Publications

Filter by type:
(2019) The blocks task; comparative analyses with other proportion tasks, and qualitative reasoning skills among 7th grade children in solving the task Cognition and Instruction, 9, pp. 45 - 96
(2019) Students’ proof schemes revisited: Historical and epistemological considerations P. Boero (Ed.), Theorems in School, Kluwer,
(2019) Reid, D.A. and Knipping, C.: Proof in mathematics education: Research, learning, and teaching ZDM Mathematics Education, 45, pp. 497 - 499
(2014) Common Core State Standards for Geometry: An Alternative Approach Notices of the AMS, pp. 24-35
(2013) The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two Cases Canadian Journal of Science, Mathematics, and Technology Education, 13 (2), pp. 154–168
(2013) The Kaputian program and its relation to DNR-based instruction: A common commitment to the developmnent of mathematics with meaning The SimCalc Vision and Contribution, (Fried, M., & Dreyfus, T., Eds.), Springer, pp. 438 - 448
(2013) Intellectual Need Vital Direction for Mathematics Education Research, Leatham, K. Ed., Springer,
(2013) DNR-based curricula: The case of complex numbers Journal of Humanistic Mathematics, 3 (2), pp. 2-61
(2013) Classroom-based interventions in mathematics education: Relevance, significance, and applicability ZDM Mathematics Education, 45, pp. 483 - 489
(2012) Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions Notices of the AMS, Instructional Science, 40, 4,
(2012) Deductive reasoning in mathematics education Encyclopedia of Mathematics Education, Springer,
(2011) The state of high school textbooks Notices of the AMS, 58, pp. 823 - 826
(2011) Intellectual need and problem-free activity in the classroom International Journal for Studies in Mathematics Education, 4 (1), pp. 80 - 114
(2010) Teaching practices that can promote the authoritative proof scheme Canadian Journal of Science, Mathematics and Technology Education, 10, pp. 139 - 159
(2010) Teaching practices associated with the authoritative proof scheme Journal for Research in Mathematics Education, 41, pp. 14 - 19
(2010) DNR-Based Instruction in Mathematics as a Conceptual Framework Theories of Mathematics Education, Barath, S., & English, L., Eds., Springer, pp. 343 - 367
(2010) Commentary on the Theoretical, conceptual, and philosophical foundations for research in mathematics education In Theories of Mathematics Education, Barath, S., & English, L., Eds., Springer, pp. 87 - 94.
(2010) An operational definition of learning Journal of Mathematical Behavior, 29, 3, pp. 115 - 124
(2009) Current contributions toward comprehensive perspectives on the learning and teaching of proof.*Teaching and Learning Proof Across the Grades: A K-16 Perspective Routledge / Taylor & Francis, pp. 275 - 289
(2009) College instructors’ views of students vis-a-vi proof Teaching and Learning Proof Across the Grades: A K-16 Perspective, Routledge/Taylor & Francis, pp. 275 - 289.
