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PUBLICATIONS
A.)
Mathematics 1. Factoring of Second Order Difference Equations with Periodic Coefficients, Mich. Math. J., 10 (1963), 17-24. 2. Fixed Points in Non-normed Spaces, Ann. Acad. Sci. Fen., A.I., No. 331 (1963). 3. Differential Equations and Differential Calculus in Montel Spaces, Trans. Amer. Math. Soc., 1(110) (1964), 1-21. 4. Note on Regular Sequence Spaces, J. Math. Soc. Japan, 17(4) (1965), 409-410. 5. (with F. Birtel) Bounded Analytic Functions of Two Complex Variables, Math. Zeit., 93 (1966), 293-310. 6. (with J.R. Retherford) Schauder Bases in Compatible Topologies, Studia Math., 28, (1967), 221-225. 7. (with J.R. Retherford) Schauder Bases and Kothe Sequence Spaces, Bull. Acad. Pol. Sci., 14(9) (1967), 497-501. 8. Perfect Fréchet Spaces, Math. Anal., 174(3) (1967), 186-194. 9. (with G. Crofts) Nuclear Maps in Sequence Spaces, Duke Math. J., 36(1) (1967), 207-214. 10. (with J.R. Retherford) Schauder Bases and Kothe Sequence Spaces, Trans. Amer. Math. Soc., 130(2) (1968), 265-280. 11. (with T. Husain) Solutions of Homogeneous Elliptic Equations, Can. Math. Bull., 13(1) (1970), 99-104. 12. Equivalent Nuclear Systems, Proceedings Warsaw Symposium on Nuclear Spaces and Ideals of Operators, Stud. Math., 38 (1970), 373-379. 13. (with T. Husain) Space of Solutions of Homogeneous Elliptic Equations, Can. Bull. Math., 41(2) (1971), 17-24. 14. A New Definition of Nuclear System with Applications to Bases in Nuclear Spaces, Stud. Math., 41(2) (1971). 15. A Remark on a Paper of M.S. Ramanujan, Math. Ann., 190 (1971), 231-32. 16. (with M.S. Ramanujan) Inclusion Theorems for Absolutely l-Summing Maps, Math. Ann., 192 (1971), 177-180. 17. Every Separable Fréchet Space Contains a Non-Stable Dense Subspace, Stud. Math., 40(1) (1971). 18. Examples of Nuclear Systems, Stud. Math. 42(1) (1972), 29-42. 19. (with M.S. Ramanujan) On λ-Nuclearity, Memoirs of the Amer. Math. Soc., 128 (1972). 20. Projective and Inductive Limits of Banach Spaces, Stud. Math., 42 (1972). 21. (with M.S. Ramanujan) Λ(α)-Bases, J. Ind. Math. Soc., 36 (1972), 333?345. 22. Lectures on Partial Differential Equations WDN, Warszawa (1972). 23. (with A. Pelczynski and H. Rosenthal) On Banach Spaces X with the Property that B(L¥,X) = L (L ¥,X), Stud. Math. 44 (1972), 617-648. 24. (with W.B. Robinson) A Characterization of ω by Block Extensions, Stud. Math., 48(1a) (1973), 153-159. 25. Infinite Type Power Series Subspaces of Finite Type Power Series Spaces, Israel J. Math., 15(3) (1973), 257-281 26. Linear Pincherle Sequences, Pacific J. Math., 55(2) (1974), 361-369. 27. Concrete Subspaces of Nuclear Fréchet Spaces, Stud. Math., 52(3) (1974), 209-219. 28. Infinite Type Power Series Subspaces of Infinite Type Power Series Spaces, Israel J. Math., 20(3-4) (1975), 359-368. 29. (with L. Crone and W.B. Robinson) Regular Bases in Products of Power Series Spaces, J. Funct. Anal., 24(3) (1977), 211-222. 30. Basic Sequences in (s), Stud. Math., 59 (1977) 283-293. 31. Subspaces Without Bases in Nuclear Fréchet Spaces, J. Funct. Anal., 26(2) (1977), 121-130. 32. (with W. Robinson) Quotient Spaces of (s) with Basis, Stud. Math., 63(3) (1978), 39-53. 33. (with B. Mitiagin) Quotient Spaces without Bases in Nuclear Fréchet Spaces, Can. J. Math., 30(6) (1978), 1296-1305. 34. (with C. Bessaga) Nuclear Fréchet Spaces without Bases, III, Archiv Der Math, 31(6) (1978), 597-604. 35. The Structure of Nuclear Fréchet Spaces, Lecture Notes in Mathematics 720, Springer (1979). 36. Nuclear Fréchet Spaces without the Bounded Approximation Property, Studia Math. 3 (1981), 85-105. 37. Basic Sequences in a Stable Finite Type Power Series Space, Stud. Math., 63 (1980), 117-130. 38. Approximation Properties in Nuclear Fréchet Spaces. Proceedings of the Seminar on Functional Analysis, Holomorphy and Approximation Theory Rio De Janeiro (J.A. Barroso, ed.), North Holland (1982), 215-234. 39. (with S.F. Bellenot) Fréchet Spaces with Nuclear Köthe Quotients, Trans. AMS 273(2) (1982), 579-594. 40. Complemented Basic Sequences in Nuclear Fréchet Spaces with Finite Dimensional Decomposition, Archiv Der Mathematik 38(2) (1982), 138-150. 41. Non-Linear Analysis in Different Kinds of Fréchet Spaces. In Non-Linear Analysis and Applications (S.P. Singh and J.H. Burry, eds.), Dekker (1982), 91-116. 42. On (LB)-Spaces and Quotients of
Fréchet Spaces, In Functional Analysis, 43. (with L. Holmstrom) Nuclear Fréchet Spaces with Locally Round Finite Dimensional Decompositions, Monat. Für Math., 97 (1984), 257-275. 44. (with Dietmar Vogt) Fréchet
Spaces with Quotients Failing the Bounded 45. (with Dietmar Vogt) Bases in Complemented Subspaces of Power Series Spaces, Bull. Acad. Polon. Sci. 34(1-2) (1986), 65-67. 46. Approximation Properties of Nuclear
Fréchet Spaces in Advances in the Theory of Fréchet Spaces (T. Terzioglu,
ed.), Dordrecht: Kluwer (1991). 1. (with E. Doberkat and J.T. Schwartz) Reusability of Design for Complex Programs: An Experiment with the SETL Optimizer, Proceedings of the Workshop on Reusability in Programming, ITT (1983), 106-108. 2. Review Essay, Mathematical Structures for Computer Science, by Judith L. Gersting. Amer. Math. Monthly 91(6) (1984), 379-381. 3. (with E. Schonberg, S.
