math questions

[meganursula]

Yesterday i posted something, a quick and dirty post referring to a 'math test', and a blog entry from a local scientist and professor. The test was meant to test students coming into a science class for basic math skills, and the blog entry reflects this guy's frustration with the math curricula in our state that is turning out more and more college students who don't have the math skills to succeed in his science classes.

Now, i've read a lot by this guy, and i was just intrigued by the two minute math test, and i didn't bother to read the whole blog entry. I was surprised to see a few (mostly non-math) students complain the entry was really condescending and insulting. I was not expecting, but upon reflection, am not surprised that not everyone got through the whole test easily.

So, i figured i'd better go back and read the whole post. Here is the thing - i do not see it as being condescending and insulting (except, perhaps, to a few policy makers with whom he has a recognized feud over math curriculum decisions). I did not see in there a place where he claimed that everyone who could not pass the test was to be pitied or looked down upon, and i did not see a lot of blame being placed on the students who are being harmed by the current system. I did see some vitriolic words about the 'discovery math' approach. I guess that doesn't bother me, because i, too, would be frustrated if i felt like the public schools that are supposed to be educated our students were continually making decisions to use a math system that has been shown to decrease competency in college bound kids, and pretty much panned by all scientists and mathematicians who have evaluated it.

But, perhaps i cut him too much slack because i believe our public schools are NOT turning out students who are mathematically and scientifically literate, and i believe the current curriculum choices probably are a significant problem when it comes to teaching college bound students the skills they need to succeed.

On the other hand, i was thinking about the math test in question. I understand why it is a decent test for his class - a science class. Clearly, science students need to have some specific math skills that literature students don't. I'm not sure it is a good class for overall mathematical literacy.

Still, i'm not sure what is. I generally hate 'closed book' exams, because i think it is more important to be able to look up something and use the information than it is to remember it off hand. This is particularly true when you are dealing with something that you are not currently working with on a daily basis, but i also felt like it was true with engineering equations i was working with a lot. My memory is such that i often stumble on simple names, dates, equations, etc.

Why should someone who isn't working with geometry know the equation for the area of a circle? (On the other hand, that is a basic equation, so it doesn't seem like it is asking that much. Is it okay to draw a line somewhere?)

It seems like our curriculum should turn out students who are confident enough to discover the skills they need in life, if they don't have them at their finger tips. How do you test for that? At the same time, it is unreasonable for a intro level science professor to have to teach all the math skills needed for that class, so the curriculum also has to touch on that material. No matter whether we like it, it does seem like the students leaving high school should be able to pass a test with some of the basic information. It seems like it would be harder to pass the same test if the material went out of practice for ten years, but hopefully those same students would be able to catch up faster with a refresher if they needed to.

(And, for my non-math friends in particular, please note that i'm not trying to say that these math skills are more important, easier to obtain, or somehow intrinsically 'better' than the equivalent writing or debating skills. It is a problem for me, actually, because while i believe strongly that math and science education must get better, i also believe that history, reading comprehension, and writing education must get better. I happen to have more of the math and science than a lot of people, which makes me realize exactly how much i am lacking in the other fields. It is really hard to improve all this stuff at once.)

Comments

[cheesepuppet.livejournal.com]

I think public schools do a terrible job with math, so I don't feel you're being unreasonable at all. High School students should graduate with a testable body of knowledge about math concepts. Adults, I think, should at least be able to identify and look things pretty easily. For instance, I was able to articulate, "I need to find the circumference; can I get that from the diameter?" While Jason's ability to walk in and do it all in his head in ten seconds was intimidating for me, I do think I would have gotten it myself eventually because I knew what I was looking for. A lot of people I know would literally have no idea how to solve that, except, "Go to the jewelry store and ask for a ring sizer." Which I really think is sad.

I don't think the article was that bad, but I did bristle at this part:

If many of our state's best students are mathematically illiterate, as shown by this exam, can you imagine what is happening to the others--those going to community college or no college at all?

For many years the only college I had was two years of community college, and it was amazing to me how to many people (like this blogger) that seemed to be equivalent to no college at all. When I was interviewing endlessly (I think I had five meetings altogether) for a sales position at lucy.com, I finally reached a meeting with the CIO, and we had great rapport. Eventually he asked what I majored in, and I said I had a couple years of work at PCC (Portland Community College) but I hadn't completed a 4-year degree.

The guy in the fancy suit made this big show of being impressed, and then said, "REALLY? Well that's just AMAZING! You're so well-spoken and intelligent for someone who never went to college!"

I was completely stunned. I ended up getting the job, but I ran into that attitude over and over. What's funny is that now that I've gotten into two universities and I have a half-finished Bachelor's degree in an Actual Declared Major, I get a lot more respect, even though the classes at the university were not nearly as challenging as some of the classes I had at community college, and my classmates were not any smarter (see: the girl who openly admitted to our professor how she'd cheated on every test so far that quarter). If anything, they were a little better dressed, and I paid three times as much to do the same level of work.

