TL;DR: The writer, a math teacher, is quitting (edit: his) job because of increased bureaucracy and standardized tests. Mostly, it seems, standardized tests.
The problem is, math is the subject which is BEST served by standardized tests. There is really no fuzzy aspect to K-12 math: answers are right or wrong. And there are of course many benefits to standardized testing like teacher and school evaluation, providing structure to the curriculum, etc.
His rant reminds me of another front-page HN article today (http://news.ycombinator.com/item?id=4712230), where the author claims that tough technical interview questions at Google bear no correlation with programming skill. Sure....
Consider the last few real-world problems I've solved (or attempted to solve) with math:
If you have a widget (roughly shaped like a cone with the tip chopped off) held at angle a and the widget is tapered at angle b and the tip of the widget has a diameter d, how far is it in x and y from the center of the tip of the widget to the theoretical tip were the taper continued to a point?
If two 14" pizzas feed five people, how many 16" pizzas do you need to feed eleven?
If a gallon of paint covers 400 ft^2 once, how many gallons cover a 12'x36' room with a 9' ceiling twice?
And to counter your claim that it no K-12 math can be fuzzy, if you live in a family-friendly neighborhood of x square miles, how many pieces of candy do you need to be prepared for trick-or-treating children? (This problem could easily be approached by a high school student, has real world application, but is a lot like the kind of interview problems that are often criticized as being irrelevant.)
But even if you feel these problems fit with standardized tests, the more important point is that none of these problems was presented to me the way I am presenting them to you. No one told me that angles a and b and diameter d would be both easily available and sufficient to calculate the necessary x and y. No one told me that comparing square inches would be the best way to determine how much pizza to buy. I was certainly not given multiple choices like a normal standardized test.
The real world mistakes people make with math are often more about knowing how and when to apply math, than doing the math itself. Almost everyone knows that Google can multiply and divide numbers. The real math skill is knowing what numbers to multiply and divide to see how many gallons of paint, or pizzas, or pieces of candy, you need.
Being able to pass a trigonometry test is useless if you can't figure out what to do with your widgets. Likewise for the other examples.
I'm not saying standardized tests have no correlation to real-world math ability. They obviously have some. But it's not exact. And there are lots of real-world situations that are poorly reflected in standardized tests.
I agree with all this, but consider that the type of math being tested on a standardized test is a subset of the skills you mention. You certainly can't perform complex word problems unless you can do the algebra or geometry calculations, whereas the converse is not true.
IOW, standardized testing of math is testing the bare minimum, and a successful teacher should be able to teach this bare minimum. If a teacher can do better, great!
But if "what gets measured gets done", then teachers will likely take time away from these more complex skills to spend more time going over what's on the test. This is especially true if you tie compensation and continued employment for teachers, and college admission and scholarships for students to test performance.
Functional Skills Maths and English tests were introduced nationally in the UK after concerns from employer's organisations and other stakeholders. Preparing students to take these is mostly a vocabulary exercise I have to say. I would be interested in any reactions people have to these tests. They are aimed at mature adults who work in factories, administration, medical services with non-degree qualification levels. We use them with non-academic teenagers as well as stepping stones to the 16+ standard exam called the GCSE.
There is a lot to the idea that learning needs to be situated in a context... but then assessment gets expensive!
The standardized tests I've seem often ask question similar to the ones you give, and are actually not all that bad.
The real world alternative to standardized tests is usually tests designed by the teachers themselves. There's little reason to believe that those are somehow better (or even close to the standardized ones, which are usually well thought out).
If math is best served by standardized tests, and a well-regarded and skilled math teacher is quitting because they're drowning his class in tests and test preparation rather than giving him the time to actually educate...
What does that say for non-math areas like English or Art or History?
I read this as "if any area is well-served by standardized tests, it's math" rather than "standardized tests are the best thing to happen to math". Sort of like a honey badger is best served by a snake bite.
