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References on Proof
Abramovich, S. (1996). Diagrammatic reasoning, technology and geometrization of proof in secondary mathematics. In E. Jakubowski & D. Watkins & H. Biske (Eds.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Panama City, Florida.
Alcock, L.J., (2004). Uses of example objects in proving. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Alcock, L.J. & Simpson, A.P., (2002), Definitions: dealing with categories mathematically. For the Learning of Mathematics, 22(2), 28-34.
Alcock, L.J. & Simpson, A.P., (2004). Convergence of sequences and series: interactions between visual reasoning and the learner’s beliefs about their own role. Educational Studies in Mathematics, 57(1), 1-32.
Alcock, L.J. & Simpson, A.P., (in press), Convergence of sequences and series 2: interactions between non-visual reasoning and the learner’s beliefs about their own role. Educational Studies in Mathematics.
Alcock, L. J. & Weber, K. (2004) Using a warranted conception of implication to validate proofs. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Alexander, D. & DeAlba, L. (1997). Groups for proofs: collaborative learning in a mathematics reasoning course. Primus, 7, (3), (pp.193-207).
Alibert, D. (1988). Towards new customs in the classroom. For the Learning of mathematics, 8, (2), (pp.31-35).
Alibert, D., & Thomas, M. (1991). Research on mathematical proof. In Tall, D. (Ed.), Advanced mathematical thinking, (pp.215-230). Dordrecht, Netherlands: Kluwer.
Almeida, D. (1995). Mathematics undergraduates’ perceptions of proof. Teaching mathematics and its applications, 14.
Almeida, D. (1996). Variation in proof standards: Implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 27, (pp.659-665).
Almeida, D. (1996). Proof in undergraduate mathematics in the UK: A case of bridging from the informal to the formal? Proccedings of the 8th International Congress on Mathematics Education. Seville, Spain.
Anderson, I., van Asch, B., & van Lint, J. (2004). Discrete mathematics in the high school curriculum. Zentralblatt für Didaktik der Mathematik, 36 (6), 105-116
Anderson, J.R. (1983). Acquisition of proof skills in geometry. In Carbonnel, J.G., Michalski, R., & Mitchell, T. (Eds.), Machine Learning: An Artificial Intelligence Approach, (pp.191-219). Paolo Alto, C.A.: Tioga.
Anderson, J.A. (1994). The answer is not the solution - inequalities and proof in undergraduate mathematics. International Journal of Mathematics Education in Science and Technology 25, (pp.655-663)
Anderson, J. (1995). The legacy of school: Attempts at justifying and proving among new graduates. Proceedings of the Mathematical Sciences Institute of Education Conference on Proof, (pp.47-58). London, U.K.: University of London.
Antonini, S. (2004). A statement, the contrapositive and the inverse: intuition and argumentation. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Antonini, S. (2003). Non-examples and proofs by contradiction. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Arzarello, F. (2000). Inside and outside: spaces, times, and language in proof production. In T. Nakahara & M. Koyama (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan.
Baker, J. (1996). Students’ difficulties with proof by mathematical induction. Paper presented at the AERA meeting. New York, N.Y.
Baker, D. & Campbell, C. (2004). Fostering the Development of Mathematical Thinking: Observations From a Proofs Course. PRIMUS, 14 (4)
Balacheff, N. (2004). The researcher epistemology: A deadlock for educational research on proof.
Balacheff, N. (1991). The benefits and limits of social interaction: The case of mathematical proof. In Bishop, A., Mellin-Olsen, S. & van Dormolen, J. (Eds.), Mathematical knowledge: Its growth through teaching, (pp.175-192). Dordrecht, Netherlands: Kluwer Academic Publishers.
Balacheff, N. (1991). Treatments of refutations: Aspects of the complexity of a constructivist approach to mathematics learning. In von Glasersfeld, E. (Ed.), Radical constructivism in mathematics education , (pp.89-110). Dordrecht, Netherlands: Kluwer.
Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In Pimm, D. (Ed.) Mathematics, teachers and children, (pp.216-230). London, U.K.: Hodder & Stoughton.
Barbeau, E. (1990). Three faces of proof. Interchange, 21, (pp.24-27).
Barki, R. & Tirosh, D. & Tsamir, P. (2004) Is it a mathematical proof or not? Elementary school teachers’ responses. Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Baylis J. (1983). Proof – the essence of mathematics. International Journal of Mathematics Education and Science Technology, 14 (4), 409-414
Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, (pp.23-40).
Bell, A. (1979). The learning of process aspects of mathematics. Educational Studies in Mathematics 10, (6), (pp.361-387).
Bergren, J. (1990). Proof, pedagogy, and the practice of mathematics in medieval Islam. Interchange 21, (pp.36-48).
Bittinger, M. (1969). The effect of a unit mathematical proof on the performance of college mathematics majors in future mathematics courses. Dissertation Abstracts, 29, 3906A.
Blackmore, D., Cluett, G., & Reid, D. (1996). Three perspectives on problem-based mathematics learning. In Jakubowski, E., Watkins, D., & Biske, H. (Eds.), Proceedings of the Eighteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, v.1, (pp.258-262).
Blanton, M.L. & Stylianou, D.A. (2002). Exploring socio-cultural aspects of undergraduate students’ transition to mathematical proof. In Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education, v.4, (pp.1673-1680). Athens, G.A.
Blanton, M.L., Stylianou, D.A. & David, M.M. (2003). The nature of scaffolding in undergraduate students' transition to mathematical proof. In the Proceedings of the 27th Annual Meeting for the International Group for the Psychology of Mathematics Education, v.2, (pp.113-120). Honolulu, Hawaii: Center for Research and Development Group, University of Hawaii.
Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? Educational Studies in Mathematics, 52 (1), 3 - 28
Blum W., & Kirsch A. (1991). Pre-formal proving: examples and reflections. Educational Studies in Mathematics 22, v.2, (pp.183-203).
Bobos, G. (2004) Is theoretical thinking necessary in linear algebra proofs? In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Boero, P., Garuti, R., & Mariotti, M. (1996). Some dynamic mental processes underlying producing and proving conjectures. In Puig, L. & Gutierrez, A. (Eds.), In the Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, v.2, (pp.121-128). Valencia, Spain: Universitat de Valencia.
