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01 Nov 2005 - 19:27

math brain


Each year I come to realize more and more that very few of my students are like me. This even goes for the good students, and I need to stop teaching the type of course where I excelled.

The main differences, I think, stem from my experiences in math classes in sixth through twelfth grades. Don't think that this is shaping up to be an anti-calculator rant. It's not....

Middle School Math
I didn't take middle school math. My parents were absolutely furious when I was in sixth grade. The math teacher had a system by which before the beginning of each unit, we could take the unit test, and if we scored at least 90%, we didn't need to sit through the class. Instead we were given packets to work through (independently) while sitting in the back of the classroom. I learned all sorts of things: the difference between accuracy and precision, all manner of tests for divisibility, combinations and permutations, vectors. Most importantly I learned how to ignore someone yapping in front of a chalkboard and how to learn math by reading a textbook and doing problems until I understood the material. As an added bonus, sixth grade math was the time when most students were indoctrinated that "taking notes in math class" equalled "copying every glyph on the chalkboard onto a sheet of paper." This set the stage for years and years of listening in class instead of taking notes. About halfway through sixth grade the school district was sick of my mom's complaining, so they put a bunch of us in an enrichment class where we flew kites to learn about right triangle trig; in seventh grade they enrolled us in algebra.

Math Homework
From eighth grade through twelfth grade I took seven different math classes, and in none of them did anyone ever check my homework. Homework was assigned, and we were supposed to do it, but no one ever collected it or even walked around the room to verify its existence. (One class also had occasional "problem sets" that were turned in for a grade.) If the problems were interesting, I did the homework. If the material was too difficult to learn just by sitting and listening in class (like max-min problems), I did the homework. If I failed a test (integration by trig subs), I would go back afterwards and do the homework. Sure I made some stupid choices (like doing close to ZERO math homework in all of tenth grade), but in the end I knew what I needed to, and I had learned what I needed to in order to learn math.

My students, on the other hand, seem to prefer being told what to do. Do all these problems by this day. Write this down. Memorize this. Show up in this room at 8am on MWF. And I can't get through to them that they wouldn't need to wake up early and trek across campus in the cold and dark to come to my class if they would just read the textbook and do the problems. That's all it takes: read the book, do the problems. Aside from setting the pace and verifying achievement, I'm inessential. The two things that my students are most reluctant to do (read the book and do the problems) are the keys to learning the material in my class.




Of course I read this and I'm identifying with the mom.


It Seemed Like a Bad Idea at the Time



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I made a comment there, and I think it may make sense to make it here. I need external motivation structures. I know myself well enough to know that if I intend to sit down and study maths from a textbook, I am going to procrasinate and I am not going to do it.

However, I can set up external structures that commit me to learning. Like signing up for a maths course and showing up to lectures where there's nothing to do but listen to the lecturer, and where I have to do homework or I lose marks.

This may be a moral failing, and I may be a terrible person for not being so self-motivated, but that doesn't make it not true. And I don't know how to create that sort of internal motivation. I have certainly beaten myself up over it enough without having any effect. But by creating external motivation structures, I got an honours degree in electrical engineering, and another one in economics, I can support myself in comfort, have an enjoyable life and I think contribute something to society. Though I do get frustrated by theorists who think that the whole point to exams is simply to rank people.

-- TracyW - 01 Nov 2005


My mom was the biggest pain in the butt that year. It was so embarrassing. I believe that she may have shown up at more than one school board meeting to make her fuss. In the end things worked out pretty well, though.

I think that the take-away lesson from how math was taught at Iroquois Middle School in the mid 1980s is that there are not 3 years' worth of math in middle school math. I took 6th grade math in 5th grade (as did about half of the 5th-graders), did "enrichment" (random stuff) in 6th grade, and then moved on to NYS Course I without having taken either 7th or 8th grade math. With the exception of the dozen+ kids who were accelerated due to parental complaining, all the rest of the 300 or so kids in my grade were heterogeneously grouped at "grade level." Yes, that's right: 95% of 7th graders were taking 7th grade math. Yet, the following year about 100 of the 8th graders were enrolled in Course I (and were whittled down to the 3 sections of calculus offered my senior year), and the other 200 were enrolled in 8th grade math.

Technical aside (which I emailed earlier to the webmaster account): I am only logged in as my Registered User Name from the home computer; I am perennially a guest from my office computer (despite my searching high and low for a place where I had the option to sign on or off!). Probably this is a sign that I should be doing more work at work.

-- RudbeckiaHirta - 01 Nov 2005


Rudbeckia,

I have this happen sometimes too -- I unaccountably become RobertStacy. if you have a password manager on your browser at home, then you can probably get rid of the KtmGuest login just by cleaning out that cache.

I had the same experience teaching as well, back when I was doing it in the early 90s; thinking that everyone I was teaching learned like I do. I plan to post or comment on it later.

-- CarolynJohnston - 02 Nov 2005


Hey, I hope my kid will someday have fond memories of being embarassed by his pushy mom.

-- CarolynJohnston - 02 Nov 2005


If you're using Mozilla or Mozilla Firefox, the password manager is accessible from the Preferences (under Edit).

-- CarolynJohnston - 02 Nov 2005


Christopher just looked over my shoulder and said, 'That's exactly like you. You're really embarrassing.'

-- CatherineJohnson - 02 Nov 2005