Tuesday, September 6, 2011

Two things for (from) your first day...

Today was the first day back for my school, and for many others.  Leading up to it, and reflecting on the drive home, I had two thoughts about what makes for a good year teaching and learning.

First, micro: do actual math on the first day.  It's easy to get caught up in going over rules, procedures, grading standards, etc.  But why do we implement those systems in the first place?  For the most part, the point is to ensure that our students do, actually, learn some math.  How ironic to then spend the first day not doing math in order to communicate that math is the main thing!  Much better is to communicate that math is the main thing by actually spending a chunk of the period doing math!

(For the record, I doubt that going over lists of rules or procedures is even helpful. I myself have a personal capacity of learning about five rules, procedures, or standards at a time--tops--and maybe ten per day.  I doubt most students are much better.  Even at just two rules per period, the students are effectively done by lunchtime.  So there's no point in going through every detail; instead, provide a handout with the fine print, mention the big picture, and make sure to go over rules as (just before) they come up.)

This math doesn't have to be hard.  In Geometry, we go through a sequence of folds on a circle and talk about angles, symmetry, terminology, etc.  It's a great pre-assessment of what kids know coming in, and it allows us to "get through" a lot of vocabulary in a context where that vocabulary is meaningful.  In Calculus, we watched a video of a speedometer:


 and a video of my dog's ability to do calculus while fetching a ball--which wouldn't upload, so here's the original "Dogs know Calculus" video.



Both videos generated lots of mathematical discussion, and allowed me to preview the main ideas of the course.  And the students were engaged--doing math.  How excited can a kid get about the details of a quiz makeup policy?


Second, macro: do something new.  Obviously (?) do NEW math with the class on the first day: spending several weeks "just reviewing", as far as I can tell, only communicates to kids that it doesn't really matter whether they learn it the first time around.  But mostly I'm talking about you, the teacher.  Try something new this year.  Change your grading system.  (My department did: regular nightly homework, as such, is no longer counted towards student grades; instead, we'll quiz more often, and assign more interesting out-of-class work that we can collect and grade thoughtfully.)  Or change your pedagogy:
  • use videos (á la Dan Meyer), or
  • incorporate more formative data into your lesson planning, or
  • plan quizzes and tests collaboratively, or
  • create tiered work on which students can select for themselves the appropriate level of challenge (aka Challenge by Choice), or
  • design (or borrow) writing prompts that get students to think mathematically, or
  • anything else you haven't done very well before, like in that cool presentation you heard at last spring's conference.
It doesn't have to be a complete overhaul.  But if you don't set your sights on growing at the start of the year, you're not going to be able to when you can't even see above the stack of exams you need to grade.  Pick something and try it.  And if it doesn't work so great, well, as we Chicagoans know all too well, there's always next year.

Good luck, and do some great math!  In the comments: what math did you do on the first day?

== pjk

2 comments:

  1. I couldn’t agree more. Doing math early and often on the first day is essential!

    On the first day (we started about two weeks ago) in one of my courses, my students attempted to tackle both the “valentine exchange problem” and the “high five problem.” (also known as the “handshake problem”). The valentine exchange and the high five problem are related and are part of a bigger picture leading to algebraic generalization of a found pattern.

    What struck me was that the next day we looked at the “staircase problem”, which is nearly identical to the “high five problem”. However, my students really could not connect the two. As one student told me, in the “high five problem”, there are kids showing up and giving each other high fives, but in the staircase problem, there is not action, just towers of blocks making staircases. Looks like there is work to be done! And this is why it is critical that the students are thinking and doing in the classroom. If I had just stuck to “telling” what is to be learned, rather than getting students to experience it, I believe very little would be learned….both for my students and myself.

    Have a great year!

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  2. Thanks PJ, I like the videos you posted to get students talking about mathematics on the first day of class that could help frame some of the work they will be doing over the semester. The speedometer caught my eye because I had thought about using something like this before as well. What questions came up after watching it? What big ideas were hinted at?

    I thought I'd take a break from my work and have some fun :) so I made a graph based on the video you posted:

    http://tinyurl.com/supraturbo150

    I think it could be really neat to watch the video, discuss what mathematical questions could be pursued, then show the graph, and discuss what they see. It could hammer home the idea that math is a tool to analyze the physical world in which we live. I bet we could do a regression on this graph and get a pretty good function to model this situation....then what could we do with that ???? Thanks for the post!

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