Solving real problems is messy. Sometimes, we don’t even know what problem we are trying to solve, and it doesn’t become obvious until some investigation and discovery takes place. We must decide what information is needed and attempt to get it, although it isn’t always available. Sometimes there are so many variables that they distract or even confuse us from defining a course to follow. And, frequently there may not be one absolute solution. The solution that we reach may have corollaries or disclaimers, or it may simply be a best guess given all of our efforts. I hope this is starting to sound like real life because it doesn’t make a lot of sense to devote a huge chunk of time in school to learning math that is not useful in real life. And, if our students don’t get opportunities to use math in real life situations, then they will continue to see it as a boring, inert process that must be slogged through just to get to the next math course; or, even worse, as the way to a better score on the SAT. Math is so much more than a way to get into college -- it is a way to view the world, and it gives us the ability to understand, seek, and find solutions to the world around us.
This week, we started working on one of what we call our Big Problems -- a real problem. I told the students that I had been thinking about replacing the long, rectangular tables in our lunch room with circular tables. Because our students are primed from years of practice as problem solvers, it took them all of ten minutes to come up with the following questions and comments in some small group discussions. Although as a school administrator, I have thought of changing out the tables for a long time, I hadn’t considered several of their ideas as variables:
- Are round tables more ergonomical? Forearms naturally form triangles when on the table.
- How big can a round table be to hold a conversation with someone across the table in our lunchroom?
- Does looking at someone when talking to them help conversation and relationships?
- Would there be more space to move between the tables?
- What happens to aisle space? Will it open the flow or restrict it?
- How would moving to round tables affect cleaning? How big can it be and still be easily cleaned?
- Storage? (We move our tables every day to clean the floor.)
- Will round tables hurt or help inclusivity?
- Will they fit in the lunchroom?
- What will be the cost?
- Will the cost be worth the benefit (if any)?
- Unintended consequences?
- Other stakeholders (the LS students who use the lunchroom also).
What kind of math tools will we need to pursue this problem? Some things are obvious like measuring, performing simple arithmetic calculations, working with geometric shapes, and spatial reasoning. However, we may look at hearing as a function of distance from speaker (this is an algebra class after all). Or the number of seats available as a function of the circumference of a table. We are going to have to figure out some way to apply a dollar amount to something that is not easily counted (building relationships) and this will definitely involve some statistical analysis. We are going to have to do some data collection, analysis, and interpretation. More statistics. Finally, we are going to have to reach beyond our collective knowledge base to get information and possibly even help.
So, how does this assignment hold up to the teaching of skills that have become a fundamental element of our middle school: collaboration, problem solving, communication creativity, perseverance, grit. We can check all of these off.
I told the students that if we decide that replacing the tables would be a good idea that we would present our findings to our Chief Financial Officer and other stakeholders. We are not sure if the school will take our advice; this is the real world after all, and there are all sorts of other claims on school dollars than lunch room tables. But, regardless of the outcome, the process of working through this problem will give the students and teachers some practice with the utility and function of math.
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