Conference Countdown
Atlanta, Ga.
April 2-4, 2016
  • membership
  • my account
  • help

    We are here to help!

    1703 North Beauregard Street
    Alexandria, VA 22311-1714
    Tel: 1-800-933-ASCD (2723)
    Fax: 703-575-5400

    8:00 a.m. to 6:00 p.m. eastern time, Monday through Friday

    Local to the D.C. area: 1-703-578-9600, press 2

    Toll-free from U.S. and Canada: 1-800-933-ASCD (2723), press 2

    All other countries: (International Access Code) + 1-703-578-9600, press 2


  • Log In
  • Forgot Password?


ASCD Annual Conference and Exhibit Show

2016 ASCD Annual Conference and Exhibit Show

Learn. Teach. Lead.
Get the tools to put it all together at this can't-miss education conference—with more than 200 sessions and five inspirational keynote speakers.

Learn more and register.



ASCD respects intellectual property rights and adheres to the laws governing them. Learn more about our permissions policy and submit your request online.

Policies and Requests

Translations Rights

Books in Translation

Sale Book (Jun 2006)

Concept-Rich Mathematics Instruction

by Meir Ben-Hur

Table of Contents


Allen, D. (Ed.). (1998). Assessing student learning: From grading to understanding. New York: Teachers College Press.

Anderson, J. R. (1995). Cognitive psychology and its implications (4th ed.). New York: W. H. Freeman and Company.

Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education (pp. 1–32), CBMS Issues in Mathematics Education (Vol. 6). In A.H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in College Mathematics Education. Providence, RI: American Mathematical Society.

Atkinson, R., & Shiffrin, M. (1968). Human memory: A proposed system and its control processes. In G. H. Bower & J. T. Spence (Eds.), The psychology of learning and motivation: Advances in theory and research (Vol. 2). New York: Academic Press.

Baird, J. R., Fensham, P. J., Gunstone, R. F., & White, R. T. (1991). The importance of reflection in improving science teaching and learning. Journal of Research in Science Teaching, 28(2), 163–182.

Ball, D. L., & Bass, H. (2000). Making believe: The construction of public mathematical knowledge in the elementary classroom. In D. Phillips (Ed.), Constructivism in education (pp. 193–224). Chicago: University of Chicago Press.

Bartsch, R. (1998). Dynamic conceptual semantics: A logico-philosophical investigation into concept formation and understanding. Stanford, CA: CSLI Publications.

Baxter, J. (1989). Children's understanding of familiar astronomical events. International Journal of Science Education, 11(5), 502–512.

Beeth, M. E. (1993, April). Classroom environment and conceptual change instruction. Paper presented at the annual meeting of the National Association of Research in Science Teaching, Atlanta, GA.

Bell, A. W., Fischbein, E., & Greer, B. (1984). Choice of operation in verbal arithmetic problem: The effects of number size, problem structure and content. Educational Studies in Mathematics, 15(2), 129–147.

Ben-Hur, M. (Ed). (1994) On Feuerstein's Instrumental Enrichment: A collection. Arlington Heights, IL.:IRI/SkyLight Training and Publishing, Inc.

Ben-Hur, M. (2004). Forming early concepts of mathematics: A manual for successful mathematics teaching. Glencoe, IL: International Renewal Institute, Inc.

Ben-Hur, M. (2004). Investigating the big ideas of arithmetic: A manual for successful mathematics teaching. Glencoe, IL: International Renewal Institute, Inc.

Ben-Hur, M. (2004). Overcoming the challenge of geometry: A manual for successful mathematics teaching. Glencoe, IL: International Renewal Institute, Inc.

Ben-Hur, M. (2004). Making algebra accessible to all: A manual for successful mathematics teaching. Glencoe, IL: International Renewal Institute, Inc.

Ben-Hur, M. (2004). Mediating probability and statistics: A manual for successful mathematics teaching. Glencoe, IL: International Renewal Institute, Inc.

Biggs, J., & Collins, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.

Blythe, T., Allen, D., & Powell, B. S. (1999). Looking together at student work: A companion guide to assessing student learning. New York: Teachers College Press.

Borovcnik, M., & Bentz, H. J. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 73–105). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(1), 155–192.