Freudenberger, and J.T. Schwartz) An Optimization Experiment with SETL, In Software Review
(T. Biggerstaff, ed.), Addison-Wesley, (1989), 275-293. C.) Mathematics Education - Refereed Papers 1. The Cognitive Effect of Computer Experiences on Learning Abstract Mathematical Concepts, Korkeakoulujen Atk-Uutiset 2 (1984), 41-47. 2. (with T. Ayers) Learning
Mathematics Concepts: Using Computers with 3. Computer Experiences as an Aid in Learning Mathematics Concepts, Working paper for the Conference on the Influence of Computers and Informatics on Mathematics and Its Teaching, Strasbourg, March 1985. 4. The Use of Computers in Mathematics Education, SIAM Newsletter, June 1985. 5. (with P. Lewin) Reflective Abstraction and Mathematics Education, Journal of Mathematical Behavior, 5(1) (1986), 55-92. Download as PDF file. 6. Reflective Abstraction and Computer Experiences, Proceedings of the Eighth Annual Meeting of PME-NA, September 1986. 7. On Teaching Mathematical Induction, I., Journal of Mathematical Behavior, 6(1) (1987), 305-317. Download as PDF file. 8. (with T. Ayers, G. Davis, and P. Lewin) Computer Experiences in the Teaching of Composition of Functions, Journal for Research in Mathematics Education, 19(3) (1988), 246-259. Download as PDF file. 9. Anatomy of a Question, Journal of Mathematical Behavior 6(3) (1988), 363-365. 10. (with F. Elterman and C. Gong) The Student's Construction of Quantification, For the Learning of Mathematics, (1989). Download as PDF file. 11. On Teaching Mathematical Induction, II, Journal of Mathematical Behavior, 8 (1989), 285-304. Download PDF file (866K, 27pages) 12. (with J. Hawks, D. Nichols) Development of the Process Conception of Function by Pre-Service Teachers in a Discrete Mathematics Course, Proceedings, Thirteenth Annual Meeting of PME, June 1989, Paris. 13. (with B. Cornu) Using a
Cognitive Theory to Design Educational software, 14. Programming in Calculus, Proceedings
Ohio State Technology Conference, 15. (with Keith Schwingendorf) Calculus, Concepts and Computers - Innovations in Learning Calculus, in T. Tucker (ed.), Priming the Calculus Pump: Innovations and Resources, MAA Notes #17, Reston: MAA, pp. 175-198, 1990. 16. Reflective Abstraction in Advanced
Mathematical Thinking, in Advanced 17. (with D. Tall) Advanced Mathematical Thinking and the Computer in Advanced Mathematical Thinking (D. Tall, ed.), Kluwer (1991), 231-250. 18. The Constructive Aspects of Reflective Abstraction in Advanced Mathematics, in (L.P. Steffe, Ed.) Epistemological Foundations of Mathematical Experiences, New York: Springer-Verlag, 1991. 19. (with Keith Schwingendorf) Constructing Calculus Concepts: Cooperation in a Computer Laboratory, in Carl Leinbach (ed.) The Laboratory Approach to Teaching Calculus, MAA Notes, 20 1991. 20. (with Keith Schwingendorf) Calculus, Concepts and Computers: Some Laboratory Projects, in Carl Leinbach (ed.) The Laboratory Approach to Teaching Calculus, MAA Notes, 20 1991. 21. Mathematics Computer Laboratories for Education and Research, in Carl Leinbach (ed.) The Laboratory Approach to Teaching Calculus, MAA Notes, 20 1991. 22. A Learning Theory Approach to Calculus, in (Z. Karian, ed.) Symbolic Computation in Undergraduate Mathematics Education, MAA Notes, 24, pp. 48-55, 1992. 23. (with Daniel Breidenbach, Julie Hawks, and Devilyna Nichols) Development of the Process Conception of Function, Educational Studies in Mathematics, 23 (1992), 247-285. Download as PDF file. 24. (with G. Harel) The Nature of the Process Conception of Function, in (G. Harel and E. Dubinsky, ed.) The Concept of Functions: Aspects of Epistomology and Pedagogy, MAA Notes, 25 (1992), 85-106. 25. A Theory and Practice of Learning
College Mathematics, in (A. Schoenfeld, ed.) Mathematical Thinking and
Problem Solving. Hillsdale: Erlbaum, pp. 221-243,
26. Reaction to James Kaput's paper, Democratizing Access to Calculus: New Route to Old Roots, in (A. Schoenfeld, ed.) Mathematical Thinking and Problem Solving. Hillsdale: Erlbaum, pp. 157-171, 1994. Download as PDF file (236K, 14 pages) 27. (with J. Dautermann, U. Leron, R. Zazkis) On Learning Fundamental Concepts of Group Theory, Educational Studies in Mathematics, 27, pp. 267-305, 1994. Download as PDF File (725K, 38 pages) 28. Pedagogical Change in Undergraduate Mathematics Education in Bettye Anne Case, Editor You're the Professor, What Next, MAA Notes, 35, 1994, pp. 114-119. Download as pdf file (127K, 8 pages) 29. (with I. Arnon and P. Nesher) Actions which can be Performed in the Learner’s Imagination: The case of Multiplication of a Fraction by an Integer. Proceedings of the Eighteenth /International Conference for the Psychology of Mathematics Education, PME XVIII, University of Lisbon, Lisbon, Portugal V. II, 1994, pp. 32-39 30. (with U. Leron) An Abstract Algebra Story, American Mathematical Monthly, 102, 3, March 1995, pp. 227-242. Download as pdf file (79K, 32 pages) 31. Is Calculus Obsolete? Mathematics Teacher, 88, 2, February 1995, pp. 146-148. Download PDF file (111K, 4 pages) 32. ISETL: A Programming Language for Learning Mathematics, Comm. in Pure and Appl. Math., 48, 1995, pp. 1-25. Download PDF file (269K, 23 pages) 33. (with J. Cottrill, D. Nichols, K. Schwingendorf, K. Thomas and D. Vidakovic) Understanding the Limit Concept: Beginning with a Coordinated Process Schema, Journal of Mathematical Behavior, 15, 2 (1996) pp. 167-192. Download as PDF File (553K, 25 pages) 34. (with R. Zazkis, J. Dautermann) Using Visual and Analytic Strategies: A study of students' understanding of permutation and symmetry groups, Journal for Research in Mathematics Education, 27, 4, 1996, pp. 435-457. Download as pdf file (107K, 39 pages) 35. (with R. Zazkis) Dihedral Groups: A Tale of Two Interpretations, Research in Collegiate Mathematics Education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education 6, 1996, pp. 61-82. Download as PDF file. 36. (with R. Noss) Some Kinds of Computers for Some Kinds of Math Learning, Mathematical Intelligencer, 18, 1, 1996, pp. 17-20. Download PDF file (21K, 7 pages) 37. (with M. Asiala, A. Brown, D. DeVries, D. Mathews, K. Thomas), A Framework for Research and Curriculum Development in Undergraduate Mathematics Education, 1996. Research in Collegiate Mathematics Education II, Issues in Mathematics Education (CBMS), American Mathematical Society. Download as PDF file 38. Una Aplicacíon De La Perspectiva Piagetiana A La Educacíon Matemática Post- Secundaria Educacíon Matemática, 3, 8, 1996. Download as PDF File (228K, 23 pages) 39. Some Thoughts on a First Linear Algebra Course, in (D. Carlson, C.R. Johnson, D.C. Lay, R.D. Porter, A. Watkins, and W. Watkins, Eds) Resources For Teaching Linear Algebra, MAA Notes, 42, (1997), pp. 85-106. Download as PDF File (249K, 24 pages) 40. (with J. Dautermann, U. Leron and K. Schwingendorf) A Reaction to Burn’s “What are the Fundamental Concepts of Group Theory?” Educational Studies in Mathematics, 34 (1997) pp. 249-253. Download PDF file (93K, 6 pages) 41. A Reaction to “A Critique of the Selection of ‘Mathematical Objects’ as a Central Metaphor for Advanced Mathematical Thinking” by Confrey and Costa. International Journal of Computers for Mathematical Learning, 2, 1997, pp. 67-91. Download as PDF file (269K, 25p) 42. On Learning Quantification, Journal of Computers in Mathematics and Science Teaching, Journal of Computers in Mathematics and Science Teaching 16(213) (1997) 335-362. Download PDF file (411K, 43 pages) 43. Research on Undergraduate Mathematics Education, MAA Online, 1997. 