Boero, P. & Garuti, R. & Lemut, E. (1999). About the generation of conditionality of statements and its links with proving. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Boero, P., Garuti, R., Lemut, E., & Mariotti, M. (1996). Challenging the traditional school approach to the theorems: A hypothesis about the cognitive unity of theorems. In Puig, L. & Gutierrez, A. (Eds.), In the Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, v.2, (pp.113-120). Valencia, Spain: Universitat de Valencia.
Boero, P., Chiappini, G., Garuti, R., & Sibilla, A. (1995). Towards statements and proofs in elementary arithmetic: An exploratory study about the role of teachers and the behavior of students. In Meira, L. & Carraher, D. (Eds.), In the Proceedings of the 19th Conference of the International Group for the Psychology of Mathematics Education, v.3, (pp.129-136). Recife, Brazil: Universidade Federal de Pernambuco.
Brown, S. (2004). Implementing the NCTM's Reasoning and Proof Standard with Undergraduates: Why Might This Be Difficult? In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Campbell, C. (2004). Active Learning Projects for a Proofs Course. PRIMUS, 14 (3)
Canadas, C. & Gomez, P. & Castro, E. (2002). Didactical reflections about some proofs of the Pythagorean proposition. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Casselman, B. (2000). Pictures and Proofs. Notices of the AMS 47, v.10, (pp.125-126).
Chang, K. (2004). In math, computers don’t lie. Or do they? New York, N.Y.: The New York Times.
Chazan, D. (1990). Quasi-empirical views of mathematics and mathematics teaching. Interchange 21, v.1, (pp.14-23).
Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics 24, (pp.359-387).
Chazan, D. (1993). Instructional implications of students’ understandings of the differences between empirical verification and mathematical proof. In Schwartz, J. Yerushalmy, M. & Wilson, B. (Eds.), The Geometric Supposer: What is it a case of?, (pp.107-116). Hillsdale, NJ: Erlbaum.
Chen, I. & Lin, F. (2002). The evolution of a student teacher’s pedagogical views about teaching mathematics proof. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Chin, E. (2003) Mathematical proof as formal procept in advanced mathematical thinking. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Christou, C. & Mousoulides, N. & Pittalis, M. & Pitta-Pantazi, D. (2004) Proofs through exploration in dynamic geometry environments. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Coe, R. & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal 20, (1), (pp.41-53).
Contreras, J. N. (1998). Effects of instruction on students’ construction of proofs: prospective elementary and secondary teachers and the case of the angle sum in the a triangle theorem. In S. Berenson & K. Dawkins & M. Blanton & W. Coulombe & J. Kolb & K. Norwood & Lee Stiff (Eds.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Raleigh, North Carolina.
Csikos, C. A (1999). Measuring students’ proving ability by means of Harel and Sowder’s proof-categorization. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Cyr, S. (2004). Conceptions of Proof Among Preservice High School Mathematics Teachers. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Dauben J. (1996) Arguments, logic, and proof: Mathematics, logic, and the infinite. In Jahnke, H., Knoche, N., & Otte, M. (Eds.), History of mathematics and education: Ideas and experiences. Gottingen: Vandenhoeck & Ruprecht.
Davis, R. (1985). A study of the process of making proofs. The Journal of Mathematical Behavior 4, (pp.37-43).
Davis, P.J. & Hersh, R. (1981). The mathematical experience. Boston, MA: Houghton Mifflin.
DeBellis, V. & Rosenstein J. G. (2004). Discrete Mathematics in Primary and Secondary Schools in the United States. Zentralblatt für Didaktik der Mathematik, 36 (2), 46-55
Deloustal-Jorrand, V. (2004). Studying the mathematical concept of implication through a problem on written proofs. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
DeVilliers, M. (1990). The role and function of proof in mathematics. Pythagoras 24, (pp.7-24).
De Villiers, M. (1990). Proof in the mathematics curriculum. Paper presentation at the National Subjects Didactics Symposium. University of Stellenbosch.
DeVilliers, M. D. (1991). Pupils' need for conviction and explanation within the context of geometry. Pythagoras 25, (pp.18-27).
DeVilliers, M.D. (1995). An alternative introduction to proof in dynamic geometry. Micromath 11, (1), (pp.14-19).
DeVilliers, M.D. (1998). An alternative approach to proof in dynamic geometry. In Lehrer, R. & Chazan, D. (Eds.), New directions in teaching and learning geometry, (pp. 369-393). Hillsdale, N.J.: Erlbaum.
DeVilliers, M.D. (1999). Rethinking proof with the Geometer’s Sketchpad. Emeryville, C.A.: Key Curriculum Press.
DeVilliers, M.D. (2004). The Role and Function of Quasi-empirical Methods in Mathematics. Canadian Journal of Science, Mathematics and Technology Education 4, (pp.397-418).
Dhombres, J. (1993). Is one proof enough? Travels with a mathematician of the baroque period. Educational studies in Mathematics 24, (4), (pp.401-419).
Doerr, H. M. (1995). Evidence and proof: explaining vector relationships. In D. Owens & M. K. Reed & G. M. Millsaps (Eds.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Columbus, Ohio.
Dorier, J. L., Robert, A., & Rogalski, M. (2002). Some comments on “The role of proof in comprehending and teaching elementary linear algebra” by F. Uhlig. Educational Studies in Mathematics, 51 (3) 185 - 192
Douek, N. (1998) Argumentative aspects of proving: Analysis of some undergraduate mathematics students’ performances. Psychology of Mathematics Education, v.2, (pp.273-280).
Douek, N. (1998). Some remarks about argumentation and mathematical proof and their education implications. Paper presentation at the First European Conference of Research in Mathematics Education. Osnabruck, Germany.
Douek, N. (1999). Argumentation and conceptualization in context: a case study on sunshadows in primary schools. Educational Studies in Mathematics 39, (1/3), (pp.89-110).
Douek, N. (1999). Argumentative aspects of proving: Analysis of some undergraduate mathematics students’ performance. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Dreyfus, T. (1999). Why Johnny can't prove. Educational Studies in Mathematics 38, (1/3), (pp.85-109)
Dreyfus, T. & Hadas, N. (1996). Proof as answer to the question why. Zentralblatt für Didaktik der Mathematik 28, (1), (pp.1-5).
Dubinsky, E. (1989). On the teaching of mathematical induction. Journal of Mathematical Behavior 8, (pp.285-304).
Dubinsky, E., Elterman, F. & Gong, C. (1988). The student’s construction of quantification. For the Learning of Mathematics 8(2), 44-51.