Bruner, J. (1991). Acts of meaning. Cambridge, MA: Harvard University Press.

Bunge, M. (1962). Intuition and science. New York: Prentice-Hall.

Byrnes, J., & Wasik, B. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777–786.

Campbell, K. J., Collis, K. F., & Watson, J. M. (1993). Multimodal functioning during mathematical problem solving. In B. Atweh, C. Kanes, M. Carss, & G. Booker (Eds.), Contexts in mathematics education (pp. 147–151). Brisbane, Australia: Mathematics Education Research Group of Australasia.

Campbell, K. J., Collis, K. F., & Watson, J. M. (1995). Visual processing during mathematical problem solving. Educational Studies in Mathematics, 28(2), 177–194.

Carpenter, T. P. (1989). Teaching as problem solving. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp.187–202). Reston, VA: National Council of Teachers of Mathematics.

Carpenter, T. P., Ansel, E., Franke, M. L., Fennema, E., & Wiesbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem-solving processes. Journal for Research in Mathematics Education, 24(5), 428–441.

Carpenter, T. P., Fennema, E., Franke, M. L., Empson, S. B., & Levy, L. W. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.

Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19–32). Mahwah, NJ: Lawrence Erlbaum Associates.

Case, R. (1974). Structures and strictures: Some functional limitations on the course of cognitive growth. Cognitive Psychology, 6(4), 544–574.

Cawley, J. F., Fitzmaurice-Hayes, A. M., & Shaw, R. A. (1988). Mathematics for the mildly handicapped: A guide to curriculum and instruction (p. 174). Boston: Allyn and Bacon.

Clement, J. (1993). Using bridging analogies and anchoring intuitions to deal with students' preconceptions in physics. Journal of Research in Science Teaching, 30(10), 1241–1257.

Columba, L., & Dolgos, K. A. (1995). Portfolio assessment in mathematics. Reading Improvement, 32(3), 174–176.

Cook, M. (2001). Mathematics: The thinking arena for problem-solving. In A. Costa (Ed.), Developing minds (3rd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Cooperative Learning Center at the University of Minnesota, codirected by Johnson and Johnson. Available:

Corbett, H. D., & Wilson, B. L. (1991). Testing, reform and rebellion. Norwood, NJ: Ablex Publishing Corporation.

Curio, F. R., & Schwartz, S. L. (1998, September). There are no algorithms for teaching algorithms. Teaching Children Mathematics, 5(1), 26.

Davis, G. E., & Tall, D. O. (2002). What is a scheme? In D. O. Tall (Ed.), Intelligence, learning and understanding in mathematics (pp. 133–137). Flaxton, Australia: Post Press.

Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Norwood, NJ: Albex.

DeBono, E. (1985). Six thinking hats. New York: Little, Brown and Company.

De Lisi, R., & Golbeck, S. (1999). The implications of Piagetian theory for peer learning. In A. M. O'Donnell & A. King (Eds.), Cognitive perspectives on peer learning (pp. 3–37). Mahwah, NJ: Lawrence Erlbaum Associates.

Derry, S. J., Levin, J. R., Osana, H. P., & Jones, M. S. (1998). Developing middle school students' statistical reasoning through simulation gaming. In S. J. Lajoie (Ed.), Reflections on statistics: Agendas for learning, teaching, and assessment in K–12. Mahwah, NJ: Lawrence Erlbaum Associates.

Dewey, J. (1933). How we think. Chicago: Henry Regnery.

Dienes, Z. P. (1960). Building up mathematics. London: Hutchinson.

Dillon, J. T. (1988). The remedial status of student questioning. Journal of Curriculum, 20(3), 197–210.

Echevarria, J., & Graves, A. (1998). Sheltered content instruction: Teaching English-language learners with diverse abilities (p. 35). Boston: Allyn and Bacon.

Ellis, A. K. (Ed.) (2001). Research on educational innovations (p. 105). New York: Eye on Education, Inc.

Ellis, K. A. (2001). Research on educational innovations (3rd ed., pp. 86–91). New York: Eye on Education, Inc..

