As shown on the scanned answer key, this was an anonymous quiz. College students have a tendency to put in pathetically minimal effort on things they're not being directly graded on. Also, the quiz's stated purpose was to help the teacher calibrate the assignments; maybe some students purposely answered questions wrong in hopes of dumbing down the class. (Though I don't dispute the author's central point.)
The author says that UW students taking Atmospheric Sciences s101 "should be the creme of the crop of our high school graduates with high GPAs".
1) Atmospheric Sciences 101 sounds like a "blowoff" class that liberal arts students would take only to fulfill a science requirement. In other words, the students are likely self-selected for lack of math/science ability.
2) UW is a public university. It may very well be the best public university in Washington, but I'd bet the best students have a nontrivial rate of private school attendance. (So as to dispel any illusions of elitism, I attended the University of Michigan, which is also a public research university.)
"UW is a public university. It may very well be the best public university in Washington, but I'd bet the best students have a nontrivial rate of private school attendance."
Don't kid yourself. This is an epidemic problem at all schools, public and private. I have friends who teach at both public and private universities, and they all have the same horror stories. My own personal experience (private undergrad / PhD at UW) bears out their anecdotes. With certain institutional exceptions, private school kids are richer, not smarter.
Also, the GPA and SAT scores of incoming UW freshman are astonishingly high right now (IQR of 3.60-3.91 GPA, 570-680 SAT math, according to http://admit.washington.edu/Numbers). Admittedly, those aren't Harvard numbers, but one would still expect a 600 math SAT student to be able to do well on a basic high-school algebra quiz.
Perhaps, but your argument was a challenge to the statement that the students represent the best and brightest of the state, and that's what I was addressing. When the test is as easy as this one, the argument that these students aren't elite isn't important.
Yes, but the questions were really easy. Even a liberal arts major should've been able to answer them. They would have seen problems like these in the first 2-3 years in high school many, many times.
In all reality most high school students don't pay attention in their math courses and only do minimal effort for what grade they required.
To be honest I was taught how to do scientific notation in one day in high school and if you asked me the rules for how many places to keep through operations I could guess but I truthfully wouldn't know. I have taken 2 chemistry courses and many other high level lab courses in college and have only heard that scientific notation was preferred not required (for the chem courses) and given no refresher course.
From personal experience I have met people who made it through AP Calculus in high school (passing grade in class not test) who really have difficulty understanding and passing a basic college algebra course.
Summary: just because people are introduced to problems in high school doesn't mean they can do them.
I'm just as upset with the state of math education in the US as anybody, but if UW is anything like my alma mater, then "Atmospheric Science 101" is a class that liberal arts majors take to satisfy their math & science general education requirements. A lot of these students (my wife, for example) have serious math anxiety. She could probably get a 70% on this test, even today, so many years after school, but throw it at her without warning on the first day of a non-math class and she'd literally cry.
Now there's a case to be made that a good high school math curriculum should not leave anyone anxious about math, but I still think it's a bit of a leap to take this test and extrapolate to all students.
Same experience with my girlfriend. She has a good analytical mind (she graduated near the top of her law class) but she's just terrified of math.
The weirdest aspects of this phenomenon are that: a) there's a very real fear of math unlike any other subject and b) there's no stigma against being mathematically illiterate as there is for other subjects (most likely because so many people just accept that "math is hard" and not for them).
I know the same story. I'm not sure what it is, but people do have a real fear of math. I graduated from the UW's ACMS ( Applied Computational Mathematical Sciences ) department which mainly focuses on scientific computing, as is obvious from the name, so I do know something about Math at the UW.
First off, let me say that UW students are not the cream of the crop. They're not daft, but the UW admits a very wide array of people. Many of them absolutely terrified of math. I don't know why this is, I looked at the test and it took me roughly one minute to complete the test in my head. However, I do know some very, very bright people who wouldn't touch math with a 10 foot pole.
Mainly, it is my liberal arts friends who have this attitude ( and I really do think it is an attitude problem ) and freeze when they encounter problems such as these.
I suppose that my point, is really that just because these kids scored low on your test, doesn't mean that they are stupid. I think they are just scared.
On a separate but related note: Until I was 14 I was in public school in Utah, and when I came to Washington in the 8th grade I was 2 to 3 years ahead of my peers in math ( this was the most advanced level offered to my grade at my school ). There really is something very wrong with math education in WA.
I have had a few friends take your class ( I don't know if it really was your class )and they've all said that it was a very hard class and they learned a lot. Unfortunately, I didn't actually have any friends take it because they were generally interested in it, they actually took it because they needed the credit. I think it's a 'Natural World' credit.
I actually wish that I had taken a few years of atmos. Given what I chose to study, I think I would have liked it. There are lots of numbers to be crunched in the weather. :-)
Is it any surprise, though? Math is taught in a manner that focuses very much on the how but rarely ever the why. And while Discovery Math/Reform Math/etc are lambasted for not teaching kids to memorize certain algorithms, they do something else that's very important: encourage students to use creative problem solving skills to develop their own solution algorithms.
I'm not going to advocate reform math in its current form, but I have to question traditional "drill and kill" teaching methods in today's modern world. If I can't remember how to find the area of a triangle, I just Google it. Drilling it into my brain would have made sense in the 1920's when there was no internet, no assurances my peers had the appropriate level of education to know such a thing, and possibly no ability to reach an "expert" via telephone to tell me the algorithm. I'd be completely reliant on my memory and (possibly) a math book if I was fortunate enough to have one with me. For all practical purposes, memorizing one half times base time height would have been the way to go in a pre-Internet era. Today, it seems like it's far more worthwhile to develop students who are solid problem solvers with strong information retrieval skills, as opposed to wasting precious time memorizing trivial algorithms that are readily available.