The AMS Notices has an interesting article about a mathematician using his sabbatical to teach high school math that overlaps a little bit with this post: http://www.ams.org/notices/201210/rtx121001408p.pdf
I read it the same way as you did, that math is the best-case area for standardized testing. Thus my point: If standardized testing leads to this kind of 'driving out the good' in math, where it's most easily and effectively used to measure performance, what does that mean for less-well-served areas?
It's possible that there was a state-wide hiring freeze on teachers. State revenues, like federal revenues, declined substantially during the economic downturn. And since education is usually a major part of state budgets, it becomes a primary target for spending cuts if the state government is trying to reduce the amount of debt they're accumulating. A lot of states have balanced budget requirements, but I don't know if Oregon is one. Even if Oregon doesn't have a balanced budget requirement, there will still be substantial political pressure for the state government to reduce spending.
I'm related to two teachers, and the answer is yes, if not worse.
In IT/CS we're used to extreme pigeon-holing of personnel (So, I'm the guy who was hired to install using LVM and ext2 but we'd never hire a guy who listed ext3 on his resume...) Its all about the pigeon-holing and resume keyword scanning.
In the teaching world, its simpler, more like "we want to hire a grade school teacher". Aside from some HR fluff, that's pretty much it for the hiring ad. If there are 200 districts in your state, all of whom hire "someone" every year because of quitting / retirement / firing / whatever, then you have to send out 200 resumes to each district, just like every other unemployed teacher and/or new grad. The majority of new grads end up as retail clerks or waitresses, of course, but some do get hired. Most get hired because someone knows them... but the eternal hope of being the only applicant somewhere springs eternal, and each application only costs a small amount of time and money, so its a lotto mentality.
Sadly, that is indeed normal for people looking for jobs as teachers in Oregon, and has been normal for at least the last several years. The only districts that are really hiring are the very rural ones, and even then it is usually just one or two positions.
Looks like memorization to me. Looks like the questions are formulaic, and that students are expected to memorize both the formulas needed to answer the questions and the formula that the question itself follows. Sure, a student who actually understands the material will pass the test; but a student who does not actually understand the material can pass too, and will have an easier time doing so.
If you accept the notion that computer programming is math, then these tests are about math: you could write a computer program that uses some basic pattern matching and symbolic manipulation to pass those tests.
I disagree that using memorized formulas to solve math problems isn't meaningful learning. But granting you that, I'd argue that a student who has memorized the formulas and can apply them to that test and get correct answers is a success story. That's better than most people, and enough of a tool to make math an asset for that person in life.
Students who conceptually get it, and those who have just "memorized" will do well on atest. The test will help identifying the students who can do neither, and the teachers who are underperforming, which is the real problem.
> I'd argue that a student who has memorized the formulas and can apply them to that test and get correct answers is a success story.
but what is the goal here? I assume the goal is to teach that person how to notice a situation in real life, and use the knowledge learned at school to cope with that situation.
Does rote learning actually help for such a goal?
I argue that it _might_, but only if the situation "looks" similar to one of the pre-prepared situations that the student has studied.
Those who have grasped the concept, and is able to gain deep understanding of fundamental principles, will be much better prepared for that eventual situation mentioned above. And if i was an employer, I'd want to hire that person, instead of the one who learnt by rote.
Now, granted, there isn't really an easy way to distinguish between the two above. Which is why the standard test is used - its the best we've got. But if the teaching method is allowed to be influenced by these standarized tests such that the student, instead of gaining a deep understanding, is relegated to just rote learning, he/she will never really be able to apply what they've learnt to situations they've never encountered before, and thus, the goal is not fullfilled.
And I'm teaching someone grade 7 math in North Carolina, so this is something I care about a lot.
There's not a whole lot of secret sauce in a multiple-choice test. Yes, you can do them well or you can do them poorly. But even if you were to assume that California has super-awesome math tests, it would be pretty easy to duplicate them elsewhere.
I disagree that math is best served by these particular standardized tests. Testing can be useful (particularly something like the AMC or AIME), but when you're given meaningless problems like calculating how many watermelons Jack can carry to the store, there's better ways of assessing a deep understanding of mathematics.
