Monday, June 27, 2005

How Much Math Should A College Graduate (Teacher) Know?

I've had a difficult time with the idea that all college graduates should be literate but not necessarily numerate (thank you, John Allen Paulos, for your book Innumeracy). What exactly is the point of a college education? Shouldn't a "well-rounded", "well-educated" person have at least some facility with numbers and computation? Students can enter the California State University or University of California systems having passed only Algebra II, and depending on their major, never again have to take a math course. This is worse than silly.

In his aforementioned 1988 book Innumeracy, Paulos had this to say in the introduction:

Innumeracy, an inability to deal comfortably with the fundamental notions of number and chance, plagues far too many otherwise knowledgeable citizens. The same people who cringe when words such as "imply" and "infer" are confused react without a trace of embarrassment to even the most egregious of numerical solecisms. I remember once listening to someone at a party drone on about the difference between "continually" and "continuously." Later that evening we were watching the news, and the TV weather caster announced that there was a 50 percent chance of rain for Saturday and a 50 percent chance for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend. The remark went right by the self-styled grammarian, and even after I explained the mistake to him, he wasn't nearly as indignant as he would have been had the weathercaster left a dangling participle. In fact, unlike other failings which are hidden, mathematical illiteracy is often flaunted: "I can't even balance my checkbook." "I'm a people person, not a numbers person." Or "I always hated math."

Yet no one would ever proudly say, "I can't read."

So this takes us back to my original point: how much math should a college graduate know? And then, how much math should a teacher know?

I won't rely on the following argument: I was a math/science/engineering major and I had to take several English, philosophy, history, and other humanities courses, why shouldn't the liberal arts majors have to take some math? It's an interesting question but not really an argument. Rather, I want to discuss what a college graduate should know, and how much math even an elementary school teacher should know.

If you want to dance, go to Juilliard. If you want to be an artist, go to the Academy of Arts in San Francisco. If you want to get a college degree, you should have a well-rounded education. In fact, the liberal arts originally included math courses, but what did those Renaissance people know, anyway? I assert that high school Algebra II is not sufficient for a college graduate. But that's just an opinion.

Teachers, however, are another story. Teachers need to know more than what they teach. A third grade teacher who cannot do fourth grade math--and that includes fractions, folks--cannot adequately prepare students for the next grade. If they could, why not just have smart high school students teach elementary level math? They know plenty more than the third-graders.

It's no secret that our math and science education in this country is subpar, especially in elementary schools. Perhaps it will take another Sputnik to wake us up. They'll stay asleep in Virginia.

Number 2 Pencil reports that Virginia is eliminating the requirement for the Praxis I exam for prospective teachers because the math was too hard. Instead, they'll take a test that "will require teachers to analyze readings, write an essay, interpret tables and graphs, and demonstrate knowledge of grammar and vocabulary, all 'on a college level,' said Charles Pyle, spokesman for the Virginia Department of Education." And Kimberly asks the $64,000 question: Why is no one asking why so many teachers - who are, after all, college graduates - are having so much trouble with basic math skills?

Update, 6/28/05 9:02 am: Showing that it's not just Kimberly who demonstrates logic and common sense on Number 2 Pencil, here's one of the comments from her post on this same topic:

At the risk of sounding horribly naive, it bothers me that a teacher of any subject would express antipathy towards another subject. I frankly don't want my son being taught by someone who can't pass a high school freshman math test by the time they are a college senior. If they have so little dedication to a fundamental area of learning, why should I believe they will be any better at English?

