The goods [#NCTMDenver]

Good turn out for my session Saturday morning (EIGHT O’CLOCK!).

Thanks to Ashli Black (@Mythagon) for the shot of title screen.

Alternate title: “Slaughtering Sacred Cows w/ Your Host, Prof. @trianglemancsd.” #NCTMDenver

— Dan Meyer (@ddmeyer) April 20, 2013

Rate of change & accumulation – BIG ideas for Middle School and beyond. @trianglemancsd #NCTMdenver

— Marc Garneau (@314Piman) April 20, 2013

We’re taking simplifying radicals, rationalizing denominators, factoring, cubics, quartics, & functions to the woodshed here. #NCTMDenver

— Dan Meyer (@ddmeyer) April 20, 2013

@trianglemancsd emphasizing experiencing ideas in informal contexts as a foundation for higher, formal math. RME everywhere! #NCTMDenver

— Raymond Johnson (@MathEdnet) April 20, 2013

Haven’t thought about rates of change, derivatives, etc in a long time. @trianglemancsd stretching my brain this morning!

— Katherine Bryant (@MathSciEditor) April 20, 2013

I’ll get some more details up here sometime soon. In the meantime, here’s the handout (.pdf). And here’s the slide deck (.zip, and which—to be honest—was just a photo album on the iPad; the simplicity of this was liberating).

Here are Alison Krasnow’s notes from the session.

One last thing…this is the absolute best form of session feedback, as far as I am concerned—getting to read someone else’s notes on the session speaks volumes about what participants experienced (in contrast sometimes to what I think we did).

The slides:

Does anybody at TI check the math?

I get that the images below are not real classrooms. These are combinations of staged and stock photos. I get that. But seriously, a waterfall with a straight-line cross-section? And just what answer do we expect to the “shade 1/6 of the hexagon” task? Is the resolution on that screen good enough to detect the difference between 1/4 and 1/6? And how will the teacher tell that difference at a glance? Do YOU know which of those responses is correct?

Note the right triangle on the NSpire screen. And the "Real-world" connection: "Diagonal distance of a waterfall".

We're filling from the bottom up. If height of hexagon is 1 unit, what fraction SHOULD we fill to? And how exactly do these images help me assess whether students can find it?

Modern Algebra or Common Core?

Let’s play a little game. We’ll call it Modern Algebra or Common Core?

For each of the following learning targets, determine whether it comes from my undergraduate Modern Algebra textbook or from the Common Core State Standards for Algebra I.

1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
2. Discuss… exponential functions with continuous domains.
3. The polynomial ring…has features that have no analogues in the ring of integers.
4. Polynomials form a system analogous to the integers.
5. By “abstracting” the common core of essential features…develop a general theory that includes as special cases the integers…and the other familiar systems.
6. With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system—integers, rational numbers, real numbers, and complex numbers—the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings.

Answers in the comments.

My 6 year old’s definition of algebra

Overheard in a conversation between Griffin, 6 years old, and Tabitha, 4:

Griffin: I hate algebra.

Tabitha: What is algebra?

Griffin: Algebra is a piece of paper with math problems that are very hard.

So much prep work, and I got it (partly) wrong…

I know I messed this up.

My pH videos came out clean and distraction free. I am satisfied with their quality. I spent two hours getting 20 minutes of footage and have edited it down to tidy, manageable packages.

But I know I didn’t get a really important one into the mix.

See if you can guess what’s missing…

I have the pH of water, of 100 ml of water with 1 ml of orange juice concentrate, of 100 ml of water with 10, then 20, then 100 ml of concentrate. And I have the pH of straight concentrate.

So what’s missing? Orange juice made correctly-in a 3:1 ratio of water to concentrate. I have 1:1 and 5:1 but not 3:1.

Now I understand that the pH difference between 5:1, 3:1 and 1:1 is virtually unnoticeable. But that’s not the point. The point is that when I do this lesson on Wednesday I know one of the student questions in the “What can we ask here?” part will be about the pH of properly made juice. And it’s a less compelling answer to have me say “It’s between these other two” than to see it play out on screen (this is the whole point of the effort, after all, right?)

Too late for this time around. Lesson learned.

Continued…