The vast majority of the lessons in this site were piloted in middle school classrooms over a three year period. The lessons were then refined based on student performance and, in many cases, piloted again. In addition to what we have learned from our field tests, we draw on a wider framework for each instructional strand.
The following references are a sample of research studies and curriculum materials that are related to: 1) conceptual approaches to mathematics 2) integrated instruction where students work on complex, "ill-defined" problems and 3) writing as a method for enhanced understanding. This list is far from exhaustive, but we feel that it is useful for those interested in the research that supports the materials in this site.
Math Concepts Strand
Bennett, A., Maier, E., & Nelson, T. (1994). Math in the mind's eye: Modeling rationals. Salem, OR: Math Learning Center.
Bottge, B., & Hasselbring, T. (1993). A comparison of two approaches for teaching complex, authentic mathematics problems to adolescents in remedial math classes. Exceptional Children, 59(6), 556-545.
Carpenter, T., & Fennema, E. (1991). Research and cognitively guided instruction. In E. Fennema, T. Carpenter, & S. Lamon (Eds.), Integrating research on teaching and learning mathematics. (pp. 1-17). Albany, NY: State University of New York Press.
Carpenter, T., Fennema, E., & Romberg, T. (1993). Rational numbers: An integration of research. Hillsdale, NJ: Erlbaum.
Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In E. Forman, N. Minick, & C. Stone (Eds.), Contexts for learning: Sociocultural dynamics in children's development (pp. 91-119). New York: Oxford University Press.
Grouws, D. (1992). Handbook of research on mathematics teaching and learning. New York: Maxwell Macmillan.
Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
Hiebert, J., & Behr, M. (1988). Number concepts and operations in the middle grades. (Vol. 2). Reston, VA: The National Council of Teachers of Mathematics, Inc.
Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics research and teaching. (pp. 65-100). New York: MacMillan.
Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Erlbaum.
Lappan, G., & Ferrini-Mundy, J. (1993). Knowing and doing mathematics: A new vision for middle school students. Elementary School Journal, 93(5), 625-641.
Lappan, G., Fitzgerald, S., Friel, S., Fey, J., & Phillips, E. (1996). Connected mathematics. White Plains, NY: Dale Seymour Publications.
Leinhardt, G., & Smith, D. (1985). Expertise in mathematics knowledge: Subject matter knowledge. Journal of Educational Psychology, 77(3), 247-271.
Leinhardt, G., Putnam, R., & Hattrup, R. (1992). Analysis of arithmetic for mathematics teaching. Hillsdale, NJ: Erlbaum.
Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics. (pp. 41-58). Hillsdale, NJ: LEA.
Montague, M. (1995). Cognitive instruction and mathematics: Implications for students with learning disorders. Focus on learning problems in mathematics, 17(2), 39-49.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
Nesher, P. (1986). Are mathematical understanding and algorithmic performance related? For the Learning of Mathematics, 6(3), 2-8.
Parmar, R., & Cawley, J. (1995). Mathematics curricula frameworks: Goals for general and special education. Focus on learning problems in mathematics, 17(2), 50-66.
Putnam, R., Lampert, M., & Peterson, P. (1990). Alternative perspectives on knowing mathematics in elementary schools. In C. Cazden (Ed.), Review of Research in Education (Vol. 16, pp. 57-149). Washington, D.C.: American Educational Research Association.
Resnick, L. (1989). Developing mathematical knowledge. American Psychologist, 44(2), 162-169.
Resnick, L., Bill, V., & Lesgold, S. (1992). Development of thinking abilities in arithmetic class. In A. Demetriou, M. Shayer, & A. Efklides (Eds.), Neo-piagetian theories of cognitive development: Implications and applications for education. (pp. 210-230). London: Routledge.
Romberg, T. (1992). Mathematics learning and teaching: What we have learned in ten years. In C. Collins & J. Mangieri (Eds.), Teaching thinking: Agenda for the twenty-first century (pp. 43-64). Hillsdale, NJ: Erlbaum.
Romberg, T. (1995). Reform in school mathematics and authentic assessment. Albany, NY: State University of New York Press.
Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. (pp. 334-370). New York: MacMillan.
Skemp, R. (1987). The psychology of learning mathematics. Hillsdale, NJ: LEA.
Stein, M., Grover, B., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 489-509.
Woodward, J., Baxter, J., & Robinson, R. (1997, ). Rules and reasons: Decimal instruction for academically low achieving students. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, Il.
