Sunday, June 19, 2011

The sad state of American mathematics education

Some recent discussions via various media have spurred me to post something about how pathetic mathematics education in this country has been for a long time -- long enough that I myself was influenced by its sorry state. As a boy, I began to encounter math phobia in grade school, where a tyrannical math teacher instilled the fear of math in me. I suppose her intentions were good, perhaps hoping to motivate me to greater achievement, but her methods were not successful in stimulating the response she probably wanted. Many subsequent teachers reinforced my fears, including my math teacher for 4 years in high school. His plan was to humiliate me into doing better, not unlike the tactics adopted by the fearsome math teacher in grade school. It worked no better in high school than it did in grade school. Instead, I began to doubt my ability to master the subject. Those doubts grew with time, to the point where in my college days, it was undermining my confidence that I could pursue the career I wanted for myself because I was performing so badly in math. Meteorology is a subject that uses mathematics to a considerable extent -- being incompetent at math was simply not an option.

It took the insight of a graduate student teaching assistant at the University of Wisconsin to begin the process of overcoming my math phobia. At that point, I had two C's and a 5-credit D in 3rd semester Calculus behind me, with no prospect for a good performance in Differential Equations. But Mr. Hunter found a way to open my eyes to the subject and I managed a B! He showed me that I could understand the material and enjoy it at the same time!

In graduate school, my advisor looked over my transcript and made it clear to me I needed to minor in mathematics! I swallowed the lump of fear in my throat and did what I was told. By some miracle, I had three straight excellent math teachers (in Tensors and Vectors, Complex Variables, and Fourier Series & Boundary Value Problems) and aced all three!! My first A's in math since 2nd grade!! My fears were vanquished and I became fully confident regarding math from that point on. It was math phobia that had been holding me back, not my ability! I wonder how many people that applies to? If I overcame my fear, then I came to believe others could, too.

Since then, I've seen many people who have been denied a career in my field owing to their lack of math skills, and I believe that the abysmal teaching of math is largely responsible. Learning how to do math can be inspiring and insightful -- skills that are useful in a technological world that can be fun and exciting to apply to real-world problems. Why are so many turned off by math? I believe it's because math teachers are among the worst at teaching their subject. Math isn't about cookbook recipes that need to be memorized -- it's about understanding the abstract world that math occupies and being able to use it to solve problems of significance to the real world. Math teachers usually suck at connecting the abstract world they inhabit to reality. Most math teachers have no clue why anyone besides a mathematician might need mathematics!

It's a universal truth that no one can teach a topic they themselves don't understand. Most math teachers feel at home in their abstract world but can't relate to those who seek to see the value of those abstractions in their reality! These so-called teachers can't relate to the reality inhabited by their students because those mathematicians don't inhabit it! When I was a graduate student, the Engineering School at OU taught several math courses because the Math Department pretty much sucked at teaching those subjects, and the topics were very relevant to engineering. I benefited from several good teachers of applied mathematics in the Engineering School!

If you have math phobia, believe me when I say it's largely been manufactured in your own mind, likely the result of lousy teaching. If you believe me when I say that math skills are useful to you, no matter what your profession, then you should accept the responsibility to learn math in spite of the lousy teachers!! I promise you it will be worth it!!


Danny Brouillette said...

Your experiences and observations are fairly consistent with mine. One difference is that I have done well, on paper, in my mathematics courses from grammar school all the way to the university level. However, I am the first to admit that my successes remain only a series of A's on paper. I do not see what I have learned as relevant or applicable to my meteorology studies. My foray into the research environment at the National Weather Center this summer is making clear that I need to look to my university's physics or engineering programme for some quality applied math courses (and more computer programming!).

A case in point is my Partial Differential Equations professor last semestre. I grant that he is an amiable man (outside the domain of math--pun intended) and a genius. However, he proclaimed often that "you should have learned that at your high school," with 'that' being eigenvalues and advanced calculus proofs, among other advanced topics. He also regularly bashed applied mathematicians, engineers, and scientists. One day, for instance, he randomly told this story about some oil drilling operation off the coast of Norway that went wrong and wasted $7 million because "a pure mathematician wasn't consulted; they relied on those silly applied mathematicians and engineers." (That's a direct quotation that I wrote in my class notes!) Ironically, in an e-mail exchange with me, this professor discussed at length, as you have, what he saw as a sad mathematics education state. Too bad that he's part of the problem--in my opinion, of course.

Anonymous said...

I thought I was reading my own story. That was me completely. It took a reboot of math when I decided to toss the 20 year law enforcement career and go back for my Met. degree. I started from square one with a community college math staff that was second to none and ended up with A's and B's in Calc and DiffEq once I got to them at university. I was one class short of a minor and was bummed, but it was time to graduate. Looking back now 35+ years my elementary and high school math teachers were no less than inadequate and performed a disservice.

Chuck Doswell said...

Danny ...

If you don't grasp the relevance of math to your meteorology studies, then indeed your A's on paper are without meaning. There can be a large gap between getting an A and actually learning the course content. I definitely recommend more programming, btw.

Bamawx said...

