kitchen table math, the sequel: no stacking at school

## Saturday, February 19, 2011

### no stacking at school

SteveH said...

They need lots of paper and a big eraser. If they skip the erasing part, maybe they could track down errors. My first reaction was that the school must have taken a LONG TIME to teach that method. Wouldn't partial sums be more effective? If this is for visual learners, do they separate kids by learning type? What is the downside of teaching non-visual kids with a visual technique? If all of that was just to learn the concepts before using the calculator, then what do they do with percents and fractions? When do they drop the pictures of pie and teach symbolic math?

This is more about low expectations than understanding. You can always trade time for more understanding, but it this case, they don't seem to get that right.

At the very least, they could define a more compact picture for 1000 and 100. The picture for 1000 could consist of a vertical line followed by three O's. The picture for 100 could be a vertical line followed by two O's.

SteveH said...

It's one thing to try for deep understanding, but quite another to define it and decide when and if it happens. Go ahead and use boxes and other symbols. Does it work? How can you tell? Everyday Math uses stacking and partial sums to teach understanding. Is that not good enough for TERC? Some kids understand perfectly well with stacking and carrying. Does TERC believe that that can't happen by definition? Should math be reduced to some sort of lowest common denominator of understanding? Do TERC students EVER understand what lowest common denominator means? How do they test for that? If they get the wrong answer, can teachers figure out whether students really understand the concept? How many wrong answers can you get and still receive an "A". Oops, the school probably uses authentic rubrics.

They live in an eduland of fairy-thought. How many TERC students can dance on the head of a pin?

How many TERC students ever get to algebra in 8th grade without outside help? Of course, they will say that it's just a matter of engagement and motivation. It couldn't be TERC. Blame the kids. Blame the teachers. Blame the parents and society. However, they did seem to figure out that in the old days the problem was "traditional math". As the SNL Church Lady would way: "How con-VEEN-ient!".

Anonymous said...

SteveH, your idea about representing numbers with marks (a line and three circles for a thousand) is very much like an idea that ancient Hindu mathematicians used! You have constructed a very good representation for numbers, and if it works for you, then go ahead and use it!

SteveH said...

On top of that, there is additional understanding in the symbols and positions. You can talk about the numbers of zeros. You can talk about how the columns match up. Imagine. You can teach understanding with that picture! You can then teach partial sums and follow that up with an understanding of why carrying works.

With their picture tecnique, a line is 10, a square is 100, and a cube is 1000, but then what happens to their symbolism? What is a 1? What shape is 10000? What pictures do they use when they try to teach scientific notation?

SteveH said...

I wrote my first letter to the editor of our state newspaper over 10 years ago about TERC. At the time, our school was using the even worse MathLand, but was looking at moving to TERC. It ended up choosing Everyday Math. Our schools talk about how their math scores are better than before ... with MathLand.

ChemProf said...

SteveH, I was thinking the same thing. She labeled all of her pictures 1000 or 100, although not her 10's and 1's. It would have been faster if she'd just written the numbers out, even as 1000, 100, 100, 100, etc., and she probably would have been able to keep better track than with her mess of pictures.

Niels Henrik Abel said...

Missed it - the video is now unavailable.