I have started a separate blog devoted to helping students learn to find mistakes in worked problems (their own, or someone else’s). If this is of interest, check it out:
7/17/11 Update: There can be great value in work that contains mistakes. Learning to catch your own mistakes is a critical life skill, as is learning to review other people’s work while seeking to understand it fully (the best way to do this is by looking for mistakes).
Along these lines, I came across an interesting blog posting by Kelly O’Shea. She came up with the idea of insisting that each group who is presenting try to sneak a mistake in their work past their peers. Brilliant!
This is great! I’ll ask my college students to read this regularly. How often do you plan to post?
Thanks for the shout out, here! 🙂
What I’ve found to be much more productive in class is for the goal of The Mistake Game to be including a mistake that your classmates might have made rather than trying to hide a mistake (that usually leads to worthless Where’s Waldo type mistakes with just changing units or spelling or something). Everyone knows there is a mistake on the board anyway. The real purpose is to go through the process of working out the mistake by having the other students ask questions that make the presenters change their answer. The presenters don’t really have to argue back, but the questioners do have to work to ask good questions that are better than, say, “Why is your answer wrong?” or “Why didn’t you do XYZ?” Learning to make good mistakes is tough, but learning to make good questions that point out inconsistencies is tougher. And they get better at both as they practice the game. 🙂
Depending on the subject and the topic at hand, any number of approaches could be productive. Your comment describes what I envision working best when you wish students to focus on applying the correct concept or approach. When working on basic skills for algebra, I would seek to have students sneak in procedural errors that are common, such as failing to distribute a negative sign. And when working with more advanced algebra topics, I would seek to have students present work that does not use the most efficient route to a solution (or in fact uses an outright obscure route), but is nevertheless algebraically correct. There should be many, many variations on this theme.
All serve to make each member of the audience pay attention to their intellectual and emotional reactions to a presented solution, think about why they are reacting as they are, then present a concise question or proposed improvement with justification. Students need to spend time talking about the subject, using the correct vocabulary to communicate accurately and efficiently, and thinking about multiple potential solution paths – perhaps each with its own advantages and disadvantages. Many traditional classroom approaches make such goals challenging to meet.