Woodward, J., Baxter, J., & Scheel, C. (1997). It's what you take for granted when you try to take nothing for granted. In T. Scruggs & M. Mastropieri (Eds.), Advances in learning and behavioral disorders (Vol. 11, ). New York: JAI Press.
Integrated Lessons Strand
Bos, C. S., & Anders, P. L. (Ed.). (1990). Interactive teaching and learning: Instructional practices for teaching content and strategic knowledge. New York: Springer-Verlag.
Bransford, J., Sherwood, R., Vye, N., & Rieser, J. (1986). Teaching thinking and problem solving. American Psychologist, 41, 1078-1089.
Bransford, J., Sherwood, R., Hasselbring, T., Kinzer, C., & Williams, S. (1990). Anchored instruction: Why we need it and how technology can help. In D. Nix & R. Spiro (Eds.), Cognition, education, and multimedia: Exploring ideas in high technology. (pp. 115-142). Hillsdale, NJ: Erlbaum.
Cognition and Technology Group at Vanderbilt. (1990). Anchored instruction and its relationship to situated cognition. Educational Researcher, 19(6), 2-10.
Cohen, D., McLaughlin, M., & Talbert, J. (1993). Teaching for understanding. San Francisco: Jossey-Bass.
Collins, A., Brown, J., & Newman, S. (1989). Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In L. Resnick (Ed.), Knowing, learning, and instruction. (pp. 453-494). Hillsdale, NJ: Erlbaum.
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-21.
Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.
Means, B., Chelemer, C., & Knapp, M. (1991). Teaching advanced skills to at-risk students. San Francisco: Jossey-Bass.
Newman, D., Griffin, P., & Cole, M. (1993). The construction zone: Working for cognitive change in school. Cambridge: Cambridge University Press.
Prawat, R. (1991). The value of ideas: The immersion approach to the development of thinking. Educational Researcher, 20(2), 3-10.
Raizen, S. (1989). Reforming education for work: A cognitive science perspective. Berkeley, CA: National Center for Research in Vocational Education.
Tharp, R., & Gallimore, R. (1988). Rousing minds to life: Teaching, learning, and schooling in social context. New York: Cambridge University Press.
Barnett, C., Goldenstein, D., & Jackson, B. (1994). Fractions, decimals, rations, and percents: How hard to teach and how hard to learn? Portsmouth, NH: Heinemann.
Burns, M. (1995). Writing in math class. White Plains, NY: Math Solutions Publications.
Connolly, P. & Vilardi, T. (1989). Writing to learn mathematics and science. Teachers College Press.
Corwin, R., Storeygard, J., & Price, S. (1996). Talking mathematics: Supporting children's voices. Portsmouth, NH: Heinemann.
Countryman, J. (1992). Writing to learn mathematics. Portsmouth, NH: Heinemann.
Englert, C., Raphael, T., & Anderson, L. (1992). Socially mediated instruction: Improving students' knowledge and talk about writing. Elementary School Journal, 92(4), 411-449.
Englert, C., Raphael, T., Anderson, L., Anthony, H., & Stevens, D. (1991). Making strategies and self-talk visible: Writing instruction in regular and special education classrooms. American Educational Research Journal, 28(2), 337-372.
Flower, L., & Hayes, J. (1980). The dynamics of composing: Making plans and juggling constraints. In L. Gregg & E. Steinberg (Eds.), Cognitive processes in writing. (pp. 31-50). Hillsdale, NJ: LEA.
Fulwiler, T. (1987). Teaching with writing. Portsmouth, NH: Heinemann.
Harris, K., & Graham, S. (1996). Making the writing process work: Strategies for composition and self-regulation. Cambridge, MA: Brookline Books.
Langer, J. & Applebee, A. (1987). How writing shapes thinking: A study of teaching and learning. National Council of Teachers of English.
Mayher, J., Lester, N. & Pradl, G. (1983). Learning to write/writing to learn. Portsmouth, NH: Heinemann.
Miller, L., & England, D. (1989). Writing to learn algebra. School Science and Mathematics, 89, 299-311.
Nahrgang, C., & Peterson, B. (1986). Using writing to learn mathematics. Arithmetic Teacher, 79, 461-465.
Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge & Kegan Paul.
Raphael, T. & Englert, C. (1990). Writing and reading: partners in constructing meaning. The Reading Teacher (February), pp. 388-400.
Rivard, L. (1994). A review of writing to learn science: Implications for practice and research. Journal of Research in Science Teaching, 31 (9), pp. 969-983.
Zinsser, W. (1985). On writing well. (3rd Ed). New York: Harper & Row Publishers.