Keynote and Plenary Addresses

1. Pedagogical principle in teaching mathematics, with particular reference to the teaching of linear algebra; The International Conference of the International Linear Algebra Society (ILAS); Athens, Georgia; August 1995.
2. A fundamental principle of learning and its application in modifying students’ conception of proof; The Annual Joint Meeting of the MAA-MAS; San Diego, California; January 1997.  
3. A developmental model of students’ conception of mathematics: cognitive, epistemological, and historical considerations; The International Conference of the International Linear Algebra Society (ILAS); University of Wisconsin; June 1998.
4. Students’ conception of mathematical proof; Research in Undergraduate Mathematics Education (RUME); Chicago, Illinois; September 2000. 
5. The role of mathematical knowledge in mathematics education, Erupean Society for Research in Mathematics Education (ERME), Summer School for Graduate Study, Poděbrady, Czech Republic; August 2004.
6. Disequilibria in transitioning between proof schemes, Conference on Understanding Linkages Between Social And Cognitive Aspects Of Students’ Transition to Mathematical Proof, Providence, RI; September 2004.
7. What mathematics do mathematics teachers need to know to be effective?  Annual Conference of Mathematics Diagnostic Testing Project, University of California, Los Angles; March 2005.  
8. DNR-based instruction in mathematics; focus on diagnostic teaching, Annual Conference of Mathematics Diagnostic Testing Project, University of California, San Diego, March 2005.
9. A Research-based framework for teaching mathematics effectively, 46th Annual CMC-South Fall Conference; Palm Spring, California; November 2005.
10. What is mathematics? A pedagogical answer to a philosophical question; European Society for Research in Mathematics Education (ERME), Summer School for Graduate Studies; University of Jyväskylä; Jyväskylä, Finland; August 06.
11. DNR’s definition of mathematics: Some Pedagogical Consequences; The Mathematical Association of America, New Jersey Section; Seton Hall University, South Orange, New Jersey; October 06.
12. Transitions between proof schemes; Annual Conference of Research in Undergraduate Mathematics Education (RUME); San Diego, California; February 07.
13. Thinking in terms of ways of thinking; Annual Conference of Mathematics Diagnostic Testing Project, University of California, San Diego; San Diego, California; March 07.
14. What Is Mathematics? A Pedagogical Answer with a Particular Reference to Proving; Asian Pacific Economic Cooperation (APEC)-Tsukuba International Conference III: Innovation of Mathematics Teaching through Lesson Study; Tokyo, Japan; December 07.
15. DNR-Based Instruction in Mathematics: Focus on Teacher’s Knowledge Base; The 1st Conference on Preparing the Next Generation of Secondary Mathematics Teachers: How Pedagogy Emerges from Learning Mathematics; University of California, San Diego; San Diego, California; May 08.
16. Intellectual Need and Its Role in Mathematics Instruction; The American Mathematical Association, MathFest; Madison, Wisconsin; August 08.

Invited Talks

17. Some essential algebraic ways of thinking for success in (beginning) collegiate mathematics; Critical Issues in Education Workshop: Teaching and Learning Algebra; Mathematical Sciences Research Institute (MSRI); Berkeley, California; May 08.
18. DNR-Based instruction in mathematics and its application in physics education; Kharkov Pedagogical University; Kharkov, Ukraine; April 08.
    Mathematics curriculum and instruction: A DNR perspective; University of Munich; Munich, Germany; April 08.
19. Categories of intellectual need in mathematical practice, University of California, Los Angeles Mathematics Department’s 2nd annual Mathematics and Teaching Conference; Los Angeles, California; March 08.
20. Building a community of mathematicians, teachers, and educators secondary teacher preparation in mathematics: a reaction to Stevens’ presentation; University of Arizona; Tucson Arizona; March 08.
21. Mathematics curriculum and instruction: A DNR perspective; Illinois Institute of Technology; February 08.
22. Advancing teachers’ knowledge base through DNR-based instruction in mathematics; Principal Investigators Meeting; US Department of Education; Washington DC; January 08.
