Building Bridges to Algebraic Thinking

In spite of the fact that middle school teachers have been urged to develop algebraic thinking in their students (Lawson 1990; NCTM 1989; Phillips et al. 1991), the question of how to initiate that process may still be problematic for many teachers. Although it is important to suggest that explorations into algebraic thinking should emphasize “physical models, data, graphs and other mathematical relationships” (NCTM 1989, 102) and to recognize that “numerical and graphical problem-solving techniques become accessible strategies … through the use of technology” (Demana and Waits 1990, 53), teachers need help in building a bridge between their current instructional goals and new goals that emphasize an earlier introduction to algebraic thinking. In this article, we describe and illustrate an approach to algebraic thinking that is based on an extension of the problem-solving tasks typically investigated by elementary and middle school students.