Incorporate Interactive, Colorful Activities into Your Mathematics Classroom by Tom ReardonI thought colorful activities meant crayons, but it actually meant TI-nSpires in color. However, I was still really happy to have attended this session. Tom was a great speaker and he was really practical - he knows that tech should supplement the lesson, not be the lesson. Most of the applets he showed us were meant to be quick explorations or models. Best of all, there's a TI-nSpire player which is free! Students can interact with files that other people made, but it only works with the mouse (no keyboard inputs) and you can't edit the files without buying the software. One really nice example was a visual for summing a geometric series. The geometric interpretation worked especially well for this limits problems as students could quickly see that we were filling up the box, but would never finish. Check out his website, the link to "all my stuff" gets you to a dropbox folder, choose the folder Player Files which is filled with files he hand selected for the player (no keyboard inputs required), the word document at the bottom gives you a list sorted by topic. I need to take some time to really go through that list and see which ones are worth reserving the laptop cart for, and which other ones I can use on the smart board.
"Green" Geometric Modeling by Sharon McCrone and May ChaarThis session was about packaging and Sharon made an interesting point about how we teach Geometry. So much of the course (sometime all of the course!) is spent on two dimensional objects, but we live in a three dimensional world. These projects start with physical objects, but then students examine them in ways that allow them to practice skills in 2-D. For example, if you consider sports drinks, they have to fit onto the shelf at the store. So you examine a rectangular shelf surface and the footprint of the bottle. Students can create layouts, calculate areas of various shapes and determine how efficiently they used the space. Then if you consider packaging there are a variety of ways to look at it, but examining surface area and drawing nets lets us continue to practice area while including visualization skills and continuing to discuss a "real world" object. The bonus question was to look at a bike helmet; they assumed that the highest and widest part was a semi-circle and then asked us to design packages that would fit the helmet with some wiggle room. It would be interesting to ask students to compare the assumption to a real helmet, and of course this is a great time to make a joke about physicists: "assume a spherical cow."
Radian Protractor by Jennifer SilvermanDid you read that title? Radian. Protractors. Why haven't they existed for as long as degree protractors have? I have no idea, but Jennifer decided to remedy this problem and the first run just arrived on Tuesday. I feel so cutting edge! They are sleekly designed with measurements only going in one direction (so much more logical than the confusing 2 directional ones) and they come in both fractions of π and straight numbers. She has also provided us with some carefully scaled drawings that are easy to measure using the new protractors. Check out the website for the lessons and to buy your own radian protractors ($3.14 each, so funny).
The original presentation is now available as a pdf.
Reasoning, Sense Making and Proof by Fred DillonI went to PCMI with Fred and he's great fun. We got to do the locker problem, which is one of my favorites. Then we talked about limits in terms of stocking fish in a pond. Here Fred shared the 5 different representations he uses; I've seen what some people call the rule of four (graph, table, equation, words) but he also includes an area model (like Tom's geometric series box). Finally, we worked on a puzzling probability problem. That was the most interesting one: Two people take their lunch break from 12 to 1. They plan to meet up for coffee during their hour, but don't plan a time. Both are rather impatient though, so they will only wait 10 minutes until they give up and leave. What's the probability they meet?
Making Sense of Similarity by Terry CoesTerry has been teaching for a long time and he had some good, solid ideas to share. Since I developed a 10 hour PD on proportional reasoning as part of my grad program the challenges he listed for studying similarity weren't a surprise to me. However, I think many teachers think like he once did "Oh, it's February, that's why this isn't going well." (That comment also made me question what other topics I blame on timing...) Thinking multiplicatively is hard for students after so many years of being trained to think additively. Terry made an excellent point that I am going to try to keep in mind at all times: complete sentences make sense. So often we let kids (and ourselves) get away with phrases that are meaningless out of context. The Pythagorean Theorem is not "a squared plus b squared equals c squared." Instead, the theorem states "If you have a right triangle with legs a and b, hypotenuse c, then a squared plus b squared equals c squared." The math practice Attend To Precision doesn't just mean be careful when you round, it also means to communicate precisely.
I hope you found something useful in my session summaries, I found it useful to summarize since now I have all of the ideas from two intensive days more organized (both online and in my brain). If you haven't been to an NCTM conference I would recommend checking out the schedule and trying to make the next one near you. You'll get a lot more out of it than the tidbits I managed to share here.