The last math class I took in High School was Algebra II. That was during my junior year... My final grade was a D... That's surprising when you consider that in college I got A's in Calculus, Predicate Calculus, Group Theory, Linear Algebra, Numerical Analysis, Discrete Mathematics, Advanced Statistical Analysis, Boolean Algebra and Mathematical Theory of Computation... OK - I have to admit that I got a B in Multivariate Calculus, but that was at Reed College - they grade a bit tougher there - and it was all proof based... Yeah - if I ever have to do another Epsilon-Delta proof I swear I'll scream :-)
It took me many years to figure out exactly why I did so poorly in high school Algebra - I finally realized that it was partly because nobody ever explained to me that math is totally bogus. (If it wasn't bogus there would be no such thing as imaginary numbers.)
Here's an example of what I mean:
During Algebra II at Orange Glen (spring of 1969) we were introduced to inequalities and we had to graph them on a "number line"... When I found out that the number line is defined as being continuous through zero it struck me as completely absurd... I mean - the positive axis represents real values, while the negative axis sort of represents real values, and zero represents the total absence of a value... So how can you have continuity from a value - through the absence of a value - to a value???
That was probably the only time during high school I was actually curious enough about something to ask a question :-) And the teacher had no clue how to answer it... After a number of minutes of back and forth I was told I was being disruptive and we moved on...
As it turns out it is the height of folly to think of mathematics in terms of reality. Mathematics is a collection of abstract concepts that are exactly what they are defined to be (no more and no less). Yes, math provides tools for solving real world problems - but that doesn't mean math itself has anything to do with reality... And that should have been the answer to my question :-)
Aside: That's why I get so irritated by the use of "manipulatives" to teach math in grade school... Yeah - it helps kids "visualize" math. But that only works for problems that can be visualized... It must come as a shock later on when they discover that there are a heck of a lot of problems that can't be represented in 3 dimensional space. And unless you've been taught to do math based purely on the definitions you're screwed... But I digress...
The reality issue wasn't the only reason for my low grade:
Our teacher was out sick for a few days and we had a substitute... The sub taught at a much quicker pace and (in my opinion) explained things much more clearly. I learned an incredible amount in those few days...
Then our regular teacher came back and all the other students in the class were like "We are so glad you are back! We couldn't understand a thing that other guy was saying!"
That was when I realized that the class was actually moving too slow for me... I was getting bored and drifting off...
Well, I suppose all those days I skipped might have had something to do with the low grade too :-)
One final story - just one of those things that stuck in my mind:
According to a recent study teenage boys think about sex roughly every 17 seconds. And from what I can remember that's about right :-) But at that age you don't have to be thinking about anything for your body to "betray" you...
One morning I was anxiously watching the clock waiting for Algebra class to end. Not a thought in my head other than wanting to get out of there :-) Then a girl in the next row reached up and brushed her hair away from her face... That was all it took - I was instantly at "full attention"...
I was like "You have got to be kidding me! I wasn't thinking a darn thing!!!" The class was ending 5 minutes and there was no way I could stand up without my "condition" being obvious.
I was in a state of absolute panic... I was thinking about sports statistics (that actually does seem to help) and roadkill and anything else I could come up with to put myself "at ease"... I ended up having to spend a couple of extra minutes in the room after class "organizing my notes" before I was finally able to head off...
Yeah - it's one of those things that happens to teenage boys... But it's really not our fault :-)
About Me
- pdx70rt
- The title of my blog is "Screws fall out all the time". This, of course, is a line from "The Breakfast Club". What follows is "we live in an imperfect world" and that is the thing I found most interesting (and amusing) about life...
3 comments:
And how quite you got from math to the, er, teenage boy problem is..interesting. Talk about MATH going from one thing to another through something quite different! You seem VERY able to do that ;-)
(I was terrible at math--I read a lot of stuff that claimed that a disfunctional family background was a reason for poor math skills in children. Could that have contributed to your low grade at that time, do you think? Though clearly the slow pace and resultant boredom was the REAL problem).
Dysfunction probably has a lot to do with it... It affects confidence and that has a LOT to do with the ability to grasp challenging material...
It wasn't until tech school in the military that I became aware that I was actually capable of understanding technical material... And not just merely capable - I excelled...
That's a great way of looking at math. That's exactly the problem people have with logic. It always seemed to me like those who couldn't grasp it were the ones who wanted it to be impossible to prove something that is false in reality. They couldn't accept that what we were doing was working with a system of rules into which we had to plug certain assumptions (and the assumptions don't have to be true). The rules have practical applications but it's up to the user to apply them in practical ways!
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