This is why my little college-math-ed blog has so many readers:

Because I am Everycollegeinstructor.

In U.S. report released this month, 40 per cent of professors who were surveyed said that most of the students they teach lack the basic skills for university-level work. Further, the survey conducted by the Higher Education Research Institute at the University of California at Los Angeles found that 56 per cent cited working with unprepared students as a source of stress.

Count me among both groups.

The rest of the article is essentially a quantitative, snark-free summary of everything I’ve written about teaching over the past year. Incoming university students, reports the Globe, are woefully unprepared for the demands of university; it’s hard to know how to deal with them; their high school grades mean nothing. Nothing new here, but I’m glad this issue is getting national attention.

Unfortunately, I think the remedies described in the article – more remedial classes! extra help for students who lack basic skills! diagnostic tests for students whose math marks are below 70% or whose English marks are below 80%! – are remarkably short-sighted, and contribute to the unfortunate trend of students paying universities to learn what they used to be able to learn in high school, for free.

The main problem, as I see it, is an increasingly incoherent high school curriculum that is quickly diverging from the goals of a university education. And this problem won’t be solved until high school and university educators start talking to one another.

I’ve got a lot to say about this piece, and I’m finding that my thoughts are all over the place, so bear with me. Or don’t, I guess.

First, a quote from Ann Barrett, managing director of the University of Waterloo’s English language proficiency program, that dovetails with the experience of every single college calculus instructor who’s ever taught students who took calculus in high school:

“I have seen students present high school English grades in the 90s, who have not passed our simple English test.”

And the proposed reasons for this?

Some officials blame grade inflation at the high school level. Others say that in this primarily visual world, there’s little focus on the written word. And one professor points to the high school curriculum being so jam-packed with content that teachers have no time to instruct on the basic skills.

My thoughts on these, respectively, are: kind of, but that’s beside the point; give me a break; and ok, now we’re getting somewhere.

Let’s start with grade inflation, becuase it’s the most frequently-cited cause for students obtaining A’s in high school and flunking out of college. I stand by what I wrote on the subject back in January, but I think that the A-students-flunking issue is a lot more complicated than that.

If grade inflation were the main culprit, then we could say that a student who gets an A has what may once have been considered C-level understanding of the material; that is, an A in 2005 is equivalent to a C in (say) 1995.

I disagree. My A-minus student does not have a C-level understanding of the grade twelve course that I took a decade ago, the one that prepared me reasonably well for my university math classes. He doesn’t even have a D-level understanding of such material.

To say that an A-minus means anything in terms of a student’s understanding of the math they need to succeed in university is to say that there’s any correlation whatsoever between college level math and grade twelve math as it’s taught in BC. And there isn’t.

My student’s A-minus is a in fact pretty accurate reflection of his knowledge. My student does indeed have an A-minus grasp of the material taught in grade twelve math in BC. My student has acquired A-minus-level proficiency at storing formulas in his fucking graphing calculator and memorizing the solutions to homework problems so that he can recall them when he faces the test.

He’s quite good at all that, really. It’s just that this proficiency would help him not one whit if he were to take a university-level math class, taught by professors who naïvely expect their A-minus students to be minimally numerate, not to mention vaguely proficient in reasoning mathematically.

Reducing this issue to grade inflation suggests that the problem lies in the evaluation of students, not in the choice or presentation of material. Absolute mastery of BC’s garbage grade 12 math curriculum doesn’t prepare students for university, because BC’s garbage grade 12 math curriculum is virtually disconnected from university.

My colleagues and I have griped amongst ourselves about this, but as far as I can tell, there is no communication between high school curriculum developers and university educators. Tweaking grades won’t fix that.

On to the next idea – we live in a visual world, with little emphasis on the written word, so no wonder Johnny can’t read – am I missing something here? Did our world become significantly more visual in the last decade – a time during which universities have reported tremendousincrease in unprepared students? The high school texts I’ve seen are jam-packed with the written word.

