• Anderson, C.W., & Smith, E.L. (1987). Teaching science. In Richardson-Koehler, V. (Ed.), Educators’ Handbook: A Research Perspective (pp. 84-111). New York, NY: Longman, Inc.
• Anderson, J.R. (1976). Language, Memory, and Thought. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Anderson, J.R. (2002). Spanning seven orders of magnitude: A challenge for cognitive modeling. Cognitive Science, 26, 85-112.
• Ashlock, R.B. (2002). Error Patterns in Computation: Using Error Patterns to Improve Instruction. Upper Saddle River, NJ: Prentice Hall.
• Ausubel, D.P. (1968). Educational Psychology: A Cognitive View. New York, NY: Holt, Rinehart and Winston.
• Ball, L.D. (1992). Magical hope: Manipulatives and the reform of mathematics Education. American Educator, 16 (2), 14-18.
• Ball, L.D. (2003). Mathematics Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education. Santa Monica, CA: RAND Corporation.
• Barcellos, A. (2005). Mathematics misconceptions of college-age algebra students. PhD dissertation, University of California at Davis, CA.
• Behr, M., Erlwanger, S., & Nichols, E. (1980). How the children view the equals sign. Mathematics Teaching, 92, 13-15.
• Booth, L.R. (1984). Algebra: Children’s Strategies and Errors. Windsor, England: NFER-Nelson.
• Booth, L.R. (1988). Children’s difficulties in beginning algebra. In A.F. Coxford & A.P. Shulte (Eds.), The Ideas of Algebra, K-12 (pp. 20-32). Reston, VA: NCTM.
• Brown, J.S., & Burton, R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155-192.
• Brown, J.S., & VanLehn, K. (1980). A generative theory of bugs in procedural skills, Cognitive Science, 4 (4), 349-377.
• Brown, J.S., & VanLehn, K. (1982). Toward a generative theory of “bugs”. In T.P. Carpenter, J.M. Moser, & T.A. Romberg (Eds.), Addition and Subtraction: A Cognitive Perspective (pp. 117-135). Hillsdale, NJ: Lawrence Erlbaum Association, Inc.
• Bruner, J. (1960). The Process of Education. Cambridge, MA: Harvard University Press.
• Butler, F., Miller, S., Crehan K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research and Practice, 18, 99-111.
• Capraro, M., Capraro, R., Harbaugh, A., Kulm, G., Sebesta, L., Sun, Y., et al. (2004). Representational models for the teaching and learning of mathematics. Paper Presented at the Annual Conference of National Council of Teachers of Mathematics, Philddelphia, PA.
• Carpenter, T.P., Franke, L.P., & Levi, L. (2003). Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Portsmouth, NH: Heinemann.
• Chi, M.T. (1997). Creativity: Shifting across ontological categories flexibly. In T.B. Ward, S.M. Smith, R.A. Finke & J. Vaid (Eds.), Creative Thought: An Investigation of Conceptual Structures and Processes (pp. 209-234). Washington, DC: American Psychological Association.
• Chi, M.T. (2005). Commonsense conceptions of emergent process: Why some misconceptions are robust. The Journal of the Learning Science, 14, 161-199.
• Chi, M.T., & Roscoe, R.D. (2002). The processes and challenges of conceptual change. In M. Limon & L. Mason (Eds.), Reforming the Process of Conceptual Change: Integrating Theory and Practice (pp. 3-27), Dordrecht, The Netherlands: Kluwer Academic.
• Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13, 16-30.
• Clement, J., Lochhead, J., & Monk, G. (1981). Translation difficulties in learning mathematics. The American Mathematical Monthly, 8, 286-290.
• Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of Research in Education, 16, 3-56.
• Cuban. L. (1984), How Teachers Taught. New York, NY: Longman.
• Davis, R.B., & Vinner, S. (1986). The notion of limit: Some seemingly unavoidable misconception stages. Journal of Mathematics Behavior, 5, 281-303.
• Ding, M., Li, X., Capraro, M.M., & Kulm, G. (2006). Teacher Responses to Students’ Errors in Transition from Verbal to Symbolic Representation. New York, NY: Basic Books.
• Dubinsky, E. (1995). After examples and before proofs: Constructing mental objects. PhD dissertation, Purdue University: West Lafayette, IN.
• Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In G. Harel & E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy (pp. 85-106). Washington, DC: Mathematical Association of America.
