harel, G. (1990). Higher order knowledge involved in the solution of algebra speed word problems, Journal of Structural Learning, 10, 305-328.
  9. 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.
  10. 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.
  11. Behr, M., & Harel, G. (1990). Students’ errors, misconception, and cognitive conflict in application of procedures, Focus on Learning Problems in Mathematics, 12, 75-84.
  12. Harel, G., & Tall, D. (1991). The general, the abstract, and the generic, For the Learning of Mathematics, 11, 38-42. Download
  13. Harel, G., & Behr, M. (1991). Ed's Strategy for solving division problems, Arithmetic Teacher, 39, 38-40. Download
  14. 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
  15. 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
  16. 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.
  17. 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
  18. Harel, G., & Behr, M. (1992). The blocks task on proportionality: Expert solution models, Journal of Structural Learning, 11, 173-188. Download
  19. 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.
  20. 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.
  21. 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.
  22. Harel, G. (1993). On teacher education programs in mathematics, International Journal for Mathematics Education in Science and Technology, 25, 113-119.
  23. 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
  24. 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
  25. 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.
  26. 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
  27. Harel, G., Behr, M. (1995). Teachers' solutions for multiplicative problems, Hiroshima Journal for Research in Mathematics Education, 31-51.
  28. 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
  29. 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
  30. 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.
  31. Harel, G., & A. Trgalova (1997). Higher Mathematics Education. In A. Bishop (Ed.), International Handbook in Mathematics Education, Kluwer Academic Publishers, 675-700.
  32. 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.
  33. Greer, B., & Harel, G. (1998). The role of analogy in the learning of mathematics, Journal of Mathematical Behavior, 17, 5-24. Download
  34. 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
  35. 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
  36. Sowder, L., & Harel, G. (1998). Types of students’ justifications. Mathematics Teacher, 91, 670-675.
  37. 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
  38. 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.
  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., & 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.
  41. Harel, G. (in press). Students’ proof schemes revisited: Historical and epistemological considerations. In P. Boero (Ed.), Theorems in School, Kluwer.
  42. 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
  43. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. International Journal of Mathematics Thinking and Learning, 5, 157-189. Download
  44. Harel, G., & Rabin, J. (2003). Polygons whose vertex triangles have equal area. The American Mathematical Monthly, 110, 606–610.
  45. 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.
  46. Harel, G., & Sowder, L. (2005). Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development, Mathematical Thinking and Learning, 7, 27-50. Download
  47. 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
  48. Hitt, F., Harel, G., & Selden, A. (2006). Preface , Research in Collegiate Mathematics Education, 6.
  49. 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
  50. 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
  51. Koichu, B. & Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65(3), 349-365. Download
  52. Harel, G. (2008). 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 American Association. Download
  53. 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.
  54. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction: Focus on Proving, Part I. Zentralblatt fuer Didaktik der Mathematik, 40, 487–500. Download
  55. Harel, G. (2008). DNR Perspective on Mathematics Curriculum and Instruction, Part II. Zentralblatt fuer Didaktik der Mathematik. Download
  56. Harel, G., Fuller, E., & Rabin, J. (2008). Attention to meaning. Journal of Mathematical Behavior, 27, 116–127. Download
  57. Harel, G. & Sowder, L. (in press). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge/Taylor & Francis.
  58. Harel, G. & Fuller, E. (in press). 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.
Refereed Proceedings Articles
  1. Harel, G., Behr, M., Post, T., & Lesh, R. (1987). Theoretical Analysis: Structure and hierarchy, missing value proportion problems. In J. C. Bergeron, & N. H. Herscovics, C. Kieran (Eds.), The Proceedings of the 11th Annual Conference of the PME. Canada : University of Montreal , pp. 269-274.
  2. Harel, G., & Martin, G. (1986). The concept of proof held by preservice elementary teachers, The proceedings of the 10th Conference of the PME. London : University of London Institute of Education , pp. 241-246.
  3. Behr, M., Reiss, M., Harel, G., Post, T., & Lesh, R. (1986). Theories applied to sequential length-measuring-knowledge in young children, The proceedings of the 10th Conference of the PME. London : University of London Institute of Education , pp. 235-240.
  4. Harel, G. (1986). A comparison between two approaches to embodying mathematical models in the abstract system of linear algebra. In G. Lapan & R. Even (Eds.), The Proceedings of the 8th Annual Conference of the PME-NA. Michigan : Michigan State University , pp. 127-132.
  5. Harel, G., Behr, M., Post, T., & Lesh, R. (1987). Qualitative differences among 7th grade children in solving a non-numerical proportional reasoning blocks task. In J. C. Bergeron, & N. H. Herscovics, C. Kieran (Eds.), The proceedings of the 11th Annual Conference of the PME. Canada : University of Montreal , pp. 282-288.
  6. Harel, G., Smith, D., & Behr, M. (1987). Aggregate versus individual elements interpretations to facilitate Part-Whole representations. In J. Novak (Ed.), The Proceedings of the 2nd International Seminar of Misconceptions and Educational Strategies in Science and Mathematics, Vol. III. NY: Cornell University , pp. 211-215.
  7. Harel, G., & Hoz, R. (1987). Declarative and procedural knowledge and isomorphism of speed problems. In J. Novak (Ed.). The Proceedings of the 2nd International Seminar of Misconceptions and Educational Strategies in Science and Mathematics, Vol. III. NY: Cornell University , pp. 203-210.
