Category Archives: Teaching

The Fibonacci in Tool’s Lateralus

Posted on by

http://www.youtube.com/watch?v=wS7CZIJVxFY

On Friday we rocked out to Tool’s Lateralus for a while before math class.
Even though there was a flood in our building,
and now we had the baseboards and 2 feet of wallboard removed in my classroom and in others.
Sound travels much better than usual.
No one came down the hallway to complain to me for making too much noise.
I did close the doors just in case.

I was sad to turn the video off, but it’s long.
We missed a day Monday, and we had to start class.
Back to business as usual.

I remember one day,
I played that video in linear algebra,
where we also studied the Fibonacci Sequence.
A young man turned to me and with incredulity in his voice asked,
“Where in the hell did you find that?”

I had to laugh, because everyone sends me math things,
but my magic is to know when to use them.
Even when no one reacts, I know that sitting in my classroom
some student is listening and thinking.
Maybe this little bit of inspiration is enough to take them in a direction
that neither of us ever imagined.

One thing we forget in math class
while we are doing calculations,
trying to remember which angle is which on the unit circle,
Is that all of this math and the fact that it works out the way it does,
in such neat little packages,
all of these are miracles, one right after the other.
That we can understand this at all,
that means each of us is also a miracle.

It took thousands of years before calculus was invented,
and we’ve forgotten all the intermediate steps,
all the times someone tried something and it didn’t work out,
all that got thrown away like scratch paper.
All we see is the final result, the neat little packages,
and we dare to think, “how boring.”
Stop before you say that.
Be amazed for a moment that we figured this out at all.

—
From Edward Frenkel’s recent article in The Atlantic

Charles Darwin wrote in his autobiography: “I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.” Mathematics is not about studying boring and useless equations: It is about accessing a new way of thinking and understanding reality at a deeper level. It endows us with an extra sense and enables humanity to keep pushing the boundaries of the unknown.

Walking out of class

Posted on by

Friday is quiz day. I give a quiz. I try not to make it an easy quiz. This week inspiration came in the form of an online homework problem everyone said was difficult. I didn’t think it was that bad, but I took time to write up a solution and post it for them. Then I recycled it for the quiz question, figuring that after they had tried to do it, and after I had posted a solution, it was fair game. And if we still didn’t know how to do it, it was time to learn.

I could tell that many were unprepared for the question, and they were too flustered to come up with a coherent strategy for dealing with it.

And that’s fine. That’s why I solve quiz questions immediately after giving a quiz. If you don’t know how to do it and you should, well, now I’ll show you again and hope that this will impress the method on your brain.

Five students stood up and walked out before I started doing the quiz solution.

That kind of blatant display of disrespect for me and their own learning annoys the daylights out of me. I know that we are a learning environment, not a forced learning environment. You can lead a horse to water, blah blah blah.

But. Wow.

I’ve seen this happen in other people’s classes, including one I was sitting in on for fun. I know this has nothing to do with the quality of the instructor, and everything to do with the quality of the student. Still … it can be hard to sit/stand there and take it.

I pointed out to the ones who stayed that they were at a competitive advantage in the class.

Before we went home, I reminded them that I would love to see them in office hours. “Maybe I am weird, but I love to watch you do math,” I said, “I guess that’s why I am a math teacher. So if you are wondering if you would be `bothering’ me in my office hours, don’t. Working with students is the best part of my day. So come.”

Three new ones did. Maybe the day was not without its successes.

Honors Class

Posted on by

The challenge with teaching an honors class is making sure you have interesting enough questions to keep your smartest students on their toes while not intimidating the hard-working middle of the class into hatred and helplessness.

First exam was Thursday evening, and so Friday’s quiz question was the following:

Have a conversation with the exam you took last night. Was it a victory lap or a street fight? Did it go better or worse than you expected? In the conversation start figuring out what message your exam has for you.

Everyone thought the exam was a formidable opponent. There was plenty they knew how to do, and also some spots where I made them think. Many are concerned to see how they did, but they also express having better knowledge of what to do to prepare and resolve to destroy the next exam.

My favorite comments:

  1. I kind of enjoyed it. I’ve never had a challenging math test. They have always been straightforward and procedural. This one made me think. … This class has been helping me break my habits of memorize, plug and chug. I would not have done well had I used those methods.

  2. I wish you would just give me numbers, but you are an Honors Exam and that’s what I should expect. By the end, I felt better about you. You made me think and you were challenging, but I think we may be friends. … You taught me that I can think through a problem, even if I am not sure where to start.

    (This second commenter, a young lady, got a 100 on the exam!)

Now I better hope I can come up with a good next exam …

Teaching

Posted on by

One downside to teaching is that there are days when, in another job, I’d just stay home in bed and allow myself to be ill. But I’m not in another job. I’m a university teacher.

Today was one of those days.

My throat was in agony whenever I tried to talk, and I had to get the microphone working in order to teach.