Is it any surprise, though? Math is taught in a manner that focuses very much on the how but rarely ever the why. And while Discovery Math/Reform Math/etc are lambasted for not teaching kids to memorize certain algorithms, they do something else that's very important: encourage students to use creative problem solving skills to develop their own solution algorithms.
The idea sounds really great, but everything i've ever seen is that the students just end up terrible at everything. I even tried to teach it some, and the material seemed great to me as a teacher, but the students just never got it. I feel like the discovery idea makes a lot more sense in hindsight, but when learning that way, doesn't work out like hoped.
However, I study applied math and I would say i learn in a more discovery way... But thats at the graduate level.
If students are ending up terrible at everything, then the problem is deeper than just tradition vs reform. What's likely occurring is we are much better at teaching plug-and-chug than we are at developing problem solving. That's to be expected, as it's significantly harder to develop problem solving skills than it is to simply memorize steps, grade, correct, and repeat until perfect. This is especially true when you consider most math teachers really aren't trained in the art of problem solving, and were likely taught in a traditional manner themselves. As such they have no real frame of reference to go off of when attempting to foster problem solving skills in their students.
Also with a triangle it can be easily shown how you arrive at 1/2 bh, and I agree teaching this is much more valuable than formula memorization. Throwing in some practical use cases school kids can actually relate to wouldn't hurt either. I mean, when you're in 4th grade, who gives a fuck how tall a light pole is.
If you're interested in reading anecdotes from dozens of genuinely smart people who were or are scared of math, you can visit this fascinating Metafilter thread in which posters address the issue.
"Why do elementary school teachers teach multiplication tables for 6 years and call that math?"
Recently my mother told me a story of when I was in elementary, a teacher told my mother that while I was quite good in English in the like, I was bad at math. My mother (who likes math and is pretty good at it) got pissed off at the teacher and told her that she couldn't possibly know if I was good at math or not, because we weren't doing math.
I actually did not ever learn my full multiplication tables, but I did learn techniques to get around not knowing them, and can know consequently multiply much larger numbers in my head than most other people. So I don't regret my hatred of memorization.
And that might be behind it. The only thing I hated more than memorizing multiplication tables was memorizing poems, but there was very little of the latter in my education; much more of the former.
I'm sorry but there is no excuse for not being able to write down the equation for finding the area of a circle. Even if you completely suck in geometry and can't remember a damn thing pi*r^2 should roll of the tongue without a second thought.
I'm almost a decade out of university and it only took me a second to spool up my basic math part of the brain. (Scientific notation took me a second to remember what it meant) But a freshman with only a 3 month break between schools should get 100% on this exam.
And I remember in France how my university professors used to complain that high school students became weak in set theory...
I didn't know that the level in the US had fallen that far... but it's true that I remember helping a girl in the nearby community college on her math classes and the level of the exercises she had was about the french 7-8th grade math.
But of course, I think the emphasis on math in europeans countries is maybe different than in the us. In France, for example, ability in math is the main selection criteria and students who took the scientific curriculum in highschool had 6-8 hours/week of mathematics and for calculating the gpa, mathematics had a coefficient of 7-9 (compared to 3 for english for example).
And because the scientific curriculum is considered the most prestigious a lot of students who intend to later study non-scientific specialities like law or business take it.
Interesting premise, questionable conclusion. Kids can't do simple concept problems, so they need more drilling? Failure to calculate 1/.1 is not due to lack of practice, it is due to fundamental lack of understanding of fraction division. This is not a problem you fix via repeated long division of 4 digit numbers. This is a problem stemming from the fact that these students were never given a good idea of what the symbols they are being forced to move around really mean.
And who cares that they don't know the definition of cosine, or the formula for the area of a circle? These are not fundamental ideas for non engineers.
In my opinion, those are fundamental ideas for human beings in the year 2010; obviously we have to lower our expectations to match reality, but we shouldn't pretend they are unreasonable. Really, how difficult is the idea of a cosine? That's not exactly an unapproachable level of abstraction.
Remember, these are people who have had 12 years of full-time mandatory schooling, and have signed up for a few more years on top of that. If anyone with an average IQ cared even a tiny bit about such things, they could learn all of it in half that time; and if they don't care at all, parents and teachers didn't do their job.
Of course, I agree with the main thrust of your post. Somehow, you have to actually encourage (and allow) the students to understand what they're dealing with, instead of giving up, moving numbers and letters on paper, and passing to the next class. If that doesn't happen, there's no surprise that they've forgotten it six weeks after the course.
I agree that just drilling on the mechanics of long division doesn't help. But, drilling the concepts can help. The point of the article is that instead of letting kids discover everything on their own and then feeling happy, teachers should direct their learning. In doing so, I would say they should drill the same concept repeatedly and ask questions that test both the ability to do the procedure and understand the concept.
Anecdotally, this is how I taught my sister multiplication and how my friend tutored someone in calculus.
and scroll down to 'Washington State Facts'. Anecdote: I attend a community college in California, found the problems laughably easy, and have met tons of people in my classes who would feel much the same way.
I would bet these students got excellent grades in math.
EDIT: As in, I'm sure that during high school they got high marks in math class without actually understanding the fundamentals of what they were 'learning'.
