Wednesday, March 26, 2014

The Subtraction MathWars

I'm sure everyone has seen this "letter" from a"frustrated parent" who claims that despite having a degree in "electronics engineering", can't figure out the child's homework.

I call "Shenanigans", both on the letter and on the responses.

First, we must accept that the "parent" can't read instructions, is pre-disposed to being an asshole over the ways in which our children are taught math, and is probably not all that capable of understanding basic principles.

In addition, when claiming that "simplification is valued over complication", he failed to note that , in business, "Completing the Assigned Task" is given far more weight than "Over-simplification and pedantry."

 ... but I digress.

In the "Bad Old Days", I recall many instances in which people browbeat math teachers with the anecdote, "I went to the store and bought $13.82 of stuff and the kid behind the counter couldn't make change for a $20. You teachers need to teach them the basics."

The standard algorithm vs. The New Way (which isn't so new; it's "Making Change") - look at that problem up there. Pretend you just bought something worth $111 dollars and you handed the clerk a $427 check. How much money do you get back? Follow the little jumps and imagine someone slapping bills into your hand. Makes a lot of sense now, doesn't it?

So here's what needs to happen: Kids need both.

Sorry, Reforministas, the standard algorithm is more useful and easier sometimes.
Sorry, Ostrich-Headed Blowhards, the "New Way" is more useful and easier sometimes.

Let's face facts.
- 316
is much easier when done vertically. No borrowing, no hassle.

Even a problem that contains a "borrowing" is often easier done with the standard algorithm. It's more compact and it's cleaner. 492 - 327, for example. On the other hand, the "Counting Up or Down" is easier when you are close to certain values, such as the infamous 30001 - 29999 question.

A professor suggests that anything that can't be done with the New Way should be done with a calculator or WolframAlpha, but I disagree completely. He provides research that states teaching algorithms to young elementary students is harmful. I read the studies but I don't agree that we should NEVER teach the standard algorithm and borrowing; I just feel we should be more intelligent about it.
  1. Kids should eventually be comfortable with both ways. 
  2. Timing is critical. Maybe the New Way should be taught before the Standard Algorithm. 
  3. Also, be more willing to MAKE kids learn the SA, even if it's temporarily painful. If they understand place value and the counting up and down, they can learn the SA.
  4. Be less anal-retentive about the size of the problems and the difficulty of the subtractions (7 digit from 8-digit is extreme).  
  5. Stop insisting that the calculator is the Deus Ex Machina of mathematics. It is a tool and should be used to make already-understood work easier, but not if it replaces the understanding with No-Think Monkey Push-Button
Teach them both and then let them choose. Each method has advantages and each has disadvantages.

We can't be doing this:
DC: "Go ahead, use your standard algorithm to compute: 4,000,002 - 3,999,999"
Me: "This problem is better solved by counting up. 41036 - 28569 is easier solved by subtraction algorithm.
DC: "That is better solved with a calculator. #justsayin"

No. NO. Goddamn it, NO.

"There's no longer a reason to memorize a mindless math algorithm."
What if it's NOT meaningless?
Jumping to the calculator the instant the problem gets slightly weird can only lead to disaster for students. If I gave the student four hundred of these, I'd expect him to cut and paste into a spreadsheet or WolframAlpha, but one problem and he gives up and reaches for a calculator?

"There's no longer a reason to memorize a mindless math algorithm. There's plenty of reasons to understand thinking behind them." I agree with that. Proper teaching starts with understanding ... but then, once you understand the method, the algorithm is no longer meaningless; memorization occurs organically. The algorithm NEEDS understanding of place value.

When I reply that "Algebra, messes it up for many: 410x - 36y - 285x + 69y, as does calculator madness" (see the madness) and the response is, "Thankfully WolframAlpha", well that's when you know someone is not dealing from the top of the deck.

Yeah, Wolfram gives you the answer, coupled with

How in the bloody blue blazes of hell is that useful to someone who can't subtract?

1 comment:

  1. Curmudgeon, what do you think about this: mental math, short cuts, re-arranging numbers in your head, etc., are very important skills. Anyone who is proficient at the basic operations also still uses the more idiosyncratic ways all the time. BUT, each person ends up using the tricks that work best for them, and they develop a menu of tricks and methods over time, with no threat of failure if any particular trick just doesn't do it for them. To my mind, requiring young children to use complicated tricks in order to solve problems and to write about them, for crying out loud, is a terrible pedagogical mistake.