I'm licensed to do what now?

After about 18 hours spent in a classroom and on the, uh, range, I am now the proud holder of a motorcycle license. I also have a bit of a sunburn on the back of my neck. The latter I earned by tooling around a paved lot while never getting above 2nd-gear. The former was acquired the same way. I've spent some time reflecting on the whole experience—T says possibly too much time.

True to form, The T turned my commentary on the course into an example of learning theory. Let me explain. A student in the class said she was taking the class because she bought a 400cc scooter to ride to work and she'd heard that if she was caught on the road, it would be taken away. She does not have a permit for the scooter. She seemed to think that it would be impounded because it was a scooter. I tried to explain to her that it would be impounded because she didn't have a driver's permit to ride it on the road. I guess she didn't believe me because the next day when the instructor asked her why she was taking the class, she said the same thing. She wanted her motorcycle license because she thought she needed to get a motorcycle because a scooter could not be on the road. She did not understand the role the driver's permit played in the situation. The scooter is completely street legal. It would have been impounded because of the lack of a permit, not because it is not a motorcycle.

It was fascinating to me to watch how my suggestion of necessary paperwork was ignored. This is where T's learning lesson comes in. People, i.e., students, will hold on to their beliefs until they can mesh new information with their old (possibly incorrect) understanding to come to a new understanding. This woman had it in her head that it was the mere existence of the scooter on the road that was the problem and not the lack of paperwork. I wonder if she's shopping for a Harley right now because she still doesn't get it.

(Is this where I mention she is in the country on a green card and that little bit of paperwork she seems to understand just fine?)

When The T has talked about how people hold on to what they understand during our many education conversations, I've nodded my head and agreed. It makes sense. I've then walked into a classroom and wonder why my students make mistakes that were addressed and discussed previously. Their understanding of the math is similar to the scooter-chick's understanding of impounding: each party is holding on to what they know because new info has not been integrated into their belief structures—yet (hopefully 'yet'). Now I'm pondering my role as an instructor to help students with this integration of new info. This falls into Leading a Horse to Water scenario so I know I can't just give them the info and think that they'll immediately believe in it and integrate it and understand it. But how far do I lead? Do I walk right to the water? Do I just provide a map and compass? Do I try to come up with more detail in this analogy when I could be doing other things?

ponder ponder ponder

That won't be on the test

In precalculus, we've spent the last few days looking at various solution techniques for systems of equations. If you are a math-o-phobe, all you need to get from the last sentence is "looking at various solution techniques." In street lingo, it means we've been solving problems by hand and building up to the crescendo (in my mind anyway) of getting the calculator to do it for us. I prefer setting the stage for the Magic Button Method by first working problems by hand and analyzing why the steps are done and why they are allowed, etc. etc.

Today was the moment. What had been taking a minimum of 15 minutes of arithmetic agony took a mere minute of set-up and a second of waiting for the calculator to spit out the answer. One student immediately asked, "Are we going to be able to solve these with the calculator on the homework?"

What I wanted to say was, "Once the genie's out of the bottle, it's impossible to put him back."

What I heard myself say was, "It's like finding out that the wizard is just a creepy old man behind a curtain. There's no going back once you've seen that."

Six days and counting before break begins. Not a second too soon, me thinks.

But how do you really feel?

So there I am yesterday, at my first day of school, all shiny and happy and ready to face the challenges of the new year. I will not actually identify those challenges each by name in this post—they are Legion and I would rather focus on here what was the focus of my yesterday.

The year began as is the tradition here at the CC on the Hill ... how have I not thought to call it CCHill before, folks, eh? (I now have David Bowie in my head singing "ch-ch-ch-chill" to the tune of "ch-ch-ch-changes") ... what was I talking about? Oh yes, I was heading off to the traditional morning coffee hour and welcome back by the Prez when I saw my new colleague's door open. Remembering all too well what it was like to be the fresh meat, I offered to walk over with him and introduce him around. We had a lovely chat during which I assured him, a southwest desert transplant, that the rain this corner of the continent is famous for would get here soon enough. And what's the rush, anyway?

