Category Archives: math

Past, present and future

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I had a Thanksgiving visit to a faculty colleague’s house. We got to talking about graduate school after dinner and the feelings of inadequacy it seems to bring out in everyone. These feelings relate back to my earlier post on shame. He described the dogged persistence by which he finished up, and he is glad to not have research responsibilities anymore in a teaching-focused faculty position.

As for me … I am glad I am not in a research position, and as I wrote earlier, I feel like a failed researcher. Graduate school sure kicked the stuffing out of my ego. But there’s a part of me that isn’t convinced that I couldn’t be a good researcher now (although exactly at what is still an open question) or couldn’t have been a good one then. The one thing I am sure of is that you can put a perfectly motivated, intelligent, creative person in the wrong circumstance with the wrong people, and you can tear her down so badly that she is almost unable to function. So that she starts to hate things that were enjoyed activities to begin with.

Yes, a good part of that was my own damn fault, and I know it. No one teaches you when to quit; that sometimes the only way to make something better is to run away from it. I should have found other people and another direction, but when things didn’t work, I was far too busy blaming myself, feeling like a failure. That does not help give you strength to pick yourself up, walk away, and start over.

I got on Project Euler this summer; discovering that I do really like programming was a revelation. After leaving my last software job, I thought I had made a huge mistake going into the field. Must’ve been guilt or pressure, being one of the few women who could to go on and pursue math and software. But that’s not right either. Over the past years of teaching, I keep discovering that I do love problem-solving, math, and programming, and not just when I am working with students. I enjoy them in their own right. And what does that mean?

I am always going to be a teacher first; give me students and they will take priority in my life. I want more than that out of life too. I want to write articles and books; I really want to write things that people read and care about. I don’t want to just write musty math articles.

I know I approach problems differently now than back then; now I’m all about finding the low hanging fruit and plucking it down. Way back when I was in graduate school, I wanted to understand the things that most confused me. Which is, for the record, not the best way to pick a thesis topic.

One thing for certain is that we cannot go back and fix the past. The only thing we can do is learn from it, and use our lessons to help ourselves and others. I don’t know where my journey will take me; maybe into more research and maybe not. One thing I am always telling my students is that they are capable. They are worthy. They are strong. They will find a way, even though it may not be what they currently imagine. And that is the message I need to bring to myself. I am capable. I am worthy. I am strong. I will find a way, even if it is nothing that I currently imagine.

Shame

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A friend and I had dinner last night, and one of the topics we talked about was shame. Something else in our conversation made me think that he would like to watch Brené Brown’s TED talk on The Power of Vulnerability (one of the most-watched TED videos)

I hadn’t quite processed at that time, that she had a second video about shame, but when I watched it again, I knew I’d seen it before.

Shame is one of the hardest things for people to talk about. It is painful to live through, and just as painful to hear, and so we try to hide it. But shame thrives on secrecy and isolation.

Dr. Brown defines shame this way:

Shame is the intensely painful feeling or experience of believing we are flawed and therefore unworthy of acceptance or belonging.

The last time I had an intense bout of shame was during my first semester when I started working at a university after a long sojourn as a software developer. I gave a talk to the Numerical Analysis seminar, about a paper I had recently gotten published. The talk was too short, and I didn’t have to do anything beyond some fairly basic mathematics to get my result. It felt like everyone filed past me, not speaking to me, and I had days of crisis, tears, trying to get help from my therapist, not knowing where to go or what to do. But definitely not talking about the incident with anyone who was there; I wanted to avoid all of them. I think I told a friend who advised me to ask someone there how it went, and one thing I knew for sure was that I couldn’t do that. I was completely terrified of what the response would be. I am still not sure I could ask someone who was there that day about it, and that was 5 or more years ago now.

This stirs up all the memories of my graduate school experience, where, no matter what I did, I felt like I had disappointed my advisors and hadn’t met the standard. I remember going home from an oral exam that I passed and crying for hours, feeling like a failure. I remember words, “Maybe you are like a retarded third grader who can’t learn how to read.” I remember many days where my one success was not starting to cry until I got out of the building. And the sense that my Ph.D. represented my ultimate failure as a human being to be what I wanted to be.

Clearly one of my shame triggers is being unworthy as a mathematician. Of being unable to do anything but second rate or easy work.

Today I was videotaping a lecture. A student asked how I knew a certain equation was the equation of a plane, and on tape, I couldn’t figure out what to say. I was stumped, although I know I know this answer. I said it was because a linear constraint in 3 dimensions solves to a 2 dimensional space. Because I just do. You’ll learn more about this in the next section on the cross product, and more yet in linear algebra.

In office hours I struggled with a few questions (some were hard) and eventually managed to put together the neat answer to the plane equation for my student, after several tries to write the notation properly. It’s not like I don’t know the notation. I was feeling queasy and uncertain and anxious and uncomfortable. That was enough to keep the notation from coming out properly.

I kept thinking, I caught that on videotape. I can’t show that videotape to anyone, They will think I am stupid, or that I don’t know my subject matter, that I am incompetent.

And that is shame. Not as bad as those other, earlier, times. But shame. I am writing here, so that maybe these things can see the light of day. So that they can be exposed to empathy. Because openness and empathy are the two antidotes to shame.

And I wonder, dear readers, what stories you might be brave enough to tell me about shame. Maybe not publicly. Maybe not here. Maybe in person, sometime, or by private message. I hope that if you honor me with your confidence, that I can provide the empathy that helps ease the experience of unworthiness and isolation.

The Fibonacci in Tool’s Lateralus

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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

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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

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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 …

The Advantages to Being Female

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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.

90% of Success

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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.)

Project Euler

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Lately I’ve been thinking about what I wanted to do with an honors class I am teaching in the fall. The three things you can give a student that will help them most in the future are: good communication skills (make them write, make them give presentations), programming skills, and work on decent-sized projects that go beyond the routine weekly homework. These are discussed in this Washington Post article: Starting College? Here’s how to graduate with a job.

I’m getting burned out on teaching large projects and lots of writing. That’s not appropriate for this class anyhow. But I could throw in some programming problems. And we might do a small project with some writing/presentation. Or we might not! #1 Rule for the Moment: take it easy on yourself, Dr. Jinx. You have a lot of irons in the fire, and you work too hard.

One of my students recently pointed me to the Project Euler (http://projecteuler.net) website, which is a compendium of nice problems requiring programming and basic mathematics to solve. I am sure friends into math and programming have mentioned this site to me in the past, but I didn’t have the motivation to go check it out.

There are several small problems early on the site that I can use for my students. Then they get more interesting/harder. What I wasn’t expecting was how much fun I would have solving these.

I’m 21 problems in. The problems are getting harder. I am building a small library of general-purpose tools to make solving them easier.

I worked in software for 10 years, and when I got out, I questioned myself on many counts. Did I really like doing math, or was I just sucked in because I was one of the few women who could, and I seemed to be reasonably good at it? Did I really like programming, or did I just get sucked into it, too? While it seems possible that other paths might have been good ones for me, it also seems that I got a first-hand look on how environment can deeply effect your enjoyment of things. A poisonous environment can cause you to start to dislike and feel incompetent at activities that you are actually reasonably competent at and enjoy.

The number one advice I tend to have for students is to find people and environments that make them feel good about themselves and spend more time in them. I wish I had gotten and taken that advice myself.

Whether you are a supervisor or a teacher or a Ph.D. advisor, good advice to keep in mind is to put some thought into keeping the environment supportive and healthy. While yes, whatever you are doing is work, if you can make work fun, you win. Your employees and students will work hard and happily for you in that case.