Thanks for making this point today. I ended up in conversations with my precalc classes earlier about notation and how it can make maths unnecessarily hard (exhibit a: vectors in math books and physics books often use different letters for the same things).

Will put more thought into the definition/work before the word itself as we head into the wild fields of trigonometry.

And now I’m going to spend the evening thinking about forces around a curve. Cheers :)

I remember being in an upper division math class and being ‘introduced’ to ordered pairs. The book defines an ordered pair as follows: “Let S be a set and let a and b be members of S. The ordered pair (a, b) is the set {{a},{a, b}}. The element a is called the first term of (a, b), and the element b is called the second term of (a, b).”

I had no idea what this book was talking about; perhaps the proper schema was not activated. If someone mentioned a Cartesian Coordinate System or even said “x’s and y’s” then I think I would have saved a lot of time and energy.

In the same sense, while I’m sure all students have been introduced to annulus in various forms, I doubt many know the mathematical name or formal definition (if they did they wouldn’t need a teacher). Our challenge becomes to help them understand the mathematics behind the shape and give them the tools/language to express that understanding without conveying the idea that mathematics is anything other than natural.

Oh, you and your tuna casserole lifestyle, making those DOT engineers’ whole year, I’ll bet. :-)

Dan – the time you spent with us here in Indiana was awesome – faculty are still buzzing about the day! Thanks so much.

What’s exciting about this post+comments is the enthusiasm for real-world application of things that cause most high school (and junior high) students to roll their eyes. It’s not just telling or showing them how they COULD use it, but allowing them to interact with people who DO

We have, for example, a rather (actually, it’s very) steep driveway that needs to be paved. In my research on road construction techniques (once a student, always a student), I found clear explanations, wonderful diagrams, and (wait for it…) the same geometric equations my high school sophomore is doing for homework. Instant Teaching Moment…

I have forwarded several of your posts to a friend, and she just sent me a message asking if you have (or plan to create) a book of these concrete, real-world examples.

Based on the comments I see here, you could ask for examples from your readers and put them together as a collection.

Terri

I agree. I try to use as little Greek in my classes as possible. I think Greek letters can be very off-putting and they’re often unnecessary. What’s wrong with sin(A+B) rather than sin(alpha+beta)?

Similarly, I don’t like Latin plurals. Is it so wrong to say “formulas” rather than “formulae”?

Check out my blog :P

I once did an inservicey thing in Beaverton, OR in which I assigned teachers to go out to stoplights with a partner, a watch, and a notepad. they were to observe and collect data about the vague question, “How do you tell if a light is timed well?” (Or something like that; at any rate, the timing of lights is something I had churned about for years without actually taking data, so I thought, ¿que oportunidad?)

Before the debriefing the next day, besides taking data of my own, I thought I’d call up a traffic engineer. It took a while to figure out what they were called, but (as you suggest) when I got hold of Portland’s chief guy, he was thrilled to talk to someone, anyone! who cared about what he had devoted his life to.

And a big takeaway: is there a control room where they can control the lights? Yes, for downtown only. Under what circumstances so they alter the timing? Answer: for emergency vehicles. Not for traffic. Their experience was (at that time) that any attempt to do that in real time just made things worse.