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.

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.

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.

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.

Mathematics curriculum and instruction: A DNR perspective; Illinois Institute of Technology; February 08.

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.

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.

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.

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.

Research on the learning and teaching of proof; University of Tsukuba; Tsukuba, Japan; December 07.

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.

Intellectual Need and Its Role in Mathematics Instruction; Arizona State University; Phoenix, Arizona; October 07.

The necessity principle and its implementation in mathematics instruction; University of Arizona; Tucson, Arizona; August 07. 

Development of mathematics teachers’ knowledge base through DNR-based instruction; National Science Foundation; Washington DC; August 07.

What is mathematics? A DNR perspective; Arizona State University; Phoenix, Arizona; October 07.

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.

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.

Ways of understanding versus ways of thinking in mathematical practice; Institute for Curriculum and Instruction; Glagenfurt, Austria; April 07.

What is mathematics? A DNR perspective; University of Essen; Essen, Germany; April 07.

DNR-based instruction in mathematics; University of London; London, England; April 07.
Transitions between proof schemes; University of Georgia; Athens, Georgia; April 07.

A definition of mathematics and its pedagogical consequences; Eastern Carolina University, Greenvile, North Carolina; March 07.

Thinking in terms of ways of thinking, California State University at San Marcus; San Diego, California; February 07.

Students’ ways of understanding and ways of thinking; Ben-Gurion University of the Negev; Beer-Sheva, Israel; January 07.

DNR as a conceptual framework for curriculum development and instruction in Mathematics; Technion—Israel Institute of Technology; Haifa, Israel; January 07.

On the transition between proof schemes; Tel-Aviv University, Tel Aviv, Israel; January 07.

DNR’s definition of mathematics: Some Pedagogical Consequences; Kharkiv National V.N.Karazin University; Kharkov, Ukraine; January 07.

Workshop on students’ intellectual needs; The Mathematical Association of America, New Jersey Section; Seton Hall University; South Orange, New Jersey; October 06.

Students’ engagement with mathematics of change: the Kaputian program; The Annual Meeting of the American Educational Research Association; San Francisco, California; April 06.

Students’ mathematical experience; International Linear Algebra Society; Drexel University; Philadelphia, Pennsylvania; March 06.

The role of proof in mathematics curricula; Marquette University; Milwaukee, Michigan; March 06.

DNR-based instruction in mathematics; Indiana University Purdue University at Indianapolis (IUPUI); Indianapolis, Indiana; March 06.

What is Mathematics? A Pedagogical Answer to a Philosophical Question; Leibniz Laboratory; Grenoble, France; January 06.

On the development of students’ conceptions of proof; University of Delaware; Newark, Delaware; November 05.

What is Mathematics?  Pedagogical and Philosophical Considerations, ILAS (International Linear Algebra Society); Regina, Canada; June 05.

DNR-Based Instruction, Center for Research in Mathematics and Science Education, San Diego State University; San Diego, California; February 05.

On the Development of Students’ Proof Schemes, Department of Mathematics, University of Oregon; Eugene, Oregon; December 04.

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.

Disequilibria in Transitioning Between Proof Schemes; Department of Cognitive Science, University of California, San Diego; San Diego, California; October 2004.

The Causality of Proof Scheme, Conference on the History and Pedagogy of Mathematics; Uppsala, Sweden; July 04.

On the Learning and Teaching of Proof; Department of Mathematics, University of Michigan, Ann Arbor, Michigan; April, 04.

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.

DNR-Based Instruction in Mathematics, with Particular Reference to the Concept of Mathematical Proof; First Joint International Meeting; Pisa, Italy; June 02.

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.

Didactique of Mathematics and Mathematics Education; Las Vegas, Nevada, Annual Meeting of the National Council of Teachers of Mathematics Research Presession; April 02.

DNR-Based Instruction in Mathematics; Department of Mathematics, Cal Poly, San Luis Obispo, California; March 02.

Principles of Learning and Teaching: Application to School Algebra; Great San Diego Mathematics Conference; San Diego, California; February, 02.

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.

Proof Understanding Production and Appreciation; University of California, Los Angeles; May 01.

