Some thoughts about why American math education stinks

Some thoughts about why American math education stinks

In theory, at least, I should be the very last person to weigh in on this topic. As I usually joke, most of my students could tutor me in math. My mathematical education was mediocre in every way imaginable, and let’s not even talk about that 200+ point score gap between my SAT and Math and Verbal scores. With competent instruction, I probably could have become an excellent — or at least a decent — math student, but alas, that ship sailed many years ago.

So why on earth should anyone listen to me spout off about what ails math education? Well, because by this point, I know a fair amount about the functions and dysfunctions of the American educational system, about pedagogical trends, and about just how difficult good teaching really is. If you’re willing to hear me out, I’m going to start with an anecdote. (more…)

The knowledge deficit in action

Occasionally I’ll stumble across a passage that seems perfectly straightforward to me, but that I see students get confused about over and over again. One such passage begins in the following way:

Through a friend’s father, Elizabeth found a job at a publishing company.
Her parents were puzzled by this. The daughters of their friends were
announcing their engagements in the Times, and those who joined the Peace
Corps or had gone to graduate school were filed under the heading of
“Useful Service” as if they had entered convents or dedicated themselves to
the poor.

The passage continues for another couple of sentences, but that’s pretty much the gist of it.

That my students should have such difficulty with this of all passages was a mystery I had filed away in a mental drawer somewhere, to be trotted out an examined from time to time but never yielding sufficient clues for me to draw any real conclusions from.

Then I had a couple of illuminating moments.

First, I had a student miss a Writing question because she did not know what the Peace Corps was. This was a girl who liked to read and had already scored a 750 in CR — not the type of kid I’d expect to have that sort of gap.

Next, a friend of mine who teaches high school told me that her AP students did not understand what a mistress was — as in, they had never been exposed to the concept and couldn’t really grasp it.

She also told me the following anecdotes about her son, who had just finished his freshman year of high school: One, he had accidentally bubbled in, on a practice ACT, that he intended to pursue a two-year college degree because she’d recently explained to him that it took her two years to get her master’s, and he didn’t realize that people go to school for four years of undergraduate education before they go to graduate school. And two, while going over a newspaper article with him, she discovered that he did not know what pesticides were. This despite his having attended an über-progressive middle school with a community garden!

Incidentally, her son is a very smart boy (albeit not much of a reader), but no one had ever bothered to explain to him these very basic pieces of information that most adults take for granted. Everyone, his mother included, assumed he knew them and therefore never saw any reason to discuss them. His mother was absolutely gobsmacked when she discovered what he didn’t know. (If you’re a teenager reading this, don’t be so quick to laugh. I guarantee that there are some very important pieces of information about life in the real world that you don’t know either.)

The moral of the story? Every time I think I’ve stopped taking things for granted, I discover that I need to strip away yet more of my preconceptions about what pieces of knowledge I can and cannot assume students possess.

After all that, I started taking a look at the SAT from another angle: that of cultural reference points that most adults don’t give a second thought to but that plenty of kids taking the SAT haven’t picked up. I was inspired, of course, by E.D. Hirsch, but the reference points aren’t so much Great Events in Western Civilization as they are things you learn from reading a newspaper on a regular basis. Even a really bad newspaper.

Then today I happened to be going over the passage cited at the beginning of the post, and suddenly I had a lightbulb moment. It’s chock-full of references that wouldn’t give most adult readers pause, but that the average teenager wouldn’t be able to make heads or tails of.

1. “Announcing engagements in the Times”

Assumed knowledge: The Times refers to a newspaper, e.g. The New York Times. When people get engaged, they sometimes post announcements in the local newspaper. Usually the people who do this are relatively well-off or socially prominent, especially in a newspaper like The New York Times. This piece of information suggests that Elizabeth’s family is probably at least upper-middle class, if not outright wealthy, which in turn suggests why her parents are surprised that she doesn’t want to take money from them.

2. The Peace Corps(!)

Assumed knowledge: The Peace Corps is a governmental organization that places American volunteers (usually college graduates) in various high-need areas in the developing world. Members may teach English, help preserve wildlife, or run recycling programs. In general, they have a reputation for being left-leaning tree huggers.