England, D. A., & Flatley, J. K. (1985). Homework—and why (PDK Fastback No. 218). Bloomington, IN: Phi Delta Kappa Educational Foundation.

Feuerstein, R. (1980). Instrumental enrichment: Intervention program for cognitive modifiability. Baltimore, MD: University Park Press.

Feuerstein, R., Rand, Y., Hoffman, M. B., & Miller, R. (1994). In M. Ben-Hur (Ed.), Feuerstein's instrumental enrichment. Arlington Heights, IL: SkyLight.

Feuerstein, R., Feuerstein R., & Schur, Y. (1997). Process and content in education, particularly for retarded performers. In A. Costa & R. Liberman (Eds.), Supporting the spirit of learning: When process is content. Thousand Oaks, CA: Corwin Press.

Feuerstein, R., & Rand, Y. (1997). Don't accept me as I am (Rev. ed., pp. 337–339). Arlington Heights, IL: SkyLight.

Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving problems in multiplication and division. Journal of Research in Mathematics Education, 16(1), 3–17.

Fullan, M. (2000). The return of large-scale reform. Journal of Educational Change, 1(1), 1–23.

Fuson, K. C., & Kwon, Y. (1992). Korean children's understanding of multidigit addition and subtraction. Child Development, 63(2), 491–506.

Gange, R. M. (1985). The conditions of learning and theory of instruction (4th ed.). New York: Holt, Rinehart and Winston.

Geary, D. C. (1994). Children's mathematical development: Research and practical implications. Washington, DC: American Psychological Association.

Gelman, R. (2000). The epigenesis of mathematical thinking. Journal of Applied Developmental Psychology, 21(1), 27–37.

Gleitman, L., Carey, S., Newport, E., & Spelke, E. (1989). Learning, development, and conceptual change. A Bradford Book. Cambridge, MA: MIT Press.

Good, T. L., & Brophy, J. E. (2000). Looking in classrooms (8th ed.). New York: Longman.

Good, T. L., & Grouws, D. A. (1979). Teaching and mathematics learning. Educational Leadership, 37(1), 39–45.

Grasser, C. A., & McMahen, C. L. (1993). Anomalous information triggers questions when adults solve quantitative problems and comprehend stories. Journal of Educational Psychology, 5(1), 130–151.

Grasser, C. A., & Person, N. K. (1994). Question asking during tutoring. American Education Research Journal, 31(1), 104–137.

Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal fur Mathematikdidatik, 21(2), 139–157.

Harris, J. R. (1998). The nature of assumption: Why children turn out the way they do? New York: The Free Press and Simon & Schuster.

Hert, K. M. (1981). Children's understanding of mathematics (pp. 11–16). London: John Murray.

Hewson, P. W., & Hewson, M. G. (1989). Analysis and use of a task for identifying conceptions of teaching science. Journal of Education for Teaching, 15(3), 191–209.

Hewson, P.W., & Thorley, N. R. (1989). The conditions of conceptual change in the classroom. International Journal of Science Education, 11(5), 541–553.

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook on research in mathematics teaching and learning. New York: Macmillan.

Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 199–223). Hillsdale, NJ: Erlbaum.

Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer.

Jungck, J. R., & Calley, J. N. (1985). Strategic simulations and post-Socratic pedagogy: Constructing software to develop long term inference through experimental inquiry. American Biology Teacher, 47(1), 11–15.

Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press.

Kerman, S., & Martin, M. (1980). Teacher expectations and student achievement: Teacher handbook. Bloomington, IN: Phi Delta Kappa.

Kerslake, D. (1986). Fractions: Children's strategy and errors: A report of the Strategies and Errors in Secondary Mathematics Project. Windsor, Berkshire, England: NFER-Nelson.

Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.). (2003). A research companion to principals and standards for school mathematics (p. 225). Reston, VA: National Council of Teachers of Mathematics.

Kilpatrick, J., Swafford, J., & Bradford, F. (2001). Adding it up: Helping children learn mathematics. Washington, DC: Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council, and National Academy Press.

Koedinger, K. R., & Nathan, M. J. (1994). The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 12(2). Available:

Konold, C. (1989). Informal concepts of probability. Cognition and Instruction, 6(1), 59–98.