Dubinsky, E. & Lewin, P. (1986). Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. Journal of Mathematical Behavior 5, (pp.55-92).
Dubinsky, E., & Yiparaki, O. (2000). On student understanding of AE and EA quantification. In Dubinsky, E., Schoenfeld, A.H., & Kaput, J. (Eds.), Research in collegiate mathematics education IV, (pp.239-286). Providence, R.I.: American Mathematical Society.
Duval, R. (1991). Structure du raisonnement déductif et apprentissage de la demonstration. Educational Studies in Mathematics, 22, (pp.233-261)
Easterday, K.E. & Galloway, L.L. (1995). A comparison of sentential logic skills: Are teachers sufficiently prepared to teach logic? School Science and Mathematics 95, (pp.431-436).
Ebert, C., Ebert, G., Klin, M., & Sheva, B. (2004). From the principle of bijection to the isomorphism of structures: An analysis of some teaching paradigms in discrete mathematics. Zentralblatt für Didaktik der Mathematik, 36 (5), 172 – 183
Eisenberg, T.A. & McGinty, R.L. (1974). On comparing error patterns and the effect of maturation in a unit on sentential logic. Journal for Research in Mathematics Education 5, (pp.225-237).
Epp, S.S. (2003). The role of logic in teaching proof. American Mathematical Monthly 110, (10), 886-899
Epp, S. (1998). A unified framework for proof and disproof. Mathematics Teacher 91, (8), 708-713
Evans, J. & Saint, B. T. (1982). The psychology of deductive reasoning. London, U.K.: Routledge & Kegan Paul.
Fallis, D. (1996). Mathematical Proof and the Reliability of DNA Evidence. American Mathematical Monthly 103, (6), (pp.491-497).
Fawcett, H. (1938). The Nature of Proof. Thirteen Yearbook of the National Council of Teachers of Mathematics. New York, N.Y.: Bureau of Publications, Teachers College, Columbia University.
Finlow-Bates, K., Lerman, S. & Morgan, C. (1993). A survey of current concepts of proof held by first year mathematics students. In Proceedings of the 17th International Conference for the Psychology of Mathematics Education, v.1, (pp.252-259).
Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics 3, (2), 9-18.
Fischbein, E. & Kedem, I. (1982). Proof and certitude in the development of mathematical thinking. In Vermandel, A. (Ed.), Proceedings of the Sixth International Conference for the Psychology of Mathematics Education, (pp.128-131). Anthwerp, Belgium: Universitaire Instelling Antwerpen
Fitzgerald, J. (1996). Proof in Mathematics Education. New England Journal of Education, v178, n1, p35-45.
Fonseca, L. (2002). Preservice teachers, geometry and proof. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Furinghetti, F. & Domingo, P. (1996). Presentation of a questionnaire for evaluating the influence of the semantic context in mathematical proof. Proccedings of the 8th International Congress on Mathematics Education. Seville, Spain.
Furinghetti, F. & Paola, D. (2003). To produce conjectures and to prove them within a dynamical geometry environment: a case study. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Galbraith, P.L. (1981). Aspects of proving: A clinical investigation of process. Educational Studies in Mathematics 12, 1-28.
Gardiner, T. (2004). Learning to prove: using structured templates for multi-step calculations as an introduction to local deduction. Zentralblatt für Didaktik der Mathematik, 36 (2), 67-76
Geeslin, W. E. (1995). College students’ early ideas about mathematical proof. In D. Owens & M. K. Reed & G. M. Millsaps (Eds.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Columbus, Ohio.
Gholamazad, S. & Liljedahl & Zazkis, R (2003). One line proof: what can go wrong?. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Gholamazad, S., Liljedahl, P., & Zazkis, R. (2004). What Counts as Proof? Investigation of Pre-service Elementary Teachers' Evaluation of Presented 'Proofs'. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Gibson, D. (1998). Students’ use of diagrams to develop proofs in an introductory analysis course. In Schoenfeld, A.H., Kaput, J. & Dubinsky, E. (Eds.), Research in College Mathematics Education III, (pp.284-305). Providence, RI: AMS.
Glass, B. (2004). Students problem solving and justification. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Goetting, M. (1995). The college students’ understanding of mathematical proof. Dissertation Abstracts International 56–A, 3016.
Goff, C. D. (2002). Using composition techniques to improve classroom instruction and students' understanding of proof. PRIMUS, 12 (3)
Goldberg, D.J. (1975). The effects of training in heuristic methods on the ability to write proofs in number theory. Dissertation Abstracts International 35, 4989B.
Goldin, G. (2004). Problem Solving Heuristics, Affect, and Discrete Mathematics. Zentralblatt für Didaktik der Mathematik, 36 (2), 56-60
Govender, R. & DeVilliers, M. (2004). A dynamic approach to quadrilateral definitions. Pythagoras, 59, (pp.34-45).
Gutierrez, A. & Lawrie, C. & Pegg, J. (2004) Characterization of students’ reasoning and proof abilities in 3-dimensional geometry. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Hadas, N. (1977). Children's conditional reasoning: an investigation of 5th graders' ability to distinguish between valid and fallacious inferences. Educational Studies in Mathematics 9, (pp.98-140).
Hadas, N. &Hershkowitz, R. (1999). The role of uncertainty in constructing and proving in computerized environment. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Hadas, N., Hershkowitz, R. & Schwarz, B. (2000). The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments. Educational Studies in Mathematics 44, (1-2), (pp.127-150).
Hanna G. (1989). More than formal proof. For the learning of mathematics 9, (1), (pp.20-25).
Hanna, G. (1990). Some pedagogical aspects of proof. Interchange 21, (pp.6-13).
Hanna, G. (1991). Mathematical Proof. In Tall, D. (Ed.), Advanced Mathematical Thinking, (pp. 54-61).
Hanna, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics 15, (3), (pp.42-49).
Hanna, G. (1996). The Ongoing Value of Proof. PME Conference 20th, v1, p. 1-21 - 1-34. Valencia, Spain.
Hanna G. (1998). Proof as understanding in geometry. Focus on Learning Problems in Mathematics 20, (2&3), (pp.4-13).
Hanna, G. (2000). Proof, Explanation and Exploration: An Overview. Educational Studies in Mathematics 44, (1-2), (pp.5-23).