Update #2, 6/28/05 9:45 am: The best work on this subject is Liping Ma's 1999 book Knowing and Teaching Elementary Mathematics, which should be on the reading list in every teacher education school in the country. Ma posits that our elementary teachers do not possess PUFM, "profound understanding of fundamental mathematics", which involves both expertise in mathematics and an understanding of how to communicate that subject matter to students. PUFM includes the ability to not only solve a math problem, but to understand why your solution is mathematically sound (that is, to understand why the algorithm you used works) and perhaps to create a word problem which can be modeled by your algorithm and computation. She gives the example of dividing 1 3/4 by 1/2 as an example of the type of problem that stymied US elementary teachers in her studies, but that didn't trouble Chinese teachers (who often have less formal training and significantly less college than their American counterparts).


Kimberly Lloyd said...

I used to say that people never bragged about not being able to read well -- until I taught an SAT prep course last summer. I had students (all of whom were very wealthy) who PROUDLY stated they were illiterate (one actually used that word). They didn't read so much as the back of a cereal box unless it was directly required for school, and even then used Cliff Notes and the like to get out of anything that required brain power. Most of the proud un-readers were boys and I was at least able to talk some of them into reading the sports columns in the newspaper to get a sense of writing styles. But I still remain frightened of what happens when these children of the wealthy and the powerful bribe their way through college and become my bosses...

Darren said...

Write them nasty memos--they won't understand them, and they'll probably give you a raise because it'll look like you're working so hard.

L'oiseau rebelle said...

I took a look at the sample Praxis 1 math exam, and gosh... The math portion of the sixth-grade national exam in Singapore is way harder than this.

You mean college graduates can't even do this?

Darren said...

That's what we mean, yes.

Go ask an English teacher to do *any* of those problems. Or an elementary school teacher.

I agree with the Number 2 Pencil commenter I quoted in my update to this posting.

Anonymous said...

As a physics tutor at a relatively well-known university, I was amazed to find biology majors, food and excercise science majors, and education majors who simply could not do math. Forget understanding Newton's laws of motion, I had students who butchered fractions, made mistakes in algebra problems that are generally introduced at the junior high school level, were completely unfamiliar with the distributive property of multiplication, and one who honestly asked me how many zeros are in one million. If our schools can produce such mathematical ignoramuses and call them college-ready then we deserve to be eaten alive by other countries.

Anonymous said...

I agree, but I am an English teacher who also finds this ridiculous. I went up through Integral Calculus in college-though I must admit that my understanding was a HUGE stumbling block in Calculus. The math up to that point (basic arithmetic-Trig) I had found rather effortless. But Calc kicked my bottom!

At any rate, I am an English teacher who feels quite comfortable with math and math concepts and have even used them in my classes to show relationships (analogies, for example).

I agree there should be more focus on math literacy, but please don't paint all us English folks with the same brush-some of us do find other disciplines important.

Darren said...

You're right, Doug. Broad brushstrokes are usually a bad idea. You must admit, though, that you're closer to the exception than the rule, at least in my experience. I've had both English and social studies teachers, in a parent/teacher/student conference, say the forbidden "I wasn't any good in math at school, either." Makes me want to kick some butt.

And first year calculus kicked my butt for awhile, too! In all honesty, one morning I just woke up and it all made sense. I guess all that banging of the head against the wall paid off in some subconscious way!

NYgirl said...

You make a good point. However, teaching more material requiers more time, & at present, a good portion of the teaching hours are dedicated to politcal indoctrination.
What did you learn more in your humanites & soc sci classes, subject matter or propaganda? This is the real why reason everyone is requiered to attend humanities & social science classes.
As of yet, math classes do not do this & until they do, we will not see an extensive math requierment of college or secondary school students.

Edward said...

Here's a word problem for some of the dumber math teachers:

It takes 1/2 a cup of sugar to make one batch of marijuana brownies. You have 1 3/4 cups of sugar. How many times are you going to get stoned this weekend?


Darren said...

NYgirl, go read *this* post!

Batya said...

My math-gifted daughter suffered terribly because of teachers who were weak in Math to the extent that she failed it in jhs. Her mind was so much faster than the teacher's that she ended up sleeping during the lessons.

NYgirl said...

Thanks for the link Darren.