The Backward-Forward Method
Unfortunately, little or no time is spent in most math classrooms discussing "heuristics," the art of problem solving. This often leaves students grasping at straws, struggling even to know where to begin when staring down an unfriendly, unfamiliar math question. George Pólya's How to Solve It is a classic on this subject, required reading for all serious math students. In another classic, How to Read and Do Proofs , author Daniel Solow advances a powerful problem solving approach he calls the “Forward-Backward Method.” I’ve found it helpful in my own teaching and mathematical work to reverse the method, first thinking backward from the ultimate goal to various subgoals which, if achieved, would enable direct progress to the original objective. Whether writing complex proofs or tackling simple algebra problems, this “Backward-Forward” process provides students with a simple yet powerful structure for solving problems. Just as an archer would prefer to move the target ...