Monday, April 23, 2012

Math in the Media: To save this math class, we must destroy it!

Words failed me (mostly) when I read this article today in the Washington Post:
At Virginia Tech,  Computers Help Solve a Math Class Problem
It is a common problem that the transition from high school mathematics courses to those at university can be quite difficult to make.  Even in courses whose content is basically the same, like Calculus AB in the AP system and what most universities call Calculus I, the treatment of that content is much different here at the university.  Of course, students sometimes do not do well.  And I am sure that sub-standard teaching from some of us up here may be a part of it.  We need very much to analyze how we teach and learn to do a better job!  And many of us are.  IN fact, here at Hopkins, we are devoting a LOT of resources precisely to this problem of how to better and more comprehensively educate our incoming students.

But to help cure the "problem" of not-high-enough passing rates by essentially removing instructor face-time from teaching!?!  That is patently absurd in my book.

Mathematics is absolutely NOT about learning a few techniques to apply to standard problems set up to test those techniques, which is exactly what many unit-based, worksheet driven, math courses seem to be like pre-college level.  Porting that type of course to the university level may in fact raise passing rates.  But without the ability to study nuanced mathematical ideas and relationships via discussion and debate (think Socrates), one never learns how to THINK mathematically.  Only to calculate.

Maybe that is what VTech is looking for.  I, for one, am not.  


Anonymous said...

I disagree.

Virginia Tech is limiting the new approach to remedial courses like pre-calculus and trigonometry. Remedial courses require smaller class sizes then service courses. The problem sets are repetitive and drill oriented. The goal is not to teach abstract thinking, but to learn to apply techniques by rote.

As best, teaching remedial courses is not the most productive use of a tenure track professor's time. As such, at most colleges, remedial courses are taught by adjunct professors or graduate students from other departments. This practice enables remedial classes to have low student/teacher ratios. Unfortunately, the quality of instruction is often just as bad, if not worse then high school.

JHU is lucky that the vast majority of undergraduates do not require remedial math courses. As such, the department can provide service courses without placing an undue burden on the facility. For a school like Virginia Tech, I can understand the desire explore alternatives to a costly system of remedial instruction that only produces mediocre results

Richard Brown said...

Thank you for the clarification. But I have two issues that remain:

(1) The article quotes: "Emporium courses include pre-calculus, calculus , trigonometry and geometry, subjects taken mostly by freshmen to satisfy math requirements." I find no value in teaching a topic as intricate and conceptual as calculus as a techniques class.

And (2), even in pre-calculus and geometry, abstract reasoning is a necessary gateway to real mathematics learning and real understanding. Treating these topics like drill-oriented, repetitive techniques-based courses simply makes the transition to calculus and beyond that much harder. Graduate students and adjuncts can be quite effective as idea-based educators at this level. And graduate students can and should use this type of educator-training as part of their training as mathematicians.

I fear the effort to save on costs is costing the education.

Jake said...

I feel like I'd be happy with that kind of course only if the homeworks/quizzes/tests were so hard as to make it nearly impossible for students to pass. Then at least you'd know the students who passed learned something. Of course there's no way students will learn unless they spend time thinking about it themselves, and it seems to me that this kind of class encourages students to do the bare minimum (show up to the lab, go through the assignment, and leave). Since everything is spelled out for them, students don't even have to go to their textbooks to see what's going on when they can't do a problem. And that's the bare minimum in more traditional math courses.

This reminds me why Carothers's Real Analysis is my favorite textbook: every few sentences the book will stop and say something like, "And that means this. (Why?)" So you are pointed towards the kinds of questions you should be asking, and then you're left to answer them yourselves. Eventually, after several hundred pages of this - and countless hours trying to answer the "why"s - you know analysis really well, because you can ask the right questions yourself.