Sunday Samples 76
I’ll be taking another short hiatus this week. I hadn’t mentioned this before because there was one more person I wanted to tell in person rather than let her read it here, but I’ve managed to forestall the death of my career by one more year. So in the fall I take up at Western Kentucky University, and I have to go this week to hunt the wild apartment.
So I figured that it would be appropriate to use the Kentucky state song, “My Old Kentucky Home”. This version is sung by Paul Robeson, and it includes the pre-bowdlerization lyrics. So I suppose I should make clear that my quoting them in no way means that I endorse their use. Ahem.
The sun shines bright in the old Kentucky home
‘Tis summer, the darkies are gay
The corn-top’s ripe and the meadow’s in the bloom
While the birds make music all the dayThe young folks roll on the little cabin floor
All merry, all happy and bright
By ‘n’ by hard times comes a-knocking at the door
Then my old Kentucky home, goodnightWeep no more my lady
Oh, weep no more today
We will sing one song for the old Kentucky home
For the Old Kentucky Home far awayThe head must bow and the back will have to bend
Wherever the darky may go
A few more days, and the trouble all will end
In the field where the sugar-cane growA few more days for to drop the weary load
No matter, ’twill never be light
A few more days ’til we totter on the road
Then my old Kentucky home, goodnightWeep no more my lady
Oh, weep no more today
We will sing one song for the old Kentucky home
For the Old Kentucky Home far away
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Congrats on the new job! Do you know what courses you’ll be teaching?
Congrats, glad to hear you found a place.
Not precisely sure what courses I’ll have, but probably more calculus. Also it’s likely I’ll have to try my had at teaching below the calculus level, which I’m sort of nervous about. There’s a lot more “how” and a lot less “why” down there, and I’m not as good with that.
Does there have to be less “why”? Wouldn’t the why’s help “down there” too?
Some, maybe, but the emphasis in college algebra and pre-calculus has to be on being able to use things. I can’t just wave my hands past “the sine is a function that takes an angle around the unit circle and gives back the y-coordinate”. I need to make sure they can actually recite the standard sine and cosine tables, for instance. I just don’t have much experience in teaching those sorts of practicalities.
I’ve been pondering this quite a bit recently. Do they need to “recite” these immediately when asked? Or is it enough that they can figure it out in a minute or two after thinking it through?
Maybe I worded it badly. My point is that whatever output value the sine gives for this or that input value is somewhat beside the point when it comes to the why of “what the sine function is”. I can use it in all sorts of situations without ever knowing that
. But at the end of a precalculus class they need to be able to say that (with or without thinking), or I haven’t done my job.
UPDATE: Sridhar, below, is right. See? Even I can’t recite the values off the top of my head.
Math below Calculus is a good thing for a teacher to experience. I taught Algebra 1, Algebra 2, and Geometry for 5 semesters at Woodbury University, and a year of those (plus pre-Algebra and pre-Calculus and other courses) in middle schools and high schools in Pasadena. I am better for the experience.
Your primary role is to balance instruction (which is usually all that the naive think that teachers do), assessment, and management (lesson planning and classroom management). The assessment is not just about grading homework and exams; it is to determine the learning style of each unique student. What matters is NOT what you know, but what you can find out about what is going on in the head of the student. Give at least half credit on homework and esxams under my mantra: if you can’t write the equation, draw me a picture, or write me an English paragraph, but show my what you think. What the student knows that is right, build on, using their learning style.
What the student knows that is wrong, usually the result of a bad teacher in the past, you solve by regressing them to just before that mistake, and then rolling forwards on the right path. The student usually knows where and when they went off-track, and still resents the teacher who did that.
Read papers on Dyscalculia — Mathematics Disorder. It is real, it is insidious, and in only 1/3 of the clinical cases is neurological; the rest can be cured by good teaching. This is your chance to save lives!
Thanks for the clarification John. I’ve been in a questioning frame of mind as of late.
Jonathan – Having the students showing what (and how) they are thinking is one of my goals – however students find this discomforting. They are too used to giving only an answer (and knowing if it is “right” or “wrong”). I’m interested in how they got that answer, which tells me more about their understanding (or lack thereof).
I agree with Jackie. “What is in the student’s head” is more dynamic than static. Asking them to draw a picture is dynamic hand-eye, albeit falls short of “draw me an animation.” Writing a paragraph is to get a narrative — given the storytelling dynamics of the human brain, which is part of what we repurpose to do Math at all.
We also repurpose the visual system (neural mechanisms to abstract the graph of horizon, trail edge, tree trunk edge), kinaesthetics (“grasping” the truth), and spoken language (in that we must teach English-to-Math and Math-to-English translation, and mjost students hate “word problems).
“It seems that mathematics is carried in people’s heads, and that it is malleable in the sense that experts ‘know’ almost instinctively whether it is possible to modify standard theorems to fit the context being discussed; perhaps this is the definition of an expert.”
“Whither Mathematics?”, Brian Davies, Notices of the AMS, Vol 52, No. 11, Dec 2005, pp.1350-1356]
Re: comment 7, it might be even more useful for them to be able to recite that sin(pi/4) = 1/sqrt(2).
[Sorry, I don't know how to use LaTeX in comments]
The same issue, Notices of the AMS, Vol 52, No. 11, Dec 2005, but p.1317 has an editorial by Richard O. Hill “Future High-School Math Teachers and Upper-Lvel Math Courses” with things that future high school teachers don’t know, but should. Example:
sqrt(-4) * sqrt(-9) =/= sqrt(36)
The article, expanded, is at:
http://www.math.msu.edu/%7Ehill/
4 relevant papers there, all good:
A Capstone Course for Prospective High School Mathematics Teachers
On the Transition in Mathematics from High School to Michigan State University
Future High School Math Teachers and Upper Level Math Courses
What (Future) High School Teachers Need to Know about Trigonometry
These are good points. Maybe I’ll open a thread…
Oh, and I updated my comment #7 to credit Sridhar FTW.
[...] Mathematics Courses (open thread) As I mentioned in the comments yesterday, I may well have to be teaching math courses below the calculus level this year. The closest [...]
Pingback by Pre-Calculus Mathematics Courses (open thread) « The Unapologetic Mathematician | July 7, 2008 |
good that you’ve landed *something* of course.
this thread might be some sort of evil omen,
though … the “dept head at WKU” has a post near the end …
Troubling indeed, but it seems restricted to an institution where some other shady goings-on had already been noted.
As for the department head, I don’t recognize that name. Maybe there’s a statistics subdepartment, or a separate department, or something, but that’s not the chair of the math department.
good to know. anyhow, i hope it’s safe to assume
that titled faculty in *any* university still have
a heck of a lot more academic freedom than that
poor norasteh fella. no wait. any university
rightly so-called. my ex-college now styles itself
a U (but is actually still a liberal-arts college;
in particular, no grad-level math program) …
and there’s a diploma-mill down the street
that i’ve never applied at (i’ve taught in four
colleges in this city) that’s been using that
ivy tech “do it by the script every minute” model
and *calls* itself a university.
more at CO9.