Teaching Badly: Change

Back in the saddle after allowing the blog to quiesce for a few weeks.  With the fall term starting up at St. Anselm’s, it’s time to start writing about teaching again.

Change is an important element in facing each new school year.  Things that didn’t work the previous year have to be improved or removed, whether that is an approach to discipline or a topic or an assignment.  Some topics grow stale over time, sometimes because the teacher has lost interest in them; they have to go.  And sometimes it’s just important to do something new, for your sake and the sake of the students.

This is a bit of a scary thing: I spent so many years early on just trying to figure out what worked and holding on to that.  What if I change things now and screw it all up?  What if a class goes badly?  What if a whole week is lost?

Quelle horreur!  Get over it (and yourself) and do something new.  You are not the pinnacle of the educational experience, no matter how good you are.  You’re not risking perfection here; you are risking your pride.

So what am I doing differently this year? Continue reading Teaching Badly: Change

Teaching Badly: Oppose, Redirect, Prevent

I have never taken an education class and, Deo volente, never will.  We can get into why another day.  For now, I thought I would jot down my basic theory on how to run a classroom.

When I consider the ways in which I handle behavior problems in class, I really see just three: I can confront and oppose misbehavior, I can redirect it, or I can prevent it from happening in the first place.

It’s worth noting that misbehavior doesn’t (just) mean throwing paper airplanes or talking out of turn.  It can be any behavior that destabilizes the class or diverts you from accomplishing the goals of the day.  Sometimes it manifests as wildness but it could be anything that’s stopping you or slowing you down.

Now, the three basic teacher responses to such behavior: Continue reading Teaching Badly: Oppose, Redirect, Prevent

Vergil to Augustine: Inanitas

My friend Adam has hit upon a quite nice little idea in his translating of the Aeneid.  The general idea is that Vergil is a cynic who ends all his most epic scenes by throwing shade on them.  I’ll let Adam speak for himself on the details, but I was pleased to play a small auxiliary role in the hashing out of the idea.

Initially I resisted his take on the pictura inani, or empty picture, that Aeneas used to feed his soul.  Why not instead stay local and contrast Aeneas feeding his soul (animus) with a soulless (inane) picture?  But once we got talking, his cynical read started to grow really nicely.

While Adam ran off to do some real work (prep for a class), I played the role of research assistant gunning down every use of the adjective inanis in the Aeneid.  Again, God bless the internet.  And indeed, it is quite remarkable how often inanis shows up just in an amateur little word search, and what it ends up modifying (hope, rage, tears, etc.).

It was also fun because our discussion of Vergil’s agenda–pro Augustan or not?–sparked an idea about another field full of expert scholarship: the writings of St. Augustine. Continue reading Vergil to Augustine: Inanitas

Is Math Persuasive?

Continuing my flogging of the issue: is it the essence of a mathematical proof to be persuasive, such that someone who fails to persuade has failed to engage in “mathing?”

I ran across this fun little Numberphile video which raises in passing an interesting and important point.  Fermat came up with an idea (not his super-famous one) about some primes being the sum of two squares (like 17=16+1).  What the video goes on to mention is that many mathematicians after Fermat–the super-heavyweights like Euler and Gauss and Dedekind and Co.–all came up with proofs of this idea.

Each of those proofs is different.  Very different.  If the goal of mathematical proof were simply to persuade, the proofs would be valued for getting different “mathematical demographics” to agree to the truth of the conclusion.  Or perhaps, even more simply, one could insist that everyone should agree to the conclusion of the first, rational proof and then get on with life.

But this is not the role of mathematical proofs, any more than it is the role of the scientific method or logical argumentation.  The various proofs are valued because each of them illuminates different aspects of the problem as well as different areas of the wide world of mathematics. Continue reading Is Math Persuasive?

Notes

Why should I think artificial intelligence is on the near horizon when we can’t even make artificial animals?

Teaching is not like astronomy.  It’s like saddle-making.  You know, except with living beings instead of leather.

(Almost?) every child I’ve ever taught has or will turn out just fine.  Not all of them will do it at my school though.