In my morning room, I can’t tell that the mike is working, but I need to talk quietly or it won’t be long before I’m not talking at all. And when I can’t hear that it is working, I keep trying to compensate.

Then there’s the muzzy-headedness, and mistake after mistake after mistake where I just don’t line my points up very well. This is frustrating for the students; I get it. They begin to talk amongst themselves, and then I try to compete with my voice which is a painful disaster.

You know that moment when you are about to start to cry, from feeling like you are the biggest screw-up in the world and nothing you can do right now will change it, right in the middle of class, in front of the 60 students out of a hundred who bothered to show up the day after an evening exam …

I managed to channel it into irritation instead. “Look, guys, I know I stink today, and I know I’m hard to follow, but I can’t compete with you (talking while I’m talking). So make up your minds whether you are going to help me out or whether we just want to go home and don’t really care about learning this after all.”

It got better after that, but I was still wet-eyed in line to order my lunch.

The honors class in the afternoon was better, but I appealed to their mercy straight off. We laughed at a few things and did one problem with minimal talking to help save my voice. The no-talking problem … now something about that was interesting. I want to try that again.

The Advantages to Being Female

Posted on by

One of my students was rubbing his face this morning in a characteristic gesture that I recognize from my past week of extreme stress.

“Hey,” I called out, “is everything all right?”

He told me he was really stressed. I don’t know what I said; we got started with class. We talked for a moment about questions and concerns with regards to the exam tomorrow night. Then I taught my lesson.

I had a crowd after class, someone wanting to learn some math, some concerned with logistics, and the young man who was rubbing his face, who wanted to tell me what was up.

Apparently he made an error in recording his exam schedule, and missed an exam he was supposed to take yesterday at the disability center. The instructor wouldn’t make alternative arrangements, and he has to take the exam with the rest of the class without the additional time he’d normally get.

You don’t see young men get to the crying point often, and when you do, you know they are under a phenomenal amount of stress.

You can’t bullshit someone in a situation like that. “Oh, it will be all right,” that’s just empty words. We know it’s just one exam, but to this student at this time, it’s the entire world.

You want comfort at times like that from a caring authority figure who can let you know absolutely that you are okay and you are not a fuck up.

I’ve been paying careful attention to how this one has been doing all semester; he’s not getting the disability accommodation on my quizzes, and it’s my responsibility to make sure that situation is working for both of us.

I put my hand on his shoulder, and I told him that if he was doing in that other class what he was doing in mine, and he could calm down between now and that exam, that I was confident that he would get through it okay. More than okay. I’m convinced he’ll do well.

I know that’s still just empty words; it requires my authority and his conviction of my ability to stand in judgment to carry that message through. It couldn’t make everything better, but I think it helped.

Scholarships

Posted on by

I have a prize student. Some insane luck brought us together. I got assigned to teach a class no one else wanted to teach and decided to make the best of it. He happened to be in the class that first semester when I didn’t know what on earth it was I should be doing. Since I didn’t know what I should have them do, I threatened to make them do two final projects unless they came up with one of their own. I didn’t need threats on this one, to be honest, he had an idea for me. I remember looking at his project proposal, with the professional looking diagrams, and thinking, “Oh my gosh, look at this.”

Thus began a great run for both of us. I thought his work was pretty cool, so I asked him to submit it to the local journal of undergraduate research. He got that published. He made a video for my class that blew my mind, so I had him enter that in another contest. Won that one too.

I saw an advertisement for the undergraduate thesis program. He seemed interested in doing more with his project, so I asked him to apply. He did. Got in. Wrote an undergraduate thesis, and was named runner up for outstanding STEM thesis. He got the nomination for the Goldwater Scholarship and picked that up ($7500!) He went to MathFest this past summer, and walked away with another $150 award.

Now, my student is amazing, but the #1 reason he’s won all this stuff is that he’s had things he wanted to do, and when he was encouraged to apply for things he went out and did it, bringing all of his diligence and conscientiousness into play.

My job has been to stand behind him and cheer, see the opportunities, and apply the professorial push when needed.

He’s the nominee for the Marshall Scholarship, which is one of the 2 year fellowships to do graduate study in the UK. I was proud of that. Today I found out he’s also going to be the nominee for the Churchill Scholarship, which is similar to the Marshall, and maybe slightly better known. Why? Because the original nominee wasn’t working on the application materials, and he was.

So, lesson: Apply. And when you apply, be conscientious about it. Do the work in front of you. I don’t know if he’ll win either scholarship, but in my mind, he just improved his odds. And by doing nothing more than keeping on top of the things he needed to do.

I hope he knows how proud of him I am. Watching all this evolve is more than I ever thought I’d get to see as a teacher. I’m going to miss him when he graduates. What a ride, what a ride! these last 2 years have been.

