I’m alive, I’m alive // And I’m sinking in.
Acknowledgements
First off, thank you very much to Bowman for his amazing, thoughtful, well-written guest blog posts. I told you he was a tour-de-force and I can only say that I hope you’re finding his ideas as inspiring as I have. I’m stealing everything I can from him. I hope you are doing the same. I’m all about the concrete, and he gives me the concrete. Inspirational, he is.
Personal Update
So I’m now back in New York City. Home. I attended 5 weeks of professional development. Two weeks at the Klingenstein Summer Institute in Lawrenceville, New Jersey, followed almost immediately by three weeks at the Secondary School Teacher’s Program at the Park City Math Institute in Park City, Utah.
Yes, I’ve gone from this to this:
Current Status of My Thoughts
I have to say: I am burned out. Five weeks is a long time. I am also inspired, and hope to soon sort through all that I’ve taken away to make some serious changes in my classroom. And next year, I am only teaching two preps (Algebra II and Calculus, but not the AP Curriculum). So I will have the breathing room to make changes, I hope.The changes will involve intentional group work and formative assessments, coupled with much more intentional atmosphere building of a place where mathematical thinking (right or wrong) is valued and errors are celebrated and not something to be feared.
Yeah, I know. These are small changes and you think I need to be more ambitious.
JK. I know these are huge. It will take a lot of thinking to figure out how concretely to enact them. It’s easy to say these ideas, but it’s way harder to actually visualize them happening, if I close my eyes. I have some ideas, but not nearly enough.
I’m also worried about finishing the curriculum (especially in Algebra II) next year I try to go for depth and misconceptions and mathematical thinking, rather than try to go at those things but then succumb to the expediency of the moment and don’t allow time for grappling and productive struggling and discussion. But I’m less worried than in previous years, for some reason, and I’m ready to just go for it and see what happens. I suppose it’s because I’ve taken a vow to not underestimate my kids and their thinking abilities. Which I think I’ve done, unintentionally, and now I have to correct that. So if any of you have experiences of making the transition from teaching procedures to teaching thinking, any want to share any advice, puh-leese help me out here in the comments. (I don’t only teach procedures, to be fair to myself, but if I had to put myself in a camp, I would put myself more in a procedural camp than the thinking camp.)
I promise I’ll share my thoughts about changes I’m going to make in the classroom next year, as I sort through things, just like I did with my maybe-too-extensive blogging about standards based grading last summer.(That being said, I also suppose I have to talk about how I’m going to revise SBG for next year in calculus. Which means I have to figure out how I’m going to revise SBG first. Hu-uh. Feeling daunted now.)
Last year I was timid about making changes. I did Standards Based Gradings, and I felt that was “enough.” I think that was a good start. But it was like a bandaid on a bigger problem. I need to work on my craft in the classroom, and SBG didn’t change that too much. And so this year: I’m going for a sea change. No more glacial change, I’m jumping in whole hog, and mixing metaphors like similes are to analogies. Or something.
Contradictions
I praised Bowman for being specific and concrete, and look at me here, being all musing. Sorry. It almost feels like I’m trying to psyche myself up for next year, and committing myself to change by announcing it publicly. Yes, I suppose that that’s exactly what this is.
I hope to be more concrete soon. It’s just that, well, this here blog has always been for me, partly to archive what I do (the concrete) and partly for me to sort through what I’m thinking and get some ideas down… because when they slosh around in my head: 1. I can’t sleep 2. I get a headache 3. I get paralyzed with the overwhelming sense that I need to do something but I don’t know what. It’s the paralysis that I hate the most. So I’m hoping to avoid that by starting to put thoughts to page. But I know: I hate reading these kinds of posts too. So if you got to this point: sorry.
Continuous Everywhere but Differentiable Nowhere 
I’d love to swap notes. I’ll be teaching Intermediate Algebra at the community college, which is pretty much the same as Algebra II.
Try the Exeter problems – they are free on the web and they are not the standard textbook procedural problems. I will be sprinkling those problems both in my SBG quizzes as well as in class work and HW.
Best of luck
Dean Schonfeld
confidentlylimited.wordpress.com
In truth, all any one of us can do is choose a goal and chip away at it. In fact, “chipping away” has become one of my main spiritual and creative practices. In the moment, I get frustrated that all I’m doing is dripping water drop by drop on a rock. But then I take a deeper breath and remember that this is how the Grand Canyon was formed.
– Elizabeth (aka @cheesemonkeysf on Twitter)
Look at the Art of Problem Solving texts for problems that encourage thinking rather than procedures. The books are written for kids who love math and are good at it, so I’m not suggesting them as general textbooks, but they do have some great problems.
I came across your blog because I am teaching Multivariable next year and am planning on stealing (sorry) some of your ideas. Regarding your current conundrum, I am roughly in the same boat. I have been teaching Honors Geometry for some time now but, being at a private school, have a bit of liberty with the program. I am trying desperately to change my lecture based teaching into a Moore Method, or student driven, learning environment. My plans include Dean’s ideas of peppering in Exeter’s problems after entire chapters have been covered (and possibly after the chapter assessments have been given) as well as GasStationWithoutPumps ideas of using Art of Problems Solving questions. My first day of class is actually going to be introducing the students to the Tower of Hanoi problem as well as a standard “you have a 3 L beaker, a 5 L beaker, and an 8 L beaker full of water. How can you get two beakers of 4 L each?”. The purpose of these exercises on the first day is to demonstrate to the students that math, all math, is problem solving. The correct answer is rarely found on the first try, and making mistakes, or failing, is part of the learning process and only helps to refine how you go about finding the solution. Maybe they’ll see the metaphor or maybe I’ll have to cram it down their throats. We’ll see…
I, too, will be blogging about my ideas and successes (or failures) as the year goes on as this is quite a Herculean task.
Best of luck to you.
Hooray for another MV teacher! Next year there are no kids eligible, but the year after there will be a lot. As you probably know, I do a mixture of smaller assessments (worth little) and problem sets. And a huge final project, which seems like kids either love it or they come to hate the work because it’s so involved but then are really proud of their final product so in the end they love it.
I do a lot of lecturing, and then we go off on tangents a fair amount, sometimes in weird directions that take a week or so for us to truly fully investigate (e.g. we had a period where we tried to stack books to get the maximum overhang). It works well for me, but I’m excited to read/hear about what you do so I can modify for the following year.
I thought I’d seen the Exeter problems, but I can’t find them. Can someone point me to the right page?
http://www.exeter.edu/summer_programs/7327_7401.aspx
Hi all,
Thanks for your thoughts. For those proposing integrating Exeter or AoPS type questions in the course, I wonder how you transitioned your kids to that sort of work. What did it look like, how did you have them work on it, how long did it take for them to get used to it?
For me it’s not about finding the problems (I have both AoPS and the Exeter problem sets), but about getting kids used to using the mathematical habits of mind, and how to make that normal for them…
Sam
Sorry, I can’t help you there. I’ve not been teaching a high school class. I’ve done lunch-time math team coaching in middle school, voluntary summer school computer programming, and robotics club coaching in high school, but these are all smaller groups with no obligation for the kids to show up, so they were very self-selected groups.
I think that the two intro AoPS contest math books (http://www.artofproblemsolving.com/Store/viewitem.php?item=ps:aops1 is part one) do a good job of introducing mathematical thinking (at least of the problem-solving variety) to kids, but I’ve not tried using them in a disciplined way.