Hanna G. (2000). A critical examination of three factors in the decline of proof. Interchange 31, (1), (pp.21-33).
Hanna, G. & Barbeau, E. (2002). What is Proof? In Baigrie, B. (Ed.), History of Modern Science and Mathematics, (pp. 36-48). Charles Scribner's Sons.
Hanna, G., de Bruyn, Y., Sidoli, N. & Lomas, D. (2004). Teaching Proof in the Context of Physics. Zentralblatt für Didaktik der Mathematik 36, (3), (pp.82-90).
Hanna G., & Jahnke, H.N. (1993). Proof and Application. Educational studies in Mathematics 24, (4), (pp.421-438).
Hanna, G. & Jahnke, H.N. (1993). Aspects of proof. [Special issue] Educational Studies in Mathematics 24, (4).
Hanna, G. & Jahnke, H. N. (1996). Proof and proving. In Bishop, A., Clements, K., Keiterl, C., Kilpatrick, J., & Laborde, C. (Eds.), International handbook of mathematics education, Part 2, (pp. 877-908). Dordrecht, The Netherlands: Kluwer
Hanna, G. & Jahnke, H. N. (1999). Using arguments from physics to promote understanding of mathematical proofs. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Hanna G., & Jahnke N., (2002). Another Approach to Proof: Arguments from Physics. Zentralblatt für Didaktik der Mathematik 34, (1).
Hanna, G. & Jahnke, H. N. (2002). Arguments from physics in mathematical proofs: an educational perspective. For the Learning of Mathematics 22, (3), (pp.38-45).
Hanna, G., & Jahnke, N. (2004). Proving and modeling. In Henn, H.W. & Blum, W. (Eds.), Proceedings of the ICMI study 14: Applications and Modeling in Mathematics Education, (pp.109-114). Dortmund, Germany: University of Dortmund.
Harada, K. & Gallou-Dumiel, E. & Nohda, N. (2000). The role of figures in geometrical proof-problem solving: Students’ cognitions of geometrical figures in France and Japan. In T. Nakahara & M. Koyama (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan.
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, (pp.601-613).
Harel, G., (2001). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In Campbell, S. & Zazkis, R. (Eds.), Learning and teaching number theory. Journal of Mathematical Behavior (special issue).
Harel, G. (in press). Greek versus modern mathematical thought and the role of Aristotelian causality in the mathematics of the Renaissance: Sources for understanding students’ conception of Proof. In Boero, P. (Ed.), The concept of mathematical proof. Dordrecht, The Netherlands: Kluwer.
Harel, G. (in press). The DNR system as a conceptual framework for curriculum development and instruction. In Lesh, R., Kaput, J., Hamilton, E. & Zawojewski, J. (Eds.), Foundations for the future. N.J.: Erlbaum.
Harel, G., & Lesh, R. (2003). Local conceptual development of proof schemes in a co-operative learning setting. In Lesh, R. & Doerr, H. (Eds.), (?). Mahawah, N.J.: Erlbaum.
Harel, G. & Sowder, L. (1998). Students’ proof schemes: Results from an exploratory study, In Schoenfeld, A.H., Kaput, J., & Dubinsky, E. (Eds.), Research in College Mathematics Education III (pp. 234-283). Providence, RI: AMS.
Harel, G., & Sowder, L (In Press). Toward a comprehensive perspective on proof, In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Reston, VA: National Council of Teachers of Mathematics
Hart, E. (1994). An exploratory study of the proof-writing performance of college students in elementary group theory, Dissertation Abstracts International 47, 4313A.
Hart, E. (1994). A conceptual analysis of the proof-writing performance of expert and novice students in elementary group theory. In Kaput, J. & Dubinsky, E. (Eds.), Research issues in undergraduate mathematics learning: Preliminary analyses and results, (pp. 49-63). Washington, DC: The Mathematical Association of America.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra, Journal for Research in Mathematics Education 31, (pp.396-428).
Heinze, A. (2004). The proving process in mathematics classroom - method and results of a video study. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Heinze, A., Anderson, I., & Reiss, K. (2004). Discrete Mathematics and Proof in the High School. Introduction. Zentralblatt für Didaktik der Mathematik, 36 (2), 44-45
Heinze, A., Cheng, Y. H., & Yang, K. L. (2004). Students’ performance in reasoning and proof in Taiwan and Germany: Results, paradoxes and open questions. Zentralblatt für Didaktik der Mathematik, 36 (5), 162-171
Heinze, A. & Kwak, ; J. Y. (2002). Informal Prerequisites for Informal Proofs. Zentralblatt für Didaktik der Mathematik, 34 (1), 9–16
Heinze, A. & Reiss, K. (2004). The Teaching of Proof at the Lower Secondary Level – A Video Study. Zentralblatt für Didaktik der Mathematik 36, (3), (pp.98-104).
Herbst, P. (2003). Using novel tasks in teaching mathematics; Three tensions affecting the work of the teacher. American Educational Research Journal 40, (1), (pp.197-238).
Herbst, P. (2003). Enabling students’ interaction with diagrams while making and proving reasoned conjectures. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Herbst, P. (2002). Establishing a custom of proving in American school geometry: evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics 49, (3), 283-312.
Herbst, P. (2002). Engaging students in proving: A double bind on the teacher. Journal for Research in Mathematics Education 33, 3, 176-203.
Herbst, P. (2002). Enabling students to make connections while proving: The work of a teacher creating a public memory, In Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education - North America, v.4, (pp. 1681-1692). Athens, GA.
Herbst, P. (2004). Interactions with diagrams and the making of reasoned conjectures in geometry. Zentralblatt für Didaktik der Mathematik, 36 (5), 129-139
Herbst, P. & Brach, C. (2004). Proving and proof in high school geometry: What is “it” that is going on for students and how do they make sense of it? Paper presentation at the AERA annual meeting.
Herbst, P. & Chazan, D. (2003). Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: the case of engaging students in proving. For the Learning of Mathematics 23, 1, (pp.2-14).
Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics 24, 389-399.
Hoyles, C. & Kuchemann, D. (2002). Students’ understanding of logical implication, Educational Studies in Mathematics 51, 193-223.
Hoyles, C. (1997). The curricular shaping of students’ approaches to proof, For the Learning of Mathematics 17, 1, 7-16.
