Thursday, January 28, 2010

"Community" TV Show

The NBC comedy "Community" gets way more things right than they have to. For example: The sexpot statistics professor.

But wait, there's more. I've long held a theory about performance that, "No actor can play more intelligent than they are in real life". Largely this is a matter of diction: I hear actors stumbling over, or putting incorrect emphasis on, pieces of vocabulary that they don't really know or use themselves in daily life. "Community" places really great actors throughout the ensemble; they're delivering lines like "as long as we keep the work/fun ratio the same I want to keep seeing you", and "the deception is making the sex 36% hotter" so fluidly that they slide by almost without me realizing that they were meant to be jokey.

Tuesday, January 26, 2010

Elementary Teachers

Did you know?
Beilock, who studies how anxieties and stress can affect people's performance, noted that other research has indicated that elementary education majors at the college level have the highest levels of math anxiety of any college major.

This in a larger article finding:
But by the end of the year, the more anxious teachers were about their own math skills, the more likely their female students — but not the boys — were to agree that "boys are good at math and girls are good at reading." In addition, the girls who answered that way scored lower on math tests than either the classes' boys or the girls who had not developed a belief in the stereotype, the researchers found.

http://news.yahoo.com/s/ap/us_sci_fear_of_figures

Sunday, January 3, 2010

Phonics and Bases

Speaking of the "Math Wars", here's an observation I made about teaching the most basic elementary-school subjects.

When I was very young, we were taught reading by "phonics", i.e., sounding out the letters of unknown words, and then thinking about how those sounds related to words we already knew. Sometime after that, phonics was dropped for a "whole word" approach, but it seems like the pendulum might be swinging back these days.

Why do "phonics" make sense as an instructional strategy? Because our system of writing is a technology based on exactly that principle. The whole point to our alphabet is that it is phonogrammatic, i.e., written symbols represent spoken sounds. This system of writing is meant for there to be an obvious connection between what we write, and what we say. (Of course, this is totally different from logographies such as Chinese whole-word characters and Egyptian heiroglyphics, but that's an entirely different story.) In teaching a child to read, why would you not use the language tool the way it was designed to be used?

Similarly, the traditional way of teaching arithmetic is to memorize a small number of basic facts (addition and multiplication tables), and then learn fundamental written procedures for adding, subtracting, multiplying, etc., large (many-digit) numbers. More recently, we've had to deal with the "Math Wars" is which training in time-tested prodecures has been frowned upon as too authoritarian (or something). Rather, there appears to be extensive time spent in base-10-system conceptual understanding, and then inventive or creative exhortations to make up your own multifarious addition, subtraction, etc., algorithms.

Why do "procedures" make sense as an instructional strategy? Again, because our system of written numbers is a technology based on exactly that principle. The whole point to our place-value system (base-10) is that it is intended to make the specific procedures for adding, subtracting, and multiplying simple, straightforward, and consistent for everyone! Consider the history of written numbers: With ancient systems like, again, Egyptian numerals or Roman numerals, there was no way to get addition or multiplying accomplished by simple writing or mental effort. Without a fixed base system, numbers don't "line up" the way they do for us. To get any arithmetic done (including total sales or tax calculations), you had to go to a licensed counter (think: public notary) with their counting board or abacus tool for use as a mechanical calculator, and trust that the computations they did there were correct. You were entirely at the mercy of this elite, cryptic profession, just to do simple addition.

At some later point, our Hindu-Arabic numeral system was invented and made its way to the West. This system of writing numbers is meant for there to be an obvious connection between the numbers we write, and how to add and multiply them, via a specific written procedure. Kings and princes were astounded at the prospect of people being able to do arithmetic on paper, or in their head, without using an abacus as a calculator. It's like magic! It's not some kind of accident that we use a positional-number system, it was engineered that way only so that we could use a specific adding and multiplying algorithm. In teaching a child to do arithmetic, why would you not use the written number tool the way it was designed to be used?

In summary, it's fascinating that both reading & writing instruction have taken almost exactly parallel paths in the last few decades in America. In each case, they have abandoned the rationale for which the writing tool was designed in the first place. It's like showing someone a power saw for this first time and them asking them, "Can you think of something you might use this for?" To leave out the intention of the tool is to miss the whole point of it. We should play to the strengths of our writing technology, and not frustrate ourselves fighting against it.

Math Wars

Recently I've had some discussions about the wacky stuff being taught in elementary math classes these days. Not something I deal with directly in the college classes I teach, but turns out there's a whole history to the current situation actually referred to as the "Math Wars"!

http://en.wikipedia.org/wiki/Math_wars

Basically, there's been a dispute over whether to emphasize "procedural" (algorithmic, memorized step-by-step processes) or "conceptual" (creative, inventive, big ideas) skills in the earliest grades. In the last 2 decades or so the "conceptual" camp has basically won the debate in teacher education schools, claiming to have research backing up the approach. Recently there have been calls for a more middle-ground approach.

Interesting articles in this month's American Educator magazine. One by cognitive psychologist Daniel T. Willingham: http://www.aft.org/pubs-reports/american_educator/issues/winter09_10/willingham.pdf
In cultivating greater conceptual knowledge, don't sacrifice procedural or factual knowledge. Procedural or factual knowledge without conceptual knowledge is shallow and is unlikely to transfer to new contexts, but conceptual knowledge without procedural or factual knowledge is ineffectual. Tie conceptual knowledge to procedures that students are learning so that the "how" has a meaningful "why" associated with it; one will reinforce the other. Increased conceptual knowledge may help the average American student move from bare competence with facts and procedures to the automaticity needed to be a good problem solver. But if we reduce work on facts and procedures, the result is likely to be disastrous.

And another article by professor E.D. Hirsh: http://www.aft.org/pubs-reports/american_educator/issues/winter09_10/hirsch.pdf
The victory of the progressive, anti-curriculum movement has chiefly occurred in the crucial early grades, and the further down one goes in the grades, the more intense the resistance to academic subject matter with the greatest wrath reserved for introducing academic knowledge in preschool. It does not seem to occur to the anti-curriculum advocates that the four-year-old children of rich, highly educated parents are gaining academic knowledge at home, while such knowledge is being unfairly withheld at school (albeit with noble intentions) from the children of the poor. For those who truly want equality, a common, content-rich core curriculum is the only option. It is the only way for our disadvantaged children to catch up to their more advantaged peers.