Inventing Problems

I’m sure many of you have been annoyed by the story problems in math classes. They are often boring, worded funny, and require a large suspension of disbelief. You may ask yourself what kind of idiot would write questions like those.

Well, I would.

In my Probability class, one of the projects assigned was to come up with unique questions that would need to be solved using the methods we were learning in class. We didn’t do that well. Now, I don’t mean to insult my classmates. Our questions were clever and fun to think about. However, they fell short when we were asked to solve each others. They became as mundane and silly as the work we had done our of textbooks in previous math classes.

In Jo Boaler’s class, she mentioned a different approach to assigning larger problems. In most American classroom, Mathematics is taught as a subject, rather than a tool. Teachers search for a circumstance applicable to their current curriculum, rather than providing problems and giving the students tools and resources to solve it how they see fit. The questions my class and I came up with were synthesized with answers and a process already chosen. We had worked backward to get the problem, which made them straightforward and fake.

Jo spoke of a school that taught Mathematics as a tool. Instead of giving their students a procedure out of thin air and asking cookie cutter question that didn’t really apply to life outside the classroom, teachers would assign a project, then make a number of tools available for their class. These tools would include what the teachers would think would be of use, such as protractors and straight edges, along with random ones that were unlikely to be necessary. Students would have to think critically about how to go about solving the problem. Some students would even use the ‘unnecessary’ items to problem solve in a new, unconventional way. The students had to choose the procedure, rather than being force-fed one to plug-and-chug throughout the class period. When groups came to the teachers with questions, they would be led in the right direction, or given a concept or procedure useful for how the group decided to overcome their current hurdle. Students would understand why and how the procedure they had just learned worked and how it could be applied to real-world situations. The groups would even share what they learned with others. (I mentioned in an earlier entry how explaining to peers solidifies understanding of the material.) Mathematics was no longer a thing to be memorized and regurgitated, but something to experience first-hand and apply.

Inventing problems with specific information in mind does have a place in the classroom, though. By creating our own, personal questions in my stats class, we were deepening our understanding of how the procedures worked as well as where we could use them in our own lives. It gave us a chance to be creative and invent the most complicated (yet solvable) problem we could.

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