Mathematics Departments and the Talented Mr. Teacher

Today we have a guest post from a colleague named Mathprof. The pseudonym perhaps is needed as Mathprof's colleagues might not be pleased to read all mathprof's comments. I did some very minor editing, but otherwise the content is Mathprof's.

I asked Mathprof about Alexander Coward. You can read some background here: http://alexandercoward.com/BlowingTheWhistleOnUCBerkeleyMathematics.html

Mathprof's response to me:

Nationwide, mathematics departments, higher education or otherwise, mirror his [Alexander Coward's] interpretation and description of events. He perfectly described my department. Just today, some of my students alerted me that my peers have been complaining that I try too hard and that my approach is hurting students. In their opinion, it is not proper for the teacher to try to teach - it is the student’s responsibility to try to learn. I am, supposedly, doing my students a disservice as I raise their knowledge base through the use of sound, research based, pedagogical practices by letting my students become accustomed to a style of learning they will likely never experience again.

Most mathematicians at large universities are grounded in pedagogical, epistemological, ontological, and methodological paradigms that uphold and maintain the current mathematics education paradigm. There are deep seated beliefs about what is education, who can and should access it, how it should look, and to what end. Although the socialization in this manner of thinking occurs mainly in colleges, it is often introduced in early education, as mathematics undergraduates fill most of the K12 mathematics teacher positions, and they often bring this paradigm with them. This is how the system perpetuates itself and how it constructs continuity between K-12 and higher education.

What I have learned in the few years of reading and writing extensively on this topic is that the form and function of education are completely at odds with one another. This is particularly true in mathematics. If you ask math teachers what they hope to achieve and then observe their method of approach, it is quickly evident that for the majority of teachers, form rules over function. Strategies whose function is to increase learning are aggressively de-emphasized and de-legitimized simply because they clash with the dominant paradigm view of education. This occurs both in practice and in research. Recreating their learning experience in not a means to an end, but an end onto itself. The demonstration of a superior capacity and knowledge in mathematics is the form that must rule over function. For these teachers, learning is a mere externality. Those that are meant to learn math do - everyone else learns their place. There is no maximization of exposure, customization of approach, or an intellectualization of the process. It is complete madness.

I could go on forever but I will stop. I feel bad for the guy [Alexander Coward]. It sounds like he is doing it the right way. That said, welcome to education. Watch out for gravity - you never know which way it will pull tomorrow.

-- Mathprof

How To Be A Kick-A## Teacher

25 helpful pieces of advice.

  1. Comportment:
    1. Walk like you're walking away from an explosion in a Hollywood movie.
    2. Tuck your chin in, tilt your head down and look at people from out of the top of your eyes.
    3. Squint.
  2. Lecturing:
    1. Show up late, then run over time because there is so much to cover.
    2. Bring to your lectures more hardware, dry erase markers, computers, tablets,
      cell phones and piles of paper and printed references than any one else.
    3. Consider lecturing in Esperanto so that your international students can learn as much as your native students.
    4. Liberally sprinkle your lectures with Fisher quotes in Latin and French.
  3. Questions:
    1. Take 5 minutes to respond to every question.
    2. Always ask if there are any questions, but don't wait for people to raise their hands.
    3. You have several options for answering questions:
      1. Give a lot of fake life philosophy type advice, but don't actually answer the question.
      2. Point out that you'll get to that answer later in the lecture. It doesn't matter if you actually do get to it later.
      3. Explain how semantic deconstruction enables a pithier answer. Never give the pithier answer.
  4. Give homeworks that are impossible to answer correctly, but don't grade them. Give everyone 100% but only after the quarter ends.
  5. Do not follow the syllabus.
    1. The syllabus should cover everything from Moby Dick to Playfair to Rise and Fall of the Roman Empire to the complete first edition of F. N. David's first book to John Graunt's tables of mortalities and a summary of Biometrika, but only through 1900.
    2. Do not update your syllabus. The syllabus your mentor, who retired the year after you joined the faculty, first wrote during world war II should suffice. He worked hard enough on it after all.
    3. If there are any pre-med students in the class, make sure you cover all the material on the MCAT.
    4. If there are any pre-law students you need not cover the material on the LSAT as there are currently enough seats in first year law classes for all applicants in the United States.
  6. Explain at length that the class really should satisfy distribution requirements in a different area.
  7. Direct everyone to read your blog where you post:
    1. Frequent links to XKCD and phdcomics.
    2. On semantic deconstruction and quantum mechanics.
  8. Teach your students how to do a better job of simulating real data.
  9. Explain the grading policy in detail, but don't follow it.
  10. Orthogonal decomposition theorem. Homeworks, lectures and tests should form an orthogonal basis in knowledge space.
  11. Jokes. Humor always makes difficult material more interesting. If you don't know any statistics jokes, here are some that you can use, preferably without attribution.
    1. Q: How many statisticians does it take to screw in a lightbulb? A: It depends on your model.
    2. Q: What's purple and commutes? An Abelian Grape. (Yeah, well).
    3. An applied statistician, an econometrician, a theoretical statistician and a psychometrician walk into the faculty bar on campus and don't talk to each other. Bose-Einstein statistics at work.
    4. Q: Why don't theoretical statisticians play hide and seek? A: Because no one will look for them.
    5. Q: How many econometricians does it take to make chocolate chip cookies? A: Ten. One to stir the batter and nine to peel the M&Ms.
    6. A statistician came home and found his house burned to the ground. When he asked what happened, the police told him "Well, apparently the chair of the math department came to your house, and ...".