    What is mathematics?; Project NExT (New Experiences in Teaching); Joint Mathematics Meeting; San Diego, California, January 08.
23. Mathematical induction: cognitive and instructional considerations; Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (SIGMAA on RUME); Joint Mathematics Meeting; San Diego, California, January 08.
24. A definition of mathematics and its pedagogical consequences; AMS-MAA-MER Special Session on Mathematics and Education Reform; Joint Mathematics Meeting; San Diego, California, January 08.
25. The Necessity principle and its implementation in mathematics instruction; AMS-MAA Special Session on Scholarship of Teaching and Learning in Mathematics; Joint Mathematics Meeting; San Diego, California, January 08.
26. Research on the learning and teaching of proof; University of Tsukuba; Tsukuba, Japan; December 07.
27. Setting instructional objectives in terms of mathematical ways of thinking; The Annual Meeting of the California Mathematics Council North; Monterey, California; November 07.
    Setting instructional objectives in terms of mathematical ways of thinking; The Annual Meeting of the California Mathematics Council South; Palm Springs, California; November 07.
28. Intellectual Need and Its Role in Mathematics Instruction; Arizona State University; Phoenix, Arizona; October 07.
29. The necessity principle and its implementation in mathematics instruction; University of Arizona; Tucson, Arizona; August 07. 
30. Development of mathematics teachers’ knowledge base through DNR-based instruction; National Science Foundation; Washington DC; August 07.
31. What is mathematics? A DNR perspective; Arizona State University; Phoenix, Arizona; October 07.
32. Thinking of the learning and teaching of fractions in terms of ways of thinking; A Workshop on the Learning and Teaching of Fractions; Preparing Mathematicians to Educate Teachers (PMET), a Project Sponsored by the MAA and Funded by NSF; University of Michigan; Ann Arbor, Michigan; July 07.
33. Analyzing different modeling perspectives in undergraduate mathematics education; A DNR’s view; The Bi-annual Meeting of The International Community of Teachers of Mathematical Modelling and Applications (ICTMA); Indiana University; Bloomington, Indiana; July 07.
34. Ways of understanding versus ways of thinking in mathematical practice; Institute for Curriculum and Instruction; Glagenfurt, Austria; April 07.
35. What is mathematics? A DNR perspective; University of Essen; Essen, Germany; April 07.
36. DNR-based instruction in mathematics; University of London; London, England; April 07.
    Transitions between proof schemes; University of Georgia; Athens, Georgia; April 07.
37. A definition of mathematics and its pedagogical consequences; Eastern Carolina University, Greenvile, North Carolina; March 07.
38. Thinking in terms of ways of thinking, California State University at San Marcus; San Diego, California; February 07.
39. Students’ ways of understanding and ways of thinking; Ben-Gurion University of the Negev; Beer-Sheva, Israel; January 07.
40. DNR as a conceptual framework for curriculum development and instruction in Mathematics; Technion—Israel Institute of Technology; Haifa, Israel; January 07.
41. On the transition between proof schemes; Tel-Aviv University, Tel Aviv, Israel; January 07.
42. DNR’s definition of mathematics: Some Pedagogical Consequences; Kharkiv National V.N.Karazin University; Kharkov, Ukraine; January 07.
43. Workshop on students’ intellectual needs; The Mathematical Association of America, New Jersey Section; Seton Hall University; South Orange, New Jersey; October 06.
44. Students’ engagement with mathematics of change: the Kaputian program; The Annual Meeting of the American Educational Research Association; San Francisco, California; April 06.
45. Students’ mathematical experience; International Linear Algebra Society; Drexel University; Philadelphia, Pennsylvania; March 06.
46. The role of proof in mathematics curricula; Marquette University; Milwaukee, Michigan; March 06.
47. DNR-based instruction in mathematics; Indiana University Purdue University at Indianapolis (IUPUI); Indianapolis, Indiana; March 06.
