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Thursday, October 20, 2011

Analogies are to teaching as...

My boyfriend's daughter is applying to colleges so there has been a whole lot of SAT and ACT talk going on lately. She's actually focusing more on the ACT, which I know nothing about since I only took the SAT, so we've talked a little about the differences. In general when interacting with this young lady, I have tried very hard to avoid using the phrase "When I was younger..." (since apparently nothing makes you sound older to a teenager than referring to your own childhood) but when I found out that the SAT no longer has analogy questions, I couldn't stop myself. When did the analogies get dropped?!?* Of course, back in high school, I had no idea why the analogy questions were even on the test (not that I spent a lot of time thinking about it back then either but I do remember thinking that they were sort of weird). But as a teacher, I've found that a well-constructed analogy can often make a world of difference in my students' understanding. I was reminded of this the other day by Dr. Goose who uses what struck me as an awesome analogy related to the standard conservative argument for cutting taxes:
"Writing in the Wall Street Journal on the "Three Policies That Gave Us the [Steve] Jobs Economy," Amity Shlaes cites the slashing of the capital gains rate from a confiscatory 49% to 25% in 1978. Building on this evidence, she reaches the silly conclusion that "taxes on capital should always be lowered, and dramatically." One might just as easily conclude that, because a diet improved one's physique, that mealtime portions should always be dramatically lowered, too."
On the other hand, a poorly-constructed analogy can create even more confusion than you started with. Case in point: I had read about Herman Cain's 'apples and oranges' comments during the Republican debate the other night and like a lot of people, I thought he was making no sense (if you didn't hear about it, you can read the transcript and see the clip here). But somewhere in the third time I watched/read Cain's exchange with Romney, I finally realized that Cain's point is that his plan is intended to replace the federal tax structure (that's the oranges) and regardless of what one thinks we should do about that federal structure, no one is talking about any changes to state tax structures (that's the apples). The problem is that because his plan includes a sales tax, which everyone associates with state tax structures, it's not unreasonable for people to wonder how his plan would interact with the state taxes. So Cain's oranges and apples analogy was referring to who collects the tax (which is different: federal or state) but everyone else was talking about the type of tax (which is the same: sales) so his analogy seemed to make no sense.

One of the principles in How Learning Works: Seven Research-Based Principles for Smart Teaching is about how students' prior knowledge can help (or hinder) their learning. Analogies in teaching are all about connecting new ideas to other ideas that students already understand. Do you have favorite analogies you use when teaching?

* If anyone reading this doesn't know what I'm talking about when I refer to the SAT analogy questions, well, go ask your parents...

Wednesday, October 5, 2011

Supply and demand without the curves?

We discussed supply and demand in my Econ for Teachers class this week. This is usually one of my favorite weeks in this class because we do an in-class double-oral auction, which I don't get to do in principles anymore (since I'm not brave enough to try it with 500 students) - I use Aplia for that class instead and while it's better than not doing it at all, it's just not the same. I love watching the students get into their buyer and seller roles. There is always a few who surprise me, some students that I think of as being relatively quiet but they end up being enthusiastic negotiators. And students always tell me at the end of the semester how memorable the auction is for them.

But as I was preparing the materials for class, it dawned on me that no where in the California content standards, or in the national standards, are supply and demand curves mentioned. That is, standard 12.2.2 of the California standards says, "Discuss the effects of changes in supply and/or demand on the relative scarcity, price, and quantity of particular products" and standard 12.2.5 says "Understand the process by which competition among buyers and sellers determines a market price." National standards 7 and 8 say "(Students will understand) Markets exist when buyers and sellers interact. This interaction determines market prices and thereby allocates scarce goods and services" and "Prices send signals and provide incentives to buyers and sellers. When supply or demand changes, market prices adjust, affecting incentives." On the one hand, it certainly is possible to just talk intuitively about market prices and quantities adjusting to changes in supply and demand, without using a graph of the curves; but on the other hand, it seems like the intuition is so much easier when paired with the visual of the graph. But maybe it just seems that way to me because that's how I've always done it?

Partly, I'm thinking about how difficult it seems to be for students to go from the experiment data (giving the number of buyers with different buyer values and sellers with different seller costs) to graphing the curves. It feels a bit like just a graphing problem because when I go datapoint by datapoint (for example, asking, "At a price of $5, how many sellers will be willing to sell?"), they have no trouble answering and they intuitively understand the relationship between price, buyer value or seller cost, and willingness to buy or sell. But when left to finish drawing the curve, they often get lost again, as if they just can't connect the intuition they understand to the grid in front of them.

So I'm wondering how weird it would be to try to discuss supply and demand and equilibrium price and quantity without the curves. I just don't know if it would 'work'. I'm particularly thinking about student confusion about what I think of as the 'never-ending story' problem: something happens that causes demand/supply to change (shift) and that leads to a change in price, which students then think causes demand/supply to change as they confuse shifting the curve with moving along the curve. Of course, if they actually follow that argument through, that shift should cause price to change again, which causes demand/supply to change again, etc. Since that process could just continue forever (and yet we know it doesn't in reality), there must be a flaw in that argument, and I think the curves can help clarify that flaw. I can't really figure out how I would explain what's wrong with that argument without using the curves. Yet, I think there are a lot of high school economics courses that do not introduce supply and demand curves. Do they just not do supply and demand at all (that would be my own high school experience)? Or are they talking about supply and demand without the curves somehow? If anyone has taught it that way, I'd love to hear from you in the comments!