In Principles and Standards for School Mathematics (NCTM 2000), understandings of patterns, relations, functions, mathematical models, and quantitative relationships are recognized as key facets of algebraic thinking. In essence, algebraic thinking “embodies the construction and representation of patterns of regularities, deliberate generalization, and most important, active exploration and conjecture” (Chambers 1994, p. 85). Algebraic thinking should function as a means of shifting from arithmetic concepts to algebraic concepts (Chappell 1997). This shift would have occurred if there exists reasoning about relationships between quantities, rather than the specific quantities themselves (Ferrini-Mundy, Lappan, and Phillips 1997; Yackel 1997). Research shows that this arithmetic to algebraic shift is difficult for students (Stacey and MacGregor 2000). Therefore, it is imperative to explore students' reasoning as they approach problems that elicit algebraic thinking. For this reason, we will present and discuss samples of student work regarding problems that promote algebraic thinking.
Bannister's research interests include teachers' and students' conceptions of functions and rational numbers. Wilkins' research interests include quantitative literacy, educational opportunity, and the teaching and learning of probability and statistics.