48. What is Mathematics? A Pedagogical Answer to a Philosophical Question; Leibniz Laboratory; Grenoble, France; January 06.
49. On the development of students’ conceptions of proof; University of Delaware; Newark, Delaware; November 05.
50. What is Mathematics?  Pedagogical and Philosophical Considerations, ILAS (International Linear Algebra Society); Regina, Canada; June 05.
51. DNR-Based Instruction, Center for Research in Mathematics and Science Education, San Diego State University; San Diego, California; February 05.
52. On the Development of Students’ Proof Schemes, Department of Mathematics, University of Oregon; Eugene, Oregon; December 04.
53. Disequilibria in Transitioning Between Proof Schemes, Conference on Understanding Linkages Between Social And Cognitive Aspects Of Students’ Transition to Mathematical Proof; Providence, Road Island; September 04.
54. Disequilibria in Transitioning Between Proof Schemes; Department of Cognitive Science, University of California, San Diego; San Diego, California; October 2004.
55. The Causality of Proof Scheme, Conference on the History and Pedagogy of Mathematics; Uppsala, Sweden; July 04.
56. On the Learning and Teaching of Proof; Department of Mathematics, University of Michigan, Ann Arbor, Michigan; April, 04.
57. Promoting Ways of Thinking Through Ways of Understanding, and Vice Versa, Center for Research in Mathematics and Science Education, San Diego State University; San Diego, California; March 04.
58. DNR-Based Instruction in Mathematics, with Particular Reference to the Concept of Mathematical Proof; First Joint International Meeting; Pisa, Italy; June 02.
59. DNR-Based Instruction in Mathematics: Application to the Learning and Teaching of Linear Algebra; Meeting of the International Linear Algebra Society; Auburn University, Alabama; June 02.
60. Didactique of Mathematics and Mathematics Education; Las Vegas, Nevada, Annual Meeting of the National Council of Teachers of Mathematics Research Presession; April 02.
61. DNR-Based Instruction in Mathematics; Department of Mathematics, Cal Poly, San Luis Obispo, California; March 02.
62. Principles of Learning and Teaching: Application to School Algebra; Great San Diego Mathematics Conference; San Diego, California; February, 02.
63. Mathematical Symbolism and the Development of Advanced Mathematical Thinking; Center for Research on Educational Equity, Assessment, and Teaching Excellence, University of California, San Diego; September 01.
64. Proof Understanding Production and Appreciation; University of California, Los Angeles; May 01.
65. Advanced Mathematical Thinking: Its Nature and Its Development; Joint Mathematics-Education Program Annual Reunion; University of California, Los Angeles; May 01.
    Reasoning Algebraically; Mathematics Diagnostic Testing Project Conference, University of California, Los Angeles; January 01.
66. Justification and Proof in School Mathematics; Annual Conference of the California Math Council-Southern Section; Palm Spring, California; November 00.
67. Historical, philosophical, and cognitive considerations in analyzing students’ conception of proofs: Implications to the teaching of geometry and linear algebra; San Diego State University; November 99.
68. Students’ understanding of mathematical proof: Implications for instruction; Department of Mathematics, Indiana University Purdue University at Indianapolis; October 99.
69. My students are Greeks to me; Park City Mathematics Institute, Park City, Utah; July 99.
70. Greek versus modern mathematical thought and the role of Aristotelian causality in the mathematics of the Renaissance: Sources for understanding epistemological obstacles in college students' conception of proof; Department of Mathematics, University of Northern Colorado; June 99.
71. Teachers’ knowledge of mathematics, pedagogy, and epistemology; Department of Mathematics, University of Northern Colorado; June 99.
72. Greek versus modern mathematical thought and the role of Aristotelian causality in the mathematics of the Renaissance: Sources for understanding epistemological obstacles in college students' conception of proof; Department of Mathematics, San Bernardino State University; May 99.