44. (with M. Asiala, J. Cottrill, K. Schwingendorf) The Development of Students" Graphical Understanding of The Derivative, Journal of Mathematical Behavior, 16, 3, 1997. Download as PDF File (794 K, 37 pages) 45. (with A. Brown, D. DeVries, Karen Thomas) Learning Binary Operations, Groups, and Subgroups, Journal of Mathematical Behavior 16, 4, 1977. Download PDF file (262K, 45 pages) 46. (with M. Asiala, D. Mathews, S. Morics and A. Oktac) Development of Students’ Understanding of Cosets, Normality and Quotient Groups, Journal of Mathematical Behavior 16,4, 1997 download as pdf file (543K, 144 pages) 47. (With D. Mathews) Calculus, Concepts, Computers and Cooperative Learning: A Research-Based Approach to Calculus Instruction, in (R. Cantoral, Ed) El Futuro Del Calculus, 1998, Readings in Cooperative Learning For Undergrad Mathematics. 48. Review Essay on Mathematical Reasoning by Lynn D. English, Notices, American Mathematical Society, April, 1999. Download PDF file (270K 8 pages) 49. (with B. Czarnocha, S. Loch, V. Prabhu, D. Vidakovic), Calculus Students Intuition of Area and the Definite Integral: Chopping Up or Sweeping Out, Collegiate Mathematics Journal. Download as PDF File (258K, 10 pages) 50. (with O. Yiparaki), On Student Understanding of AE and EA Quantification. Download as PDF file (1206K, 67 pages) 51. A theory-based approach to help students learn post-secondary mathematics: The case of limits. Research reports in mathematics education, 1,2000, Umea University, pp. 1-18. Download as PDF file (1153K, 18 pages) 52. (with M. McDonald), APOS: A Constructivist Theory of Learning in Undergrad Mathematics Education Research, 2001. In D. Holton et. (Eds.), The teaching and Learning of Mathematics at University Level: An ICMI Study, Kluwer Academic Publishers, 273-280. Download as PDF file (73K, 22 pages) 53. What is mathematics really?, Review essay, Notices of the American Mathematical Society, 46, 9, October, 1999, 1062-1066. Download as PDF file (273K, 5 pages) 54. A better way of learning requires major changes in the teaching environment, Proceedings of RECAM Conference, in press. Download as PDF file (426K 13 pages) 55. Meaning and formalism in mathematics, International Journal for Computers in Mathematics Education. Download as PDF file (293K, 35 pages) 56. De la investigacion en las matematicas teoricas a la investigacion en las matematicas educativas: un viaje personal, RELME Journal. 57. Using a theory of learning in college mathematics courses, Teaching and Learning Undergraduate Mathematics Newsletter. 58. Moving our Focus from Teachers to Students, FOCUS. Download as PDF file (11K, 2 pages) 59. Mathematical Literacy and Abstraction in the 21st Century. In Maggie Niess, ed., Vision for Science and Mathematics Education in the 21st Century. School Science and Mathematics. October, 2000. Download as PDF file (202K, 22 pages) 60. (with Ilana Arnon) Research, Theory, Technology and Other Dangerous Pedagogical Considerations, in preparation. Download as PDF File. (223 K, 25 pages) 61. Assessment in one Learning Theory Based Approach to Teaching. Download as PDF File (133K, 7 pages) 62. (with Olga Yiparaki) Predicate Calculus and the Mathematical Thinking of Students. Download as PDF File (218K, 19 pages) 63. (with Despina Stylianou) Determining Linearity: The Interplay between Visualization and Analyses. Download as PDF File (8 pages) 64. UME Trends: Observing a Decade of Change and Preparing for the Future. Download as PDF File (96K, 7 pages) 65. Computers in Teaching and Learning Discrete Mathematics and Abstract Algebra. Download as PDF File (146K, 8 pages) 66. Undergraduate Mathematics Needs Your Critical Concern. Download as PDF File (90 K, 5 pages) 67. Writing Programs to Learn Mathematics. Unpublished report. Download as PDF File (109K, 8 pages) 68. (with Anthony Ralston) Undergraduate Mathematics - Now and Then. Unpublished report. Download as PDF File (249K, 27 pages) 69. (with Weller, Clark, Loch, McDonald and Merkovsky) An examination of Student Performance Data in Recent RUMEC Studies. In Review. Download as PDF File (1278K, 33 pages) 70. A Radical Constructivist does CL. Unpublished report. Download as PDF File (7K, 2 pages) 71. (with Asiala) Evaluation of Research - Based on Innovative Pedagogy in Several Math Courses. Unpublished report. Download as PDF File (168K, 16 pages) 72. (with K. Weller, A. Brown, M. McDonald, C. Stenger), August 2004. Intimations of Infinity, Notices of the AMS, pp. 741-750 Download as PDF File 73. (with K. Weller, A. Brown, M. McDonald), To appear. Some Historical Issues and paradoxes regarding the Infinity Concept: An APOS analysis, Part 1. Educational Studies in Mathematics. Download as PDF File 74. (with K. Weller, A. Brown, M. McDonald), To appear. Some Historical Issues and paradoxes regarding the Infinity Concept: An APOS analysis, Part 2. Educational Studies in Mathematics. Download as PDF File
1. Influence of Piaget and Related Work on K-12 Curriculum Development. Position Paper for CBME Task Force on a Framework for K-12 Curriculum Development. 2. Using Computer Experiences to Implement a Piagetian Theory of Learning Mathematics Concepts, "Influence des Moyens de Calcul et de l'Informatique sur l'Enseignement des Mathematiques," La Nouvelle Encyclopêdie, DIDEROT, Paris: PUF, 1992 237-270. 3. La Reforme Du Calculus Aux USA, Gazette Des Mathematiciens, 58, 1993, pp. 6-10. 4. Showing, Using and Making Mathematics: A CAS Can Only Go So Far, Computer Algebra Systems Newsletter, 1993. 5. After Examples and Before Proofs, Constructing Mental Objects, in press. Download as PDF File (58K, 2 pages) 6. Reflections on Krantz’ How to
Teach Mathematics: A Different View. In S.G. Krantz, How to Teach
Mathematics, American Mathematical Society: Providence, 1998, pp. 197-213.
