This is my complaint about the Chicago Math that is discussed in this article. It had infiltrated the local school district here, spending so much time telling kids the many different methods that they learn nothing at all. It spirals through all the topics, eliminating any chance to establish a foundation and build upon it. My oldest daughter had to take a basic Algebra class her first semester of college so she could feel confident that she actually knew how to go on from there. (She later completed Calculus with an A).
I have learned from this experience, though. Next daughter is only getting placed with teachers that will work on the basics instead of following the damn Chicago math curriculum as explained in the teacher’s guides. She is doing quite well.
I say BS. In most cases I find it faster to do it in my head. I don’t know how many times people have had to hunt down a calculator and start typing in numbers just to have me give them the answer. Now that isn’t true if it’s something complicated, but everyone should be able to do simple calculations in their head. At the very least be able to get an approximate answer. I mean are you going to carry a calculator around to decide whether it’s cheaper to buy the 5 or 15 lb bag of potatoes?
They spent the first week of school in math class learning about the calculator they are using this year. (TI-30X IIS thank gosh it was the cheap one) the same thing they have done his last few years according to him. (7th grader this year)
I have, no lying, seen library patrons pull out a calculator when the computer tells them they have 45 minutes left in their session and somebody’s picking them up at 5:30. Is our kids really learning, then?
And I know you said “arithmetic”, but you have got to know in your head at least an approximation of how much this shirt is going to cost if the whole store is 20% off. If you have to pull out a calculator for that, you’re as crippled as you would be if you lived in a foreign country with another language and never learned the words for the numbers, so salespeople have to write everything down for you or you end up holding out a handful of money and telling them to take the right amount.
Well, it seems clear to me that a major problem with the way I was taught math is the absence of “applied” math - in other words, when we learn percentages we should learn to estimate them in our heads because that’s when we use that the most. Of course, you also need to learn to do it precisely, but it’s absolutely essential for that particular skill that you should be able to estimate in your head. Figuring out the other leg of a triangle, it’s a lot more important to know the exact length… and to be able to express it in a variety of units, particularly the ones that wood and pipe and such come in. I mean, there ought to be a common sense portion to this whole math education thing. I’ve never, ever, EVER used my calculus. I’ve used simple trig many a time to find out how much lumber I’ll need, and I figure up tips in my head close to every day.
It disappoints me deeply to see how many tip calculators are available for the iPhone. What are you, retarded? 20% is moving the decimal over and doubling it. Don’t want to leave 20%? Figure 20 and take some off. Rocket surgery it ain’t.
The problem with teaching arithmetic by calculator only is that you end up with people who can’t check if the answer makes sense. So if they mistype, or the calculator runs out of batteries, or they don’t know how to phrase the question in the first way (that’s why text questions are so hard - you have to find the correct formula first, then solve using the normal tools), they are completly lost.
Similarly, it’s only smart to teach sailors and hikers how to orient themselves with map and compass, because GPS can fail.
There is the question of why we teach math, which, as I said, I struggle with above (of course, the same could be asked of many other subjects). As far as development of logical skills and understanding the concepts of mathematics, rote memorization of the traditional arithmetic algorithms often does nothing. As far as having the ability to compute, use of a calculator for extended arithmetic is compelling over pen-and-pencil/in-head calculation in precisely the way that use of one is compelling over interpolation from sine tables or manual extraction of decimal expansions of square roots. As far as having a general idea of an approximate outcome, such an intuition can be built in various ways, part of which can be “cluster problems”, and none of which requires full mastery of the traditional arithmetic algorithms. And as far as “What if you were lost at sea, your batteries went dead, and you needed to perform a complicated calculation?”, this is too contrived to matter for most people and can be dealt with as part of the special skills required for those for whom it is a reasonable concern.
Certainly, the traditional arithmetic algorithms are pieces of knowledge which interested people can learn at some point, just as, say, interested people can learn the details of differential equations or spherical geometry or combinatorics or whatever floats their boat. But are they fundamental life skills that everyone must learn early on, before any other math? I am dubious.