Konold, C. (1991). Understanding students' beliefs about probability. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 139–156). Dordrecht, The Netherlands: Reidel.

Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2(1), 1–23.

Kozulin, A., Mangieri, J. N., & Block, C. (Eds.). (1994). The cognitive revolution in learning in creating powerful thinking in teachers and students: Diverse perspectives. New York: Harcourt Brace College Publishers.

Kramarski, B., & Mevarech, Z. R. (1997). Cognitive-metacognitive training within a problem solving based Logo environment. British Journal of Educational Psychology, 67(4), 425–445.

LaConte, R. T. (1981). Homework as a learning experience: What research says to the teacher. Washington, DC: National Education Association (ED 217 022).

Larrivee, B. (2000). Transforming teaching practice: Becoming the critically reflective teacher. Reflective Practice, 1(3), 293–308.

Lehman, D. R., Lempert, R. O., & Nisbett, R. E. (1988). The effects of graduate training on reasoning: Formal discipline and reasoning about everyday life. American Psychologist, 43(6), 431–443.

Lester, F. K., Jr., Masingila, J. O., Mau, S. T., Lambdin, D. V., dos Santon, V. M., & Raymond, A. M. (1994). Learning how to teach via problem solving (pp. 152–166). In D. Aichele & A. Coxford (Eds.), Professional Development for Teachers of Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Lindsay, C. H., Greathouse, S., & Nye, B. (1988). Relationships among attitudes about homework, amount of homework assigned and completed, and student achievement. Journal of Educational Psychology, 90(1), 154.

Lipman, M. (1984). The cultivation of reasoning through philosophy. Educational Leadership, 42(1), 51–56.

Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense: Large numbers discrimination in human infants. Psychological Science, 4(5), 396–401.

Lochhead, J., & Zietsman, A. (2001). What is problem-solving? In A. Costa (Ed.), Developing minds (3rd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Long, M., & Ben-Hur, M. (1991). Informing learning through the clinical interview. Arithmetic Teacher, February, 44–47.

Marzano, R. J., Pickering, D. J., & Pollak, J. E. (2005). Classroom instruction that works: Research-based strategies for increasing student achievement. Upper Saddle River, NJ: Merrill Prentice-Hall.

Mason, J. (1993). Assessing what sense pupils make of mathematics. In M. Selinger (Ed.), Teaching mathematics (pp. 153–166). London: Routledge.

A Math Forum Project Elementary Problem of the Week: April 19, 1999. Good Fences—posted April 26, 1999. Available:

Mayer, R. (2000). Intelligence and education. In R. Sternberg (Ed.), Handbook of intelligence (pp. 519–533). Cambridge, MA: Cambridge University Press.

Mayer, R. E., & Wittrock, M. C. (1996). Problem solving transfer. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 47–62). New York: Macmillan.

Mevarech, Z. R., & Susak, Z. (1993, March/April). Effects of learning with cooperative-mastery learning method on elementary students. Journal of Educational Research, 86, 197–205.

Miller, A. (1996). Insights of genius: Imagery and creativity in science and art. New York: Springer-Verlag.

Minsky, M. L. (1975). A framework for representing knowledge. In O. H. Winston (Ed.), The psychology of computer vision (pp. 211–277). New York: McGraw-Hill.

Morris, A. (1999). Developing concepts of mathematical structure: Prearithmetic reasoning vs. extended arithmetic reasoning. Focus on Learning Problems in Mathematics, 21(1), 44–71.

Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebraic development. Cognition and Instruction, 18(2), 209–237.

National Commission on Mathematics and Science Teaching for the 21st Century (The Glenn Commission). Press Release. Sept. 27, 2000.

National Council of Teachers of Mathematics (NCTM). (1989). Professional standards for teachers of mathematics. Reston, VA: Author.

Nesher, P. (1986). Are mathematical understanding and algorithmic performance related? Learning of Mathematics, 6(3), 2–9.

Nesher, P., & Hershkovitz, S. (1994). The role of schemes in two-step problems: Analysis and research finding. Educational Studies in Mathematics, 26(1), 1–23.

