The Irascible Professor^SM

"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." ... ... Albert Einstein.
 

Commentary of the Day - December 21, 2005:  Great Expectations.  Guest commentary by Poor Elijah (Peter Berger).

Nearly twenty years ago a movie about math class won an Oscar nomination.  Stand and Deliver told the story of a room full of poor, mostly Hispanic potential dropouts and their teacher, Jaime Escalante.  In the film Mr. Escalante's high school students progressed from not knowing arithmetic to mastering calculus in a single term, largely because he expected great things of them.

In real life it didn't happen that way.  Mr. Escalante spent over a decade building his math program, including a sequence of feeder courses beginning in junior high.  The real kids who made it through his high-flying calculus class worked for years to get there.

Expectations are important.  Some students never get a chance to attempt rigorous coursework because they're constrained by stereotypes rooted in race and poverty, what former Education Secretary Rod Paige termed "the soft bigotry of low expectations."  At the same time, many poor, minority students bring significant disadvantages from home, which genuinely limit their prospects for success at school.  In addition, for thirty years the education reform movement has instituted low expectations for all races, colors, and classes.

Schools, like any enterprise, need to shed faulty assumptions.  The persistent issues of race and poverty merit our attention as a nation.  But Mr. Escalante's students didn't go from zero to calculus after a period of  simply believing in themselves.  It took years of individual commitment and toil.

Believing in yourself, especially in the absence of actually having to do anything, is relatively easy.  In fact, thanks to our national self-esteem crusade, American kids score quite well when it comes to believing in themselves.  In a 1992 analysis of Asian and American math students, for instance, American students ranked highest when it came to expressing confidence in their math abilities. Unfortunately, American math students ranked lowest when it came to actual "mathematical competence."  In other words, American kids think highly of themselves as math students, despite the fact that they aren't very good at mathematics.

More alarming still, it's likely that they don't know much math in part precisely because they've been encouraged to think so highly of themselves.  The same study reported that most American teachers value sensitivity to their students above clarity of instruction.  In contrast, Asian teachers are more concerned with clearly presenting subject matter.  American teachers, worried about damaging self-esteem, tended to gloss over students' errors, while their Asian colleagues didn't shy away from their students' mistakes and instead pointedly examined them as part of the learning process.

You can't blame our national math mediocrity solely on the cult of self-esteem.  Over the past few decades, the decades that have seen the decline in achievement that everybody's talking about, reformers have replaced more traditional programs that build on fundamentals with approaches that sideline the basics in favor of "higher order" math and "problem solving."  These innovations, nicknamed "fuzzy math" by critics, are responsible as well.  In the same way, whole language, another touted reform, is culpable for many American students' inability to read.

The merits of these instructional methods, and their defects, are worth discussing.  But beyond debating the efficacy of one math program over another, we need to confront a more worrisome question.  Why have schools found fuzzy math, or fuzzy anything, so appealing?

Why are the multiplication tables passé?  Why do experts disdain memorization?  Why did schools relegate phonics to the ash heap?  How did content become a dirty word?  Why did we banish facts from history classes and textbooks from science courses?  When did "How do you feel about that?" become the central question in American classrooms?

Reformers recite a familiar litany of reasons, from "engaging" students to developing "higher order" skills for the twenty-first century.  But these justifications are smoke screens.  Logic and creativity are neither new nor more necessary in this century than they were in the last.  And not everything we need to do and learn in this life is engaging.  Some of it's pure drudgery; but, that's hardly an excuse not to do it.

We stopped doing and learning a lot of things in school because they weren't fun.

Experts justify calculators on the grounds that it's more important for students to focus on those higher order skills.  That's true if you're talking about high school math or physics.  But it's not the reason we're handing out calculators to nine-year-olds.  The real reason is memorizing addition facts and the multiplication tables is a pain in the neck.  Requiring that kids learn the basics and practice their skills might make them not enjoy math.  We don't want that to happen, so instead we deny them those skills, which means they can't do math.

Experts point out that poor, minority students lack the basic skills and learning foundation that middle class kids are more likely to acquire at home.  While they're sadly overstating how many middle class kids come to school with those advantages anymore, growing up middle class clearly conveys learning benefits.

These same experts are also quick to insist that poor, minority students need college prep courses like algebra, trig, and Mr. Escalante's calculus.  The trouble is their solution to lacking the basics is to skip them in the name of social equality and jump right to the flashy stuff.  This is exactly the wrong approach.

All students need to master the fundamentals.  Kids who start out at a deficit are precisely the kids who need them the most.  The less familiar you are with the basics, the more time, not the less time, you need to spend on them.

Despite all the rhetoric and good intentions, there's nothing that schools can do to eliminate hardships at home or even to substantially compensate for them.  Starting out behind necessarily means you have further to go to catch up.

There is no shortcut to learning.  That's the expectation we need to pass on to all students, whether they like it or not.

And whether we like it or not.

© 2005, Peter Berger.
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Peter Berger teaches English in Weathersfield, Vermont. Poor Elijah would be pleased to answer letters addressed to him in care of the editor.

The IP comments: The IP agrees only in part with Poor Elijah's comments.  The IP was lucky enough to have gone through elementary school in Cambridge, MA in the late forties and fifties, well before the self-esteem movement took hold.  We slogged our way through the multiplication tables, learned long division, how to take square roots by hand, and all that.  But, in truth, the level of mathematics teaching and learning really wasn't all that much better than it is today.  The reason for that was that most of the IP's elementary school teachers knew very little mathematics themselves.  They viewed elementary mathematics as a set of facts to be memorized, rather than as a set of logical procedures.  We memorized the multiplication tables, and rules for multiplying and dividing fractions.  However, we did not learn why those rules worked.  Our teachers had never studied the axioms of arithmetic, so they were about as clueless as their students when it came to the why of arithmetic.  In the intervening years it seems that students not only don't learn the why of elementary mathematics, they also don't learn the what.  In recent years, the National Council of Teachers of Mathematics (NCTM) has tried to introduce more of the why into school mathematics; however, they too often have succumbed to the excess emphasis on constructivist teaching that prevails today and a desire to avoid the unpleasant realities of associated with learning the what of school math.  For better or worse, the what and the why of elementary mathematics are inextricably connected.  And, one can't really learn one without also learning the other.
 

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