73. Fostering students’ reasoning ability; Mathematics Diagnostic Testing Project Conference; University of California, San Diego; April 99.
74. Critical components of teachers’ mathematical knowledge; Center for Research on Educational Equity, Assessment, and Teaching Excellence; University of California, San Diego; March 99.
75. Greek versus modern mathematical thought and the role of Aristotelian causality in the mathematics of the Renaissance: Sources for understanding epistemological obstacles in college students’ conception of proof; Working Group on the Multiplicative Conceptual Field, University of California, San Diego; March 99.
76. Historical, philosophical, and cognitive considerations of students’ conception of proof; The Annual Regional AMS Meeting, Depaul University, Chicago Illinois; September 98.
77. The concept of mathematical proof; Park-City Mathematics Institute, Park City, Utah; July 98.
78. Advanced mathematical thinking; University of Northern Colorado; February 98.
    Transformational reasoning; University of Genoa, Italy; January 1998.
79. The concept of proofs: historical and cognitive considerations; University of Modena, Italy; January 98.
80. Teaching the concept of mathematical proof; Tel Hay College, Israel; January 98.
    Instructional principles for the teaching of mathematics, with particular reference to proofs; Technion, Israel; January 98.
81. Students’ proof schemes; Technion, Israel; January 98.
82. Proofs and technology; Weizmann Institute, Israel; January 98.
83. Students’ proof schemes; Weizmann Institute, Israel; January 98.
    Instructional principles for the teaching of mathematics, with particular reference to proofs; University of Northern Colorado; January 98.
84. A taxonomy of proof schemes; Department of Mathematical Sciences; Northern Illinois University; November 96.
85. Pedagogical issues in mathematics; Park-City Mathematics Institute; July 96.
    Students' transformational proof schemes; Conference on Proof; Institute of Education, University of London; January 96.
86. Elementary school teachers’ knowledge of mathematics; Department of Education, Ben-Gurion University, Israel, July 94.
87. Teaching linear algebra conceptually; Meeting of the Society for Industrial and Applied Mathematics; San Diego, California; July 94.
88. On moving from multiplicative reasoning to algebraic reasoning; Working Group on the Multiplicative Conceptual Field; Aix-en-Provence, France; September 93.
89. Conservation of operation and the multiplicative conceptual field; Center for Research on Mathematics and Science Education, San Diego State University; March 93.
90. Epistemological aspects of mathematical proof; Department of Mathematics, San Diego State University; March 93.
91. Epistemological aspects of mathematical proof; Department of Mathematics, University of California, San Diego; March 93.
92. The multiplicative conceptual field; The University of Georgia; January 93.
    On the construction of mathematical proof; School of Education; Purdue University; April 92.
93. Constancy of intensive quantities; Working Group on the Multiplicative Conceptual Field; Purdue University; November 91.
94. Ratio and rate in children's reasoning on speed and mixture problems; Department of Mathematics; San Diego State University; May 91.
95. Epistemological obstacles in mathematical knowledge construction; Department of Mathematics, Indiana University Purdue University at Indianapolis; January 91.
96. On the transition from the additive structure to the multiplicative structure; Leuven University, Belgium; December 90.
97. Students’ difficulties in learning linear algebra; Conference on the Learning and Teaching of Linear Algebra; College of William and Mary; August 90.
98. Proportional reasoning as a foundation for multiplication and division concepts; Department of Chemistry, Purdue University; October 89.
99. A mathematical/cognitive/instructional analysis of the multiplicative conceptual field; National Center for Research in Mathematical Sciences Education; University of Wisconsin; September 89.
100. Proportional reasoning as a foundation for the concepts of multiplication and division problems; Rutgers, the State University; Center for Mathematics, Science, and Computer Education; April 89.
101. The multiplicative conceptual field; National Center for Research in Mathematics Science Education; San Diego; January 89.
102. Teachers’ understanding of multiplication and division concepts; Department of Mathematics; University of Illinois at Chicago; December 88.