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.

Justification and Proof in School Mathematics; Annual Conference of the California Math Council-Southern Section; Palm Spring, California; November 00.

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.

Students’ understanding of mathematical proof: Implications for instruction; Department of Mathematics, Indiana University Purdue University at Indianapolis; October 99.

My students are Greeks to me; Park City Mathematics Institute, Park City, Utah; July 99.

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.

Teachers’ knowledge of mathematics, pedagogy, and epistemology; Department of Mathematics, University of Northern Colorado; June 99.

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.

Fostering students’ reasoning ability; Mathematics Diagnostic Testing Project Conference; University of California, San Diego; April 99.

Critical components of teachers’ mathematical knowledge; Center for Research on Educational Equity, Assessment, and Teaching Excellence; University of California, San Diego; March 99.

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.

Historical, philosophical, and cognitive considerations of students’ conception of proof; The Annual Regional AMS Meeting, Depaul University, Chicago Illinois; September 98.

The concept of mathematical proof; Park-City Mathematics Institute, Park City, Utah; July 98.

Advanced mathematical thinking; University of Northern Colorado; February 98.
Transformational reasoning; University of Genoa, Italy; January 1998.

The concept of proofs: historical and cognitive considerations; University of Modena, Italy; January 98.

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.

Students’ proof schemes; Technion, Israel; January 98.

Proofs and technology; Weizmann Institute, Israel; January 98.

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.

A taxonomy of proof schemes; Department of Mathematical Sciences; Northern Illinois University; November 96.

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.

Elementary school teachers’ knowledge of mathematics; Department of Education, Ben-Gurion University, Israel, July 94.

Teaching linear algebra conceptually; Meeting of the Society for Industrial and Applied Mathematics; San Diego, California; July 94.

On moving from multiplicative reasoning to algebraic reasoning; Working Group on the Multiplicative Conceptual Field; Aix-en-Provence, France; September 93.

Conservation of operation and the multiplicative conceptual field; Center for Research on Mathematics and Science Education, San Diego State University; March 93.

Epistemological aspects of mathematical proof; Department of Mathematics, San Diego State University; March 93.

Epistemological aspects of mathematical proof; Department of Mathematics, University of California, San Diego; March 93.

The multiplicative conceptual field; The University of Georgia; January 93.
On the construction of mathematical proof; School of Education; Purdue University; April 92.

Constancy of intensive quantities; Working Group on the Multiplicative Conceptual Field; Purdue University; November 91.

Ratio and rate in children's reasoning on speed and mixture problems; Department of Mathematics; San Diego State University; May 91.

Epistemological obstacles in mathematical knowledge construction; Department of Mathematics, Indiana University Purdue University at Indianapolis; January 91.

On the transition from the additive structure to the multiplicative structure; Leuven University, Belgium; December 90.

Students’ difficulties in learning linear algebra; Conference on the Learning and Teaching of Linear Algebra; College of William and Mary; August 90.

Proportional reasoning as a foundation for multiplication and division concepts; Department of Chemistry, Purdue University; October 89.

A mathematical/cognitive/instructional analysis of the multiplicative conceptual field; National Center for Research in Mathematical Sciences Education; University of Wisconsin; September 89.

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.

The multiplicative conceptual field; National Center for Research in Mathematics Science Education; San Diego; January 89.

Teachers’ understanding of multiplication and division concepts; Department of Mathematics; University of Illinois at Chicago; December 88.

The textual structure of multiplication and division problems; School of Education; University of Minnesota; March 88.

The Concept of Proportion; Department of Mathematics, Statistics, and Computer Sciences; University of Illinois at Chicago;March 88.

The Concept of Proof; Department of Mathematics, Statistics, and Computer Sciences; University of Illinois at Chicago; May 86.

Teaching and Learning Linear Algebra in High School; Department of Science Teaching, Weizmann Institute, Israel; April 85.

Teaching and Learning Linear Algebra in High School; Department of Education, Ben-Gurion University, Israel; January 85.

Teaching and Learning Linear Algebra in High School; Teaching Center, Hebrew University, Israel; August 84.

