A Clash of Perspectives

Last week I told you about how I was doing a problem in roof rafters using pictures to calculate the length via similar triangles. It seems this is not the approved method. Let us continue the story where we left off...

-----------------------------------------------------------

 

A student once told me there is a sheet with 137 mathematical formulas on it, and those are all the formulas you need to pass your carpentry exam. One of those  137 formulas corresponds to the very rafter problem which I was doing with pictures. But of course there are a dozen or so rafter types in carpentry, which means  another dozen or so formulas corresponding to each of the  possible rafter questions the students might see on an exam. For me, the idea that you would try to calculate rafter lengths by memorizing dozens of different formulas seems completely impractical and unnecessary because I have exactly one method that works for every single problem: I just draw the picture and work it out with similar triangles. But for those students who have been indoctrinated in the method of formulas, it seems both pointless and frustrating when I insist on doing my calculations with the help of pictures.  (Murray happens to be one of those indoctrinees. One day I was showing how to do board-feet calculations, naturally with the help of pictures, when Murray walked right into my class without saying a word, wrote the formula on the board behind me, and walked out again.)

It was this clash of perspectives that precipitated the crisis which ultimately cost me my job. I was teaching hip rafters, which go at an angle in three dimensions. I drew my picture. The obvious way to draw the picture, projecting the rafter into the plan view, requires an  intermediate calculation, and this is how I did it on the board. One of the “formula” students said I was doing it wrong, so I asked him to go the board and show us how to do it. He got up and wrote a single formula, getting the same answer as me. No pictures and no middle step. I looked at it and saw that it was right but in that moment I somehow wasn’t able to put it in the form of a simple picture. So I told him he was free to use the formula if he wanted, but I preferred to keep using the method which I understood, even with the extra step. With almost no warning, the student abruptly announced, “This is a fucking waste of time. You don’t know what you’re doing.” As he got up to leave, I told him he was suspended for the duration of the class. Which was a violation of Murray’s explicit orders to me. Which Murray didn’t have the authority to issue in the first place since he wasn’t my boss. Which is what I subsequenly said in my letter to my REAL boss. Which led Murray to accuse me of not following the curriculum. Which is where this whole story began.

As I re-read the last few lines, I realize that although the sequence of events makes sense, it’s not exactly the way it happened. The truth is a little more bizarre. At the end of my class that day, I went straight to Murray to tell him what had happened. I found him livid with rage. Based only on the student’s complaining to him of being kicked out of class, he had already phoned our boss, told him that I wasn’t following the curriculum and demanded that I be fired. His words to me were “You’ll never set foot in my classoorm again!” And all this without even waiting to hear my side of the story! (His exact words were “I don’t NEED to hear your side of the story.” It’s interesting that I would hear those same words several more times in various circumstances during my year in Thompson. Nice people you have up there.) In any case, when I described this sequence of events in my letter to Selwin, it frankly made Murray look like the jackass he truly is. Murray never forgave me for that.

And that was how Level Two ended. According to the Ms. Henning’s letter, “Mr. Green was provided ample opportunity to correct these issues in Level 3, but this did not happen.” And yet the only specific example of inappropriate teaching subsequent to the Christams break which they are able to cite in their letter of dismissal is...troubleshooting the water heater, which took place not in Carpentry but in Facilites Tech 2! From Level Three Carpentry the college does not present a single instance to support its case.

How Not to Teach Slope

When I was fired six years ago by University College of the North, the College President gave three examples of improper teaching which were basis for my dismissal: the smokestack, the water heater, and "the slope example". I've talked about the first two cases already, so today we're going to pick up the story at the point where I deal with Exhibit C.

---------------------------------------------------------- 

By now it should be clear that I offended my fellow teachers by taking math outside the traditional classroom. These are the incidents which stuck in their minds as being offensive long after I was gone. Which brings us at last to Exhibit C, the one Ms Henning refers to as “the slope example”. Just what was this?

My first inkling that “slope” was an issue came during an absurd conversation late in January with my supervisor, who worked out of The Pas, five hours away. On one of his infrequent visits, he made a vague reference to problems with the way I taught slope. When I tried to ask him what kind of problems he was talking about, he became visibly flustered and said “slope is just an example”. Then he abruptly announced that he had no more time to talk because there was a taxi waiting to pick him up for his return trip to The Pas, and he rushed down the stairs and out the door! My written follow-ups were not answered, and that was the last I heard about slope.

I’m quite sure I know now what this was all about. Yes, I do teach slope differently. If a roof slope is 5:12, I draw a little triangle and label the sides. Then I draw another triangle to represent the rafter. The horizontal length is given: say, its fourteen feet. The height x is the unknown. Then, pointing at the triangles, I recite:  “Five is to x as twelve is to fourteen”; and as I say the words, I write the formula equating the two fractions. That’s how I teach it, and the reason I teach it that way is because for as long as I can remember, that’s how I’ve done it myself. And the problem is that my method is quite different from the way everyone else teaches it.

