Wednesday, September 14, 2011

Another Win for SBG: Impact on Planning

I've been starting the honors course with the traditional kinematics -> forces sequence for a few years now, after a few variations.  I do displace 2D kinematics until after we've done all of the force stuff, but before we do energy.  That gives them a great chance to really own (I guess that they say 'pwn' these days) this stuff; it's a great moment about "wow, remember when we thought this was so hard?!".  The physics curriculum, on the other hand, is dramatically different.

Anyway, I try to get the honors kids into a few great habits very quickly, like using units (not just writing them down, but using them!  More on that here) and doing algebra with no numbers until the last line.  That last bit takes some doing, because they certainly have some ingrained tendencies and, while it's not actually any different, it takes a couple of weeks for them to realize that it's just the same old algebra.

It can be a bit tricky to do that well in the first part of motion (I bit the bullet and starting framing it as CVPM this year :) ), because it really just isn't that complex.  A lot of symbolic abstraction here is, for the most part, a little forced.  There are ways to build precursors to it, but full 'no numbers until the end' (NNTE) application isn't super-well applied here, at least as a beginning.

But... I don't really have to do that yet.  Sure, some kids will get a nice 'Not Proficient' on the first assessment involving the algebra standard, because they'll be missing that core skill:

Algebra (A)
Core Skills
Apply percentages appropriately and accurately

Use no numbers in algebraic solutions
Proficiency Indicators
Recognize the need for and properly apply the quadratic formula

Be fluent in algebraic operations

Use ratios accurately in problems requiring comparison of the same expression
Advanced Indicators
Use the calculator’s solver to solve an intractable equation

That's where the SBG magic comes in: it doesn't really matter!  I'm most concerned with them nailing what we've done so far, so the feedback that comes along with that grade (lots of check marks, with that solitary little x by the NNTE skill) will speak to the idea that they're doing well, but just need to work on that one skill.  They'll have plenty of time to work on that, for sure.  The grade is much less important than the feedback, because the grade changes.
Some kids will be fine with it at this point - they'll certainly have been exposed to it, and could do it, in principle.  More power to 'em.

For many, it's less an issue of ability to do it than disbelief that I'm serious about them doing it.  In that case, this'll serve as a much more specific and tangible reminder that I am serious about it.  
At the end of all of this, I can assess a bit earlier and more often than with traditional grading, because I don't need to worry about the ethical implications of giving an assessment that I'm not sure that everyone can nail (well, that's not exactly what I mean, but the "average knowledge bar" for the assessment can be lowered).  It's just that I wouldn't want to give a big one (lots of standards, lots of time, some standards not assessed again for a long time, etc.) without lots of time, but that's why the big summative tests are at the ends of the model units.  The smaller ones leading up to it are just for the benefit of the students; I wouldn't even record a grade, if I didn't want to have as much data as I could.  All I need to do is educate the kids about why we're having the assessment and what they should do after it's over (hint: read the feedback, apply the feedback, maybe look at the grade next week); after all, taking a test is better test prep than cramming! (Can anyone find the reference to that paper?  I couldn't, after a cursory Google)

Assessments aren't for me, they're for you.

PS: Why am I so super-sold on NNTE?  Other than the fact that you need to be able to do it to work at the next level, it means that you don't have to re-derive the whole thing when you change a given quantity, allows you to actually solve any problem that involves a system of equations (two unknowns, one of which isn't the desired quantity, is enormously difficult for 99% of kids that haven't mastered NNTE), gives you a chance to check your work by checking the units of the answer (without having to carry around units in your algebra), lets you learn about function dependencies (look: the coefficient of friction's in the denominator, so increasing it will decrease the stopping distance) and lets you use those dependencies to check your work a different way (should the stopping distance decrease with increased coefficient of friction? Yes, it should - check.), and lets you evaluate (and again use to check your answer) special cases of the relationship (what happens to the acceleration of the cart if the angle of the ramp becomes 90 degrees? Well, sin(90) = 1, so the expression reduces to g - that's exactly what it should do!).  Also, that was the longest sentence e v e r.

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