It’s been a bit of a wild ride since my last post. Well, maybe not wild, but non-stop end-of-year and family stuff. I wanted to write, but simultaneously didn’t – I’ve been working out some thoughts about my teaching [and my life, I suppose] privately. It’s 7:03 am and I’m in my spacious room at Exeter, my body refusing to begin catching up on the sleep it badly needs at the end of the school year. So before the summer really begins, and suffuses last term with a [rosy?] glow, I figure I should do some reflecting.
The school year ended well – working in reverse. Our students return for 2 days and an hour (for report cards) after 11 days off for Regents exams. A brilliant plan – don’t you agree. Most of the day my room looked like the picture to the right. The few students who came to my trig classes had some questions about the Regents exam, and were then played very low key games of 24 and SET. In one of my Geometry classes, I had one student – sweet Nalain, who sat and made hexaflexagons with me for half an hour and then politely asked if he could go talk to his art teacher. But during 8th period – my last class of the year, and of the day, three Geometry students and a friend showed up; I gave them a set of Blokus and watched them go. It was absolutely delicious to listen to their banter while they challenged (and helped) each other, and when the bell which ended my first decade of teaching rang – they asked if they could stay and finish their game. Why we teach, to be sure.
My Algebra 2/Trig classes finished the year well, with engaging mini-units (all there was time for) on Statistics (regressions and normal distribution), Probability (binomial and otherwise), and Sequences and Series. The Alg2/Trig team met at the end of exams and re-organized our curriculum to better align it to the Common Core Standards (or whatever version NYS decides to go with), and I know these units will get much better attention next year because of the revised pacing. We will be using emathinstruction.com as our pacing guide with a little juggling of the units to better meet our non-annualized schedule’s needs. And my work over the last three years to teach our current curriculum conceptually rather than purely procedurally (like
many most of my colleagues) has finally paid off – my Regents scores reflect a group of students who have mastered the wide range of topics covered by the full year course. Test scores are not the be all and end all, I know. But in an environment that highly prizes success on the Regents exam by students and teachers, it feels good to meet the bar the school has set.
I never recapped my Spiky Door project. As you can see from the photo, we did, indeed, create our Spiky Door. The students drew their scaled nets, constructed pyramids, and calculated their volume and surface area. I borrowed liberally [completely] from Kate Nowak and Lisa Bejarano for this project, although I did not have the students draw three dimensional sketches of their figures; we hadn’t done anything along those lines in class, and I felt unprepared to teach them. My version of the project is here:
The year in Geometry ended with a small project on tessellations. When we returned to school after Memorial Day, there were 8 days of instruction left, broken up by a professional day and a day off for the first Algebra 2 Common Core Regents exam, with Senior Prom falling in the middle. In other words, lovely June weather, an inconsistent schedule and high absences. I wanted something hands-on that students could work on at different paces, with built in extra challenges. We talked about Escher (of course) and looked at his art work, and the geometry therein. We played with pattern blocks and made tessellations with regular polygons. I found wonderful step-by-step images of how to create tessellations using different types of transformations in this lesson from the Exploratorium. At first, I encountered some resistance (“pattern blocks are for babies.”), but the students kept each other in line, amazingly enough (“shut up – this is fun!”). And the beauty of this project, just as with Spiky Door – 100% engagement. Lots of banter, lots of math talk, and results from everyone.
Unfortunately, I do not have photos of the completed tessellations – many of which were quite lovely – although I have saved all of them as artifacts. You’ll have to take my word for it.
I am still not satisfied with all of the results I got in these classes. In Geometry for example, a unit on Coordinate Geometry came after Spiky Door and before this final assignment. We spent three weeks on equations of lines, slope, and how slope appears in lines that are parallel or perpendicular. This unit was less hands-on, and involved more direct instruction and practice (although I have a dynamite exploration on parallel and perpendicular lines, and I don’t have the correct source for it). The assessment in this unit was traditional (i.e. a quiz), and the results not great. I’ve spent a lot of time reflecting about whether my expectations for the students are not high enough, or what classroom management strategies might be more helpful in eliciting ‘better’ and more original work across the board; copying became rampant in a unit with many worksheets (lesson learned).
I have a wonderful [teacher] friend, Emma Groetzinger, who left her students and fan club in Brooklyn [me] to study at Stanford this year. Although she is far away, Emma’s new endeavor has provided us with a richer platform for professional collaboration; because of her more objective perspective and graduate studies, she is able to take a broader view of what is going on in my classroom which helps me enormously in these moments of doubt. This is what she told me – in a text, no less! – when I expressed to her some of the insecurities that continue to plague me about my teaching.
“If we can think about “doing” mathematics as not only the production of right answers but also very much tied up with being able to articulate our thinking, our process, and ask others about theirs… then we may have a broader way to evaluate our classroom spaces for productivity. Sometimes even when kids are not getting things “right” they are still learning, from their own mistakes, from each other, from the value of thinking deeply about their own thinking.”
It’s been a hell of a year. Time to go write on this amazing pad: