Reasons to be cheerful (part three)
Summer, Buddy Holly, the working folly
Good golly Miss Molly and boats
Hammersmith Palais, the Bolshoi Ballet
Jump back in the alley and nanny goats
18-wheeler Scammels, Domenecker camels
All other mammals plus equal votes
Seeing Piccadilly, Fanny Smith and Willy
Being rather silly, and porridge oats
A bit of grin and bear it, a bit of come and share it
You're welcome, we can spare it - yellow socks
Too short to be haughty, too nutty to be naughty
Going on 40 - no electric shocks
The juice of the carrot, the smile of the parrot
A little drop of claret - anything that rocks
Elvis and Scotty, days when I ain't spotty,
Sitting on the potty - curing smallpox
Reasons to be cheerful part 3
Health service glasses
Gigolos and brasses
round or skinny bottoms
Take your mum to paris
lighting up the chalice
wee willy harris
Bantu Stephen Biko, listening to Rico
Harpo, Groucho, Chico
Cheddar cheese and pickle, the Vincent motorsickle
Slap and tickle
Woody Allen, Dali, Dimitri and Pasquale
balabalabala and Volare
Something nice to study, phoning up a buddy
Being in my nuddy
Saying hokey-dokey, singalonga Smokey
Coming out of chokey
John Coltrane's soprano, Adi Celentano
Bonar Colleano
Reasons to be cheerful part 3
If the above rings no bells, you're probably too young or too old to recall the sprightly Ian Drury and the Blockheads. You owe it to yourself to download the above song immediately and listen to it several times before proceeding. This way, there be monsters.
Bad Day At School
There's nothing quite like having a classroom full (and I do mean FULL: as in 36 of 42 allegedly enrolled students in a room with desks and books for 30) of "precalculus" students with too much heat in the room and too much ire in their souls as you try to take them through a review of something that on the one hand you know they SHOULD know, and on the other you suspect with good reason is going to be news to most of them, despite having allegedly passed two years of algebra and one of geometry. The review topic in question: the point-slope form of a linear equation. The first task, having ascertained that the majority of students at least believed they knew what "slope" meant and could find it given the coordinates of two points, was to find the equation of the line that passed through them. Little did I realize just what sort of tiger trap I was about to fall into.
Picking two points from one of the textbook problems, I began guiding the students through the process of using the point-slope form, with my usual plan of showing that regardless of the point one chose to use in the equation, it would result in the same graph, the same line, and, upon applying a little algebraic manipulation into the slope-intercept form, stark evidence that the equations arrived at with either point were equivalent, as of course should be the case if they have the same slope and pass through the same two points.
Unfortunately, I never got that far. So much time had been spent dealing with logistical issues regarding the shortage of seats and books, as well as dealing with various disciplinary issues, trying to take attendance on-line (PowerSchool, where is thy sting?) given that I was using my laptop, not the promised but as yet invisible Pentium-based desktop Mac that would have made the process much less time-consuming (for reasons not worth going into here), I knew that if things continued to go less than smoothly, it would be difficult to finish what was supposed to be the only major mathematical point I thought I might be able to look at with them before class ended. However, as I started to proceed with the equation with one of the two points, I was rudely and persistently told by a vociferous subset of the class who had been making things difficult (when not making them impossible) for much of the two weeks we'd been meeting that I was clearly wrong.
At first, I thought they meant that I'd made some sort of calculation error, hardly an impossibility under the best of circumstances, and these were anything but the best. I began to recheck my work, but the sound and fury from their part of the classroom made rational thought or even simple calculation a doubtful process at best. Finally, I realized what was amiss: they had taken PART of my lesson as gospel, but refused to attend to the crucial caveat. Since I labeled the points as "point 1" and "point 2" respectively, and since the coordinates were labeled with the appropriate subscripts, clearly I was in error when I chose "point 2" as the one to plug into the equation. After all, hadn't I written the point-slope form with subscripts x1 and y1?
How could I possibly be stupid enough to now be telling them that the point that had 2s in the subscripts were kosher (okay, no one said "kosher" and in fact, none of what was said approached in any way the slightest degree of civility, but this is a family blog, after all)? Obviously, I'd made a huge mistake and anything I did from this juncture on was going to be horridly wrong.
Now, this was hardly the first time I'd taught this topic, either to high school or community college students. Indeed, having taught a lot of algebra courses over the years, I was used to there being skepticism that it didn't matter which point was used and that it would be possible to show that whichever was selected would be fine, and that the resulting equations, though initially appearing to represent different lines, would ultimately turn out to be the same, without any doubt at all.
However, nothing in my experience with non-alternative education students had prepared me for a group of students who were supposedly ready for precalculus and who not only were so confused by a notation issue, but more importantly were NOT going to be patient or trusting enough to see if just possibly their teacher had a clue about what was going on and could, in short order, demonstrate that fact and part the clouds.
I hoped, of course, for a teachable moment. I figured that either I'd get to finish the problem with input from the students, and, having tried both points, they'd start to see (or in some cases REMEMBER from previous experience) that all was indeed well, or that if I were extraordinarily fortunate, the light would go on for most of them before I even got to that point, and, mirabile dictu! they would look at me with new-found respect, paving the way for a successful and productive year.
Instead, things bogged down as no one in the class would agree to see what happened if they finished the problem with those coordinates with the OTHER subscripts and I finished it with the point I'd selected: the hue and cry became such that more time was lost trying to maintain some order, and when the bell rang, the problem remained unfinished, several students loudly agreeing with my chief antagonist in the class when he proclaimed that I "didn't know what I was doing."
While of course there have been moments in my teaching career when I really DIDN'T know what I was doing, either mathematically, pedagogically, or a combination thereof, this was most decidedly not one of the times I was unclear about the mathematics. I was very confused, however, about what kinds of experiences would lead a class of seniors and juniors to be so invested in proving that the teacher couldn't possibly right, and not by making a convincing mathematical argument, but merely by making it effectively impossible for the teacher to show that he might actually be (dare I say it?) right.
I'll stop at this point, leaving readers to consider their own experiences in similar circumstances, if any, giving everyone ample opportunity to contemplate what might have saved the day in this or similar situations. I'm sure that my "solution," such as it was, will not be terribly satisfying, so there's no hurry on my part to offer it. By all means, I'm sure others would have done much better in my shoes than did I, and I'm interested to learn about the alternatives that I might have employed but did not.
If only I'd had a Vincent Black Lightning 1952 and a red-headed girl waiting outside, instead of a Japanese sedan and a horrid, traffic-snarled 80 minute slog home.
Picking two points from one of the textbook problems, I began guiding the students through the process of using the point-slope form, with my usual plan of showing that regardless of the point one chose to use in the equation, it would result in the same graph, the same line, and, upon applying a little algebraic manipulation into the slope-intercept form, stark evidence that the equations arrived at with either point were equivalent, as of course should be the case if they have the same slope and pass through the same two points.
Unfortunately, I never got that far. So much time had been spent dealing with logistical issues regarding the shortage of seats and books, as well as dealing with various disciplinary issues, trying to take attendance on-line (PowerSchool, where is thy sting?) given that I was using my laptop, not the promised but as yet invisible Pentium-based desktop Mac that would have made the process much less time-consuming (for reasons not worth going into here), I knew that if things continued to go less than smoothly, it would be difficult to finish what was supposed to be the only major mathematical point I thought I might be able to look at with them before class ended. However, as I started to proceed with the equation with one of the two points, I was rudely and persistently told by a vociferous subset of the class who had been making things difficult (when not making them impossible) for much of the two weeks we'd been meeting that I was clearly wrong.
At first, I thought they meant that I'd made some sort of calculation error, hardly an impossibility under the best of circumstances, and these were anything but the best. I began to recheck my work, but the sound and fury from their part of the classroom made rational thought or even simple calculation a doubtful process at best. Finally, I realized what was amiss: they had taken PART of my lesson as gospel, but refused to attend to the crucial caveat. Since I labeled the points as "point 1" and "point 2" respectively, and since the coordinates were labeled with the appropriate subscripts, clearly I was in error when I chose "point 2" as the one to plug into the equation. After all, hadn't I written the point-slope form with subscripts x1 and y1?
How could I possibly be stupid enough to now be telling them that the point that had 2s in the subscripts were kosher (okay, no one said "kosher" and in fact, none of what was said approached in any way the slightest degree of civility, but this is a family blog, after all)? Obviously, I'd made a huge mistake and anything I did from this juncture on was going to be horridly wrong.
Now, this was hardly the first time I'd taught this topic, either to high school or community college students. Indeed, having taught a lot of algebra courses over the years, I was used to there being skepticism that it didn't matter which point was used and that it would be possible to show that whichever was selected would be fine, and that the resulting equations, though initially appearing to represent different lines, would ultimately turn out to be the same, without any doubt at all.
However, nothing in my experience with non-alternative education students had prepared me for a group of students who were supposedly ready for precalculus and who not only were so confused by a notation issue, but more importantly were NOT going to be patient or trusting enough to see if just possibly their teacher had a clue about what was going on and could, in short order, demonstrate that fact and part the clouds.
Be Careful What You Wish For
I hoped, of course, for a teachable moment. I figured that either I'd get to finish the problem with input from the students, and, having tried both points, they'd start to see (or in some cases REMEMBER from previous experience) that all was indeed well, or that if I were extraordinarily fortunate, the light would go on for most of them before I even got to that point, and, mirabile dictu! they would look at me with new-found respect, paving the way for a successful and productive year.
Instead, things bogged down as no one in the class would agree to see what happened if they finished the problem with those coordinates with the OTHER subscripts and I finished it with the point I'd selected: the hue and cry became such that more time was lost trying to maintain some order, and when the bell rang, the problem remained unfinished, several students loudly agreeing with my chief antagonist in the class when he proclaimed that I "didn't know what I was doing."
While of course there have been moments in my teaching career when I really DIDN'T know what I was doing, either mathematically, pedagogically, or a combination thereof, this was most decidedly not one of the times I was unclear about the mathematics. I was very confused, however, about what kinds of experiences would lead a class of seniors and juniors to be so invested in proving that the teacher couldn't possibly right, and not by making a convincing mathematical argument, but merely by making it effectively impossible for the teacher to show that he might actually be (dare I say it?) right.
What the fudge?
I'll stop at this point, leaving readers to consider their own experiences in similar circumstances, if any, giving everyone ample opportunity to contemplate what might have saved the day in this or similar situations. I'm sure that my "solution," such as it was, will not be terribly satisfying, so there's no hurry on my part to offer it. By all means, I'm sure others would have done much better in my shoes than did I, and I'm interested to learn about the alternatives that I might have employed but did not.
If only I'd had a Vincent Black Lightning 1952 and a red-headed girl waiting outside, instead of a Japanese sedan and a horrid, traffic-snarled 80 minute slog home.
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