Tuesday, October 28, 2008

Continental Math League Update:

Enthusiasm from students and parents; skepticism from teachers.

Specifically, about "stacking."  (Today's word for how we used to add, subtract, and multiply numbers by placing one number on top of the other.)

Kids love it.  And not just the ones on our team.  As Nancy Bea Miller writes:
When I showed one of my sons how I had learned addition, i.e. the "stacking" method, he was very impressed. "Wow, that's so cool! That works great! I wonder if my math teacher knows about this?" was his innocent comment.
Yes, she does, and she doesn't like it.  At least if she resembles the teacher who approached me after math practice yesterday and recounted the dismay she felt when she caught one of her students stacking numbers, thus abandoning the more "meaningful" and "faster" way he used to solve problems.

My co-coach and I tried to explain that the Continental Math League numbers are big enough, and random enough, that Reform Math's methods aren't faster and more meaningful, but inefficient and confusing. It's one thing to add 48 and 39 by reasoning that:
48 is 2 less than 50, and 39 is 1 less than 40, so add 40 and 50 and get 90 and then count backwards by 3 and get 87."
But take one of the problems we did at Continental Math League yesterday: 825 - 267. Restricting myself to the kinds of calculation that these second and third graders are able/expected to do in their heads, here's the most efficient non-stacking method I can come up with:  
The closest friendly number to 825 is 800, and the closest friendly number to 267 is 250.  825 is 25 more than 800.  250 is 10 more than 260, and another 7 gets you 267.  10 plus 7 is 17.  So 267 is 17 more than 250.  So subtract 250 from 800. Well, 800 minus 200 is 600, minus 50 more is 550.  Then subtract 17 from 25 by counting up from 17.  Seventeen plus 3 more is 20 plus 5 more is 25.  3 plus 5 equals 8.  Add 8 to 550* to get 558."
*By this point in the problem, how many people remember what they should be doing with this 8?

Anyone with a more efficient non-stacking method for subtracting 267 from 825 (no calculators allowed!) is invited to share it here.

2 comments:

Anonymous said...

825-300=525
525+33=558
I'm not sure if that's cheating with the 33 though.

Pat B said...

I do problems like this using what I call "counting on." Subtraction is how many to get from one to the other...so start at 267 and add three (easy) to get to 270, now thirty more to get to 300 (that's 33 so far) and then 500 to get to 800, (easy, 533) and we need 25 more, (533 --> 553--> 558 in baby steps)
compare to the stacking method for problems like 2003 - 978 especially..