Doing and Learning instead of Teaching

I started my Master’s program this summer. It is focused on research, and has us spending each summer working out in industry. We hope that we can learn more about how science, technology, engineering and math are used in the real world, and thus make our teaching more relevant for our students.

I am spending the summer at a company that makes those little black bug-looking things that go into electronics. Those things are called Integrated Circuits. They also probably made your favorite calculator. But I am working in the Failure Analysis Lab. We get the pieces that are sent back from customers and have failed or otherwise need to be investigated.

I just wrapped up my second week, and am still learning. But the most important thing, the thing I most want to take out of that place and into my classroom is curiosity. These men (and yes, it is all men on the team I am on) are legitimately interested and curious about each and every part that comes in. I have seen three guys crowded around a microscope and computer screen, pouring over the little details on a circuit, debating over the source of the problem. One guy suddenly remembers that he had helped someone else on the same sort of problem months ago, and runs off to find that report. Hours later, after we have done more processes and more tests to find the exact problem, the guys are asking about what we found.

This is their job, but they like it. Every day presents new challenges and puzzles, and every day they are excited to solve those puzzles. How I wish I could help my students develop that kind of curiosity about math!

This Line is Part of a Very Large Circle

I saw this on Tumblr today. If you don’t know, Tumblr is where your angst-filled students hang out. I just like the funny pictures that show up from time to time.

This is from Yoko Ono, and I hope that doesn’t make it too weird for class. I would love to throw this up in class (both geometry and calculus) and see what kids make of it.


A Prediction about the Blog-o-Sphere

Oh, how I hate that word. Blog-o-sphere. Ugh.


I’m starting my first class for my masters today. We will spend the summer learning about how to do research as a teacher, and so we of course have to read oodles of research. Our first paper to read is from way back in 1992. The authors are discussing all sorts of research that teachers do in their own classrooms, and have this cheery observation:

Increasingly, communities of teacher researchers from different parts of the country are disseminating their work to one another and developing a class-room-grounded knowledge base from the collective inquiries of teachers across contexts. (Cochran-Smith & Lytle)

I can’t imagine how teachers did that back in the day. Actual mail? I have to say, I am so thrilled to be a young-ish teacher today, instead of 20 years ago. If I didn’t have twitter, the AP Discussion Boards, and most importantly people like dy/dan and Shawn Cornally, I would cry.

(I’m going to try to be all grad-school-y and use proper AMA citation)

Cochran-Smith, M. & Lytle, S. Teacher Research as a Way of Knowing. Harvard Educational Review. 1992;62(4): 447-474.

Books Have to be Better Than This

I am taking on a AP Statistics class next year. I agreed to do it because I’m crazy and had temporarily forgotten that I have never taken a statistics course. So I get to learn stats this summer.

I am starting with the AP review guide that comes with our text. It’s called Fast Track to a 5. (Published by Cengage to go with the Peck, Olsen and Devore book) The chapters are supposed to correspond to the textbook but be more directed to the AP exam.


This evening I found this. The problem begins by saying that the Standard Deviation for the data is 4 minutes, but then proceeds as if it is 2 minutes. On the next page, it actually states the standard deviation is 2.

This is a simple mistake, a typo, just one number. But because this is my first real exposure to the concept, I thought for a bit that perhaps when they say that 68% of the data lies within +/- 1 s.d. of the mean, perhaps that meant that 68% of the data is within one s.d. of the mean. I am confident enough in my understanding of what plus and minus means to make me raise a red flag, and a little more thought cleared it up.

But is that reasonable to expect of a teenager? A teenager who doesn’t really care that much?

This one little mistake can lead to a completely wrong understanding of how the normal curve can be used. We pay for these books, we expect them to be useful. They should be better than this.

(Oh, and the publisher doesn’t have an errata page. Maybe this could be a start.)

Playing Around with Math

The seniors are done for the year, so my Calc AB class has shrunk considerably for this last week. I had promised that we would not do calculus after the AP test, so today I had some math puzzles to think about. Next year I am going to require all seniors to create something outside of class that either takes a mathematical concept to greater depth than they have seen in class, or that relates mathematics and another class. I am hoping to give the a few ideas now to stew in their minds over the summer.

We started with .99999…=1. It surprised me that no one was willing to defend this as true. I made them split into groups and try to prove it true or false. I was struck by how little they remembers about repeating decimals. They didn’t get it until I pushed them towards 1/3, and even then only about half the class was okay with it. A few girls were very wary. They wanted to know what fraction would give .9 repeating as a result. I hope it occurs to them that there is a reason no fraction they can think of yields this. A few students tried to use limits to prove the entire proposition, which made me very happy.

Next I presented an idea about ants marching along a line and turning around when then bump into each other. This one got a lot of talk and a lot of engagement, but most students were unwilling to draw anything out on paper or whiteboard. I would like to tweak the question a bit to help them feel more confident about it.

Finally, I gave them the adding odds problems from The Mathematician’s Lament. This one worked very well. They had many different ideas, including breaking apart the numbers to find the number squared, and finding the average of the numbers being added. At the end of class I showed them the visual proof in the book and they liked it as well. I think this might be a good problem to show different ways of proving something.

In the middle of all of this, one girl started showing some others that a point on the outside of a rotating circle moves faster than a point on the middle. I don’t know why this came up at all, but they were all thoroughly stunned by the idea. This might be one of the best parts about teaching – getting to see so many people discover these great ideas for the first time.

Overall, I think the class went well. They are tired and ready to be done for the year, but I got some thinking out of them. I can only hope that it leads to some interesting conversations around the dinner table tonight.

AP Day

Today was the day. My students, every last one, sat down and took the test. Since they were all taking the test, I took a day off and had lunch with my mom. I only feel lightly guilty about that. Next year I will be teaching a few other classes in addition to AP Calc, so I won’t get a day off. Ah well.

Last night I had students in my room from 2:45 until 6:30, when I had a meeting (not counting a quick trip to Chipotle). Those students who came in are, for the most part, the ones who will certainly have earned a 4 or a 5 on the test. I would have been very happy if they had not come in for extra help, and their classmates who really needed it had. But if those students were the ones who tended to come in for extra help, they of course wouldn’t need it. I am really hoping that switching to SBG in BC next year, and trying to peg quarter grades to anticipated AP scores in AB will help with that problem next year.

And now we wait for July 7th and score reports!