Hoyles, C. & Healy, L. (1999). Linking informal argumentation with formal proof through computer-integrated teaching experiments. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Housman, D. & Porter, M. (2003). Proof schemes and learning strategies of above-average mathematics students, Educational Studies in Mathematics 53 (2), 139-158.
Kleiner, I. (1991). Rigor and proof in mathematics: A historical perspective, Mathematics Magazine 64, (5), 291-314.
Jiang, Z. (2002). Developing preservice teachers’ mathematical reasoning and proof abilities in the Geomter’s Sketchpad environment. In Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Athens, GA.
Jones, K. (2000). Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations. Educational Studies in Mathematics 44, (1-2).55-85.
Jones K. (2000). The Student Experience of Mathematical Proof at University Level. International Journal of Mathematical Education in Science and Technology 31, (1), 53-60.
Jones, K. (1997). Student-teachers' conceptions of mathematical proof. Mathematics Education Review 9 .21-32.
Kleiner, I. (1991). Rigor and proof in mathematics: A historical perspective. Mathematics Magazine 64, (5), 291-314.
Koedinger, K. R. (1998). Conjecturing and argumentation in high-school geometry students. In Lehrer, R. & Chazan, D. (Eds.), Designing learning environments for developing understanding of geometry and space, (pp. 319-347). Mahwah, NJ: Erlbaum.
Knapp, J. & Zandieh (2004) Examples as tools for understanding proofs in geometry. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Knipping, C. (2004). Challenges in teaching mathematical reasoning and proof – Introduction. Zentralblatt für Didaktik der Mathematik, 36 (5), 127-128.
Knuth, E., & Sutherland, J. (2004). Student Understanding of Generality. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Knuth, E. (2002). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education 5, 1, 61-88.
Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education 33, 5, 379-405.
Knuth, E. & Elliott, R. (1998). Characterizing students’ understandings of mathematical proof. The Mathematics Teacher 91, 714-717.
Knuth, E., Choppin, J., Slaughter, M., & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education - North America, v.4, (pp. 1693-1700). Athens, GA.
Kortenkamp, U. (2004). Experimental Mathematics and Proofs in the Classroom. Zentralblatt für Didaktik der Mathematik, 36 (2), 61-66
Krummheuer G. (1995). The ethnography of argumentation. In Cobb., P. & Bauersfeld, H. (Eds.), The emergence of mathematical meaning: interaction in the classroom culture. Hillsdale, NJ: Erlbaum.
Krummheuer G. (2000). Mathematics learning in narrative classroom cultures: studies of argumentation in primary mathematics education [1]. For the Learning of Mathematics 20, (1), (pp.22-32).
Kuchemann, D. & Hoyles, C. (2002). Students’ understaning of a logical implication and its converse. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Laborde, C. (1990). Language and mathematics. In Nesher, P. & Kilpatrick, J. (Eds.), Mathematics and cognition: a research synthesis by the International Group for the Psychology of Mathematics Education, (pp. 51-69). Cambridge: MA: Cambridge University Press.
Laborde, C. (2000). Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving. Educational Studies in Mathematics, 44 (1-2).
Lakatos, I. (1976). Proofs and refutations. Cambridge, UK: Cambridge University Press.
Lam, E. (2002). Making and proving conjectures: circles. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Lavy, I. (2004). Kinds of arguments emerging while exploring on a computerized environment. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Lawson, A. E., Karplus, R., & Adi, H. (1978). The acquisition of propositional logic and formal operational schemata during the secondary school years. Journal of Research in Science Teaching 15, (pp.465-478).
Leikin, R. (2004). Towards high quality geometrical tasks: reformulation of a proof problem. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Leron, U. (1985). Heuristic presentations: The role of structuring. For the Learning of Mathematics 5, (3), (pp.7-13).
Leron, U. (1985). A direct approach to indirect proofs. Educational Studies in Mathematics 16, (pp.321-325).
Leron, U. (1983). Structuring mathematical proofs. American Mathematical Monthly 90, (pp.174-185).
Lester, F.K. (1975). Developmental aspects of children’s ability to understand mathematical proof. Journal for Research in Mathematics Education 6, (1), (pp.14-25).
Lewis, S.M. (1987). University mathematics students’ perception of proof and its relationship to achievement. Dissertation Abstracts International 47, 3345B.
Lin, F.L., Lee, Y.S., & WuYu, J.Y. (2003). Students’ understanding of proof by contradiction. In Pateman, N., Dougherty,B.J., & Zilliox, J. (Eds.), Proceedings of the 27th Annual Meeting of the International Group for Psychology in Mathematics Education, v.4 (pp. 443-449). Honolulu: University of Hawaii.
Lin, F. L. & Yang, K. L. (2002). Defining a Rectangle under a Social and Practical Setting by Two Seventh Graders. Zentralblatt für Didaktik der Mathematik, 34 (1), 17–28
Linchevsky, L., Vinner, S., & Karsenty, R. (1992). To be or not to be minimal? Students teachers’ views about definitions in geometry. In Geeslin, W. & Graham, K.(Eds.), Proceedings of the Sixteenth PME Conference, v.2, (pp.48-55). Durham, NH: University of New Hampshire.
Lovell, K. (1971). The development of the concept of mathematical proof in abler pupils. In Rosskopf, M. et al (Eds.), Piagetian cognitive-development research and mathematical education, (pp. 66-80). Washington, DC: NCTM.
Lovin, L. & Cavey, L. & Whitenack, J. (2004). Evidence and justification: prospective PREK-8 teachers’ proof-making and proff-evaluating. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Lowenthal, F., & Eisenberg, T. (1992). Mathematics induction in school; An illusion of rigor. School Science and Mathematics 92, (pp.233-238).
Maher, C.A. (2002). How students structure their own investigations and educate us: What we’ve learned from a fourteen-year study. In Cockburn, A.D. & Nardi, E. (Eds.), Proceedings of the 26th Annual Meeting of the International Group for the Psychology of Mathematics Education, v.1, (pp. 31-46). Norwich, England: University of East Anglia.
Maher, C. & Davis, R. (1995). Children’s explorations leading to proof. In C. Hoyles & L. Healy (Eds), Justifying and proving in school mathematics (pp. 87-105). London: Institute of Education, University of London
Maher, C. & Martino, A. (1996a). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education 27, (2), (pp.194-214).
Maher, C. & Martino, A. (1996b). Young children inventing methods of proof: The gang of four. In Steffe, L., Nesher, P., Cobb, P., Goldin, G., & Greer, B. (Eds.), Theories of mathematical learning, (pp. 431-447). Hillsdale, NJ: Erlbaum.