Taking Math Outside the Classroom

I've talked about two cases where I was written up by the College President for taking math outside the classroom. There were a few more similar instances that weren't cited in the reasons for my dismissal, but I still got in trouble for. Here are a couple of them:

----------------------------------

With hindsight, it’s obvious to me that my real crime was to be different from other math teachers: different from people who didn’t have the imagination or the knowledge to be able to do the kinds of things that I could. From this point of view, I could finally understand, much later, a couple of other incidents which were baffling to me at the time but which fit into a consistent pattern of behaviour. These confrontations involved, of all people, mild-mannered Dennis Cameron, journeyman carpenter and Facilities Tech program co-ordinator, who literally flew into a rage on two occasions when he encountered me out in the shop doing real-world math exercises with my students.

One incident involved stairway calculations. Dennis had given our students a worksheet. Every stairway has exactly six parameters which define its dimensions: total rise, total run, number of steps, riser height, etc. Given any three, the other three may be calculated by plugging the numbers into certain formulas. That was the gist of the worksheet.

At the end of the period I thought it might be a good idea to go out into the building and measure the dimensions of an ACTUAL staircase, to see if they agreed with what the formulas said. When Dennis saw me doing this, he basically freaked out and ordered me back into the classroom. It sounds crazy but that’s what happened. And it wasn’t the only time.

A couple of months later the students were given an assignment to draw a floor plan of the mock-up house which they had built out in the shop. I thought we ought to start by going out to the shop and taking measurements. Of course, the students had all kinds of trouble reading the tape measure. But I perservered with them until Dennis came upon us. Again...he freaked out. “Who told you to take them out here? They have the dimensions in their notes...”. Well maybe they did and maybe they didn’t. But was there really any reason for him to lose his temper? Except...there I was, the math teacher, out on the shop floor again with my students. Something was obviously very wrong with this picture, from Dennis’s perspective.

The Last Jew in Auschwitz

In yesterday's installment, I told you how I was criticized by the College Presidient for an episode involving "trouble-shooting and electric circuit". When I left off, I had just started telling you how in this particular course, we were operating under a strict imperative of keeping the students enrolled at all costs, if only for the social benefits. Let us continue with the story...

-------------------------------------------------------------------------------

In the case of Facilities Tech Level Two, we had a further motivation for keeping our students enrolled: the numbers game. In fact, our total enrollment consisted of exactly one student: quite a bright young fellow actually, and incidentally not unpopular with the ladies. But alas Pete had a weakness for the bottle. His weekends would begin Thursday afternoon and sometimes last until Tuesday...twelve days later. Still, we needed him more than he needed us: and don’t think he didn’t know it. In a moment of black humor I once called him the Last Jew in Auschwitz, in reference to the German guards who carefully protected the lives of their few remaining charges during the final months of the war, not out of any sense of guilt or sympathy, but simply because if the High Command found out they were operating a concentration camp with no inmates, those guards might find themselves suddenly unemployed and, as a consequence, liable to be sent to the Eastern Front. Similarly, we had four instructors making a comfortable living off young Pete Ross, but only as long as he was willing to grace us with his presence, if only for a few days every other week or so. The point of this digression is that in the context of Facilities Tech Level 2, in that particular winter, the “curriculum” in the Thompson campus was simply whatever subject matter you could use to hold Pete Ross’s attention on any given day. And to go back after the fact and hold me as an instructor to any higher standard makes no practical sense.

Having said all that, what exactly was my crime? In Facilities Tech, the students work on a mock-up of a house in which they have to, among other things, install a water heater, which involved both plumbing and electical. I thought this would be a good topic to take a closer look at, so I showed Pete how to draw up the circuit diagram for the controls (remember: I was responsible for teaching math AND blueprints!), and then we did some measurements on the actual building water heater to see if it worked the way the control diagram said it should. How was this possibly outside the scope of what we might teach people in a program which covers carpentry, plumbing, and electrical? All I did was to take the student outside the classroom, into the "real world", in an attempt to make the textbook knowledge more meaningful.

Failure is Not an Option

Last time I told you how the College President game me three examples of inappropriate teaching to justify my dismissal from the Carpentry Apprenticeship program in Thompson, Manitoba:

* * * * * * 

...in fact she came up with exactly three cases, the smokestack being Exhibit A. And as an argument for my dismissal, it is patently absurd.

Let's move on to Exhibit B: the water heater controls. This example comes not from the Apprenticeship program but from Level Two Facilites Tech. Now, I admit that in this program I was a little less meticulous in following the curriculum as compared to the Apprenticeship classes, where I knew that the students would be responsible for passing a Provincial Exam at the end of their program. I took the Provincial Exam very seriously: in fact, from early in the year, I made a point of meeting with Murray every single day after my class ended to confer with him about what I had just covered and what I ought to work on the next day. That’s how I handled the Apprenticeship course, so if I ever veered from the curriculum you should blame Murray, not me. But as for the Facilites Tech program, just what was the particular urgency about following the curriculum?

No one who has not seen the social problems among the native people of the North can completely understand what we are dealing with in an educational setting. Many of the students who enroll in our courses are barely functional after years of chronic alcohol abuse. It was made clear to me that failing them was not an option: we wanted to keep them enrolled at all costs, because we believed that one way or another the school is providing a positive social influence. In the case of Facilities Tech Level Two, we had a further motivation....

* * * * * * *

When we return, I'll tell you just what that "further motivation" was all about.