## Saturday, October 17, 2009

### Methodology

I am a collector of methods. I like finding new ways to do the simple operations and neat new ways to look at mathematics. I do not feel these methods should be shown to students.

Teach one method. I am in favor of the algorithms that I grew up with. Old fuddy-duddy? Maybe. Tough. The old ways work. The old ways are usually simpler and easier to use.

Think subtraction. 759-384. Do it your way. Now try to follow this.

Why are we bothering to re-invent this wheel?  Isn't one way sufficient for the students?  I feel we should wait until they have completely understood one method before we confuse them with "Other" possibilities.  If a student comes up with this on his own, great.

Sheesh.  No wonder kids get confused if this is what they're taught.
h/t to parentalcation

1. That is actually the method I use for adding/subtracting sans calculator or paper. But I arrived at it on my own while in college.

I agree the traditional method works better for instilling a sense of place value, borrowing, and regrouping. For example, it is easier to teach subtraction of mixed numbers if students can use the traditional method.

My youngest son does some weird thing with rounding and then adjusting. 760 - 400 + 16 - 1 I think that is what he does.

2. I do arithmetic 'funny' - but I was taught standard algorithms (sometimes after using place-value-emphasizing algorithms first, as a pedagogical transition)

So, your example: 759 - 384

I generally subtract left to right, a few columns at a time.
75 - 38 is 37
9 - 4 is 5
375

I teach high school students "no carry" subtraction, just to impress them with something that seems cool.
384 is 16 shy of 400.
Add 16 to both numbers, and subtract:

775 - 400 = 375.

I've done what Peggy's kid does, as well.

I've never seen this "Partial Differences Subtraction" before. Mildly interesting. It does not offend me, though I think kids should not be allowed anywhere near it before mastering standard algorithm.

Jonathan

3. This is one of the disappointing things about "standards based curricula". A belief like yours: "it's fine if a kid figures it out on his own" morphs into "everyone should learn to do it all of the possible ways"
Bleah