Mariotti, M.A., (1997) Justifying and Proving in Geometry: the mediation of a micro-world, Revised and extended version of the version published in: Hejny, M., Novotna, & J. (Eds.), Proceedings of the European Conference on Mathematical Education, (pp.21-26). Prague: Prometheus.
Mariotti, M. A. & Maracci, M. (1999). Conjecturing and proving in problem solving situations. In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Mariotti, M.A. (2001). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning 6, (3), (pp.283-317).
Mariotti, M.A. (2000). Introduction to Proof: The Mediation of a Dynamic Software Environment. Educational Studies in Mathematics 44, (1-2), (pp.25-53).
Markel, W. (1994). The role of proof in mathematics education. School Sciences and Mathematics 94, (pp.291-295).
Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics 44, (1-2), (pp.87-125).
Marshall , J. (2004). Construction of meaning: urban elementary students’ interpretation of geometric puzzles Journal of Mathematical Behavior, 23 (2), 169-182
Martin, L., LaCroix, L., & Grecki, S. (2004). Mathematical Images for Workplace Training: The Case of John, a Plumbing Apprentice. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Martin, T. S. & McCrone, S. S. (2001). Investigating the teaching and learning of proof: first year results. In Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Snowbird, Utah.
Martin, T. S. & McCrone, S. S. (2003). Classroom factors related to geometric proof construction ability. The Mathematics Educator, 7 (1), 18-31.
Martin, T. S., McCrone, S. M. S., Bower, M. L., & Dindyal, J. (in press). The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in Mathematics.
Martin, T. & McCrone, S. S (2003). The teaching and learning of geometric proof: an emerging theory. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Martin, W.G., & Harel, G. (1989). Proof frames of pre-service elementary teachers. Journal for Research in Mathematics Education 20, (pp.41-51).
Martino & Maher (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior 18, 1, (pp.53-78).
McCrone, S. S. & Martin, T. S. (2000). Tools for investigating high school students’ understanding of geometric proof. In M. L. Fernandez (Ed.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Tucson, Arizona.
McCrone, S. & Martin, T. (2004). The Impact of Teacher Actions on Student Proof Schemes in Geometry. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education - North America. Toronto
McCrone, S. & Martin, T.S. (2004). Assessing High School Students’ Understanding of Geometric Proof. Canadian Journal of Science, Mathematics & Technology Education 4, (2).
McCrone, S. S. et al (2002). An investigation of classroom factors that influence proof construction ability. In Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education - North America, v.4, (pp.1701-1712). Athens, GA.
Miyakawa, T. (2002). Relation between proof and conception: the case of proof for the sum of two even numbers. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Miyakawa, T. (2004). Reflective symmetry in construction and proving. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Miyazaki, M. (2000). Levels of proof in lower secondary school mathematics. Educational Studies in Mathematics 41, (1), (pp.47-68).
Miyazaki, M. (2000). What are essential to apply the “discovery” function of proof in lower secondary school mathematics? In T. Nakahara & M. Koyama (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan.
Moore, R.C. (1994). Making the transition to formal proof. Educational Studies in Mathematics 27, (pp.249-266).
Morgan, W.H. (1972). A study of the abilities of college mathematics students in proof-related logic. Dissertation Abstracts International 32, 4081B.
Morris, A. (2002). Mathematical reasoning: Adults’ ability to make the inductive-deductive distinction. Cognition and Instruction 20, (1), (pp.79-118).
Moshovits-Hadar, N. (1988). Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics 8, (pp.12-19).
Muter, E. M. & Maher, C. A (1998). Recognizing isomorphism and building proof: revisiting earlier ideas. In S. Berenson & K. Dawkins & M. Blanton & W. Coulombe & J. Kolb & K. Norwood & Lee Stiff (Eds.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Raleigh, North Carolina.
Nasser, L. & Tinoco, L. (2002). Argumentation and proofs in mathematical teaching. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
O’Daffer, P.G., & Thornquist, B.A. (1993). Critical thinking, mathematical reasoning, and proof. In Wilson, P.S. (Ed.), Research ideas for the classroom: High school mathematics, (pp. 39-56). New York: Macmillan.
Okazaki, M. & Iwasaki, H. (2000). Geometric construction as a threshold of proof: The figure as a cognitive tool for justification. In T. Nakahara & M. Koyama (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan.
Otte, M. (1994). Mathematical knowledge and the problem of proof. Educational Studies in Mathematics 26, (4), (pp.299-321).
Otte, M. (1990). Intuition and formalism in mathematical proof. Interchange 21, (1), (pp.59-64)
Otte, M. (2002) Proof-analysis and the development of geometrical thought. In F. Hitt (Eds.) Representations and Mathematics Visualization.
Paola, D. (2004). Patterns of reasoning in classroom. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway
Pedemonte, B. (2001). Sone cognitive aspects of the relationship between argumentation and proof in mathematics. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Piatiek-Jimenz, K. (2003). Undergraduate students’ beliefs and misconceptions about proof. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Porteous, K. (1986). Children’s appreciation of the significance of proof. Proceedings of the tenth International Conference of the Psychology of Mathematics Education, (pp. 392-397). London, England.
Powell, A., Maher, C., & Alston, A. (2004). Ideas, Sense Making, and the Early Development of Reasoning in an Informal Mathematics Setting. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Raman, M. (2000). Some beliefs about proof in collegiate calculus. In M. L. Fernandez (Ed.) Proceedings of the conference of the North American group for the Psychology of Mathematics Education. Tucson, Arizona.
Raman, M. (2003). Key Ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics 52, 3, (pp.319-325).
Raman, M. (2004). Key Ideas: The Link between Private and Public Aspects of Proof. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Rasmussen, C. (2004). The Evolution of Formal Mathematical Reasoning: A Case Study of the Uniqueness Theorem in Differential Equations. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Recio, A.M., & Godino, J.D. (2001). Institutional and personal meanings of mathematical proof. Educational Studies in Mathematics 48, (1), (pp.83-99)
Reid, D. (2003). Forms and uses of abduction. Paper presented to Working Group 4: Proof and argumentation, at the Third annual conference of the European Society for Research in Mathematics Education. Bellaria, Italy.
Reid, D. (2002). Elements in accepting an explanation. Journal of Mathematical Behavior 20, (4), (pp.527-547).
