**Keynote and Plenary Addresses**

- Intellectual Need and its Application in Curriculum and Instruction; MAA Souther California-Nevada Section; Long Beach, California; October, 2012.
- A Research-Based Framework for Teaching Mathematics Effectively; Scientia Conference on

Research and Innovation in Undergraduate Science and Engineering Education; Rice University, February, 2011. - DNR-Based Instruction in Mathematics; IX National Science and Mathematics Congress; Ismir, Turkey; September 2010.
- A Review of Four High-School Mathematics Programs: Annual Meeting of the Mathematics Diagnostic Testing Project; University of California at San Diego; March 2010.
- Math for America San Diego: Focus on Teachers’ Knowledge Base; Fundraising Event; University of California at San Diego, January, 2010.
- A Review of Four High-School Mathematics Program; 2nd Conference on Preparing the Next Generation of Secondary Mathematics Teachers: How Pedagogy Emerges from Learning

Mathematics; University of California, San Diego; San Diego, California; April 2009. - Mathematics Curriculum and Instruction: A DNR Perspective; Chicago Symposium Series on

Excellence in Teaching Mathematics and Science: Research and Practice; National Louis

University; Chicago, Illinois; February, 2009. - Intellectual Need and Epistemological Justification: Historical and Pedagogical Considerations;

Bingham Young University; November, 2008. - Two Fundamental Questions: A DNR Perspective; Young European Researchers in Mathematics Education Summer School (YESS); Trabzon, Turkey; August, 2008.
- Intellectual Need and Its Role in Mathematics Instruction; The American Mathematical Association, MathFest; Madison, Wisconsin; August 08.
- 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.
- 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.
- Thinking in terms of ways of thinking; Annual Conference of Mathematics Diagnostic Testing Project, University of California, San Diego; San Diego, California; March 07.
- Transitions between proof schemes; Annual Conference of Research in Undergraduate Mathematics Education (RUME); San Diego, California; February 07.
- 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.
- 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.
- A Research-based framework for teaching mathematics effectively, 46th Annual CMC-South Fall Conference; Palm Spring, California; November 2005.
- DNR-based instruction in mathematics; focus on diagnostic teaching, Annual Conference of Mathematics Diagnostic Testing Project, University of California, San Diego, March 2005.
- 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.
- 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.
- 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.
- Students’ conception of mathematical proof; Research in Undergraduate Mathematics Education (RUME); Chicago, Illinois; September 2000.
- 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.
- 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.
- 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.

**Invited Talks**

- Developing and Sustaining Professional Communities of Teachers around Mathematical Content and Student Intellectual Need; Joint Mathematics Meeting (JMM); San Diego, California, January, 2013.
- Intellectual Need and its Application in Mathematics Curricula; School of Mathematical and Statistical Sciences; Arizona State University; November, 2012.
- Justification in mathematics and mathematics education; Mathematics & Mathematics Education:

Searching for Common Ground: A Symposium in Honor of Ted Eisenberg; Ben-Gurion University of the Negev Beer Sheva, Israel; April, 2012. - Intellectual Need and its Application in Curriculum and Instruction; Department of Mathematics, University of Arizona; April, 2012.
- Intellectual Need in Mathematical Practice and Its Application in Curriculum and Instruction, Department of Mathematics, Virginia Tech; March, 2012.
- Mathematics Curriculum and Instruction: A DNR Perspective; School of Education, Virginia Tech; March, 2012.
- Holistic Problems and Their Role in Mathematics Curricula; Western Regional Noyce Conference; Costa Mesa, California: March, 2011.
- A Research-Based Framework for Teaching Mathematics Effectively; Annual Greater San Diego Mathematics Conference; February, 2011.
- An In-Depth Examination of Four High-School Programs; Annual Conference of California Mathematics Council; Palm Spring; November, 2010.
- DNR-Based Instruction in Mathematics: Focus on Holistic Problems; Annual Conference of California Mathematics Council; Palm Spring; November, 2010.
- Proof Schemes; School of Education, Tel-Avis University; September, 2010.
- Students’ Readiness for Algebraic Ways of Thinking; Annual Meeting of the International Linear Algebra Society (ILAS); Pisa, Italy; June 2010.
- The Role of Mathematics in Mathematics Education Research: Question for Public Debate; Annual Meeting of the National Council of Teachers of Mathematics; San Diego; April, 2010.
- A Definition of Mathematics and Its Pedagogical Consequences; Department of Mathematics, Purdue University; March, 2010.
- Teaching Calculus with Understanding; Annual Conference of California Mathematics Council; Palm Spring; November, 2009.
- Discussant of the symposium, Collaboration and the Interplay among Design, Policy Contexts, and Rigor: Building Valid, Student- Centered Mathematics Assessments; Annual Meeting of the American Educational Research Association; April, 2009.
- Intellectual Need and Its Application in the Mathematics Classroom; San Pedro High School; January, 2009.
- Intellectual Need and Its Application in Mathematics Instruction; Department of Mathematics, University of Illinois at Chicago; October, 2008.
- Intellectual Need and Epistemological Justification; School of Education, University of Wisconsin; October 2008.
- 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.

**Conference Talks**

- 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.