103. The textual structure of multiplication and division problems; School of Education; University of Minnesota; March 88.
104. The Concept of Proportion; Department of Mathematics, Statistics, and Computer Sciences; University of Illinois at Chicago;March 88.
105. The Concept of Proof; Department of Mathematics, Statistics, and Computer Sciences; University of Illinois at Chicago; May 86.
106. Teaching and Learning Linear Algebra in High School; Department of Science Teaching, Weizmann Institute, Israel; April 85.
107. Teaching and Learning Linear Algebra in High School; Department of Education, Ben-Gurion University, Israel; January 85.
108. Teaching and Learning Linear Algebra in High School; Teaching Center, Hebrew University, Israel; August 84.
109. Teaching and Learning Linear Algebra in High School: Preliminary results; Department of Mathematics, Tel-Aviv University, Israel; March 84.

Conferences Talks

110. Teachers’ use of examples as a pedagogical tool. Annual Conference of the International Group of the Psychology of Mathematics Education,Prague, Check Republic; July 2006.
111. Teachers’ ways of thinking associated with the mental act of problem posing. Annual Conference of the International Group of the Psychology of Mathematics Education,Prague, Check Republic; July 2006.
112. Effects of DNR-based Instruction on the Knowledge Base of Algebra Teachers; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.
113. Dilemma Concerning Semi-Structured Clinical Interviews: Interviewer-Interviewee Interaction Revisited; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.
114. Teachers’ Reconceptualization of Proof Schemes; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.
115. Mathematics Teachers’ Knowledge Base: Preliminary Results, Annual Conference of the International Group of the Psychology of Mathematics Education, Bergen, Sweden; July 2004.
116. Journal for Research in Mathematics Education: A Reviewer’s Perspective; Annual Meeting of the National Council of Teachers of Mathematics; Las Vegas, Nevada; April 200l.
117. The rational number project; new research questions; The Annual Meeting of the International Group For the Psychology of Mathematics Education, North America Chapter; North Carolina State University; October 1998.
118. What is advanced mathematical thinking? The Annual Meeting of the International Group For the Psychology of Mathematics Education, North America Chapter; North Carolina State University; October 1998.
119. Students' conception of linear dependence and linear independence; The Annual Meeting of the American Mathematical Association; San Diego, January 1997.
120. A reaction to approaching geometry theorems in contexts: from history and epistemology to cognition By Mariotti, Bussi, and Boero; The Annual Meeting of the International Group for the Psychology of Mathematics Education; Lahti, Finlad, July 1997.
121. The concept of proof in the context of linear algebra; The International Congress of Mathematics Education; Seville, Spain; July 1996.
122. Classifying processes of proving; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Valencia, Spain; July 1996.
123. Interviewing Undergraduate Majors about Proof; The Annual Meeting of the Mathematical Association of America; Orlando, Florida; January 1996.
124. Applications to pedagogical principles to undergraduate mathematics curriculum; The Annual Meeting of the Mathematical Association of America; Orlando, Florida; January 1996.
125. Emphasizing the concept of proof in the teaching of linear algebra; The Annual Meeting of the Mathematical Association of America; San Francisco; January 1995.
126. Factors in learning linear algebra; The Annual Conference of the PME-NA; Baton Rouge, Louisiana State University; November 1994.
127. Learning to prove mathematically; The Annual Meeting of the American Educational Research Association; Seattle, Washington; April 1994.
128. The linear algebra curriculum study group recommendations: Moving beyond concept definition; The Annual Meeting of the Mathematical Association of America; Cincinnati; January 1994.
129. Children's understanding of proportionality; The Annual Meeting of the American Educational Research Association; San Francisco; April 1992.
130. Bringing about change in mathematics teaching: A Reaction to four research papers; The Annual Meeting of the American Educational Research Association; San Francisco; April 1992.