  8. Lacampagne, C., Post, T., Harel, G., Behr, M. (1988). A model for the development of leadership and the assessment of mathematical and pedagogical knowledge of middle school teachers. In M. Behr, C. Lacampagne, & M. Wheeler, The Proceedings of the 9th Annual Conference of the PME-NA. Illinois : Northern Illinois University , pp. 418-424.
  9. Conner, G., Harel, G. & Behr, M. (1988). The effect of structural variables on the level of difficulty of missing value proportion problems, in M. Behr, C. Lacampagne, & M. Wheeler, The Proceedings of the 9th Annual Conference of the PME-NA. Illinois : Northern Illinois University , pp. 65-71.
  10. Harel, G., Post, T., Behr, M. (1988). An assessment instrument to examine knowledge of multiplication and division concepts and its implementation with inservice teachers. In M. Behr, C. Lacampagne, & M. Wheeler, The Proceedings of the 9th Annual Conference of the PME-NA. Illinois , Northern Illinois University , pp. 411-417.
  11. Harel, G., Behr, M. & Post, T. (1988). On the textual and semantic structures of mapping rule and multiplicative compare problems. In A. Borbas (Ed.), The Proceedings of the 12th Annual Conference of the PME. Hungary : Fereno Genzwein, pp. 372-380.
  12. Martin, G., & Harel, G. (1989). The role of the figure in students' concepts of geometric proof, The Proceedings of 13th Annual Conference of the PME. France : University of Paris , pp. 266-273.
  13. Harel, G., Post, T., Behr, M., & Lesh, R. (1989). Fischbein's theory: A further consideration, The Proceedings of 13th Annual Conference of the PME. France : University of Paris , pp. 52-59.
  14. Hoz, R., & Harel, G. (1989). The facilitating role of tables and forms in the solution of speed problems: real or imaginary? The Proceedings of 13th Annual Conference of the PME. France : University of Paris , pp. 123-129.
  15. Harel, G., & Kaput, J. (1990). The role of conceptual entities in constructing meaning of advanced mathematical concepts and their mathematical notational system, The Proceedings of 14th Annual Conference of the PME. Mexico : Oaxtapec, Vol. 1, pp. 53-60.
  16. Behr, M., & Harel, G. (1990). Construct theory of rational numbers; towards a semantics analysis, The Proceedings of 14th Annual Conference of the PME. Mexico : Oaxtapec, Vol. 3, pp. 3-10.
  17. Harel, G., & Behr, M. (1990). Understanding the multiplicative conceptual field, The Proceedings of 14th Annual Conference of the PME. Mexico : Oaxtapec, Vol. 3, pp. 27-34.
  18. Behr, M., Harel, G., & Post, T., & Lesh, R. (1991). The operator subconstruct, The Proceedings of 15th Annual Conference of the PME. Italy : Assisi , Vol. 1, 120-127.
  19. Harel, G., & Behr, M., Post, T., & Lesh, R. (1991). Variables affecting proportionality: Understanding of physical principles, formation of quantitative relations, and multiplicative invariance, The Proceedings of 15th Annual Conference of the PME. Italy : Assisi , Vol. 2, 125-132.
  20. Harel, G., & Dubinsky, E. (1991). The development of the concept of function by preservice secondary teachers: From action conception to process conception, The Proceedings of 15th Annual Conference of the PME. Italy : Assisi , Vol. 2, 133-140.
  21. Harel, G. (1994). Factors in learning linear algebra, The Proceedings of the 16th Annual Conference of the PME-NA. Baton Rouge , Louisiana State University , Vol. 1, 89-94.
  22. Harel, G., & Sowder, L. (1996). Classifying processes of proving. The Proceeding of the 20th Annual Conference of the PME, Valencia , Spain , pp. 59-67.
  23. Heid, K., Harel, G., Ferrini-Mundy, J., & Graham, K. (1998). The role of advanced mathematical thinking in mathematics education reform, The Proceeding of the 20th Annual Conference of the PME-NA, Raleigh , North Carolina , pp. 53-58.
  24. Cramer, K, Harel, G., Kieren, T. & Lesh, R. (1998). Research on rational number, ratio and proportionality, The Proceeding of the 20th Annual Conference of the PME-NA, Raleigh , North Carolina , pp. 89-93.
  25. Harel, G., & Lim, K. (2004). Mathematics Teachers’ Knowledge Base: Preliminary Results. Proceeding of the Psychology of Mathematics Education.
  26. Harel, G. (2008). Topic Study Group 19: Reasoning, Proof and Proving in Mathematics Education, Proceeding of the International Conference on Mathematics Education.
  27. Harel, G., & Koichu, B. (1996). Algebra teachers’ ways of thinking characterizing the mental act of problem posing. The proceeding of the Psychology of Mathematics Education, Prague, Check Republic. pp. Vol. 3, pp. 241-249.
  28. Zaslavsky, O., & Harel, G. (1996). Teachers’ use of examples as a pedagogical tool. The proceeding of the Psychology of Mathematics Education, Prague, Check Republic. Vol. 5, pp. 257-264.
  29. Zaslavsky, O., & Harel, G. (1996). Teachers’ use of examples as a pedagogical tool. The proceeding of the Psychology of Mathematics Education, Prague, Check Republic.
  30. Ignatova, O., Mezentsev, R., Kazachkov, A., & Harel, G. (2008). DNR-based Instruction in Physics: Sliding a Stick towards its Center of Gravity. Proceedings of The 8th Student's Regional Conference on Modern Problems of Physics and Their Computer Support. National Technical University and Kharkov Polytechnic Institute.
 
   
harel@math.ucsd.edu UCSD