Reid, D. (2002). Describing young children’s deductive reasoning. In Cockburn, A. & Nardi, E. (Eds.), Proceedings of the Twentieth-sixth Annual Conference of the International Group for the Psychology of Mathematics Education, v.4, (pp.105-112). Norwich, UK.
Reid, D. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education 33, 1, (pp.5-29).
Reid, D. (2002). Elements in accepting an explanation. Journal of Mathematical Behavior 20, (4), (pp.527-547).
Reid, D. (2002). Describing young children’s deductive reasoning. In Cockburn, A. & Nardi, E. (Eds.), Proceedings of the Twentieth-sixth Annual Conference of the International Group for the Psychology of Mathematics Education, v.4, (pp.105-112). Norwich, UK.
Reid, D., & Dobbin, J. (1998). Why is proof by contradiction difficult? Proceedings of the 22nd PME Conference, v.4, (pp.41-48). Stellenbosch, South Africa.
Reid, D. (1997). Jill's use of deductive reasoning: A case study from grade 10. In Dossey, J.A., Swafford, J.O., Parmantie, M., & Dossey, A.E. (Eds.), Proceedings of the Nineteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, v.2, (p.667). Columbus OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
Reid, D. (1997). Constraints and opportunities in teaching proving. In Pehkonnen, E. (Ed.), Proceedings of the Twentieth-first Annual Conference of the International Group for the Psychology of Mathematics Education, v.4, (pp.49-55). Lahti, Finland.
Reid, D. (1995). Proving to explain. In Meira, L. & Carraher, D. (Eds.), Proceedings of the Nineteenth Annual Conference of the International Group for the Psychology of Mathematics Education, v.3, (pp.137-143). Recife, Brazil.
Reid, D. (1996). The role of proving: Students and mathematicians. Proccedings of the 8th International Congress on Mathematics Education. Seville, Spain.
Reid, D. (2001). Proofs, proofs, proving and probing: research related to proof. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Reid, D. A. & Roberts, R. (2004). Adult learners' criteria for explanations. Zentralblatt für Didaktik der Mathematik, 36 (5), 140-149
Reiss, K. M & Hellmich, F. & Riess, M. (2002). Reasoning and proof in geometry: prerequisites of knowledge acquisition in secondary school students. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Reiss, K. & Klieme, E. & Heinzo, A (2001). Prerequisites for the understanding of proofs in the geometry classroom. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Reiss, K., & Renkl, A. (2002). Learning to Prove: The Idea of Heuristic Examples. Zentralblatt für Didaktik der Mathematik 34, (pp.29-35).
Rettke, L. & Zandieh, M. & Knapp, J. (2004). Overcoming difficulties with proof as a group. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Riley, K. (2004). Prospective secondary mathematics teachers’ conceptions of proof and its logical underpinnings. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Rin, H. (1983). Linguistic barriers to students’ understanding of definitions. In Hershkowitz, R. (Ed.), Proceedings of the Seventh International conference for the Psychology of Mathematics Education, (pp.295-300). Rehovot, Israel: Weizmann Institute of Science.
Rips, L.J. (1994). The psychology of proof. Cambridge, MA: The MIT Press.
Roberge, J.J. (1970). A study of children's ability to reason with basic principles of deductive reasoning. American Educational Research Journal 7 , (pp.583-596).
Roberge, J.J. (1975). Development of comprehension of logical connectives in symbolic or verbal form. Educational Studies in Mathematics 6, (2), (pp.207-212).
Roberge, J.J. (1972). Recent research on the development of children's comprehension of deductive reasoning schemes. School Science and Mathematics 72, (pp.197-200).
Rodd, M. (2000). On mathematical warrants: Proof does not always warrant, and a warrant may be other than a proof. Mathematical Thinking and Learning 2, (3), (pp.221-244).
Ron, G. & Dreyfus, T. (2004) The use of models in teaching proof by mathematical induction. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Ross, K. (1998). Doing and proving: The place of algorithms and proof in school mathematics. American Mathematical Monthly 3, (pp.252-255).
Rossi, H. (1995). When is the best proof not the best proof? CBMS Issues in Mathematics Education 5, (pp.31-53).
Rota, G. (1996). The Phenomenology of Mathematical Beauty. In Kanamori, A.(Ed.) Proof and Progress in Mathematics, Symposium, v111, n2, p. 171-182. Boston, M.A.: Synthese-Dordrecht: Kluwer.
Rowland, T. (2002). Proofs in number theory: History and heresy. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Royal Statistical Society (1995). Tackling the mathematics problem. London Mathematical Society, Institute of Mathematics and its Applications.
Ryu, A. (2002). Constructing mathematical argument in context: An analysis of processes of contextualization in interaction. In Proceedings of the 24th Annual Meeting for the Psychology of Mathematics Education - North America v.4, (pp.1713-1725). Athens, GA.
Sacristand, A. I. & Sanchez, E. (2002). Processes of proof with the use of technology: discovery, generalization and validation in the computer microworld. In A. D. Cockburn & E. Nardi (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Norwich, UK.
Sanchez, E., Sacristan, A. I., & Mercado, M. (2004). Improving the Formulation Component of Proofs Using a Network Chat Environment Within Dynamic Geometry Activities. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Sanchez,E., & Sacristan, A.I. (2003). Influential aspects of dynamic geometry activities in the construction of proofs. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Sandoval, I. (2004). Reasoning Strategies in the Solution of Geometric Problems Through Cabri Géomètre. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education . Toronto, Canada.
Schabel, C. (2005). An instructional model for teaching proof writing in the number theory classroom. PRIMUS, XV (1), 45-58
Schoenfeld, A. (1986). On having and using geometric knowledge. In Hiebert, J. (Ed.), Conceptual and procedural knowledge: The case of mathematics, (pp. 225-264). Hillsdale, NJ: LEA.
Schuster, A. (2004). About Traveling Salesmen and Telephone Networks – Combinatorial Optimization Problems at High School. Zentralblatt für Didaktik der Mathematik, 36 (2), 77-81
Sekiguchi, Y. (2000). A teaching experiment on mathematical proof: Roles of metaphor and externalization. In T. Nakahara & M. Koyama (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Hiroshima, Japan.
Segal, J. (2000). Learning about mathematical proof: Conviction and validity. Journal of Mathematical Behavior 18, (2), (pp.191-210).