• Ernest, P. (1991). The Philosophy of Mathematics Education. London: Farmer.
• Erlwanger, S.H. (1973). Benny’s conception of rules and answers in IPI mathematics, Journal of Children’s Mathematical Behavior, 1 (2), 7-26.
• Falkner, K.P., Levi, L., & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232-236.
• Gilbert, J.K., Osborne, R.J., & Fensham, P.J. (1982). Children’s science and its consequences for teaching. Science Education, 66, 623-633.
• Graham, A.T. & Thomas, M.O. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41, 265-282.
• Hammer, D. (1996). Misconceptions or P-Primes: How may alternative perspectives of cognitive structure influence instructional perceptions and intentions? The Journal of the Learning Science, 5, 97-127.
• Harper, E. (1979). The child’s interpretation of a numerical variable. PhD dissertation, University of Bath, England.
• Harper, E. (1987). Ghosts of Diophantus. Educational Studies in Mathematics, 18, 75-90.
• Hart, K. (1981). Children's Understanding of Mathematics: 11–16. London: Murray.
• Haverty, L.A. (1999). The importance of basic number knowledge to advanced mathematical problem solving. PhD dissertation, Carnegie Mellon University, Pittsburgh, PA.
• Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra (pp. 60-86). Reston, VA: National Council of Teachers of Mathematics.
• Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introduction analysis. In J. Hiebert. (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 1-28). London: Lawrence Erlbaum.
• Hibert, J., & Capenter, T.P. (1992). Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65-97). New York, NY: Macmillan.
• Jourdain, P.E. (1956). The nature of mathematics. In J.R. Newman, (Ed.), The Work of Mathematics. New York, NY: Simon and Schuster.
• Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
• Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York, NY: Macmillan.
• Kilpartick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics: Report of the Mathematics Learning Study Committee. Washington, DC: National Research Council, National Academy Press.
• Knuth, E., Stephens, A., McNeil, N.M., & Alibali, M.W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37, 197-312.
• Kulm, G. (2004). Content alignment of test items necessity and sufficiency criteria. Paper Presented at the Annual Meeting of the American Educational Research Association. San Diego, CA.
• Labaree, D. (1992). Power, knowledge and the rationalization of teaching: A genealogy of the movement to professionalize teaching. Harvard Educational Review, 62, 123-154.
• Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
• MacGregor, M., & Stacey, K. (1993). Cognitive models underlying students’ formulation of simple linear equations. Journal for Research in Mathematics Education, 24, 217-232.
• MacGregor, M., &. Stacey, K. (1997). Students’ understanding of algebraic notation. Educational Studies in Mathematics, 33, 1-19.
• Matz, M. (1982). Towards a process model for school algebra error. In D. Sleeman & J.S. Brown (Eds.), Intelligent Tutoring Systems (pp. 25-50). New York, NY: Academic Press.
• McNeil, N.M., & Alibali, M.W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance. Child Development, 76, 1-17.
• Moses, B. (1999). Algebraic Thinking, Grades K-12. Reston, VA: National Council of Teachers of Mathematics.
• Moyer, P.S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.
• National Council of Teachers of Mathematics. (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: the author.
• Newman, M.A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In M.A. Clements, & J. Foyster (Eds.), Research in Mathematics Education in Australia (Vol. 2, pp. 239-258). Melbourne, Australia: Swineburne Press.
• Payne, S.J. & Squibb, H.R. (1990). Algebra mal-rules and cognitive accounts of error. Cognitive Science, 14, 445-481.
• Philipp, R.A. (1999). The many uses of algebraic variables. In B. Moses (Ed.), Algebraic Thinking, Grades K-12: Readings from NCTM’s School-Based Journals and Other Publications. Reston, VA: NCTM.
• Piaget, J. (1952). The Child’s Conception of Number. New York, NY: Humanities Press.
• Piaget, J. (1970). Genetic Epistemology. New York, NY: Norton.
• Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10, 163-172.
• Resnick, L.B. (1982). Syntax and semantics in learning to subtract. In T. Carpenter, J. Moser, & T. Romberg (Eds.), Addition and Subtraction: A Cognitive Perspective (pp. 136-155). Hillsdale, NJ: Lawrence Erlbaum Associates.
• Resnick, L.B., & Omanson, S.F. (1987). Learning to understand arithmetic. In R., Glaser (Ed.), Advances in Instructional Psychology, (pp. 41-95). Hillsdale, NJ: Lawrence Erlbaum Associates.
