So right now I am sitting in Hynes Convention Center – room 109. In case you aren’t in the know (for shame!), I am at the National Council for Teachers of Mathematics (NCTM) conference in Boston. I just finished Day 1. I spoke to a total of three strangers, one of them who I recognized (and who recognized me) from the Phillip Exeter conference from this past summer. I don’t do well with meeting new people, which is such a shame in such a math-teacher-rich environment. But hey, three isn’t bad.
The sessions I went to today were:
#14: Identifying and Remediating Misconceptions [about CAS/TI-Nspire and developing numerical intuition]
#46: Show me the Sign! [about using sign analysis effectively in 9th, 11th, and 12th grades]
#79: Helping Students Read Math [about how to teach students to read their textbooks]
#142: Discovering Trigonometry [on how Exeter uses problem solving to teach their courses, using trigonometry as the vehicle to talk about that]
This was my first NCTM conference. Let me put this one piece of information about me: I don’t like my time wasted, so I tend to be critical of speakers [1]. I expected to really appreciate one or two of the sessions, and politely sit through the others. I thought I’d be inspired maybe once or twice.
You can see where this is going. I really, really enjoyed all four sessions. The speakers were prepared, and focused – for the most part – on concrete things in the classroom. It wasn’t about giving us the most difficult but interesting mathematical problems to work on. In other words, it wasn’t about mathematics. It was about teaching mathematics. We talked about topics and skills we work with everyday, and the speakers spoke about their approaches. None of them were zealots, saying “you should do it my way because it is the best.” It was “this is what I do, this is why I do it, and maybe you can use bits and pieces of what you hear here in your own classrooms.” I appreciated that.
I don’t know if I will have time to post about each individual session, but I will hopefully post some interesting bits later. (I said that about things I learned at the Exeter conference this past summer, and never did, though. So I can’t promise.) But maybe if (when) I actually apply some of what I’m getting to the classroom, I’ll feel more inspired to write.
(FYI, if you feel like you just absolutely need to know more about one of the sessions I went to, throw that down in the comments. You know I can’t deny you.)
[1] Yes, yes, I know our kids feel the same way, and we should always keep this in mind when we enter a classroom.
Continuous Everywhere but Differentiable Nowhere 
I love your pre-emptive footnote.
They are all very interesting. I’d like your thoughts on the following:
#79 Helping Students Read Math [about how to teach students to read their textbooks]
How much focus should there be on definitions and why do the definitions lead to the results we have? I ask because of this. Is this appropriate for the high school level? Do we need to discuss the implications of the definitions and why the conditions set in the definitions are important? Which property is more fundamental?
#142: Discovering Trigonometry [on how Exeter uses problem solving to teach their courses, using trigonometry as the vehicle to talk about that]
I’d be interesting to know how they support students through the process without giving too much away and yet still be able to reach most, if not all, students. Beyond just understanding how to get to answers in trigonometry, how much value or focus is placed on facility with trigonometric function values and trigonometric identities?
Hi Mr. H:
I think your questions re: definitions are important, but definitely need more time to flesh out my initial thoughts. In the meanwhile, though, the speaker for the “Helping Students Read Math” talk has put online all her notes and presentation here: readingmath.pbworks.com
As for the “Discovering Trig,” I left with the same questions. They did say at Exeter that the first year of math is a transition to their problem solving based courses, but by the time they are a few semesters in, they get used to it. But there is a jarring transition. The non-Exeter teacher who was using the Exeter problems in her class who spoke said that she liked the trig problem solving for her Precalculus class because although her students saw some trig in Algebra 2, the beginning part of the unit was review. So it ended up being the perfect opportunity for teaching the material in a new way, and to take them to greater depths.
As for your questions on “facility with … trigonometric identities,” I can’t answer that. I assume a lot, because the problem sets have students derive a lot of these identities geometrically (e.g. sum of angle identities).
Sam
Hi Sam,
I like the fact that the speaker acknowledges in the worksheet that filling out the worksheet for every reading may be tedious. The speaker does give students a nice checklist/tool to help them develop metacognitive skills while reading. I guess my question about the proper amount of focus on definitions (why things are defined the way they are, and what are the implications of setting those conditions) doesn’t really apply to her talk.
Problem solving is definitely a great way to keep students interested. My question was mainly about how much skills practice was done. How do they ensure that when problem solving, students didn’t miss the answer because of a lack of skills. Given the limited instructional time, I would think that trying to problem solve when students don’t have the basics would be a challenge. Imagine teaching factoring through problem solving to students who have trouble with the multiplication table. I was more interested in how “discovery of trig” is done by students. Do they derive the identities and formulas through problems or were the formulas given and then problems presented where students applied them?
Thanks for taking the time to respond to my questions.
Hi Mr. H-
The speaker gave strategies to *understand* definitions, but not to understand why they are written the way they are.
As for Exeter, my impression is that they do not do drill work at all. They get 7-8 problems a night from these problem sets (http://www.exeter.edu/academics/84_9408.aspx). I think they do derive the trig formulas — they are not given them. In the session, we derived the sum of angles sine formula and the law of sines and cosines.
Best,
Sam
I’d love to hear more about the sign analysis session, but I don’t want to add anymore to your already overflowing plate. :-)
I will try to take the time to put up a post on that for you! Once I thought about it, the key idea from the session is simple (maybe everyone but me already does it in their classrooms), but it really probably does make all the difference. Taking working with things like absolute value and quadratic inequalities to being a routine procedure to being a place where students totally understand what is going on.
I second the request for more info about sign analysis. *smile* but take your time (or have you already blogged about it and I just haven’t made it there in my reader?)
I attended the Boston Conference, too and had mixed results with the quality and appropriateness of the sessions I selected to attend. Two of the presentations were outstanding. I, like you, want to know about strategies that work. Two others were not “as advertised” and unlike you, I didn’t sit politely and listen. I headed to the exhibit halls to see what’s new from the vendors. The rest were okay…with at least something I could take away to use or at least to think about.
BTW, I presented on Thursday on using graphic organizers in algebra and geometry in middle school and high school. My room was full and people seemed to respond well to the strategies I shared that we’ve developed and used in our district. Not too many people left early, but I have developed thick skin because I know that no one speaker/presentation is appropriate for everyone and their needs.
So, I guess that somewhere, someone is blogging about me and my session and I hope it was a positive experience for them and ultimately for their students.