Download as PDF
File (230K, 27 pages) E.) Mathematics Education-Edited Collections 1. (with Rosemary Fraser) Computers and The Teaching of Mathematics: A Worldview.The Shell Centre, University of Nottingham, Nottingham, England, 1990 2. (with Gershon Harel) The Concept of Functions: Aspects of Epistemology and Pedagogy, MAA Notes, 25 (1992). 3. (with James Kaput) Research
Issues in Undergraduate Mathematics Learning, 1. (with R.B.K. Dewar, E. Schonberg, and J.T. Schwartz) Programming with Sets: An Introduction to SETL, Springer 1986. 2. (with N. Baxter and G. Levin) Learning Discrete Mathematics with ISETL, Springer Verlag, (1988). 3. (with U. Leron) Learning Abstract Algebra with ISETL, Springer Verlag, 1994. 4. (with N. Hagelgans, B. Reynolds, K. Schwingendorf, D. Vidakovic, M. Shahin, and J. Wimbish) A Practical Guide to Cooperative Learning in Collegiate Mathematics, MAA Notes 37, MAA:Washington, DC 1995 5. (with K. Schwingendorf and D. Mathews) Applied Calculus, Concepts & Computers, Revised Preliminary Edition, McGraw-Hill, 1996. 6. (with K. Schwingendorf and D. Mathews) Calculus, Concepts & Computers, Second Edition, McGraw-Hill, 1995. 7. (with K. Schwingendorf) Calculus, Concepts & Computers, Preliminary Version, Port II. West, 1992 8. (with W. E. Fenton) Introduction to Discrete Mathematics with ISETL, Springer, 1996 9. (with D. Mathews & B. Reynolds)
Readings In Cooperative Learning For Undergraduate Mathematics, MAA Notes
#44 (1997). G.) INVITED LECTURES AND CONFERENCE PRESENTATIONS SINCE FALL 1984 1. Using Computer Experiences in Learning Mathematics Concepts, Grinnell College, October 1984. 2. Cognitive Effects of Computer Experiences on Learning Mathematics Concepts, SUNY Plattsburg, November 1984. 3. Computer Experiences as an Aid in Learning Mathematics Concepts, University of Toronto, March 1985. 4. Computer Experiences as an Aid to Learning Mathematics, Turin University (Italy), April 1985. 5. A research program in epistemology and pedagogy, SESAME seminar, University of California, Berkeley, September 1985. 6. A new approach to teaching abstract concepts in Mathematics, University of North Carolina at Greensboro, October 1985. 7. A new approach to teaching abstract concepts in Mathematics, San Francisco State University, April 1986. 8. Using SETL to implement a Piagetian
theory of learning abstract mathematics, 9. Using SETL to implement a Piagetian theory of learning abstract mathematics concepts, Colloquium, Computer Science Department, Courant Institute of Mathematical Sciences, October 1986. 10. Use of computer experiences in teaching abstract mathematics, Institut Fourier de Grenoble, November 1986. 11. Use of computer experiences in teaching abstract mathematics, University of Leuven, Belgium, December 1986. 12. A theory of learning advanced mathematical topics and using computer experiences to implement this theory, University of London, September 1987. 13. A learning experience, all day workshop at Bloomsburg University, November 1987. 14. Some preliminary thoughts and observations on the student's construction of the concept of function, University of Paris, December 1987. 15. On helping students construct the concept of quantification, University of Grenoble, December 1987. 16. Teaching and learning predicate calculus, IUPUI, February 1988. 17. Research in mathematics education at the college level, Colloquium, Michigan State University, March 1988. 18. On learning undergraduate mathematics, Colloquium, Wabash College, April 1988. 19. Cognitive effects of computer experiences in learning mathematics, Colloquium, Kent State University, May 1988. 20. Using ISETL to learn mathematical conepts, Purdue Math Club, November, 1988. 21. A computer based discrete mathematics course for pre-service teachers, Weizmann Institute, Israel, December 1988. 22. Development of pre-service teachers concept of function in a computer based discrete mathematics course, Hebrew University of Jerusalem, December 1988. 23. A learning theory approach to using computers in Calculus, The Technion, Israel, December 1988. 24. A Piagetian Theory of learning mathematics concepts, Ben-Gurion University, Israel, January 1989. 25. Computers in High School Mathematics, Neiman Institute Workshop, Haifa, May 1989. 26. Educational Software for Calculus, Neiman Institute, Haifa, May 1989. 27. Computers in Calculus: Uses and Issues, IUPU, Ft. Wayne, September 1989. 28. Calculus, Computers and Concepts,
North Carolina Council of Teachers of 29. A Learning Theory Approach to Calculus, St. Olaf University, October 1989. 30. Programming in Mathematics Courses, Ohio State University, November 1989. 31. Theory and Practice of Learning College Mathematics, Berkeley, December 1989. 32. The Concept of Function for College Students, Tel Aviv, Israel, December l989. 33. The Concept of Function for College Students, Haifa, Israel, January 1990. 34. Research in Undergraduate Mathematics Education: What Can It Tell the College Teacher, Mississippi State University, February 1990. 35. Research in Undergraduate Mathematics Education: What Can It Tell the College Teacher, Wright State University, April 1990. 36. Research in Undergraduate Mathematics Education: What Can It Tell the College Teacher, Illinois Section of MAA, April 1990. 37. Workshop on Using Computers in
Calculus, New York State Mathematics 38. Programming to Learn Calculus, IBM Academic Computing Conference, June 1990. 39. Teaching Techniques for the Sciences, FASíUP, October 1990. 40. Testing, Ohio State Technology Conference - Firing Line, November 1990. 41. Research in Undergraduate Mathematics Education: What Can It Tell the College Teacher, North Carolina Council of Teachers of Mathematics, November 1990. 42. Calculus, Computers, Concepts and Cooperative Learning, Illinois State University, December 1990. 43. An Instructional Treatment for Functions That Seems to Work, AMS/MAA Special Session on Research in Undergraduate Mathematics Education, San Francisco, January 1991. 44. A Theory of Learning Advanced Mathematical Concepts, Concordia University, March 21, 1991. 45. A Novel Approach to Helping Students
Learn Abstract Algebra, Concordia 46. What Mathematical Education Research Has to Offer the College Mathematics Professor, September, 1991. 47. What it Means to be a Constructivist in Mathematics Education, Purdue Education Colloquium, October, 1991. 48. A Contribution Towards the Revitalization of Undergraduate Mathematics Education, Miami University Colloquium, February 1992. 49. A Different Approach to Helping
Students Learn Calculus, Calvin College 50 Calculus, Concepts, Computers and Cooperative Learning, Invited Talk at Grand Valley State Conference, March 1992. 51. Thoughts on Assessing Curriculum Reform Projects, Invited Talk at Grand Valley State Conference, March 1992. 52. Setting Up and Using a Mathematics Education Computer Lab, University of Alabama-Birmingham Colloquium, May 1992. 53. Some Remarks on Assessment, Invited Presentation to MAA Board of Governors, August 1992. 54. Theory in Advanced and Elementary Mathematical Thinking, Tel Aviv Seminar, January, 1993. 55. A Constructivist Approach to Undergraduate Mathematics Education, University of Connecticut Colloquium, April 1, 1993. 56. Assessment and Research in Undergraduate Mathematics Curriculum Reform, Invited Address at Texas Section of MAA, Abilene Texas, April 3, 1993. 57. Calculus, Concepts, Computers and Cooperative Learning: Some Results of the C4L Calculus Reform Project, University of Texas Permian Basin Colloquium, April 4, 1993. 58. Calculus, Concepts, Computers and Cooperative Learning: Some Results of the C4L Calculus Reform Project, University of Central Florida Colloquium, April 15, 1993. 59. What is Research in Mathematics
Education and Who Should Publish it? 60. Assessment and Research in Undergraduate Mathematics Curriculum Reform, Dekalb Conference Keynote Address, May 14, 1993. 61. Making Assessment Compatible with New Methods of Teaching, K-6 Workshop, University of Kansas, July 14, 1993. 62. Report on a Project to Improve Student Learning in Abstract Algebra, University of Kansas Colloquium, July 14, 1993. 63. Some Thoughts and Experiences Regarding Cooperative Learning in Undergraduate Mathematics, Columbia Teacher’s College, October 25, 1993. 64. Research in How Students Learn Abstract Algebra with Applications to the Use of Computers in Education, Boston University Colloquium, November 2, 1993. 65. A Theoretical Approach to Helping Post Secondary Students Learn Mathematics, TERC, March 1, 1994. 66. Report on a Project to Improve Student Learning in Abstract Algebra, Central Michigan Colloquium, March 3, 1994. 67. Why Can't College Students Think Mathematically? (And What Can Be Done About It?) Simpkins-Lee Lecture, Longwood College, April 6, 1994. 68. Using Computers to Help Students Learn College Mathematics, Baruch College SUNY Colloquium, April 21, 1994. 69. Lecture Series on Research and
Development in Undergraduate Mathematics 70. Writing Programs in a Mathematical Programming Language, Greater Kansas City Math Tech Expo, Keynote Address, October 7, 1994. 71. One Approach to Undergraduate Mathematics Education Reform, University of Cincinnati Colloquium, November 10, 1994. 72. Students' Analytic and Visual
Strategies in Thinking About Dihedral Groups, 73. The First Decade of Calculus Reform, University of Mississippi Colloquium, January 23, 1995. 74. C4L Workshop, Brevard Community College, February 25-27, 1995. 75 Learning and Teaching College Mathematics, Harvard Seminar, March 13, 1995. 76. The C4L Calculus Research Project, Inter-American University, Puerto Rico, Aracibo Campus, March 25, 1995. 77. A Theoretical Approach to Helping Students Learn Mathematics, University of Puerto Rico, Humacao, March 27, 1995. 78. An Approach to Helping Students Learn Abstract Algebra, Beer Sheva, Israel, May 16, 1995. 79. Using Computers to Help Students Learn Mathematics, Tel Aviv, Israel, May 17, 1995. 80. Coordinating Visual and Analytic Strategies, Technion, Haifa, Israel, May 23, 1995. 81. Epistomological Investigations of Concepts in Undergraduate Mathematics, Amer. Math. Soc./Israel Math. Union, Joint Meeting, May 24, 1995. 82. C4L Workshop, Goucher College, June 30-July 2, 1995. 83. Fragments of a Comprehensive Approach to Pedagogy in College Mathematics, NexT Presentation, Burlington, August 5, 1995. 84. A variety of ways of using Computers to help Undergraduates Learn Mathematics. Florida International University, February 2, 1996. 85. Thoughts and Experiences of Constructivism and Cooperative Learning, Emery & Henry University, February 22, 1996. 86. Cooperative Learning in Undergraduate Mathematics Education, US Military Academy at West Point, March 5, 1996. 87. Cooperative Learning Workshop, MAA Oklahoma/Arkansas Section, March 22, 1996. 88. Different Ways of Using Computers to Help Students Learn Collegiate Mathematics, Georgia State University, April 4, 1996. 89. An Approach to Helping Students Learn Abstract Algebra, W. Virginia University, April 11, 1996. 90. A Curriculum for Undergraduates based on Research into Learning and Using Computers to Help Students Learn, Enrique Jose Varona University, Havana, May 21, 1996. 91. Some General and Specific thoughts about Calculus Reform, University of Georgia Colloquium, February 28, 1997. 92. Putting Constructivism to Work-Spanning the Gap between Theory and Practice, University of No. Colorado Colloquium, April 15, 1997. 93. An Approach to Helping Students Learn Abstract Algebra, Kennesaw State Talk, April 23, 1997. 94. Constructivism, EDCI Seminar, Georgia State University, April 14, 1997. 95. Research In Undergraduate Mathematics
Education, Dartmouth College 96. Workshop In Teaching Abstract
Algebra, University of Cincinnatti, 97. Putting Constructivism to Work-Spanning The Gap Between Theory and Practice, PUC-RIO Colloquium, Rio De Janeiro, August 12, 1997. 98. Different Ways of Using Computers to Help Students Learn Collegiate Mathematics, Santa Ursula Colloquium, Rio De Janeiro, August 18, 1997. 99. On Students’ Understanding of
Existential and Universal Quantification, 100. Different Ways of Using Computers to Help Students Learn Collegiate Mathematics, Georgia College Colloquium, October 30, 1997. 101. Reforming the Upper Level Undergraduate Mathematics Courses, University of North Florida Colloquium, February 13, 1998. 102. How do people learn mathematics and what’s that got to do with how we teach? Ohio State Colloquium, May 1, 1998. 103 Putting Constructivism to Work-Spanning the Gap between Theory and Practice, RPI Colloquium, October 5, 1998. 104. How do people learn mathematics and what’s that got to do with how we teach? Helsinki University of Technology Colloquium, July 27, 1998. 105. Cooperative Learning, Savannah St., April 15, 1999. 106. Meaning and Formalism in Mathematics, Northeast Section, June 12, 1999. 107. Meaning and Formalism in Mathematics, Arizona State University, Colloquium, Feb. 17, 2000.