What I do see is this: I see students calling me over to their desks to ask about a word problem, and half the time me reading the word problem aloud to them is enough to answer their question. I see students skimming over paragraphs of text (not that I blame them) and then asking me what they really needed to read in order to solve the problem.

seldom see any indication that students are reading their textbooks beyond skimming over the examples so that they can match them to the homework questions. I’ve lost track of the number of students I’ve tutored, or fielded during office hours, who did not avail themselves of the indices of their textbooks. The reason they couldn’t show that two events were mutually exclusive was because they didn’t know what “mutually exclusive” meant, nor did they think to look it up.

When I was in high school, my English teachers routinely gave marks for producing drafts of essays. Producing the draft was worth half marks; the rest of our marks came from the quality of the actual essay. An incoherent essay could easily earn a B if the writer produced a draft. When I was in grade twelve, we had to submit one or more essays every week. There was plenty of emphasis on the written word; our ability to use it well, however, was virtually irrelevant.

Things have gotten worse in my home province, according to a former camper of mine. This camper was a brilliant math and science student; by his own account, he was “average” in English – and he wanted to improve. But he was having trouble doing so, because he was never assigned essays as homework. A few years earlier, he told me, teachers were reporting a rise of internet plagiarism.

The school board’s solution: stop assigning essays for homework. In 2002, the only essay-writing experience that high school English students had, consisted of sitting in class for eighty minutes or so and producing an unedited, unresearched paper. It’s not hard to imagine a student who excels at writing those sorts of papers, flunking out of a class that requires long, researched papers.

There’s plenty of emphasis on the written word. There’s virtually none on developing the skills required to use it effectively.

Moving along – I am a lot more sympathetic to the third proposed explanation for the increase in unprepared university students: the emphasis on content over skills. Erin O’Connor, from whom I pilfered the original link, puts it well:

What [the article strongly implies] is that the problem stems in no small part from an ideology of progressive education that is famously hostile to skills acquisition (which requires such child-stifling practices as memorization, drill, repetition, and so on).

This certainly rings true in math, where I labour endlessly to disabuse my students of the notion that if only they memorized more formulas, more examples, they’d be doing a lot better in my class. The idea that there is a smallish set of basic skills that, solidly understood and correctly applied, will carry them through more difficult work, is alien to them.

Pointing out that they can use material in Chapter n-k to solve a question in Chapter n risks an uprising. (True story: the precalculus 2 prof last year had a student in his office ask how to find a hyperbola’s asymptote. The prof reminded the student how to find equations of straight lines, and was met with a blank stare. “We did that last term,” she explained earnestly. “You didn’t show us how to do it this term.”)

Last April, I talked to my then-department head to suggest completely reworking the curriculum for the terrible precalculus class. He was more than receptive, and took notes as I ranted. One idea that came up: teaching half the content, but taking time to make sure that students had a solid grasp on everything that was taught.

It interests me, thought it doesn’t surprise me, that Erin and the English professor quoted in the article have come to similar conclusions about the courses with which they have experience: those courses too display an emphasis on content to the exclusion of skills that can be more broadly applied.

High school curricula are disjointed. We get a topic here, an application there – and we get nothing to tie them together. There’s no overarching theme for any course, no concept to unify the incredible mass of content. Students are understandably hard-pressed to recall any skills they learned in high school. And I can’t blame them for wondering, on occasion, “what’s the point of all this stuff?” I’m not even sure the people who designed their courses know.

At the end of the day, we’re left with two facts that are increasingly troubling, and increasingly at odds with one another:

1. High school students are discouraged from pursuing post-secondary options other than university; but

2. A high school education does not prepare one for university.

The first of these is seldom challenged among high school teachers and guidance counselors; the second is addressed at the university level alone. Unless high school and university educators start working together to figure out what they’re trying to accomplish, and how best to accomplish it, we’re still going to have unprepared students scrambling when they enter university, and we’re still going to have short-staffed universities rushing to endow them with the skills they should have acquired in high school. That’s not education; that’s damage control.

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