
PRESENTATIONS
Keynote and Plenary Addresses
 Intellectual Need and its Application in Curriculum and Instruction; MAA Souther CaliforniaNevada Section; Long Beach, California; October, 2012.
 A ResearchBased Framework for Teaching Mathematics Effectively; Scientia Conference on
Research and Innovation in Undergraduate Science and Engineering Education; Rice University,
February, 2011.
 DNRBased Instruction in Mathematics; IX National Science and Mathematics Congress; Ismir,
Turkey; September 2010.
 A Review of Four HighSchool 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 HighSchool 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.
 DNRBased 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 Researchbased framework for teaching mathematics effectively, 46th Annual CMCSouth Fall Conference; Palm Spring, California; November 2005.
 DNRbased 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 MAAMAS; 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; BenGurion 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 ResearchBased Framework for Teaching Mathematics Effectively; Annual Greater San Diego
Mathematics Conference; February, 2011.
 An InDepth Examination of Four HighSchool Programs; Annual Conference of California
Mathematics Council; Palm Spring; November, 2010.
 DNRBased Instruction in Mathematics: Focus on Holistic Problems; Annual Conference of
California Mathematics Council; Palm Spring; November, 2010.
 Proof Schemes; School of Education, TelAvis 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.
 DNRBased 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 DNRbased 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; AMSMAAMER Special Session on Mathematics and Education Reform; Joint Mathematics Meeting; San Diego, California, January 08.
 The Necessity principle and its implementation in mathematics instruction; AMSMAA 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 DNRbased 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 Biannual 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.
 DNRbased 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 DNRbased Instruction on the Knowledge Base of Algebra Teachers; Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona; February 2005.
 Dilemma Concerning SemiStructured Clinical Interviews: InterviewerInterviewee 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 PMENA; 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 EducationNorth 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 nonnumerical 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 EducationNorth 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.