108. Un acercamiento pedagogico basada en
una teoria de aprendizaje y usando la computadora y la educacion
cooperativa, Universidad de Cadiz, Colloquium, March 23, 2000.
109. Un ejemplo de un sistema total para trabajar en las matematicas educativas al nivel post secundario: Acercamiento y Resultados, Seminario Monterey, Mexico, December 17, 1999. 110. Meaning and formalism in mathematics, ASU, February 17, 2000. 111. Un acercamiento pedagogico basada en una teoria de aprendizaje y usando la computadora y la educacion cooperativo, Universidad de Castilla-La Mancha, Conferencia, March 25, 2000. 112. Constructivism in Teaching Mathematics and Computer Science, Beirut, August 12-17, 2000. 113. The life and work of Jean Piaget, ASU seminar, February 26, 2001. 114. Applications of undergraduate mathematics education research to teaching practice, ASU University Colloquium, February 26, 2001. 115. The development of logical thinking according to Piaget, ASU, March 1, 2001. 116. Seminario Un Curso de algebra lincal, basada en el Marco Teorico y el ciclo ACE, Seminario de Jueves, March 29, 2001. 117. Meaning and formalism in mathematics, Mayaguez, April 19, 2001. 118. Un acercamiento pedagogico bajado en un marco teprico, Pachuca Conferencias, April 27-28, 2001. 119. Un acercamiento pedagogico general basado en un marco teorico ejemplo de la cuantificacion, Oaxoca Conferencia, May 25, 2001. 120.De donde surgen las idea matematicas? Temuco Conferencia, July 16, 2001 121. Ensenanza y aprendizaje del algebra en educacion superior, Santiago de Chile, July 18-20, 2001. 122. Significado y formalismo en las matematicas, Montevideo Conferencia, August 1, 2001. 123. Cooperative learning and the use of computers Good news and bad news about two pedogogical strategies, Taiwan Colloquium, September 25, 2001. 124. Use of theory in mathematics education research, Taiwan Workshop I, September 25, 2001. 125. Development in undergraduate mathematics education, Taiwan Keynote, September 28, 2001. 126. Alternative pedagogies for college mathematics: potential and challenge, University of Cincinnatii Colloquium, November 15, 2001. 127. Un acercamiento a las investigan ciones en el aprendizaje y el desarrollo curricular para las matematicas al nivel post secundario, Bogota Inaugural, July 10, 2002. 128. Aplicacion de la teoria APOE y el ciclo de ensenanza ACE a un Curso en la algebra lineal, Bogota Taller, July 10-12, 2002. 129. Los numeros, las funciones y el infinito: una jerarquia de las encapsulaciones, Bogota Conferencia, July 12, 2002. 130. A theory-based approach to tertiary mathematics education, Bandung Talk Indonesia, September 18, 2002. 131. Undergraduate mathematics education research needs the critical concern of mathematicians, Bandung Talk Indonesia, September 19, 2002. 132. Undergraduate mathematics, Now and then, Bandung Talk Indonesia, September 20, 2002. 133. An approach to helping tertiary students learn abstract algebra, Bandung Talk Indonesia, September 19, 20, 25, 2002. 134. Teach and learning linear algebra, Bandung Talk Indonesia, September 23, 2002. 135. Teaching and learning discrete mathematics, Bandung Talk Indonesia, September 24, 2002. 136. A general approach to research and curriculum development in tertiary mathematics education, Bandung Talk Indonesia, September 24, 2002. 137. A better way of learning
requires major changes in the teaching environment, Bandung Talk Indonesia,
September 24, 2002. 139. Exams in abstract algebra, proof course, Bandung Talk Indonesia, September 25, 2002. 140. Cooperative learning in undergraduate mathematics eduction, Bandung Talk Indonesia, September 26, 2002. 141. Mathematical objects as central metaphor, Bandung Talk Indonesia, September 26, 2002. 142. Mental constructions of mathematical processes and objects: meaning and formalism, Bandung Talk Indonesia, September 27, 2002. 143. A decade and more of development of RUME the US, Bandung Talk Indonesia, September 30, 2002. 144. A theory based approach to tertiary mathematics education, Yogya Talk Indonesia, October 3, 2002. 145. Teaching and learning abstract algebra, Yogya Talk Indonesia, October 5, 2002. 146. Teaching and learning discrete mathematics, Yogya Talk Indonesia, October 7, 2002. 147. Teaching and learning linear algebra, Yogya Talk Indonesia, October 7, 2002.
