GOAL: develop frameworks and modes appropriate for MATH specific Whiteboarding.
I did a ton of experiments this year with whiteboarding and a lot of brainstorming, but here are my three favorite modes of math whiteboarding that I tried (some writing copied from previous posts). A good whiteboarding mode for me can be applied to many different topics and takes advantage of everything whiteboarding has to offer: collaborative, interactive, promotes risk taking and visually stimulating.
Guess and Check with a Partner
Students try to solve problems that take a certain amount of intuition or guesswork (like antiderivatives or factoring) by having one person write down a guess, and the other person check if it is correct.They would then keep doing this until they get a correct answer. After a certain number of problems solved, the two students switch roles. For example, above the students are looking for the antiderivative of – the guesser writes down and the checker takes its derivative to see if that is correct. Since does not equal , the guesser tries again. They continue this process until they finally get that back again. This mode is great for showing students that a great way to do math (at first) is to just try things and adjust their answer; it’s great for getting students to converse together about how to get a solution; and it’s great to get them in the habit of always checking their answers. I had a really hard time getting some students to follow the procedure for this one, but the ones that stuck to their roles got a lot out of it.
Color Coding Problems
Before solving a problem, students rewrite it using different colors to help them understand its important parts. For example, above is a whiteboarding exercise I did with the Chain Rule. Students were in groups of threes – for each problem, one person had to rewrite the problem in different colors to indicate which was the outside and which was the inside function, the next person had to differentiate it still using the colors to point out where each part of the new expression came from, and then the last person had to rewrite the expression in a simplified form. This was perfect because the hardest parts of the chain rule are recognizing when you need, seeing inside vs. outside and then seeing where the parts of the new expression come from.
The Mistake Game
Groups present solutions to semi-complicated/involved problems on whiteboards, but while presenting their solution, they purposely make a mistake (and not an silly arithmetic mistake like – a real hardcore-misconception-style mistake). Then, they present their work to the other students in the class, trying to sell their mistake as having been made for real. Other students ask thoughtful questions about the presenting group’s solution to try to help everyone find the mistake. This is always great with a quick class followup at the end collecting the most common mistakes. Check out the Guide to the Mistake Game from Kelly O’Shea, who introduced me to this game.
P.S. I’m realizing now that the example above actually isn’t a great example of a time to use this game… Some topics that it worked well for this year were graph sketching, solving for limits algebraically, using the quotient rule, implicit differentiation, related rates and using infinite limits in graphing exponential functions.