Neuman, Y., & Schwarz, B. (2000). Substituting one mystery for another: The role of self-explanations in solving algebra word-problems. Learning and Instruction, 10(3), 203–220.

Nisbett, R. E., Fong, G. T., Lehman, D. R., & Cheng, P. W. (1987). Teaching reasoning. Science, 238(4827), 625–631.

Novak, J. D. (1977). A theory of education. Ithaca, NY: Cornell University Press.

Novak, J. D. (1990). Concept maps and Vee diagrams: Two metacognitive tools for science and mathematics education. Instructional Science, 19(1), 29–52.

Nussbaum, J. (1985). The earth as a cosmic body. In R. Diver, E. Guesne, and A. Tiberghien (Eds.), Children's ideas in science (pp. 170–192). Milton Keynes, UK: Open University Press.

O'Day, J. A., & Smith, M. (1993). Systemic school reform and educational opportunity. In S. Fuhrman (Ed.), Designing coherent educational policy: Improving the system (pp. 250–311). San Francisco: Jossey-Bass.

Palincsar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension fostering and comprehension monitoring activities. Cognition and Instruction, 1(2), 117–175.

Palincsar, A. S., & Brown, A. L. (1985). Reciprocal teaching: Activities to promote reading with your mind. In T. L. Harris & E. J. Cooper (Eds.), Reading and concept development: Strategies for the classroom (pp. 147–160). New York: The College Board.

Piaget, J. (1995a). From science of education and the psychology of the child. In H. E. Gruber & J. J. Vonéche (Eds.), The essential Piaget: An interpretative reference and guide (pp. 703–705). Northvale, NJ, and London: Jason Aronson.

Piaget, J. (1995b). Judgment and reasoning in the child (originally published in 1924). In H. E. Gruber & J. J. Vonéche (Eds.), The essential Piaget: An interpretive reference and guide (p. 96). Northvale, NJ: Jason Aronson.

Pilkethy, A., & Hurting, R. (1996). A review of recent research in the area of Initial Fraction Concepts. Educational Studies in Mathematics, 30(1) 5–36.

Plato, Translation (1892). Meno. In B. Jowett (Trans.), The Dialogues of Plato, (3rd ed.). London: Oxford University Press.

Pólya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

Pólya, G. (1973). How to solve it. Princeton, NJ: Princeton University Press. (Originally copyrighted in 1945.)

Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal of Research in Mathematics Education, 20(1), 8–27.

Rosenshine, B., & Meister, C. C. (1994). Reciprocal teaching: A review of the research. Review of Educational Research, 6(4), 479–530.

Rowe, M. B. (1996). Science, silence, and sanctions. Science and Children, 34(1), 35–37.

Rowland, S., Graham, E., & Berry, J. (2001). An objectivist critique of relativism in mathematics education. Science & Education, 10(3), 215–241.

Schmidt, W. H., McKnight, C. C., & Raizen, S. A. (1997). A splintered vision: An investigation of U.S. science and mathematics education. Dordrecht, The Netherlands: Kluwer.

Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 190–191). Hillsdale, NJ: Lawrence Erlbaum Associates.

Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of “well taught” mathematics classes. Educational Psychologist, 23(2), 145–166.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.

Schoenfeld, A. H. (Ed.). (1994). Mathematical thinking and problem solving (p. 60). Hillsdale, NJ: Lawrence Erlbaum Associates.

Schoenfeld, A. H. (2002, January/February). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13–25.

Schoenfeld, A. H., & Herrmann, D. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning, Memory and Cognition, 8(5), 484–494.

Scholz, R. W. (1991). Psychological research in probabilistic understanding. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 213–249). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Schön, D. (1983). The reflective practitioner. New York: Basic Books

Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra, Educational Studies in Mathematics, 26(3), 191–228.

Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification: The case of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59–84). MAA Notes 25. Washington: Mathematical Association of America.

Shaughnessy, J. M. (1993). Probability and statistics. The Mathematics Teacher, 86(3), 244–248.

Shaughnessy, J. M., & Zawojewski, J. S. (1999). Secondary students' performance on data and chance in the 1996 NAEP. Mathematics Teacher, 92(8), 713–718.