H.) CONFERENCE PRESENTATIONS (REFEREED OR INVITED)
1. Using computer experiences to stimulate cognitive development, Conference on use of Computers in Education, Montreal, November 1985. 2. Computer Science as a Service Deprtment, SIGCSE Panel, Cincinnatti, February 3. Reflective abstraction in the student's construction of mathematical induction, Conference of the Jean Piaget Society, Philadelpia, May 1986. 4. Reflective abstraction and computer experiences: a new approach to teaching theoretical mathematics, Annual meeting of the International Group for the Psychology of Mathematics Education, East Lansing, September 1986. 5. Constructive aspects of reflective
abstraction in advanced mathematics, Conference on Epistemological
Foundations of Mathematical Experience, Athens, Georgia, February
1988. 7. An epistemological approach to using computers in mathematics education, ICME6, August 1988. 8. Approximation properties of nuclear Fréchet spaces, "Advances in the Theory of Fréchet Spaces," Nato Advanced Research Workshop, Istanbul, Turkey, August 1988. 9. Some Remarks on Undergraduate Mathematics Education, Israel Mathematics Union, May 1989. 10. Overcoming Some Student Difficulties in Learning Undergraduate Mathematics, Fourth Annual International Conference on Technology in Collegiate Mathematics, Portland Oregon, November 15, 1991. 11. Calculus, Concept and Cooperative Learning: The Purdue Project, Fourth Annual International Conference on Technology in Collegiate Mathematics, Portland Oregon, November 15, 1991. 12. Calculus, Concepts, Computers and Cooperative Learning, Invited Talk at RPI Conference, May 1992. 13. Using Computer Programming to Help Students Construct Abstract Mathematical Concepts in Calculus, Invited Talk at ICME7 Pre-Conference Symposium, August 1992. 14. What Do They Want From Us ? Preliminary Report on the Mathematical Needs of Client Departments, Invited Talk at ICME7, August 1992. 15. Understanding Abstract Mathematical Concepts: Epistemology, Computer Programming, and Cooperative Learning, Invited Talk at Central Regional Conference of NCTM, September 1992. 16. Calculus, Concepts, Computers and Cooperative Learning, Conference on Teaching Calculus to Underprepared Students, Howard University Conference, Washington, D.C., October 1992. 17. Applying Piaget's Theories in
College Level Math Courses, Association for 18. A Constructivist Approach to Undergraduate Mathematics Education, International Conference on Technology in College Mathematics, Chicago, November, 1992. 19 . Assessment of Groups and Individuals When Instruction is Based on Research on how People Learn, MAA Meeting, San Antonio, January 1993. 20. On Process Conceptions of Limits, MAA Meeting, San Antonio, January 1993. 21. Teaching Abstract Algebra with ISETL, Conference of South Dakota SSI, February, 1993. 22. A Research Based Abstract Algebra Course, NCTM Research Pre-Session, Seattle, March 30, 1993. 23. Pedagogy: What Works with Different Students, The Second Conference on the Teaching of Calculus, Harvard, June 25-26, 1993. 24. Understanding the Limit Concept: Beginning with a Process Conception, MER Workshop on Calculus Reform, July 31, 1993. 25. Some Results of an Approach to Helping Students Understand Quotients, MAA Meeting, Vancouver, August 1993. 26. Teaching and Assessment of Learning, Seventh Annual Leadership Conference of the New Hampshire Section of ATMNE, October 15, 1993. 27. Using Technology to Help Students See, Use, or Make Mathematics PME-NA Conference, October 19, 1993. 28. Research, Computers and Cooperative Learning - A New Pedagogy for Undergraduate Mathematics, ICTCM6, November 6, 1993. 29. Visual and Analytic Approaches to Problems in Undergraduate Abstract Algebra, MAA Meeting, Cincinnati, January 14, 1994. 30. An Innovative Approach to Helping Students Learn Abstract Algebra, MAA Meeting, Cincinnati, January 15, 1994. 31. Report on a Project to Improve Student Learning in Abstract Algebra, Rocky Mountain Calculus Conference, Ft. Collins, CO, April 5, 1994. 32. Learning Theory and Programming as Components of Curriculum Reform in Discrete Mathematics and Abstract Algebra, Greater Kansas City Math Tech Expo, October 7, 1994. 33. Connections Among Learning Pedagogy and Assessment, MAA Ohio Section, Findlay, Ohio, October 29, 1994. 34. Designing and Using Questions in Undergraduate Math Ed Research, ICTCM VII Research Pre-Session, Keynote Address, Orlando, Florida, November 17, 1994. 35 Learning Abstract Algebra, ICTCM VII, Orlando, Florida, November 18, 1994. 36. Student Understanding of Isomorphism Between 2Z/6Z and Z3, MAA Meeting, San Francisco, January 7, 1995. 37. Cooperative Learning in Undergraduate Mathematics Education, Invited Speaker, Michigan Section, MAA, May 8, 1995. 38. A Report on Recent Theoretical and Empirical Studies of Student Understanding of Concepts in Collegiate Mathematics, Plenary Talk, 9th Annual Central American/Latin American Conference on Preparation of Teachers and Research in Mathematics Education, Havana, Cuba, August 15, 1995. 39. Using Theoretical and Empirical Research into Learning as a Basis For the Design and Implementation of Instruction in College Level Mathematics Courses, Oberwolfach Meeting on New Trends in the Teaching and Learning of Mathematics, November 26-December 2, 1995. 40. (with M. Asiala, A. Brown, D. DeVries, D. Mathews and K. Thomas) A Framework for Research and Curriculum Development in Undergraduate Mathematics Education, Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1996, pp. 1-32. Download as PDF File (470K, 34 pages) 41. An Approach to Undergraduate Mathematics Curriculum Development, Project Kaleiodscope Workshop, University of Iowa, July 20, 1996. 42. El Constructivismo De Piaget y Aprendizaje De Los Conceptos Abstractos de la Matematica Avanzada, Tenth Latin American and Carribean Conference on Preparation of Teachers and Research in Mathematics Education, Puerto Rico, August 8, 1996. 43. A General Pedagogical Approach to Predicate Calculus and Induction, NExT Meeting, Seattle, August 12, 1996. 44. A Theoretical Framework for Research in Undergraduate Mathematics Education, RUMEC Conference, Mt. Pleasant, Michigan, September 6, 1996. 45. An Education Research Community in Mathematics and a Framework for its Operation, AMS S.E. Section Meeting, Chattanooga, October 12, 1996. 