Also, tests are frequently too long. This forces a student into choosing an answer quickly instead of eventually arriving at the correct solution.
Those meaningless low level problems are the basis for higher level skills. Studies have shown that students who are more capable of doing arithmetic without a calculator do better in college level math classes.*
This is not the first time I've read complaints about standardized testing being unfair, nor people rolling their eyes at defenses of testing as people who just don't "get it". What I haven't seen much of is a thorough explanations of which tests are unfair and what specifically is bad about them. I just looked at the math section of the EXPLORE test. I would be very concerned if my child was unable to answer those questions and I would want my teacher to prioritize those basic skills before his so-called "deep-thinking" classes.
Which tests are too long? It seems if tests are too long, we should shorten them. As an observer, it seems the standardized testing critics reach for any and all weaknesses of tests as a reason to shun them entirely, and it does raise suspicions they just hate the accountability.
1. Where does it say the author is a male? I didn't see that, and the name "Kris" is used as a female name just as often as a male name[1]
2. I'm not sure the parent is saying that this is the best way to test math, rather that it is better for math than any of the other subjects. i.e. 2+2 is always 4 but writing essays is a whole different ballgame.
Some very trivial parts of K-12 math can be tested, but they are the least important, imo. The main purpose of high-school math isn't to have students memorize trigonometry formulas: honestly, it doesn't really matter whether high-school students memorize trigonometry formulas or not. The main purpose that might actually have some benefit is to get kids thinking mathematically, and hopefully some proportion of them interested in STEM careers.
Same with high-school CS. You're not really going to learn a lot of specifics in high-school CS, and what specifics you learn are unlikely to be that important. What's important is to learn computational thinking. The tests, however (at least when I took the AP CS test) only tested trivialities, stuff like the syntax of a particular corner of the C++ STL, and the course was therefore set up mainly around that. We literally spent about a month on minutae of iostreams! In an introductory course where most of the students had never programmed before! I could hardly imagine a more stupid way to teach introductory CS, and can't imagine it could've been invented except via ease-of-testing brain damage.
Math may be best served by standardized tests, but it's still not very well served.
The point of a math class isn't so you can get correct answers on the test next month. It's so that for the rest of your life you have a reasonably mathematical intuition and decent math skills.
We all know people who crammed for quizzes, did ok, and forgot everything. That was a double waste; not only did they learn nothing, but they were trained to treat mathematics as hostile territory. Standardized tests reward the same sort of shallow behavior.
That's ok when there's no particular incentive to do well or poorly on the standardized test. But now that jobs and funding and careers are riding on the results, there's every reason to be suspicious of the results, and worried about a negative effect on people actually learning anything lasting.
The article you mentioned about Google's tough interview questions is from a community manager, not a programmer. If I was hiring a technical community manager, I would not subject them to the same interview process as engineers - that would probably eliminate the best community managers.
No, not guillable. We argue that there should be no upper limit on reward and equity for startups because they drive wealth / value into society, and without the incentive the startups would not get started.
The same entrepreneurial drive, to find new and better ways to teach over a 40 year career, is evident in the best teachers. And should be rewarded too for the value they drive is arguably greater.
We invented equity and shareholdings to enable rewards of entrepreneurial activity - what should we invent to enable rewards for similar achievements in teaching.
I think there's an opportunity cost as well. Standardized tests shift the focus of classroom time from teaching students math concepts to getting correct answers in the next test.
Tests are a disaster for math education: http://www.maa.org/devlin/LockhartsLament.pdf
The very essense of math is killed by tests (true for history/literature/physics etc as well).
The problem is, math is the subject which is BEST served by standardized tests. There is really no fuzzy aspect to K-12 math: answers are right or wrong. And there are of course many benefits to standardized testing like teacher and school evaluation, providing structure to the curriculum, etc.
His rant reminds me of another front-page HN article today (http://news.ycombinator.com/item?id=4712230), where the author claims that tough technical interview questions at Google bear no correlation with programming skill. Sure....