Factoring graph puzzles

Here’s the let’s-get-thinking warm up opener I used for my first Math 12 class last night.  I shamelessly stole Jason Dyer’s idea and turned it into a three-page set of puzzles.

I handed out the first double-sided page, got them going on that, and when people finished that then I handed them the extra hard follow-up.  I had them sitting in groups, gave everyone their own copy but encouraged them to discuss how to solve them.  By about 40 min, almost everyone had solved the first two sides and some were as far as the last (incredibly evil) puzzle.

Afterwards I showed them a quadratic equation and asked how many people felt comfortable factoring it to solve.  About four hands went up.  The rest of them were surprised when I told them they’d already done it.  I unpacked some of the good stuff going on in there a bit, probably got too wordy and I think I could’ve made the transition from puzzle to algebra better – maybe with a “reveal” puzzle that had more of the usual algebraic notation / structure embedded in it. Anyway, whatever, they were thinking and doing math for over half an hour on the first day of a night class – I call that a win.

Here are the files. The PDF files are ready to print; the .svg files are the source files made in Inkscape.  If you download Inkscape (a free, open-source vector graphics program) you can modify the puzzles and make your own fairly easily.  (Cut-and-paste the circles, and there’s an arrow tool to connect them.)
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The useless paper vs. computer debate

I just lost 18min of my prep time for Monday watching a Wolfram Alpha researcher give a talk on whether or not using W|A for homework is “cheating”.  The loss was that by the end, the talk had devolved into a false dichotomy of hand calculations vs. computer-based calculations.

I agree that we need to integrate tech like W|A into our classrooms, and more importantly into our assessments.  I also agree that to reach that point, we need to re-evaluate what the goals of hand-calculations are in math curriculum, and probably need to make serious cuts.

The problem of the all-or-nothing is that that kind of thinking has already been abused for years.  Elementary educators who struggle with math anxiety have used the arguments against “rote learning” as an excuse for purely calculator-based arithmetic training.  These students then get passed along and struggle with later work where it’s assumed that you can simply spot common factors because you’re familiar with your multiplication tables.

Does this matter?  Here’s the real problem: any career / lifestyle will carry with it some level of implicitly required mathematical ability in which you don’t want to pull out a computer or even your freaking iPod calculator.  This varies wildly depending on your career, from trades to warehouse work to core math skills as an engineer, but in every lifestyle some amount of rote learning and mental algorithmic skill is irreplaceable.  Math education needs to elevate people’s numeracy to an appropriate level for their life.

This isn’t just an argument for paper-based work; I want to see estimation actually taught well for once.  (Textbooks are inherently horrible at teaching estimation.)

So, don’t pretend this is all-or-nothing.  Admit it’s messy.  Then let’s dive into the real work of figuring out just how much is trash that we need to throw away.

* I’m throwing around big words because it’s quicker, easier, and I have a 1.5-yr-old next to me waiting for me to get off the computer and take him outside.  Sorry.

Night school

The update!  I am not only employed as a teacher-on-call, but I am now hired to teach an evening class of Math 12 through the district’s continuing-ed program.  This means a mostly adult group of students, widely varying levels of ability and recent math experience, and a fantastic opportunity for me to teach an upper-level math course.

It looks like I won’t likely have access to a digital projector or any of that other fancy-shmancy edumacational technology.  So I’m focusing on good ideas for how to manage notes with this group so that we can make the best of the whiteboards.  My wife has taught using a modified Cornell notes technique with some good stuff in there; I think I’d mod it further but there’s something worth stealing from there.  These other bloggers’ ideas are also theft-worthy: samjshah’s binder checks, or Kate Nowak’s homework quizzes.

Mixed in there somewhere is my desire to have downloadable notes in some format.  Bringing camera to snap pictures of whiteboards and uploading, maybe?

Also, follow-up to my official unofficial pro-d, Letters to a Young Mathematician was completely fantastic and I recommend it to any and all math educators.  I was going to blog some specific bits of awesome, but that didn’t happen and now I’ve returned the book and am far too busy prepping for Math 12 next week.  (Did I mention it starts this Monday?)

Yes, my head is spinning around full of a dozen innovative ideas I need to experiment with.  No, I am not going to try them all at once and explode.

Now to dive into the review material and see if I can pull a good collaborative challenge out of there somehow…  This is going to be interesting.