After the Prez's greeting, the Veeps introduce the new hires in their respective areas. This is when the tone for my year was set, I believe. When the Veep got to my colleague, he introduced him by saying, "And you know Dr. Math is new because he is sitting next to Lee."

ba-dum-bum. Annnnnnnd we're off.

Get OFF

Saturday was graduation. Therefore, you now know how the weather was on that day in these here parts. Two weeks earlier, the Emerald City's news-rag declared the region "Colder Than Siberia." Yet, the moment I throw on my academic robe, heavy in the felt department and just plain heavy, the mercury shoots to the top of the tube. Figures.

Anyway, I am still tickled when I see the faculty all dressed up in their regalia. I love the colors. This year The T attended graduation and we were hanging out in the student union while faculty filed in to don their robes. All of a sudden these smart people become retarded and cannot dress themselves. The T quickly became The Official Faculty Fitter, or OFF. Since my robes are relatively new, I still have the directions for how the hoods should hang in the pocket (and that slip of paper shall stay in the pocket for the duration of my career). The T began circulating and adjusting hoods, sometimes by request, sometimes unknown to the wearer.

The part that frosts my chickens was the number of times I heard someone say, "Oh, I can never get this. There must be something mathematical to it." Shoot me now. Why is it that because someone cannot do "it," then by default "it" must be mathematical in nature? Perhaps this comment was just a by-product of the pre-ceremony small-talk and deemed appropriate because both The T and I happen to "do math" but it still irked me. We all figured out how to tie our shoes when we were five. Are you now telling me you can't learn how to don a hood in your 50s? Yeah, let's blame your math skills.

Have a seat

The next time a student turns in a homework assignment or quiz or test or anything completed in ink, I'm going to ask him or her to have a seat in the chair of Carbon Honor.


After 12 weeks of handing back inky math papers with 0 points earned out of n possible points, I had a student turn in a final exam done in ink! And—get this—his name was written in pencil!! wtf? Oh, if I only had this chair eight days ago.

More photos

Yes, but when can I sleep in?

Oy. The quarter ended officially yesterday and I have finally come up for air. I say 'officially' because I believe the last thing of any value that occurred in any of my classes took place days—if not weeks—earlier, yet classes kept meeting. Spring quarter is brutal. I have a sense now of how marathon runners feel: once your legs go numb, your feet move out of habit. Well, my head has been numb for quite a while. My lips kept moving.

A sense of how bad things had gotten as we slogged toward the end was when, after a full 7 or 8 weeks into the class, I was still being asked a question that was foremost in the students minds: how many decimals should we round our answers to? I cannot tell you how low on the list of Big Ideas this issue is yet how high it is on the list of Things Asked Today. For the students to feel that the number of decimal places is a Big Idea means that they are missing the truly Big Ideas. For example, if you have just calculated when a water balloon launched from the roof of a 120-foot high platform is going to hit your younger sibling in the head, taking into account initial velocity and initial height while the variables that can really screw things up are mysteriously ignored and absent from the formula, why are you obsessing over the hundredths place versus the thousandths place?

I would much rather the question be something along the lines of "does launch angle matter" or "will it go farther if initial velocity is increased while height is decreased or vice-versa"? But no. Faith in the formula without understanding the elements of said formula trumps all and the fundamentalists do not question the legitimacy of what they have been told. They instead sweep the formula under the rug and obsess over the stem-cell of the math world: decimal place. I contend that this question would take care of itself if the scenario were considered a little more deeply. If you round to the hundredths place or the thousandths place, does not your sibling still get wet?


Ug. Apparently I'm still a little wound up. And I have 3 full inches of grading to get through between today and tomorrow. And today is graduation. Yea. I do like graduation around these parts. This is an area in which getting a degree is not the expected norm and is still an achievement that needs to be properly honored. These students are truly proud of themselves for their educational accomplishments, as are their families. It is not assumed that everyone will ever have a degree around here. Graduation is not merely a task included in my job description. It is a rite of passage that I am happy to be a part of. So, I'm off to grade a little, then don the robes of the academic mucky-muck, and then do something to help me reboot like mow the lawn and whack some weeds.

