Mathematical Problem Creation: How to Make Problems Real

In a Classroom Live 2.0 talk with Dan Meyer, the discussion dealt with mathematics text books, and the "pseudo" problem solving they require. Problems usually come out nice and even, information is laid out in an understandable manner (which is not how the real world works), and problems are forced into ridiculous situations. One example that I found particularly amusing (mainly because I have seen problems like this before) took a concept such as right triangles and the pythagorean theorem, and reduced this concept to a dog wearing a handkerchief, and how long one of the sides of the handkerchief would be if it were folded into a triangle. He had many textbook examples, but his point was that students see right through these fake problems, and begin to lose trust in mathematics.  

When problems are written and solved in such a simple capacity, people start to crow about the uselessness of mathematics. These types of problems can be put into the equation solver and figured out. Dan had received a Tweet saying that math was useless for this reason, and he was upset by this because the equation solver was not stressing the meaning of the math, just the solution. Dr. Scott Mcleod shared the sentiments of the Tweeter at a recent 1:1 conference I spoke at by reducing math to asking the AI on his phone for the answer. Dan points out in a pie chart that the answer is seen as the ultimate goal for most situations, when the process is just as important. This theory of just getting an answer simply skips a step in the important mathematical process, and I think that making better, more messy problems can alleviate this situation.

To help make problem solving more real, Dan suggests that that problems should not include all the numbers to start with. Numbers usually are not nice and neat anyway, and more than one solution is normally possible. He also showed some types of technology that he uses to help make mathematical problem solving more important. For starters, his smartphone has allowed him to take pictures on the go of any mathematical situation he comes across. He also uses Jott ("used" now because it does not exist anymore) to capture the situation with his voice and changing it to text so he can remember all of the context. YouTube or any other video site can be used to set up a real problem.

I use our text in class on occasion, but I would like to come up with better problems for my students to maximize their mathematical potential and show them that math is real...and not reduced to made up problems. I would use the techniques that Dan has outlined in the video and the technology he has suggested. After this phase has been enacted for a period of time, I would encourage students to find their own real situations out in the world to share with the class. This would not be an assignment with a deadline, because I want this to be natural, and not a stretch to find something. Many of my students have smart phones, or at least a phone that can take a picture. I would then set up a blog to display all of these questions after I have conferenced with the student presenting the problem. When students search for their own problems, it makes the learning experience more real to them. The problems would also relate to what interests each of them, adding a layer to the learning.

Credit given to reba@ghfoundation08 through flickr.com/creativecommons