Teaching and Learning Linear Algebra in High School: Preliminary results; Department of Mathematics, Tel-Aviv University, Israel; March 84.

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.

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.

Effects of DNR-based Instruction on the Knowledge Base of Algebra Teachers; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.

Dilemma Concerning Semi-Structured Clinical Interviews: Interviewer-Interviewee Interaction Revisited; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.

Teachers’ Reconceptualization of Proof Schemes; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.

Mathematics Teachers’ Knowledge Base: Preliminary Results, Annual Conference of the International Group of the Psychology of Mathematics Education, Bergen, Sweden; July 2004.

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.

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.

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.

Students' conception of linear dependence and linear independence; The Annual Meeting of the American Mathematical Association; San Diego, January 1997.

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.

The concept of proof in the context of linear algebra; The International Congress of Mathematics Education; Seville, Spain; July 1996.

Classifying processes of proving; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Valencia, Spain; July 1996.

Interviewing Undergraduate Majors about Proof; The Annual Meeting of the Mathematical Association of America; Orlando, Florida; January 1996.

Applications to pedagogical principles to undergraduate mathematics curriculum; The Annual Meeting of the Mathematical Association of America; Orlando, Florida; January 1996.

Emphasizing the concept of proof in the teaching of linear algebra; The Annual Meeting of the Mathematical Association of America; San Francisco; January 1995.

Factors in learning linear algebra; The Annual Conference of the PME-NA; Baton Rouge, Louisiana State University; November 1994.

Learning to prove mathematically; The Annual Meeting of the American Educational Research Association; Seattle, Washington; April 1994.

The linear algebra curriculum study group recommendations: Moving beyond concept definition; The Annual Meeting of the Mathematical Association of America; Cincinnati; January 1994.

Children's understanding of proportionality; The Annual Meeting of the American Educational Research Association; San Francisco; April 1992.

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.

Representations in mathematics: A reaction to four research papers; The Annual Meeting of the American Educational Research Association; Chicago; April 1991.

Teaching linear algebra with understanding; The Annual Meeting of the Society for Industrial and Applied Mathematics; Minneapolis, Minnesota; September 1991.

Variables affecting proportionality; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Assisi, Italy; June 1991.

The role of analogy in mathematical thinking; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Assisi, Italy; June 1991.

Invariance and proportional reasoning; The Annual Meeting of the National Council of Teachers of Mathematics; New Orleans; April 1991.

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.

The process conception of function; Conference on the Concept of Function; Purdue University; October 1990.

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.

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.

Understanding the multiplicative conceptual field; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.

Isomorphic thinking in advanced mathematics; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Oaxtapec, Mexico; July 1990.

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.

On Mathematical Understanding: A Reaction to Four Paper Presentations; The Annual Meeting of the American Educational Research Association; Boston; April 1990.

A scheme to represent the Multiplicative Conceptual Field; The Annual Meeting of the American Educational Research Association; Boston; April 1990.

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.

Children's implicit mathematical knowledge; The Annual Meeting of the International Group for the Psychology of Mathematics Education; Paris, France; July 1989.

Fischbein's Theory; a further consideration; The Annual Meeting of the International Group For the Psychology of Mathematics Education; Paris, France; July 1989.

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.

Developing leadership in middle school mathematics; The Annual Meeting of the National Council of Teachers of Mathematics; Orlando; April 1989.

Conceptual units, mathematics of quantity, and rational number concepts and operations; The Annual Meeting of the American Educational Research Association; San Francisco; March 1989.

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.

Teachers' understanding of multiplication and division concepts; Symposium on Mathematics Specialist in Elementary School; University of Chicago; September 1988.

Teacher's interpretation of “multiplicative compare” problems; The Annual Meeting of the National Council of Teachers of Mathematics; Chicago; April 1988.

Cognitive conflicts in procedure applications; The Annual Meeting of the American Educational Research Association; New Orleans; April 1988.

Declarative and procedural knowledge and isomorphism of speed problems; International Conference on Misconceptions and Educational Strategies in Science and Mathematics; Cornell University; August 1987.

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.

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.

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.

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.

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.

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.