(2008) What is mathematics? A pedagogical answer to a philosophical question B. Gold & R. Simons (Eds., Proof and other dilemmas: Mathematics and philosophy, Washington, DC: Mathematical Association of America, pp. 265 - 290
(2008) Mathematical Induction: Cognitive and Instructional Considerations. M. Carlson, & C. Rasmussen (Eds.), Making the Connection: Research and Practice in Undergraduate Mathematics, Mathematical American Association, 11, pp. 111 - 123
(2008) Maintaining the mathematical integrity of school curricula: The challenge For the Learning of Mathematics, 28, 10,
(2008) DNR Perspective on Mathematics Curriculum and Instruction, Part II ZDM—The International Journal on Mathematics Education, pp. 487 - 500
(2008) Attention to meaning by algebra teachers Journal of Mathematical Behavior, 27, pp. 116 - 127
(2007) Triadic interaction in clinical task-based interviews with mathematics teachers Educational Studies in Mathematics, 65 (3), pp. 349 - 365
(2007) Toward a comprehensive perspective on proof Notices of the AMS, F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, National Council of Teachers of Mathematics,
(2007) The DNR System as a Conceptual Framework for Curriculum Development and Instruction R. Lesh, J. Kaput, E. Hamilton (Eds.), Foundations for the Future in Mathematics Education, Erlbaum,
(2006) Preface Research in Collegiate Mathematics Education, 6,
(2006) Mathematics Education Research, Its Nature, and Its Purpose: A Discussion of Lester’s Paper Zentralblatt fuer Didaktik der Mathematik, 38, pp. 58 - 62
(2005) Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development Mathematical Thinking and Learning, 7, pp. 27 - 50
(2004) A Perspective on “Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity T. Carpenter, J. Dossey, & L. Koehler (Eds.), Classics in Mathematics Education Research, 98,
(2003) Problem solving, modeling, and local conceptual development International Journal of Mathematics Thinking and Learning, 5, pp. 157 - 189
(2003) Polygons whose vertex triangles have equal area The American Mathematical Monthly, 110, pp. 606 – 610
(2003) Local conceptual development of proof schemes in a cooperative learning setting R. Lesh & H. M. Doerr (Eds.). Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving. Mahwah , NJ : Lawrence Erlbaum Associates, pp. 359 - 382
(2003) Case Studies of Mathematics Majors’ Proof Understanding, Production, and Appreciation Canadian Journal of Science, Mathematics and Technology Education, 3, pp. 251 - 267
(2001) The Development of Mathematical Induction as a Proof Scheme: A Model for DNR-Based Instruction S. Campbell & R. Zaskis (Eds.). Learning and Teaching Number Theory. In C. Maher (Ed.). Journal of Mathematical Behavior. New Jersey, Ablex Publishing Corporation, pp. 185 - 212
(2000) Three principles of learning and teaching mathematics: Particular reference to linear algebra—Old and new observations In Jean-Luc Dorier (Ed.), On the Teaching of Linear Algebra, Kluwer Academic Publishers, pp. 177 - 190
(1999) Students’ understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra Linear Algebra and Its Applications, pp. 302 - 303, 601 - 613
(1998) Types of students’ justifications Mathematics Teacher, 91, pp. 670 - 675
(1998) Two Dual Assertions: The First on Learning and the Second on Teaching (Or Vice Versa) The American Mathematical Monthly, 105, pp. 497 - 507
(1998) The role of analogy in the learning of mathematics Journal of Mathematical Behavior, 17, pp. 5 - 24
(1998) Students’ proof schemes Research on Collegiate Mathematics Education, Vol. III. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), AMS, pp. 234 - 283
(1997) The role of structural and semantic factors in the solution of algebra speed problems International Journal for Mathematics Education in Science and Technology, 28, pp. 397 - 409
(1997) The linear algebra curriculum study group recommendations: Moving beyond concept definition Notices of the AMS, Carlson D., Johnson, C, Lay, D., Porter, D., Watkins, A, & Watkins, W. (Eds.). Resources for Teaching Linear Algebra,. MAA Notes, 42, pp. 107 - 126
(1997) Conceptual units analysis of preservice elementary school teachers’ strategies on a rational-number-as-operator task Journal for Research in Mathematics Education, 28, pp. 48 - 69
(1997) Three Principles of Learning and Teaching, With Particular Reference to the Learning and Teaching of Linear Algebra Jean-Luc Dorier (Ed.), Recherches en Didactique des Mathematiques, La Pensee sauvage,