Shepard, L. A., & Smith, M. L. (1988). Escalating academic demand in kindergarten: Counterproductive policies. Elementary School Journal, 89(2), 135–145.

Shepard, R. S. (1993). Writing for conceptual development in mathematics. Journal of Mathematical Behavior, 12(3), 287–293.

Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In J. Kilpatrick, W. B. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (p. 225). Reston, VA: National Council of Teachers of Mathematics.

Silver, E. A. (1979). Student perceptions of relatedness among mathematical verbal problems. Journal for Research in Mathematics Education, 10(3), 195–210.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

Silver, E. A., Alacaci, C., & Stylianou, D. A. (2000). Students' performance on extended constructed-response tasks. In E. A. Silver & P. A. Kenny (Eds.) Results from the seventh mathematics assessment of the National Assessment of Educational Progress (pp. 301–341). Reston, VA: National Council of Teachers of Mathematics.

Silver, E. A., & Cai, J. (1993). Mathematical problem posing by middle school students. Paper presented at the annual meeting of the American Educational Research Association, Atlanta, GA.

Skemp, R. R. (1962). The need for schematic learning theory. British Journal of Educational Psychology, 32(2), 133–142.

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20–26.

Skemp, R. R. (1986). The psychology of learning mathematics (2nd ed.). Middlesex, England: Plenum.

Smith, M. U. (1991). A view from biology. In M. U. Smith (Ed.), Toward a unified theory of problem solving (pp. 1–20). Hillsdale, NJ: Lawrence Erlbaum.

Smith, M., & Cohen, M. (1991, September). A national curriculum in the United States? Educational Leadership, 49(1), 74–81.

Spinelli, C. G. (2001). Interactive teaching strategies and authentic curriculum and assessment: A model for effective classroom instruction. Hong Kong Special Education Forum, 4(1), 3–12.

Staver, J. R. (1998). Constructivism: Sound theory for explicating the practice of science and science teaching. Journal of Research in Science Teaching, 35(5), 501–520.

Stein, D. (2004). Teaching critical reflection. Washington, DC: Office of Educational Research and Improvement, U.S. Department of Education. Available:

Suchting, W. A. (1986). Marx and philosophy: Three studies. Hampshire, UK: Macmillan Press Ltd.

Tall, D. (2002). Continuities and discontinuities in long-term learning schemas. In D. Tall & M. Thomas (Eds.), Intelligence, learning and understanding in mathematics: A tribute to Richard Skemp (pp. 151–178). Flaxton, Australia: Post Press.

Thorley, N. R. (1990, August). The role of conceptual change model in the interpretation of classroom interactions. Unpublished doctoral dissertation, University of Wisconsin, Madison.

University of Chicago School Math Project: Transition Mathematics. (1998). Scott Foresman integrated mathematics (2nd ed.). Glenview, IL: Scott Foresman.

Van Hiele, P. (1986). Structure and insight. A theory of mathematics education. Orlando, FL: Academic Press Inc.

Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. London: Falmer.

Von Glasersfeld, E. (1996). Introduction: Aspects of constructivism. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press.

Von Glasersfeld, E. (1998). Why constructivism must be radical. In M. Larochelle, N. Bednarz, & J. Garrison (Eds.), Constructivism and education (pp. 23–28). Cambridge, UK: Cambridge University Press.

Vygotsky, L. (1978). Mind in society. Cambridge, MA: Harvard University Press.

Vygotsky, L. S. (1986). Thought and language (A. Kozulin, Trans. and Ed.). Cambridge, MA: MIT Press.

Walberg, H. J., Paschal, R. A., & Weinstein, T. (1985, April). Homework's powerful effects on learning. Educational Leadership, 42(7), 76–79.

Watanabe, T. (2002). Learning from Japanese lesson study. Educational Leadership, 59(6), 36–39.

Wiggins, G. (1990). The case for authentic assessment. Practical Assessment, Research & Evaluation, 2(2). Available:

Wilson, L. D., & Blank, R. K. (1999). Improving mathematics education using results from NAEP and TIMMS. Washington, DC: Council of Chief State School Officers. Available: [July 10, 2001].


Log in to submit a comment.

To post a comment, please log in above. (You must be an ASCD EDge community member.) Free registration