Selden, A. & Selden, J. (1999). Can you tell me whether this is a proof? In O. Zaslavsky (Ed.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Haifa, Israel.
Selden, A., & Selden, J. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics 29, (pp.123-151).
Selden, A. & Selden J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education 34, 1, (pp.4-36).
Selden, A. & Selden, J., (submitted), Overcoming students’ difficulties in learning to understand and construct proofs.
Senk, S. (1985). How well do students write geometry proofs? Mathematics Teacher 78, (pp.448-456).
Simon, M. (1996). Beyond inductive and deductive reasoning: The search for a sense of knowing. Educational Studies in Mathematics 30, (pp.197-210).
Simon, M. & Blume, G. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior 15, (pp.3-31).
Siu, M.K. (1993). Proof and pedagogy in ancient China: Examples from Liu Hui’s commentary on “Jiu Zhang Suan Shu”. Educational Studies in Mathematics 24, (pp.345-357).
Solange de Silva, M. (2001). Argumentation reasoning and mathematics proof. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Sowder L., Harel G. (2003). Case Studies of Mathematics Majors' Proof Understanding, Production, and Appreciation. Canadian Journal of Science, Mathematics and Technology Education 3, (2).
Sowder, L., & Harel, G. (1998). Types of students’ justifications. Mathematics Teacher, 91, (pp.670-675)
Stylianides, G., & Silver, E. (2004). Reasoning and Proving in School Mathematics Curricula: An Analytic Framework for Investigating the Opportunities Offered to Students. In Proceedings of PME-NA.
Stylianou, D. & Blanton, M. (2004) Learning and teaching with proof: a “proof” story across the grades: beginning a conversation the learning of proof grades K-16. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the conference of the North American Chapter of the International group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Sutherland, R. (2004). Orchestrating mathematical proof through the use of digital tools. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway
Tall, D. (1991). The psychology of advanced mathematical thinking. In Tall (Ed.), Advanced Mathematical Thinking.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with reference to limits. Educational Studies in Mathematics 12, (pp.151-169).
Tall, D. (1979). Cognitive aspects of proof, with special reference to the irrationality of Ö2. Proceedings of the Third Conference of the Psychology of Mathematics Education, (pp.203-205). Warwick, England.
Tarlow, L. (2004). Students' Development of Meaningful Mathematical Proofs for Their Ideas. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Thompson, D.R. (1991). Reasoning and proof in precalculus and discrete mathematics. Paper presented at the AERA. Chicago, I.L.
Thurston, W. (1995). On proof and progress in mathematics. For the Learning of Mathematics 15, (1), (pp.29-37).
Tirosh, C. (2003) Prospective teachers’ knowledge of proofs and refutations. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Uhlig, F. (2002). The role of proof in comprehending and teaching elementary linear algebra. Educational studies in mathematics 50, 3, (pp.335-346).
Uptegrove, E., Maher, C. (2004). From Concrete Representations to Abstract Symbols. In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Usiskin, Z, (1987). Resolving the continuing dilemmas in school geometry. In Lindquist, M. & Shulte, A. (Eds.), Learning and Teaching Geometry, K-12, 1987 Yearbook, (pp. 17-31). Reston, VA: NCTM.
VanDormolen, J. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics 8, (pp.27-34).
van Schalkwijk, L., Bergen, T., & van Rooij, A. (2000).Learning to prove by investigations: A promising approach in Dutch secondary education. Educational Studies in Mathematics, 42 (3), 293 - 311
Vidakovic, D. & Martin, W. (2004). Small-group searches for mathematical proofs and individual reconstructions of mathematical concepts. Journal of Mathematical Behavior, 23 (4), 465-492
Vincent, J. & McCrae, B. (2001). Mechanical linkages and the need for proof in secondary school geometry. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Vinner, S. (1983). The notion of proof; some aspects of students’ views at the senior high level. In Hershkowitz, R. (Ed.), Proceedings of the Seventh International Conference of the Psychology of Mathematics Education, (pp. 289-294). Rehovot, Israel: Weizmann Institute of Science.
Vinner, S., (1991). The role of definitions in teaching and learning mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking, Dordrecht: Kluwer.
Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education 20, (pp.356-366).
Volmink, J. D. (1990). The nature and role of proof in mathematics education. Pythagoras, 23, 7-10.
Waring, S. (2000). Can you prove it? Developing concepts of proof in primary and secondary classrooms. Leicester, U.K.: The Mathematical Association.
Weber, K. (2004). Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior 23, (pp.115-133).
Weber, K. (2004). A framework for describing the processes that undergraduates use to construct proofs. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the International group for the Psychology of Mathematics Education. Bergen, Norway.
Weber, K. & Alcock, L. (2004). How do mathematicians validate proofs? In the Proceedings of the 25th Annual Meeting for the Psychology of Mathematics Education. Toronto, Canada.
Weber, K. & Alcock, L. (2004). Semantic and Syntactic Proof Productions. Educational Studies in Mathematics 56, (pp.209-234).
Weber, K. (2003). A procedural route toward understanding of the concept of proof. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Weber, K. (2002). Beyond proving and explaining: proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the learning of mathematics 22, 3, (pp.14-17).
Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics 48, (1), (pp.101-119).
Weigand, H. G. (2004). Sequences – Basic Elements for Discrete Mathematics. Zentralblatt für Didaktik der Mathematik, 36 (6), 91-97
Wheeler, D. (1990). Aspects of mathematical proof. Interchange 21, (1), (pp.1-5).
Williams, E. (1980). An investigation of senior high school students’ understanding of the nature of mathematical proof. Journal for Research in Mathematics Education 11, (pp.165-166).
Wong, K. (2001). Why and how to prove: the Pythagoras’ theorem in two classrooms. In M. Heuvel-Panhuizen (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Utrecht – The Netherlands.
Wu, H. (1996). The role of Euclidean geometry in high school. Journal of Mathematical Behavior 15, (pp.221-237).
Wu Yu, J. & Lin, F. & Lee, Y. (2003). Students’ understanding of proof by contradiction. In N. A. Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Yackel, E., & Hanna, G. (2003). Reasoning and proof. In Kilpatrick, J., Martin, W.G., & Schifter, D. (Eds.), A research companion to Principles and Standards for School Mathematics, (pp. 227-236). Reston, VA: National Council of Teachers of Mathematics.
Yackel, E