Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 1, Part A:
A Framework for Algebraic Thinking (15 minutes)

 What does algebra mean to you? For many of us, the word "algebra" conjures classroom memories of xs and ys, manipulating numbers and symbols according to prescribed rules, and solving for the unknown in an equation. It may not have been clear where the rules came from, or why x could be different in every problem. In recent years, the vision of how algebra is taught has been changing. Algebraic thinking begins as a study of generalized arithmetic. The focus is on operations and processes rather than numbers and computations. When algebra is studied this way, the rules for manipulating letters and numbers in equations don't seem arbitrary, but instead are a natural extension of what we know about computation.

 Video Segment In this video segment, participants discuss their initial impressions of algebraic thinking. Does thinking algebraically require formal "algebra?" Think of some situations in everyday life in which a person might think algebraically but would not consider themselves to be performing "algebra." You can find this segment on the session video, approximately 2 minutes and 19 seconds after the Annenberg Media logo.

 Problem A1 What would you define as algebraic thinking?

 Problem A2 When do you think students begin to think algebraically?

 Write down your answers to Problems A1 and A2, because we will return to them at the end of the course. There's no clear line separating formal algebra from informal algebraic ideas. Though you may not realize it, the kind of logical thinking required in reasoning about real-life situations and reasoning about mathematics is often very similar. As you work on the rest of the problems in this session, focus on the kind of thinking that's required to solve them and the kinds of representations that are most helpful in your reasoning. These problems may or may not be considered "formal algebra," but they will hopefully reinforce the notion that "making sense" is a big part of what mathematics is all about.