      The statistician's eyes lit up and he interrupted excitedly, "The chair? Of the math department? Came to my house?"
    7. Q: Why do statistics departments put questions on asymptotics on comprehensive exams? A: Otherwise there would be no use for asymptotics at all.
    8. Theoretical statisticians do it better, but only asymptotically. And in the long run, ... well, you know. But don't say anything, it makes them happier.
  12. Prove everything:
    1. Proofs are clearer when you use measure theory, even in an introductory class for biologists.
    2. And martingales allow for more efficient proofs. After all, life is a martingale. Biologists need to learn to appreciate that.
    3. Entropy means it really doesn't matter. Physicists should appreciate that.
    4. Note that everything in class has been proved previously in Doob (1953) or in one of Herman Rubin's Annals of Mathematical Statistics papers from the 1950's.
    5. Or was it the 1945 paper?
  13. Develop the theory of minimal length confidence intervals for the mean of a normal when n=1 and the mean and variance are both unknown.
  14. When students are confused, coding theory (Daleks and Ood 1985) provides an alternative way to derive most statistical models. Ontological science should be relegated to discussion sessions where the TA can handle the presentation.
  15. Refer every questioner to Fisher's original publications on the subject for more more information.
  16. No software need be installed the first two weeks of computer lab. Never use the same software package two weeks in a row.
  17. Use data sets from your own collaborative papers as examples, with results given in class that exactly contradict what was published in the literature.
  18. Due dates can be given in Julian date (in ISO-8601 format of course) during the first half of the semester and in Aztec calendar form for the second half. Dates outside the semester and during finals week should use Ptolemaic and Carbon dates.
  19. Office hours: check the course schedule to maximize the number of conflicts of office hours with other courses.
  20. Cancel class on leap days, during full and new moons, the 13th of every month, for faculty meetings, special seminars and Tuesday and Wednesday of Thanksgiving, Veteran's day and memorial day weeks. Go to at least two international conferences each quarter.
  21. Announce every Friday that class is canceled for Saturday and Sunday.
  22. Take attendance, but never get past the M's.
  23. Always misspell your email address. If possible, delete your email address (there is so much spam after all) and acquire a new one after posting your syllabus to the web site.
  24. Cover ethics, but don't cite your sources.
  25. Per School of Medicine policy, you are required to hold several lectures each semester in rooms other than the scheduled room. Lecture days and room numbers are subject to change even after the lecture has started.
  26. Play classical music during lectures and industrial grunge during midquarters. For a special treat (and personal favorite) arrange for a live performance of Karlheinz Stockhausen's Helicopter String Quartet during your final.
  27. Love your students. Unless that's against school policy, in which case announce that your love is strictly Platonic. Unless that might be misinterpreted, in which case explain the 7 different forms of love, (Eros also known as sorE backwards, Philia, Ludic, Aghast, ACDC, Programa, Flotus, Read-Write, FIFO and GIGO) and after you get them all straight, the first class should be over and you still won't have covered the syllabus and course information sheets. Bring lots of paper towels when you cover GIGO. (For advanced classes: discuss FIFI and FISTR (First In, Screw The Rest) instead of FIFO.)
  28. Finally, after you've mastered all that. Respect your students, love the material, and enjoy yourself.



Next week: Continued third order directed non-Riemannian fractional fast Fourier stochastic differential particle separating longitudinal Latin hyper-active swarm graphs in British bus queueing theory, and practice. Lecturer: Thorin "Missing Totally at Random" Oakenshield.

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