46. Applying A Piagetian Perspective to Post-Secondary Mathematics Education, Second International Workshop on Mathematics Education for Engineers, Havana, November 25-29, 1996. 47. Assessment in One Learning Theory Based Approach to Teaching, MAA Meeting, San Diego, January 1997. 48. Cooperative Learning, MAA Meeting, San Diego, January 1997. 49. Students’ Understanding of Quantifiers in Natural Language and In Mathematics, MAA S.E. Section Meeting, Atlanta, March 13, 1997. 50. El Entendimiento De Los Estudiantes De Las Oraciones Existenciales Y Universales En El Discorso Natural Y Matemático, Latin American Conference on Mathematics Education, July 17, 1997. 51. C4L: Calculus, Concepts, Computers and Cooperative Learning, NeXT Meeting, Atlanta, July 30, 1997. 52. Putting Conservatism to Work-Spanning The Gap Between Theory and Practice, RUMEC Conference, Mt. Pleasant, Michigan, September 4, 1997. 53. Poniendo El Constructivismo A Trabajar: Llenando El Boquete Entre La Teoria Y La Practica, Mexican Mathematical Society Meeting, October 2, 1997. 54. On Students’ Understanding of Cosets, Normality and Quotient Groups, International Conference on Technology in College Mathematics, Chicago, November 7, 1997. 55. Learning and Teaching Collegiate Mathematics: An MAA Activity of Increasing Importance, MAA Southeast Section, Georgia Luncheon Address, February 7, 1998. 56. Putting Constructivism to Work-Spanning the Gap between Theory and Practice, MAA Kentucky Section Invited Address, March 28, 1998. 57. Learning and Teaching Collegiate Mathematics: An MAA Activity of Increasing Importance, MAA Missouri Section, April 18, 1998. 58. Pedagogy Based on how Learning can happen, NSF Workshop, Atlanta G, May 8, 1998. 59. Un estudio prorrogado del entendimiento del calculo predicado por los estudiantes postsecundarios, Decima segunda reunion latinoamericana de matematica educativa, Santa Fe de Bogota, Columbia, July 6-10, 1998. 60. A Theory-Based Approach to Help Students Learn Post-Secondary Mathematics: The Case of Limits, Conference on Problem driven research in mathematics education, Umea, Sweden, August 7 1998 61. Meaning and Formalism in Mathematics, Conference on Problem driven research in mathematics education, Umea, Sweden, August 8 1998 62. Meaning and Formalism in Mathematics, Seaway Section Invited Address, Rochester, NY, November, 1998. 63. Writing programs to learn mathematics, International Commission on Mathematics Instruction, Study Conference, Singapore, December 1998. 64. Una decada de investigacion en algunos temas de matematicas avanzados, Series of Lectures, CLAME Conference, Monterey, Mexico, December 18, 1998. 65. Significado y formalismo en mathematics, Plenary Talk, Seminario Nacional de Investigacion de las Matematicas, CLAME Conference, Monterey, Mexico, December 18, 1998. 66. Meaning and Formalism in Mathematics, Association for the Advancement of Computers in Education, March, 1999. 67. Meaning and Formalism in Mathematics, MAA Seaway Section, April 23, 1999 68. Kent State Conference Keynote. Cooperative Learning, A better way of learning requires major changes in the Teaching Environment, Kent State Stark, May 9, 1999. 69. Kent Conference Talk, Meaning and Formalism in Mathematics, Kent State Stark, May 20, 1999. 70. Formalismo y Significado en las Matematicas, RELME 13, Santo Domingo, July 14, 1999. 71. One theoretical perspective in undergraduate mathematics education research, PME, Israel, July 26, 1999. 72. One theoretical perspective in undergraduate mathematics education research, ARUME Research Conference, Chicago, IL, Sptember 16, 1999. 73. Research in undergraduate mathematics education, Wisconsin NeXT Workshop, October 7-10, 1999. 74. Reaction to the papers of Ojeda and Moreno, PME-NA Conference, Cuenevaca, Mexico, October 25, 1999. 75. Calculus students intuition of definite integral and historical development of the concept, PME/NA Annual Meeting, November 2, 1999. 76. Effects on students’ learning topics in collegiate mathematics of pedagogy based on APOS theory, cooperative learning, writing computer programs, and in-class problem solving, MER talk, Washington, DC, January 19, 2000. 77. Educativa Matematica en EEUU, Mesa Redonda, Universidad de Castilla-La Mancha, Conferencia, March 25, 2000. 78. Cooperative learning in undergraduae mathematics education, AMS Central Section, Special Session on Education, April 8, 2000. 79. Usos diferentes de la computadora en las matematicas educativas al nivel post-secundarion, Mesa Redonda, RELME 14, Panama City, Panama, July 17, 2000. 80. Un marca teorico para la investigacion en el aprendizaje de las matematicas avanzadas: aplicaciones y resultados, RELME 14, Panama City, Panama, July 17, 2000. 81. ARUME Talk, How can mathematical concepts be learned? Synthesizing APOS theory and mathematical formalism to get one possible answer, ARUME Plenary, San Diego, CA, January 8, 2001. 82. Winter Meeting, RUME, Field of study or figment of our imagination? CRUME Panel, January 12, 2001 83. Aprendizaje de la algebra abstracta y la algebra lineal: acercamiento unificado basado en la teoria APDE, RELME Curso Corto, July 24, 26 2001. 84. Un acercamiento a la investigacion y desarrollo curricular; ejemplo de la algebra lineal, RELME Buenos Arires, Brasil, July 27, 2001. 85. La didactica de la matematica como disciplina de estudio, Montevideo Mesa Ronda, July 31, 2001. 86. Meaning and formalism in mathematics with implications for education, Taiwan Workshop II, September 26, 2001. 87. Meaning and Formalism in Mathematics. Research reports in mathematics education, 1,2000, Umea University, pp. 19-40. Download as PDF file (943K, 22 pages) 88. Teaching and learning abstract algebra and linear algebra: a unified approach, ICIMI Algebra Study Melbourne, December 13, 2001. 89. Aprendiendo algebra lineal con ISETL, Curso Especial, Oaxaco, December 16-20, 2001. 90. Numbers, functions and infinity: A hierarchy of encapsulations, Stark Conference Keynote, May 15, 2002. 91. Logical thinking- in studying mathemtics and in ordinary discourse, Reasoning Conference Richmond, May 21, 2002. 92. Aprendizaje cooperativa, RELME 16, Mesa Redonda, July 18, 2002. 93. Los numeroz, las funciones y el infinito: una jerarquia de las encapsulaciones, RELME 16, conferencio Especial, July 19, 2002. 94. Concerns with "Where mathematics comes from", ARUME Panel Burlington, July 30, 2002.
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