Mathematics Research

The Arithmetic-Algebra Transition.

Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59-78.

Johanning, D. I. (2004). Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies. Journal of Mathematical Behavior 23, 371–388

Understanding the Conceptual Structure of Algebra.

Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189–203.

Stigler, J. W., Givvin, K. B., &  Thompson, B. J. (undated). What community college developmental mathematics students understand about mathematics.  The Carnegie Foundation for the Advancement of Teaching, Problem Solution Exploration Papers

Kornell, N. (2012, November 17).  US Math achievement: How bad is it? [Psychology Today blog, Everybody is stupid except you]. Retrieve from  http://www.psychologytoday.com/blog/everybody-is-stupid-except-you/201211/us-math-achievement-how-bad-is-it.

Students' Concepts of the Equal Sign and Equivalent Equations.

Matthews, P. G., Rittle-Johnson, B., Taylor, R. S. (In press).  Understanding the equal sign as a gateway to algebric thinking.

Matthews, P.G., Rittle-Johnson, B., McEldoon, K., & Taylor, R.T. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43, 316-350.

Rittle-Johnson, B., Matthews, P.G., Taylor, R.S., & McEldoon, K. (2011). Assessing knowledge of mathematical equivalence: A construct modeling approach. Journal of Educational Psychology, 103, 85-104.

Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221–247.

Students' Concepts of Variables.

Christou, K.P., Vosniadou, S. & Vamvakoussi, X. (2007). Students’ interpretations of literal symbols in algebra. In S., Vosniadou, A. Baltas & X. Vamvakoussi, (Eds.). Re-Framing the Conceptual Change Approach in Learning and Instruction. Advances in Learning and Instruction Series (pp. 285-299). Elsevier Press.

Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts:  Equivalence & variable. ZDM, 37, 68-76.

Küchemann, D. (1978). Children’s understanding of numerical variables. Mathematics in School, 7, 23-26.

MacGregor, M., & Stacey, K,  (1997). Students' understanding of algebraic notation: 11-15.  Educational Studies in Mathematics, 33, 1-19.

Malisani, E. & Spagnolo, F. (2009). From arithmetical thought to algebraic thought: The role of the “variable". Educational Studies in Mathematics 71, 19–41.

Thinking like...: Hypothetical Thinking and Algebraic Thinking.

Amsel, E. (2011). Hypothetical thinking in adolescence:  Its nature, development, and applications.  In J. Smetana & E. Amsel (Eds.), Adolescence: Vulnerabilities and Opportunities. New York, NY,  Cambridge University Press.

Amsel, E., Klaczynski, P. A., Johnston, A., Bench, S., Close, J., Sadler, E., & Walker, R. (2008). A dual-process account of the development of scientific reasoning: The nature and development of metacognitive intercession skills. Cognitive Development, 23, 452-471.