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: http://www.clcrc.com/index.html#essays.

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: http://www.shodor.org/interactivate/lessons/.

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:
http://mathforum.org/elempow/solutions/solution.ehtml?puzzle=32.

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: http://ericacve.org.

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:
http://ericae.net/pre/getvn.asp?v=2&n=2.

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:
http://publications.ccsso.org/ccsso/publications_detail.cfm?PID=212. [July 10, 2001].

*The Core Six: Essential Strategies for Achieving Excellence with the Common Core**Engaging Students with Poverty in Mind: Practical**Better Learning Through Structured Teaching**The Differentiated Classroom: Responding to the Needs of All Learners, 2nd Edition**The Understanding by Design Guide to Creating High-Quality Units*