## Progress Report

It has been, as usual, a busy year. It seems that this is absolutely the norm in our professions, isn’t it? I am teaching three classes this year – AP Calculus BC, AP Statistics, and Geometry. In the next few days I want to comment on all of these classes as time allows. Unfortunately, this is the week we are working on midterm grade comments for every one of my 68 students AND my mom arrives tomorrow night for a visit as this is grandparents’ weekend here at our school. The two things I want to share today are reflections on the progress of my Geometry class and a class visit I made last week. I’ll tackle last week first.

We have a number of students who finish the Calculus curriculum before they graduate here. Those students – who have has two years of AP Calculus (we teach BC as a second-year course) move on to an Applied Differential Equations class taught by our school’s President. He is a retired Army engineer and he teaches a lovely Problem-Based curriculum using Mathematica. He ran into me in the hall last week and mentioned that his students were presenting the results of their first research problem and he invited me to join them on Friday. I was able to watch as two of my former students presented fantastic work that they had done on their own on a research topic of their choice. One was presenting a supply and demand curve. She explained her choice of parameters and shared the results. Her classmates made note of the similarities to a predator-prey problem that they had worked on together. She eloquently addressed the similarities and differences between the problems, but what most impressed me was her response after one of her first graphs. She remarked that the graph did not fit what she suspected should happen and her slide suddenly displayed the phrase “Question Results” and then she moved on to discuss her modification. I loved the directness and the simplicity of this message. Just because a fancy machine, and Mathematica is a VERY fancy machine, tells you something, it is not necessarily true. I have to incorporate such a simple response into my repertoire when looking at surprising or counterintuitive results. The second presentation was analyzing the forces involved in walking on high heels. It was a fun discussion and I was impressed by the depth that the student found in examining this situation. Unfortunately, our school President is retiring and I suspect that our new administrator might not have an engineering background. It’ll be up to me as department chair to find someone capable of carrying on this kind of high level work with our best math students.

i’ve been thinking about this all day. Remember, this is my 8 AM class. I have resisted some activities like this in the past thinking it just was not my bag. However, I am working closely with two terrific colleagues in Geometry this year and they sort of encouraged me to try. I stepped out of my comfort zone and the result – at least this time – was a relaxed and fun class. Kids were engaged, they supported E and gave her some real praise and after class one of my students who has been struggling so far came up to me to tell me how much fun she had. I think I may have earned some important personal capital in working with her and this may be a gateway to building a relationship with a student who does not seem to have much inherent love for my subject.  I also think that some valuable points were made about the challenge of explaining what you know to someone who does not know it. I am optimistic that this will help build a bridge toward understanding some important principles of proof in the next week or so. So, thanks to my colleagues for encouraging me to try something that seemed a bit silly to  me. Thanks to E for being a model of thoughtfulness and detail. The rest of her work this year has been uniformly outstanding, so I was not exactly surprised by this. Thanks to my students for trying an assignment that probably seemed a bit weird. Finally, thanks to Max Ray for this thoughtful book that got me going on this path.

## A Geometry Revelation to Remember

We are working with isometries in our Geometry class right now. We are looking at vector translations of objects, rotations (primarily around the origin), and reflections over horizontal or vertical lines. I am only teaching one section of Geometry so sometimes I feel like if I don’t get it right, I’ve missed an important opportunity. There have already been a couple of instances where I explain something after school in a way that I wish I had done the first time around. I am trying to keep note and be a smarter Geometry teacher next year.

At least it feels that way now. I’ll see (and report back) after our quiz tomorrow morning.

## That Visible Learning Business Again

I gave my AP Calculus BC kiddos some rough problems to deal with on HW last night. On one of the problems they were asked to consider the greatest integer function – to be called the floor function from here on – and they were to graph the relation (floor(x))^2 + (floor(y))^2 = 1. A tough problem for sure but a couple of students nailed it. Most did not, so I fired up Desmos to show them the graph thinking we’d spend some time discussing why the graph was what it was. Desmos gave a nice graph but one of my students insisted it was not quite right.

So, I told them (kind of bragging, honestly) that I had met Eli this past summer and I would tweet out our issue. My last blog post was about sharing my learning with my students and here was another great opportunity. Eli tweeted back with another go at the graph – found here

This happened while we were still in class! I got to show my students this graph and it still was not quite right. I wrote back to Eli again and his response was awesome. He tweeted back that this problem would be a lunch time conversation at Desmos World Headquarters. How fantastic is this? I get to share with my students tomorrow that a problem we shared out to the world was going to result in some brilliant guys reprogramming their fantastic tool so that it would tackle this thorny problem. Don’t know that it gets much better than this. Oh yeah, as an added bonus I was sent another take on the problem by Christopher Danielson. Here is his take

Days as a teacher don’t get much better than this. Oh yeah, I should note that I got so wrapped up in these tweets and talking to my Calc students after school about this problem unfolding that I was late to get my children from their bus. A friend had to call me to get me out of my classroom building to go grab them. For one afternoon math seemed more exciting than seeing my own children.

## Making My Learning Visible

I am in my 28th year of teaching high school math (with some overlapping years of middle school math thrown in as well) and some would think that I should have it all down pretty well but his point. Luckily for me, this is only partially true. Also, luckily for me I have a great community of support online (I’m looking at YOU #mtbos.)