3. Graduate school

Assumed knowledge: “Graduate school” refers to any post-college academic program leading to a masters or doctoral degree. Most masters program last two years, and most doctoral programs 5-7. The doctorate is the highest academic degree one can receive. In order to apply to graduate school, you must first obtain a bachelors degree (four-year undergraduate degree).

4. Convent

Assumed knowledge: a convent is a place where nuns live apart from the world in order to devote themselves to prayer. For a good part of European history, unmarried women were expected to enter one. By equating joining a convent with “Useful Service,” the author is being ironic — that is, suggesting that Elizabeth’s parents would have considered it more useful for Elizabeth to renounce all worldly goods and lock herself away than to take a job at a publishing house.

Are you starting to get the picture?

Technically, it is not actually necessary to understand all of these references to answer either of the questions that accompanies the passage. But that is somewhat beside the point. The point is that if the reader does not have a pretty darn good idea of what these things refer to, the passage itself has the potential to read like sheer gobbledygook. At that point, it’s not even relevant whether the questions can be answered without that information because the reader is so thoroughly lost that he or she can barely even focus on the questions.

Knowledge deficit indeed.

In praise of multiple choice tests

In praise of multiple choice tests

I have to say I never thought I’d write a post singing the virtues of multiple choice tests (well, sort of). Despite the fact that much of my professional life is dictated by such exams, I’ve never had any overwhelming liking for them. Rather, I’ve generally seen them as a necessary evil, a crudely pragmatic way of assessing fundamental skills on a very large scale. Sure, the logic and elimination aspects are interesting, but they’ve always in comparison to the difficulty of, say, teaching a student to write out a close reading of a passage in their own words. People might argue that learning to do so in irrelevant (obviously I disagree, but I’m not going into that here), but basically no one is disputing that it’s hard. At any rate, I’ve always assumed that given the alternative between an essay-based test and a multiple-choice one, the former would invariably be superior. (more…)

Can we get something straight? The SAT does not test “rote learning”

Can we get something straight? The SAT does not test “rote learning”

People seem to be throwing around the term “rote learning” a whole lot these days in regard to the SAT, without any apparent understanding of what it actually means. So in a modest — and perhaps vain — attempt at cutting through some of this linguistic obfuscation, I offer the following explanation.

This is an example of a question that tests rote knowledge:

The dates of the American Civil War were:

(A) 1849-1853
(B) 1855-1860
(C) 1861-1865
(D) 1866-1871
(E) 1872-1876

This question does not require any thought whatsoever, nor does it require the answerer to have any actual knowledge of the American Civil War beyond when it occurred. It is simply necessary to have memorized a set of dates, end of story. This is what “rote learning” actually means — memorizing bits and pieces of information, devoid of context, and without consideration of how those particular bits and pieces of information fit into a larger context. (more…)

In response to the SAT overhaul

In response to the SAT overhaul

There are many, many things I could say about the overhaul of the SAT (coming to a testing center near you in 2016!), but I don’t want this to turn into an endless rant, and so I’ll do my best not to ramble on too long.

The elimination of the sentence completions and the 1/4 point penalty, as well the changes to the essay didn’t surprise me in the least; the combination of Reading and Writing into one section caught me a bit off guard, however. In retrospect, I should have seen it coming. If more time is going to be allotted to the essay — the only possibility if you’re giving a more in-depth assignment — it’s going to get cut somewhere else. (more…)

Inverse relationships

I’ve come up with a formula

The amount of time a curriculum devotes to teaching critical thinking is inversely proportional to the actual critical thinking skills that the students acquire.

Think of it this way:

Critical thinking skills can only develop as the result of accumulated subject-specific knowledge, not as the result of learning “critical thinking” strategies in the abstract.

The more time students spend learning formal processes (e.g. identifying the main point) designed to teach them “critical thinking” skills in the abstract, the less time they spend obtaining subject-specific knowledge (e.g. biology, history).

Thus, the more time students spend learning learning formal processes designed to teach them critical thinking skills, the less likely they are to acquire the very knowledge that would allow them to think critically.

Or to put it in mathematical terms, where CT is defined as actual critical thinking ability and ct is defined as abstract, formal processes designed to promote “critical thinking:”

CT ? 1/ct