131. Representations in mathematics: A reaction to four research papers; The Annual Meeting of the American Educational Research Association; Chicago; April 1991.
132. Teaching linear algebra with understanding; The Annual Meeting of the Society for Industrial and Applied Mathematics; Minneapolis, Minnesota; September 1991.
133. Variables affecting proportionality; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Assisi, Italy; June 1991.
134. The role of analogy in mathematical thinking; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Assisi, Italy; June 1991.
135. Invariance and proportional reasoning; The Annual Meeting of the National Council of Teachers of Mathematics; New Orleans; April 1991.
136. On the construction of knowledge in mathematics: Formation of entities, abstraction, and generalization; The Annual Meeting of the Mathematical Association of America; San Francisco; January 1991.
137. The process conception of function; Conference on the Concept of Function; Purdue University; October 1990.
138. The role of conceptual entities in constructing meaning of advanced mathematical concepts and their mathematical notational system; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.
139. Construct theory of rational numbers; towards a semantics analysis; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.
140. Understanding the multiplicative conceptual field; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.
141. Isomorphic thinking in advanced mathematics; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.
142. On the learning and teaching of linear algebra; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.
143. On Mathematical Understanding: A Reaction to Four Paper Presentations; The Annual Meeting of the American Educational Research Association; Boston; April 1990.
144. A scheme to represent the Multiplicative Conceptual Field; The Annual Meeting of the American Educational Research Association; Boston; April 1990.
145. The role of figure in students' concepts of geometric proof; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Paris, France; July 1989.
146. Children's implicit mathematical knowledge; The Annual Meeting of the International Group for the Psychology of Mathematics Education; Paris, France; July 1989.
147. Fischbein's Theory; a further consideration; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Paris, France; July 1989.
148. The role of symbolization in the learning of advanced mathematics; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Paris, France; July 1989.
149. Developing leadership in middle school mathematics; The Annual Meeting of the National Council of Teachers of Mathematics; Orlando; April 1989.
150. Conceptual units, mathematics of quantity, and rational number concepts and operations; The Annual Meeting of the American Educational Research Association; San Francisco; March 1989.
151. Inservice and preservice teacher's mathematical knowledge of multiplication and division concepts; The Annual Meeting of the International Group For the Psychology of Mathematics Education-North America Chapter; Northern Illinois University; November 1988.
152. Teachers' understanding of multiplication and division concepts; Symposium on Mathematics Specialist in Elementary School; University of Chicago; September 1988.
153. Teacher's interpretation of “multiplicative compare” problems; The Annual Meeting of the National Council of Teachers of Mathematics; Chicago; April 1988.
154. Cognitive conflicts in procedure applications; The Annual Meeting of the American Educational Research Association; New Orleans; April 1988.
155. Declarative and procedural knowledge and isomorphism of speed problems; International Conference on Misconceptions and Educational Strategies in Science and Mathematics; Cornell University; August 1987.
156. The impact of mental representation of magnitude on problem solving; International Conference on Misconceptions and Educational Strategies in Science and Mathematics; Cornell University; August 1987.
157. Qualitative differences among 7th grade children in solving a non-numerical proportional reasoning blocks task; The Annual Meeting of the International Group For the Psychology of Mathematics Education; University of Montreal, Canada; July 1987.
158. Theoretical analysis: structure and hierarchy, missing value proportion problems; The Annual Meeting of the International Group For the Psychology of Mathematics Education; University of Montreal; July 1987.
159. A comparison between two approaches to embodying mathematical models in the abstract system of linear algebra; The Annual Meeting of the International Group For the Psychology of Mathematics Education-North America Chapter; Michigan State University; September 1986.
160. The concept of proof held by preservice elementary teachers; The Annual Meeting of the International Group For the Psychology of Mathematics Education; City University, London; July 1986.
161. Recent cognitive theories applied to sequential length-measuring knowledge in young children; The Annual Meeting of the International Group For the Psychology of Mathematics Education; City University, London; July 1986.