Tuesday, February 25, 2014

I did some math in high school.

I'm trying to formulate a response to an unsurprisingly popular blog post.  Jeremy Kun's post, pretentiously entitled: "You never did math in high school", seems to have enough attention that it is influencing what people are thinking about the state of math education.  Christopher Danielson wrote a response with some good points.  What makes Mr. Kun's rant get attention?  Many people sense that American education is broken, and he has written something as dramatic as it is insulting to teachers, and people eat that up.  It resonates with the need to be a victim and say, "I always knew it was the government's fault that I'm bad at math!"

He begins, "As a teacher I encounter all of the typical kinds of students. But there’s one kind of student I routinely encounter, usually in a freshman calculus course, that really boils my blood: the failing student who 'has always been good at math.'"  From there, he proceeds to blame various people before claiming that in one hour he "can teach them more mathematics than they have ever done in their entire lives."

Calculus teachers see students every year who are genuinely surprised by how difficult they find calculus to be.  If they truly understood algebra, calculus should be just a few good ideas away, right?  In reality, many of the students have decided, consciously or unconsciously, to mimic algebra rather than to wield it.  This decision could be made as a response to an uninspiring teacher, or in spite of a great teacher.  There could be any number of circumstances in a student's life that drive them to this shortcut.  In calculus, if not before, this catches up with them.  This is part of being a student with a less than complete commitment to a course.  Isn't that pretty much everyone?  This is not rare and it cannot always be blamed on the teacher or the math.  It is a bit unorthodox to imagine that the student plays a role, but maybe the individuals who arrive unprepared for calculus have in fact repeatedly spurned multiple invitations to learn math well.  Maybe even some of Mr. Kun's students could escape that magical hour harboring misconceptions about graph theory.

It is normal, it is human for students to undervalue and neglect skills until they are convinced that those skills are necessary.  If the teaching precedes the value by too much time, the learner will have a big task to catch up when finally they want to learn it well.  This is life. 

The public is clamoring for a hero like Mr. Kun who will promise to single handedly fix education, but what does he offer a student who is unmotivated?  Even his invitation to teach people "more mathematics than they have ever done in their entire lives" was extended to "disillusioned but otherwise motivated" students.  He does not suggest anything for those students who are not motivated, and even he must allow that some of the "I've always been good at math" people might not have sustained admirable motivation in the preceding years. 

I believe this shows a facet of human nature that would be observed in any sequence of courses, including the Graph Theory Revolution that Mr. Kun proposes.  If graph theory was the arena in which we taught kids reasoning, educators would develop standards to test progress, those standards would be addressed using questions, and those questions would be reduced--by some teachers and students--to tasks of symbolic manipulation that do not imply critical thinking. 

Mr. Kun's complaint is not about calculus, but about secondary math education in general, which he swiftly berates as a worthless industry full of incompetent teachers.  Precisely, a "vapid husk of an education" was his description of the product that represents so many millions of hours of work of high school math teachers around the world who have overcome challenges and enjoyed triumphs that Mr. Kun did not learn about before presuming to trivialize their careers.

While I have no use for Mr. Kun's wholesale derision of secondary mathematics educators, I do appreciate his point about graph theory, in part.  Graph theory would (for awhile) be enjoyed as a frontier in secondary education.  Mr. Kun notes that "The reason it is a nice topic for such a lecture is that teachers have no preconceptions about the “right” way to teach it, and students have never heard of it before."  However, anyone might see that this state of unexplored grandeur could only last a few years before graph theory was as familiar as calculus is now.  Not to mention, a year-long course could not dabble about for so long with the same elementary parlor tricks, so students would need to encounter concepts that are more theoretical, less practical, and more fraught with subtlety, thus encouraging them to answer the questions with an imperfect understanding, and here we are back at square one.  We would have to develop appropriate preceding courses, they would be similarly mishandled, and the freshmen Graph Theory students would again disappoint their professors by complaining that they used to be good at math.  "You have never done math," the haughty professor would fume, and beg them for an hour of their time to show them the wonders of calculus.

Here is my conclusion:  Better education will involve empathy from teachers and effort from students.  Without that, it is just educational alchemy, we are just pretending to achieve what we have not.

1 comment:

  1. Educational alchemy is a great term to describe the simplistic fixes proposed every few years. Overall, this is a well-reasoned response to Jeremy Kun's blog posting. I wish I had had Burchell (and Geometer Sketchpad) when I was mimicking algebra in high school!