Which brings me to: I'm frustrated with how an "education" is seen to be the same as "educated". It means so such thing. I live with two senior-level engineers who never finished college but can both solve just about any real-world math problem that comes their way. I'll probably get my degree before either of them, but will that make me more "educated" than Greg, who could probably outline for you on the back of a napkin every major historical event since the fall of Rome without batting an eye, or Jason, who when I said he should get an air filter, went and built one? I don't think so.

I wish I'd been taught math in a way that was relevant to my life, and I wish it had been designed to encourage the average student to succeed, instead of (at least in my painfully white high school) making math into this elite subject that only kids bound for college should really worry about - and if you are bound for college and you're not doing well in calculus, you're DOOMED. You aren't doomed, you're never doomed. I doomed myself with my own all-or-nothing thinking about it, and now that I have kids learning math at school and at home, I'm amazed at how fun it can be.

And now Miles has to go to Taekwondo and I need to go! :) I'll try to be more succinct later. I've gotten interrupted a hundred times already.....

[jedusor.livejournal.com]

My friend Gerry, who (like me) did two years of community college and then transferred to Clark last year, told me about a T.A. in our Experimental Methods in Psychology class who, during discussion (I was in the other discussion group and did not witness this personally), said, "Now you've all had experience writing research papers--oh, except you, Gerry, you went to community college."

He immediately asked her to step outside the classroom and told her that the remark was out of line. I remain impressed; I probably would have reamed her out right there in the classroom.

[cheesepuppet.livejournal.com]

Wow! I don't know what I would have said in that situation, but I'm guessing reaming would be right up there. I think he handled it extremely well.

[msde.livejournal.com]

Yeah, I've pretty much got the same stance with you regarding the test, and I don't have any interest in the blog or his viewpoint. If college freshmen majoring in a science can't handle the test, something is wrongn with our system. This is the stuff you might have hated in high school, but it's something you forget over time from disuse, not something fundamental you never learned.

The test is a bit unfair if you shove it in front of someone unfamiliar with things like scientific notation. I don't think I learned that until after I got through the minimum diploma requirement. However, it isn't a test of basic high school math competence. It's a test for undergrads who have self-selected themselves into a career in science.

[eub.livejournal.com]

He's clear that he doesn't think students (or other people) who can't answer these questions are deserving of blame. But he does use language that carries negative associations. "Crippling their ability to participate". "Embarrassing", "disaster" -- he wouldn't say people should be embarrassed personally, no, just that they're what's embarrassing? Their abilities are embarrassing. To education administrators, but whatever: he's saying, your abilities are an embarrassment to someone. That does sting.

[eub.livejournal.com]

My own ungrounded math-education rant: who cares about the long division algorithm? Drop it, along with the square root algorithm (which they used to teach in schools -- it's in old textbooks). Stop wasting time on arithmetic, use a damn calculator.

What everyone needs to be able to do in their head, fluently, is to estimate to one significant figure, or just to order of magnitude. That the arithmetic that people fail on, in practice, over and over.

I don't understand our high-school emphasis on trigonometry, either. It's fun, but it's not terribly useful, and it's not really a calculus prequisite for that matter. I'd rip it out and teach some basic probability theory, and probability applications.

[eub.livejournal.com]

About the "Discovery Math" business, I haven't read much. There may be strong reasons to believe that children taught with these texts don't learn as well (by standards without a circular definition of "well"). What I've read was on Cliff's blog, when he linked to some assessments of mathematical soundness of various textbooks. Ah, this PDF (http://www.strategicteaching.com/hs_curriculum_study_by_plat.pdf). I was expecting to be a "mathematical soundness" hardass, and I found it surprising how little I cared about what they were judging.

For example:

None
 of
 the
 reviewed
 programs
 provided
 the
 appropriate
 justifications
 for
 the
 basis
 of
 the
 graphing
 of
 linear
 functions.
 First,
 no
 program
 shows
 that
 the
 graph
 of
 a
 linear
 equation
 really
 is
 a
 line.
 
 Second,
 no
 program
 shows
 that
 a
 line
 in
 the
 plane
 is
 the
 graph
 of
 a
 linear
 equation.
 Third,
 although
 slope
 is
 defined,
 it
 is
 never
 shown
 that
 slope
 is
 well‐defined,
 namely,
 that
 slope
 is
 independent
 of
 which
 two
 points
 one chooses to compute it.

These just are not on my "must have" list for an Algebra text. Should they be?

math test

[lorraine-inwa.livejournal.com]

well, I took the math test and did not do well. I do fine with arithmetic (adding, subtracting, multiplying, dividing, knew the formula for the circle, etc.) BUT the vocabulary of Math is not present. It has been 50 years since I have had need of algebra etc. I agree that math teaching is terrible. When a sales person cannot make change, or a person cannot figure out half a recipe or how to double it, it is sad.

I don't want to rant about poorly prepared teachers in all areas but when the teacher cannot make subject and verb agree in a sentence, how can you expect the student to do better?