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.

__Journaling Strand__

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.