Math Education: An Inconvenient Truth

This video has been sweeping the internet and all across the land people are getting up in arms about it.

The video details how math curriculum is changing in regards to multiplication and division. People are furious.

The crux of their concern is 4 fold.

1. The ways being taught aren't the ways we, or our parents, were taught.


2. These new methods make math harder to do.


3. It is vital to kids' future that they be fluent in multiplication and long division by hand.


4. Calculators are sent by Satan to ruin society.

My feelings on the subject are as follows:

1. I don't think this is necessarily a valid concern. We shouldn't continue to use the same teaching methods for the sole reason that it's the way it's always been done. Now, their concern is more along the lines of "How are parents going to help with homework?" than "we fear change," but this still seems silly. Any parent that couldn't wrap their head around one of these methods in 5 minutes to aid their kids isn't going to be much help to them anyway.


2. Maybe it does look like it takes longer. First of all she takes overly simplified examples, perhaps the "new" methods are streamlined on larger problems.
   Secondly, she draws them out longer than they need to be. There's no reason to do half of the "sub steps" she does. Besides, how long they are on paper, however, is irrelevant. I'll get into that in a bit.


3. Is it? I took a crap load of math classes in college. I have a job where I invent and implement algorithms for solving problems given to me. I wouldn't be surprised if the number of times I've done multiplication by hand, since it was a school requirement, was under 30 or forty times. I wouldn't be surprised if the number of times I've done pencil and paper long division was in the teens.


4. Ok I exaggerate their stance on this point, but this one has always irked me. I've had to listen to this for years. Be it on the internet, from people like this, or from customers at some of my "joe jobs:"
   
   : None of you kids can do math without your calculator anymore! In my day we did it all in our heads! RAAAAAAA! Calculators!!!
   
   I'm really getting sick of it. It's true that 40 years ago they probably did a lot of math the long way. You know what though? There's a reason us "whipper snappers" are doing math as high school sophomores that you would have had to go to college as a math major to see 40 years ago. You know what it is? We don't have to piss away time on the most basic portions of the problem! Of course in a Utopian society we would be able to throw any math problem at a person and they could reply without hesitation. It's just not feasible to do so. Calculators are readily available, and that fact allows people to shift the focus off of that portion of the problem and onto the bigger picture.
   
   I remember cursive being beaten into my head as a kid. "You need to learn this to get into college." "No professor will accept anything in print." Do you know how many times I've used cursive in my adult and collegiate life in an assignment, report, or work matter? 0. Zero. Not one time. Should I have demanded my professors accept my cursive? After all, a good portion of my education was wrapped up in teaching me this "new language." Paper and pencil, and in turn cursive, as a mode of communicating in "official" fashion were replaced by something better. You can shift the focus off of penmanship (and for that matter, spelling) and focus on what you are actually trying to say. It's not without it's concerns, but technology that allows us to take our eyes off the nitty gritty details, and look at the big picture, is a good thing.

I think the most tragic thing in all of this is that they are failing to see that what is taking place is exactly what they are arguing should be happening. If you teach kids multiplying in the traditional "brute force" method, then they will almost always turn to a calculator over a pencil because they are bound by a very specific set of rules. The time it takes to find a pencil, a clean sheet of paper, and execute those rules exceeds the amount of time to find a calculator in most cases.

The lattice looks odd, but it's also looks pretty efficient. The partial products method is so similar to the "old" method it's hardly even worth arguing about.

If they learn to do math through the "clustering" method, on the other hand, you know what happens? They learn that math can be REASONED through. It looks like silly extra steps on paper sure. That really isn't the point. Learning that often times problems can be solved by figuring out smaller, easier, subproblems, rather than recalling and executing a rigorous set of rules for solving the larger original, is an excellent lesson to teach kids.

Besides that, if they get good enough at the clustering method, in the end they wont need to reach for a pencil or a calculator at all.