• 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 for Research in Mathematics Education, 20, 8-27.
• Rosnick, P. (1981). Some misconceptions concerning the concept of variable. Mathematics Teacher, 74, 418-420.
• Sáenz-Ludlow, A., & Walgamuth, C. (1998). Third graders’ interpretations of equality and the equal symbol. Educational Studies in Mathematics, 35, 153-187.
• Schoenfeld, A.H. (1985). Mathematical Problem Solving. Orlando, FL: Academic Press.
• Schoenfeld, A.H. (1987). Cognitive Science and Mathematics Education. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Schoenfeld, A.H. (1999). Looking toward the 21st century: Challenges of educational theory and practice. Educational Researcher, 28 (7), 4-14.
• Schoenfeld, A.H., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81, 420-427.
• Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
• Sfard, A. (1992). Operational origins of mathematical objects and the quandary of Reification: The case of function. In G. Harel & E. Dubinxky, (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy MAA Notes Vol. 25. Washington, DC: Mathematical Association of American.
• Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228.
• Silver, E.A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hibert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 181-198). London: Lawrence Erlbaum Association.
• Sierpinska, A. (1992). On understanding the notion of function. In G. Harel, & E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy (pp. 25-58). Washington, DC: Mathematical Association of America.
• Sims-Knight, J., & Kaput, J.J. (1983). Exploring difficulties in transformations between natural language and image-based representations and abstract symbol systems of mathematics. In D. Rogers, & J. Sloboda (Eds.), The Acquisition of Symbolic Skills (pp. 561-569). New York, NY: Plenum.
• Simon, M.A., Tzur, R., Heinz, K., & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35, 305-329.
• Sleeman, D. (1982). Assessing aspects of competence in basic algebra, In D. Sleeman & J.S. Brown (Eds.), Intelligent Tutoring Systems (pp. 185-200), New York, NY: Academic Press.
• Sleeman, D. (1984). An attempt to understand students’ understanding of basic algebra. Cognitive Science, 8, 387-412.
• Slotta, J.D., & Chi, M.T. (2006). The impact of ontology training on conceptual change: Helping students understand the challenging topics in science. Cognition and Instruction, 24, 261-289.
• Slotta, J.D., Chi, M.T., & Joram, E. (1995). Assessing students’ misclassifications of physics concepts: An ontological basis for conceptual change. Cognition and Instruction, 13, 373-400.
• Stephens, A.C. (2005). Developing students’ understandings of variable. Mathematics Teaching in the Middle School, 11, 96-100.
• Thompson, P.W. (1985). Experience, problem solving, and learning mathematics: Considerations in developing curricula. In E.A. Silver (Ed.), Learning and Teaching Mathematical Problem Solving: Multiple Research Perspective (pp. 189-236). Hillsdale, NJ: Erlbaum.
• Usiskin, Z. (1988). Conceptions of school algebra and uses of variable. In A.F. Coxford & A.P. Shulte (Eds.), The Ideas of Algebra, K-12 (pp. 8-19). Reston, VA: National Council of Teachers of Mathematics.
• Vergnaud, G. (1984). Understanding mathematics at the secondary school level. In A. Bell, B. Low & J. Kilpatrick (Eds.), Theory, Research & Practice in Mathematics Education (Report of ICME5 Working Group on Research in Mathematics Education, pp. 27-35). Nottingham, UK: Shell Center for Mathematical Education.
• Vergnaud, G. (1986). Long terme et court terme dans l’apprentissage de l’algebre. Paper Presented at the Colloque Franco Allemand de Didactique des Mathematique et de l’Informatique, Marseilles, France.
• VanLehn, K. (1990). Minds Bugs: The Origins of Procedural Misconceptions. Cambridge, MA: MIT Press.
• Watson, I. (1980). Investigating errors of beginning mathematicians. Educational Studies in Mathematics, 11, 319-329.
• Weinberg, A.D. (2005). A framework for analyzing functions in mathematical discourse. PhD dissertation, University of Wisconsin-Madison, WI.
• Woodward. J., & Howard. L. (1994). The misconceptions of youth: Errors and their mathematical meaning. Exceptional Children, 61 (2), 126-136.
• Young, R., & O’Shea, T. (1981). Errors in children’s subtraction. Cognitive Science, 5, 152-177.