References and Research Basis for CMET

 

Baek, J. (1998). Children's invented algorithms for multi-digit multiplication problems.  In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 151-160).  Reston, VA:  NCTM

 

Bezuk, N. S. (1988).  Fractions in the early childhood mathematics curriculum. Arithmetic Teacher, 35(6), 56-60.

 

Brandsford, J., Brown, A., & Cocking, R. (1999). How People Learn:  Brain, Mind, Experience, and School. Washington, D.C: National Academy Press.

 

Caliandro, C. K. (2000).  Children's inventions for multi-digit multiplication and division.  Teaching Children Mathematics, 6, 420-424, 426.

 

Carpenter, T. P., Fennema, E. & Franke, M.L. (1996).  Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. Elementary School Journal 97, 3-20.

 

Charles, K., & Nason, R. (2000).   Young children's partitioning strategies. Educational Studies in Mathematics, 43, 191-221.

 

Clark, F. B., & Kamii, C. (1996).  Identification of multiplicative thinking in children in grades 1-5.  Journal for Research in Mathematics Education, 27, 41-51.

 

Cobb, P., & Wheatley, G. (1998).  Children's initial understanding of ten.  Focus on Learning Problems in Mathematics, 10(3), 1-28.

 

Cobb, P., Wood, T., & Yackel, E. (1991).  A Constructivist approach to second grade mathematics.  In E. von Glasersfeld (Ed.), Constructivism in Mathematics Education. Dordrecht, Holland: Reidel.

 

Cramer, K., Post, T., & delMas, R. (2002).  Initial fraction learning by fourth- and fifth-grade students:  A comparison of the effects of using commercial curricula with the effects of using the Rational Number Project Curriculum. Journal for Research in Mathematics Education 33(2), 111-144.

 

Fuson, K. (1998). Children's counting and concepts on number. New York: Springer-Verlag.

 

Gravemeijer, K. (1994). Developing Realistic Mathematics Education. Utrecht:  CD-b Press.

 

Kamii, C. & Housman, L. (1999).  Young Children Reinvent Arithmetic: Implications of Piaget’s theory,  2nd ed. New York: Teachers College Press.

 

Madell, R. (1985). Children's natural processes. Arithmetic Teacher, 32(7), 20-22.

 

National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.

 

National Council of Teachers of Mathematics (1991). Professional Standards for Teaching Mathematics. Reston, VA: NCTM.

 

National Council of Teachers of Mathematics (1995). Assessment Standards for School Mathematics. Reston, VA: NCTM.

 

National Council of Teachers of Mathematics (2000). Principles and  Standards for School Mathematics. Reston, VA: NCTM.

 

National Research Council (CRMSTE) (1985). Mathematics, Science, and Technology Education: A Research Agenda. Washington, DC.

 

National Research Council (1985). Adding it up:  Helping children learn mathematics. J. Kilatrick, J. Swafford, and B. Findell (Eds.),  Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

 

Olive, J. (2002). Bridging the gap: Using interactive computer tools to build fraction schemes.  Teaching Children Mathematics, 8, 356-361.

 

The Open University. (1988). Stuck. London: Open University.

 

Piaget, J. (1987).  Possibility and Necessity. Minneapolis: University of Minnesota Press.  (Original work published 1983).

 

Piaget, J. (1945/1962).  Play, Dreams, and Imitation in Childhood.  New York:  Norton.

 

Pothier, Y., & Sawada, D.  (1990). Partioning: An approach to fractions. Arithmetic Teacher, 38(4), 12-16.

 

Reid, D.A. (2002). Conjectures and Refutations in grade 5 mathematics. Journal for Research in Mathematics Education 33, No. 1, 5-29.

 

Sáenz-Ludlow, A. (1994). Michael's fraction schemes. Journal for Research in Mathematics Education 25, 50-85.

 

Sáenz-Ludlow, A. (1995). Ann's fraction schemes. Educational Studies in Mathematics, 28, 101-132.

 

Schifter, D. (1997, March).  Developing operation sense as a foundation for algebra.  A paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

 

Sfard, A. (1994).  Reification as the birth of metaphor.  For  the Learning of Mathematics, 1,

            44-55.

 

Sinclair, A., Siegrist, F., & Sinclir, H. 19835).  Young children's ideas about the written number system.  In D. Rogers & J. A. Sloboda (Eds.), The Acquisition of symbolic skills.  (pp. 535-541).  New York:  Plenum.

 

Steffe, L. P. (1992).  Schemes of action and operation involving composite units.  Learning and individual Differences,4, 259-309.

 

Steffe, L., & Killion, K. (1989).  Research into practice:  Children's multiplication.  Arithmetic Teacher, 37, 34-36.

 

Steffe, L. P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children's counting types:  Philosophy, theory and application. New York: Praeger Scientific.

 

Suydam, M. (1987). Indications from Research on Problem Solving.  In F. Curcio (Ed.), Teaching and Learning: A Problems Solving Focus. Reston, VA: NCTM.

 

Tirosh, D. (2000). Enhancing prospective teacher’s knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31, 5-25.

 

von Glasersfeld, E. (1995). Radical Constructivism. London, UK: Falmer Press.

 

Wheatley, G. & Reynolds, A. (1999). Coming to Know Number. Tallahassee, FL: Mathematics Learning.

 

Warrington, M. & Kamii, C. (1998). Multiplication with fractions: A Piagetian, constructivist approach.  Mathematics Teaching in the Middle School, 3, 339-343.