You want points for what exactly?

Just came back from a visit at Kfluff's place and I can't say I'm having warm and fuzzy thoughts for the semester folks finishing up out there in Academia. We Meisterquarter Quartermeisters are only 36% of the way through Spring Quarter. The quarter of toil and drudgery. The quarter of daylight saving time when the sun stays up longer than I do. The quarter of "didn't I say that aloud already?"

Things heard in my classroom so far this quarter:

Me: The probability of Event A is 1/4. What is the probability of Event B, given that A has happened?
Student: But we don't know A has happened.
Me: We have the probability it could and will happen.
S: We have no way of knowing if it is going to happen for sure.
Me: And THAT is the definition of probability. We are calculating probabilities, folks, not guarantees.

Oh, I'm just getting warmed up here.....

Me: Are these two events independent or dependent?
Student: point-9-4-5-2
Me: That doesn't answer the question. Independent or dependent?
S: That's what my calculator says.
Me: Sure. Why not? Say another number. I'll tell you that one's right too. Independent or dependent?

And the climax thus far.....

Me: What is that you're drinking there?
Student: A can of Bawllz. I got it in the bookstore.
Me: Is this where I'm supposed to ask what it tastes like?

sigh

I can hardly wait until the pile of grading overwhelming the flat surfaces in my office starts to get handed back and the Begging for Partial Credit begins. I think I'm going to post this movie to my blackboard pages. Yeah, I know it's a viral add but it is named Millimetres Matter and—by golly!—yes they do. You want partial credit? Exactness really does matter even if you don't care. Enjoy the movie. I wonder if the insect division of the ASPCA knows about this.

People smarter than us

OK, I'm back. Sorry about the hiatus. Got busy and then I got sick and then I ... lost my password? ... got a cramp? ... got trapped in a litterbox inexplicably filled with quicksand rather than litter?

Sorry, I drifted there for a moment. I'm back now. School's been fun. I've been working with a student who is very, very close to sounding like that old joke about x: What do you mean x equals 25? Yesterday you told us it was 12!" This student—who is an absolute joy to work with and my tongue is nowhere near my cheek when I say that—really works hard and has no problem asking questions. The issue of note recently involves x and y and the issue of independence and dependence. Think back to a (stereo-)typical math problem. In such a problem, you would choose an x-value, plug it in, do the arithmetic to find the corresponding y-value. In that case, y is dependent upon x because we had no idea what y was going to be until we plugged in an x.

Well, my student is so fixated on the fact that we "usually" choose x first and find y second that when the variables change roles, it is a brand spanking new world for her. Even when the variables are given a context but remain as x and y she struggles. Here's the example from class:

Variables: Number of gallons of paint and Area to be painted

Scenario One: I want to paint my room. When I go to the store, I first need to know how much area I want to paint. Then I know how many gallons to buy.

Scenario Two: I happen upon a pyramid of stacked cans of paint in my garage. I wonder to myself, "How much area can I cover with this paint?"

The variables are the same in both cases yet in the first scenario Gallons is dependent upon how much Area and in the second scenario Area is dependent upon the number of Gallons. Make sense? To my student it made sense too. She was fine and cruising along until we substituted an x for gallons and a y for area and ran through the second scenario where where Gallons (x) is dependent. She could not see how that could be the case. How could we choose y first?

Some days I'm glad classes are only 50 minutes long.

Here's a code that could give Eniac a run for its money. This is how the wise folks at Waffle House code your order using condiments on a plate. For example, a sausage omelot is jelly at 3-o-clock where as a plain omelot is jelly at 9-o-clock.


Click for a fuller, deeper explanation that does not involve either x or y.

How many of you are still wondering what I was doing in the quicksand-filled litterbox in the first place?