Presentations

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.