Teaching grammar functionally is one of the most colossal mistakes American “grammarians” could have made.  It’s like teaching algebra before arithmetic.  Actually, now that I think of it, we have some pretty bad ideas about basic maths too.

Learning Latin would be a lot easier if my students knew English.

Justice is the state of affairs where I get my way vs. Justice is the habit by which I happily give others what is theirs.

Pokemon Go is going to be the downfall of human civilization.  Pure, unadulterated cupidity unchained.  At least we have the solar flares to save us some day.

One day I will have all the time in the world to develop notes into topics and write on them at length.

Hah!

Math Heresy

Irrational numbers can never be real magnitudes.

There, I said it.  Irrational numbers cannot exist as magnitudes of length or weight or whatever in the world of mobile substance.  My stock example: you can never forge a sword with a blade whose length is √2 feet.

(Aside: that’s a gimmick in a to-be-written short story of mine–a magical Sword of Impossibility whose blade really is √2 feet in length and instantly annihilates whatever it cuts.)

Back to my math heresy.  Why do I think this?

Well, here’s one intuitive appeal: Continue reading Math Heresy

Prime Movers

Brandon roused me from my mathematical slumber with a post on one of my hobby-horses, prime numbers.  Just enough impetus to put down a thought I was mulling over last week.

Primes are the delightful irreducibles of the number world.  As a kid I thought of them as weird exceptions to good, common-sense mathematics–the kind of things you memorized and played goofy games with.  But that has things almost backwards.

The Fundamental Theorem of Arithmetic says that any integer can be expressed as a unique prime factorization (this is what Brandon was posting about, so I shan’t repeat him).  Said in reverse, primes are the building blocks of the number world.  Everything traces back to them.  That got me thinking about primes as an example of first movers like one would use to explain the First Way or STA’s explanation of the act of the will.   Continue reading Prime Movers

Is Science Persuasive?

More clearly: is the scientific method essentially persuasive in nature?

Hold your horses; this isn’t a conspiracy theory/Scientology/anti-immunization blog.  I just mean: has a scientist who fails to persuade people actually failed to use the scientific method?

Consider any school child’s version of the scientific method: something along the lines of observation-hypothesis-experiment-conclusion or however they are teaching the kids these days.  I don’t even remember how many versions of the thing I learned as a child and I’m sure the variations have proliferated in the decades since.

What I am asking is: does “persuade” belong on that list somewhere?  So that after your experiment or conclusion, if you fail at the persuasion stage, you have to go back and rethink the hypothesis or whatever.  “Some people don’t think I’m right.  Guess I have to start again.”

The answer is obviously no, right?  Except I teach kids, and I read things on the internet, and if that has taught me anything it’s that “obviously” ain’t all it’s cracked up to be.

I’m sub-tweeting my real topic, by the way.  Give me a minute.

The essence of the scientific method–what it really is, if it has any legitimacy at all–is to explore, uncover, and make plain the causes of observed phenomena.  We could generalize it to just causes and effects, but usually we have in mind chemistry, biology, geology, etc. involving the observable, the in-principle-quantifiable, the material.  In any case, persuasion has nothing to do with it:

  • It is obvious that someone could faithfully execute the scientific method in their backyard and never tell anyone about it.  They have done science.
  • It is obvious that someone could faithfully execute the scientific method and publish a paper that no one can understand.  They have done science.
  • It is obvious that someone could faithfully execute the scientific method and publish a paper that divides the scientific community.  They have done science.
  • It is obvious that someone could faithfully execute the scientific method and publish a paper that persuades everyone except for the world’s leading expert on the topic.  They have done science.

Ok, there’s that word “obvious” again.  I need a macro to kill that every time I use it. Continue reading Is Science Persuasive?

Cool Math: Benford’s Law

If you want to be a forensic accountant (or learn to foil forensic accountants), check this out.  Ok, or if you just like numbers!  I saw a few videos on Benford’s Law and picked what I thought was the simplest to follow.  A very cool, very interesting property of numbers.

I wondered, less mathematically and more philosophically, if the strong “preference” for 1 has to do with the way we construct or think about units.  But this is just a quick post, not a think piece, and the video speaks for itself nicely.

Math on!