90% of Success

Posted on by

Monday, first day of class, one of the points I hammered was that 90(+)% of success is showing up on time prepared for whatever activity it is that you are about to undertake.

Today I gave a quiz and maybe brought this lesson home for a few of my students.

They did know that a quiz was coming today. And they did know what it was over (had they bothered to check). And they did know (if they bothered to check) that I told them to know their section number to prepare … actually, they should have just known that. I put it on the board on Wednesday.

Question one: Write your name in the upper right hand corner. Below your name put your UIN (University Identification Number). Below the UIN put your section number. (3 points on a 10 point quiz).

Most seemed fine, a few seemed put out that I required the UIN and section number, and yes, there were a few students 10 minutes late to class when I gave a 10 minute quiz at the beginning of the day. Whoops!

“Can I come by your office later and take the quiz?”

No.

90% of Success is Showing Up on Time and Being Prepared for Whatever Activity It Is You Are About To Undertake.

I solved the quiz problems in class immediately after giving the quiz. If you got them, you know you are right. And if you didn’t, then you hopefully learn something immediately, and in such a way as to embed the lesson on your memory.

Which is why I won’t generally give make-up quizzes. We take a quiz. We solve a quiz. I drop the lowest two in case you are absent, or have a bad day. But I don’t give make-ups.

There might be a side-benefit to the day’s lesson. A few might now be convinced that the nice lady who teaches their math class really is prepared to enforce logical consequences and will actually allow them to suffer now rather than suffer later. (We sometimes are under the impression that the nice lady is going to succumb to begging and whining. We are always disappointed and surprised when it doesn’t work that way.)

The Next Best Thing

Posted on by

The next best thing to having children has to be having students. The best-best thing is that you never need to change their diapers! Although college students will attempt to fertilize you from time to time, it is usually with words and not with actual natural organic matter.

I had a good first day. I only forgot a few little things, and you know what? Probably best not to do everything at once.

I got to class early enough to get the computer setup and ready, then, even in my big class, I had plenty of time to walk around and greet (with a handshake) everyone who was there a few minutes early and give them 4×6 inch note cards for the getting-to-know-you assignment. That sort of personal attention really can make a difference, and greeting about 75 of my 100 students got done in 10 minutes before class.

Most of the students are signed up for Piazza, and they’ve already been asking and answering questions there. Seeing good community spirit develop so quickly always warms my heart. And there’s an added benefit that this will hopefully reduce the clutter in my inbox, in particular, minimizing the number of times I have to intervene and help out with logistics and straightforward questions. I love working with students, but it is easy to get overwhelmed with email asking the same question over and over again.

Lots of students seemed happy to meet me and happy to be there. A happy, productive environment is definitely one of my goals since it makes learning easier. We’ll see how we fare after the first exam.

I felt like my big message for them for the day was 90% of success is showing up on-time and prepared for whatever activity it is you are about to undertake. Be prepared, be on time, do the work that is in front of you to do, and let the rest take care of itself.

We value good teaching

Posted on by

It’s a busy week, but the basic paperwork and websites for my classes have been completed, the students have been emailed, and homework has been assigned. Before the first day of class? You betcha! I figure the only way I have to warn them that my classes are work is to assign some work due on the first day of class.

As a small distraction from all those logistics, I helped facilitate two teaching programs this week.

The first was about Piazza which I and another instructor use to promote discussion outside of the classroom. In particular, we like it when students answer each other’s questions. We also like reducing the number of times we have to answer the same question (reduction to zero is a bonus). Piazza was created by a woman entrepreneur, Pooja Sankar. Quite a role model for our women students.

The second was on the theme of getting the semester started off on the right foot, and, given that there are always a few new instructors around, advice for new instructors. I think the experienced instructors enjoyed sharing some best practices, and maybe even picked up a few good tips. I think the new instructors were exposed to a great deal of community wisdom, and heard about some valuable resources. And they have some ideas of people to approach if they have questions later.

But maybe the most important outcome for me is promoting teaching as a community value in our department. It gets lip service, but often not much else. Holding an hour long workshop or two and having faculty show up is something concrete that says that it matters.

They’re back!

Posted on by

My college town is nice over the summer. Rarely a line at the grocery store, and no problems parking. Traffic? Schmaffic. No need to fuss over that. You can go to whatever popular restaurant you like and expect to get seated promptly.

Suddenly it is over. The streets are full of cars, intersections are backed up. God help me if I want to go to the grocery, or, even worse, that den of iniquity known as Walmart.

Times like these make me glad I am a bicycle commuter, a natural avoider of the worst of the traffic.

I feel not really close to prepared for the new semester, but I will surely have something ready when I need it to be. I care about my students too much to do otherwise. Right now I dread getting prepared for Monday, but I am happy to start a new semester, meet all my new students, and see what hope and possibility is ahead.

Let me do a good job with them. If there is one thing I care about more than anything else, it is providing a healthy, happy environment in which even a scared student can find the courage to learn.