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## Practice Makes Prove-It!

Sometimes I mention websites that I personally am ambivalent about. This is one of those times...

Michael Ferraro, mathematics and physics teacher at Balboa High School in San Francisco, has created an on-line tool that provides students practice with two-column proof skills in geometry. It is called ProveIt!

You are given about forty proof situations, rated on a scale from easy to hard (I am not sure if the rating reflects user success with a particular proof or if it was a judgement by Ferraro. Few directions are available, so you need to play with the process yourself before asking students to experience it.

Basically, you start by choosing a category (e.g. Parallelogram 2). Then, the "roots" of a proof appears, complete with givens, relevant diagram, and statement to prove. Your task is to choose statements and reasons from the list given. If you decide to correct your work, options are there to remove or move statements and reasons in previous lines. Once you feel your proof is complete and solid, check it using the "QED?" button.

Now, the reason I am ambivalent. On the one hand, I found the process somewhat useful, as the format served as a guide for one practicing early-level proofs. On the other hand, I found the process involved "restricted" thinking, in that the the process gives you the necessary proof statements in a "random" order...and you task is to put them in the correct order...plus select the right justification. Thus, it gives the idea that proofs are linear, and one only has to magically find the one-way route.