This is why I passed on an AFROTC scholarship to Penn State in 1983 to study meteorology. I ended up with a Master's in another field, but all of my weather pursuits now are strictly a hobby. I am even more intimidated by math now than I was 28 years ago. I have thought about going back to met school, but I doubt I ever will. Mike Wilhelm

Danny Brouillette said...

Mathematics is, indeed, extremely important to meteorology (and science, in general). That is why I am disappointed in my mathematics training. I reckon the Constructivist pedagogical philosophy that "you must make your meaning" is useful here.

Justin Reid said...

Amen Chuck, Amen.

Although I had better grades in my undergraduate mathematics courses, it was only because I was more stubborn and spent sometimes 7 hours on end in my university's math lab. It seems like your Partial Differential Equations experience was also at lot less horrifying then mine (even though PDEs was one of the most useful math courses I've taken for meteorology!)

Even with my math minor now completed before my senior year, I now understand why the US is so far behind in terms of STEM education. The worst case scenario for me was resorting to Wikipedia and Wolfram Alpha for understanding course material (even being pointed to the latter by one professor).

I hope to go to the University of Oklahoma for my graduate studies in meteorology and thankfully I will meet all of the math coursework required for incoming students. I can honestly say the majority of my math education has been close to the third world and I will work my hardest to prevent my children from going through that dystopian atrocity.

Have a nice day,
Justin Reid

Kenny Blumenfeld said...

As a still-recovering quantiphobe, I appreciate this post, but it can be made universal: crappy teaching is at least partially responsible for ruining the pursuit of knowledge in all fields. The problems we find in writing and traditional communication (writing a letter, for example) are at least as bad as those in math...and let us not even begin to discuss what's happened to the average student's knowledge of civics, basic political geography, history, and the arts! Some students are terrified to challenge their own minds, and it looks to me to be a by-product of the totally faulty system. It's not math-phobia, it's think/learn-phobia; it's systemic, and teaching is one part of the failure. There is something else at play though.

More on-topic, the English system of units should be phased out of public grade school curricula and abolished from the entire education system, effective ASAP. It is a formidable barrier against otherwise simple computations, and I have seen a number of students break down right there, in unit conversions. How many inches are there in 3.25 miles? What a ridiculous series of hoops you are asking early learners to jump through in order to solve that problem! Going from centimeters to kilometers, however, just requires adding the right number of zeros. That may help, in a minor way.

Something that would help in a more meaningful way, but has no easy solution, would be to make math either a) fascinating, or b) vital for survival--two things that have excellent track records for developing high levels of skill.

Anonymous said...

Interesting post. As a senior undergraduate in atmospheric sciences I would love to say that I have earned straight A's in math, or that I have improved my test taking ability sufficiently to earn higher scores in math by now, however that is not the case. For as far back as I can recall I have earned C's and B's in every math class that I have taken aside from a series of poor scores that I was given in algebra (D's) soon after having entered college. The likely reasoning for these mostly mediocre scores is that whenever I have taken a math course the weather was more on my mind than purely math. So in this way it was / is more a result of focus than anything else. Math is just a hammer without a blueprint.

Another component to my not having earned straight A's in math deals with how a vast majority of math courses are set up as far as grading goes. In retrospect, most math classes are more about test taking than anything else. (You could make the same argument for courses in the atmospheric sciences, though with the focus so much more in line with what I enjoy I am / was able to overcome any / all test taking difficulty.) And believe me I have had some great math professors who have nearly choaked over giving me a C or B when all was said and done! Especially considering I was the guy who showed up to class everyday and asked a lot of great questions even despite having had a more limited focus.

Anyways, despite mediocre grades in math, I have managed to earn straight A's in all atmospheric sciences coursework with B's in physics. This in combination with other coursework along the way has allowed me to earn a 3.7 GPA as calculated over the last 60 hours of undergraduate coursework. I can only hope that no one would look at my application for graduate school next fall and toss it aside because of C's and B's in math when I have earned A's in atmospheric sciences coursework with *some* research experience in there as well.

Would I take a math class as a graduate student?. Sure. I do not fear math at all, and would do reasonably well enough to maintain the threshold GPA prescribed by most programs for continued graduate enrollment, its just that it might not be my primary focus at the time and therefore yield a less than perfect score. Of course having fewer classes per semester and more access to funding through college would have been beneficial, but that's another story. (A lot of students out there wear a few hats while attending college and that usually ads to the complexity.)

Chuck Doswell said...


I don't disagree that bad teaching is far from limited to mathematics and - in fact - it would be a classic misreading of my blog to interpret it as having denied the presence of bad teachers in other disciplines. That would be putting words in my mouth that I never said.

The blog's main point is that math is particularly egregious because its teachers have so little appreciation for its importance in disciplines other than math itself. Many mathematicians take a perverse pride in the utter irrelevancy of some of its topics and there seems to a widespread lack of concern for providing meaningful applications of mathematical principles. They're simply incapable of providing contexts in which math is useful and thereby motivating students to learn it.

This pervasive failure in math instruction then reverberates throughout those disciplines that benefit from quantitative analysis.