(1995) Teachers’ solutions for multiplicative problems Hiroshima Journal for Research in Mathematics Education, pp. 31 - 51
(1995) From naive interpretist to operation conserver J. Sowder & B. Schappelle (Eds.). Providing a Foundation for Teaching Mathematics in the Middle, New York : SUNY Press, pp. 143 - 165
(1994) Invariance of ratio: The case of children’s anticipatory scheme of constancy of taste Journal for Research in Mathematics Education, 25, pp. 324 - 345
(1994) Units of quantity: A conceptual basis common to additive and multiplicative structures G. Harel and J. Confrey (Eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics. Albany , New York : SUNY Press, pp. 123 - 180
(1994) The impact of the number type on the solution of multiplication and division problems: Further considerations G. Harel and J. Confrey (Ed).*The Development of Multiplicative Reasoning in the Learning of Mathematics*. Albany , New York : SUNY Press, pp. 363 - 384
(1993) On teacher education programs in mathematics, International Journal for Mathematics Education in Science and Technology, 25, pp. 113-119
(1992) The process conception of function. In G. Harel & E. Dubinsky. The Concept of Function: Aspects of epistemology and pedagogy, MAA Notes, No. 28, pp. 85-106
(1992) The blocks task on proportionality: Expert solution models Journal of Structural Learning, 11, pp. 173 - 188
(1992) Rational numbers: An integration of research. In T. Carpenter, L. Fennema, & T. Romberg (Eds.) Learning, Teaching, and Assessing Rational Number Concepts: Multiple Research Perspectives, Hillsdale , New Jersey : Erlbaum, pp. 13 - 48
(1992) Rational number, ratio, and proportion. In D. Grouws (Ed.) Handbook for Research on Mathematics Teaching and Learning, New York : Macmillan, pp. 296 - 333
(1992) Curriculum implications. In T. Carpenter, L. Fennema, & T. Romberg (Eds.) Learning, Teaching, and Assessing Rational Number Concepts: Multiple Research Perspectives, Hillsdale , New Jersey : Erlbaum, pp. 327 - 362
(1991) The general, the abstract, and the generic For the Learning of Mathematics, 11, pp. 38 - 42
(1991) The role of conceptual entities in building advanced mathematical concepts and their symbols. In D. Tall (Ed) Advanced Mathematical Thinking, Kluwer Academic Publishers, pp. 82 - 94
(1991) Intermediate teachers’ knowledge of rational number concepts. In E. Fennema , T. P. Carpenter, and S. J. Lamon (Eds.) Integrating Research on Teaching and Learning Mathematics, Albany , New York : SUNY Press, pp. 177 - 198
(1991) Ed’s Strategy for solving division problems Arithmetic Teacher, 39, pp. 38 - 40
(1990) Students’ errors, misconception, and cognitive conflict in application of procedures Focus on Learning Problems in Mathematics, 12, pp. 75 - 84
(1990) Using geometric models and vector arithmetic to teach high-school students basic notions in linear algebra International Journal for Mathematics Education in Science and Technology, 21, pp. 387 - 392
(1990) The structure of speed problems and its relation to problem complexity and isomorphism Journal of Structural Learning, 10, pp. 177 - 196
(1990) The effect of order and coordination of the problem quantities on difficulty of missing value proportion problems International Journal for Mathematics Education in Science and Technology, 21, pp. 589 - 593
(1990) Higher order knowledge involved in the solution of algebra speed word problems Journal of Structural Learning, 10, pp. 305 - 328
(1989) Structure and hierarchy of missing value proportion problems and their representations Journal of Mathematical Behavior, 8, pp. 77-119
(1989) Proof frame of preservice elementary teachers Journal for Research in Mathematics Education, 20, pp. 41 - 51
(1989) Learning and teaching linear algebra: Difficulties and an alternative approach to visualizing concepts and processes Focus on Learning Problems in Mathematics, 11, pp. 139 - 148
(1989) Applying the principle of multiple embodiments in teaching linear algebra: Aspects of familiarity and mode of representation School Science and Mathematics, 89, pp. 49 - 57
(1988) A pedagogical approach to forming generalizations International Journal for Mathematics Education in Science and Technology, 19, pp. 101 - 107
(1987) Variations in linear algebra content presentation For the Learning of Mathematics, 7, pp. 29 - 32