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## An argument against the real world

I recently joined a joint lesson planning group. The idea is that they either (a) create a new lesson, or (b) take a previously developed lesson, and refine the details, hopefully getting more nuanced as the effort is repeated.

The lesson they had yesterday involved analyzing this question:

Sandy has saved up $120 from babysitting. She’s going to Tower Records to buy CDs and DVDs. CDs are$12 each, and DVDs are $15 each. I get that this is supposed to be real world. Except. My kids don’t get paid to babysit – that’s just what older siblings do. Tower records doesn’t exist anymore. They don’t buy CDs, they share MP3s. They buy DVDs, but they buy the bootleg ones at the corner for$3. They would spend the whole time telling me how stupid Sandy is.

What if I changed it around a bit:

Sangemord the Vampire hunter looted 120 gold pieces in his last raid. He needs to resupply for his next raid. Blessed stakes are 12 gold, and vials of Holy Water are 15.

Exactly the same problem. The graphs will look the same, the tables, the equations, everything math is the same. The difference is that, by not trying to make the real world fit my numbers, I don’t impose a cognitive dissonance. The kids won’t spend time worrying about whether the story’s reality matches with theirs – they realize it’s fiction, and will buy into it. The fact that I’m building on an established but unconsolidated mythos (from Buffy through Van Helsing and Vampire\$) only makes it easier. They know kind of what the rules are, but not enough to argue with them to the distraction of the problem.

We have a similar lesson that is commonly promoted through the district, of comparing cell phone calling plans. The problems are similar: (a) the kids don’t care about what their phones cost – mom & dad pay for them. (b) even if they did, real world calling plans are intentionally convoluted in order to confuse the customer. They do not translate well to the straight lines we want for our algebra lesson. Once again, you’d be confronted with “That’s stupid. My plan has 1500 free minutes. I wouldn’t get any of those.”

Take that problem, and switch it to leasing a flying broom (which is now thankfully cool for boys to use as well) and those arguments disappear.

When I first started thinking about this, I just thought it might be fun. I’m becoming more and more convinced that if we want to use real world examples, they better be completely real, with realia to back up the premise1. If we are going to create fictional problems to emphasize certain concepts or aspects of a problem, then it is imperative that we eliminate the cognitive dissonance from their real world. They are constantly immersed in fiction – they know how to suspend their disbelief for that, and will happily do it in your classroom as well.

1 Using real data for problems will introduce complications – the world is rarely linear, nor rational. We need to be prepared to deal with that. And there is definitely a place for making our students deal with real world messiness. But, when we are trying to clarify a concept, it seems to me that it is a worthwhile effort to remove distractions until the concepts are cemented, and then provide opportunities to use them in a messy real world situation.

1. JackieB | February 3, 2008 at 6:32 pm | Permalink

Your lesson planning group sounds interesting. How did they react to your comment about the word problem?

2. Mr K. | February 3, 2008 at 7:21 pm | Permalink

They didn’t, really. The lesson is out of the district’s lesson bank, so I don’t expect them to change much. (They did change the store from Tower to Best Buy). The point of the group is determine how you implement the lesson, and how you specify that so that someone else can duplicate the best practices.

Turning this into an argument rather than an observation would undermine the purpose of the group, I think.

You raise an interesting point, though. This theory of mine feels sound, has worked in practice every time I’ve tried it, and resonates when described to friends who remember the problems they had in their math classes. Despite that, it flies in the face of conventional wisdom, and goes against the practices of teachers with decades more experience than I have. At this point I’m going to continue exploring it for myself, and share the theory with others, but I’m not quite ready to try forcing others to change their lessons because of it.

3. JackieB | February 3, 2008 at 8:50 pm | Permalink