Lorenz Attractor

We started on the Lorenz Attractor today, hooray! Three autonomous differential equations, and so much interesting behavior. I got to show my student’s video today; who would have ever guessed that nearly 18,000 people would have viewed it a bit over a year later?

I’m so proud. I’m so proud. I’m so proud.

We started in with one of my favorite unusual ways to structure class today. I lay out some terms that they need to understand what they are doing next, and they are told to go look them up with Google and come up to the board and fill us in. I will expand on what they say, but they are expected to lead the lesson.

The afternoon class, when asked what the Lorenz attractor was a model of, answered that it was a model of chaos and the butterfly effect (true), but what I wanted and what they need to know is something about the physical system that it represents. I clarified but I didn’t fix it. I told them we’d come back to that on Tuesday.

The morning class nailed it. Afternoon … struggling. And a lot of afternoon students in office hours with homework not-very-close to completion.

It feels good to be getting into some math. Both with the Matlab assignment due today, and with the upcoming work on the Lorenz attractor. Wherein we attempt to understand the butterfly effect and chaos, and learn how to create graphs that show clearly what we are trying to demonstrate.

What’s an excellent teacher (non-tenure track) worth?

My significant other is looking for tenure-track jobs; an offer may be pending. If it is, part of the negotiation would be whether or not they’d hire me in a comparable non-tenure track position to the one I currently hold. I would really really prefer to be either in a tenure track position at a teaching college or on an instructional professor track!

It’s a come down to realize that my credentials might be an afterthought in all this. Eh, she’s got a Ph.D. She’s taught a variety of classes. Evaluations are pretty good. Why not? No need to actually interview her or see her teach.

We’ll see how that plays out.

I emailed my letter writers about having letters ready. My CV is pretty much up to date. I should be an obvious hire if there is a position open; my undergraduates won a lot of awards for research and projects from my class in the past year, both at my university and away. I won a college-level teaching award, which is no small thing either.

I can’t shake the feeling that all that great stuff about me and my teaching might be gravy but it really won’t weigh in the decision about me at all.

Grading Writing

I just posted the following on Facebook: Getting closer to the bottom of the pile of rough drafts. Maybe reading Patrick Bahls’ book has helped, maybe some advice from the TAMU Writing Center has helped, but I am feeling less stressed about it and seeing them showing some good transference of knowledge — trying to use the mathematical models from internships or research to explain what mathematical modeling is. Even if the explanations still need some work.

If you doing it right in posting to Facebook, you are using the principles of good writing. There is always *something* on our minds, but if we are smart, we are thinking about whether or not our audience of friends is interested. If we decide that enough are, we have to put our message together, usually very briefly, so that it informs and entertains. Clarity. Conciseness. Know your audience. Tailor your message for your audience.

Grading: I am trying to only give high-level comments about the papers. Content: did you cover all the points to describe what mathematical modeling is? Did you tell us what the problem of quantification is for (certain) real-world problems? Organization: does your essay flow seamlessly from point to point, or are there jarring transitions? Do you use two examples of mathematical models to explain your ideas? Or do you tack on two examples at the end? Correctness: are you saying things that aren’t true or that need further clarification?

I will circle occasional bloopers, but my job is not to fix spelling, grammar or typesetting. That’s the students’ job. I’m also not going to go through the papers and make a list for them of points they missed. I will mention that material is missing, and maybe an example. They should be able to make a list of what they should hit and go through their paper and check that off. I’m not going to fix their wording. I will react if a sentence is confusing or incorrect.

I hope that putting the final grades on these next week will also go smoothly and less stressfully than last semester. I hope I can maintain this perspective where I am better able to see that they are doing a lot of things right, instead of getting sucked into the many things that I can find wrong.

It feels good to find a paper, perhaps missing a few points that I want them to include, but to realize that the student missed those points because he was trying to transfer knowledge from another experience, and those points didn’t fit in well with that particular story. Then I can praise as well as guidance. That always feels good.


Finally, a weekend! I have a stack of rough drafts to read and grade. Grading is quick, up to 4 points and I grade only on how complete the draft is. I try to make a comment or two for everyone. We’ll see if I manage when I get further into the stack. I have 39 drafts and if I spend 15 minutes with each one, I am looking at nearly 10 hours of work. Time that I just don’t have. Energy that I just don’t have!

I managed to keep the epsilon > 0 philosophy of exercise going today by getting out for a bike ride. It wasn’t very long, and it wasn’t very fast, but it was better than nothing.

I also made it to the pharmacy today. I had old medications to throw away, and, rather than putting them in the landfill or water supply, I took them to the pharmacy and their disposal program. Well, turns out if it is a controlled substance the pharmacy won’t take it. Something else got rejected too. So what am I supposed to do with them? Put them in cat litter or coffee grounds. Okay. Unfortunately, I don’t have a cat, and we don’t drink much coffee. I’ll figure something out. So much for environmentally-friendly disposal. Most were accepted, and at least I tried?

Peer Review Review

First class: a few hiccups with students getting papers printed at the last minute. Not a huge surprise for a 9:35 am class. I think they mostly had it pulled together by 9:40 am. Things went well from there; I overheard some good conversations about organizational structure and how to use examples.

Second class: Quite a few students unprepared with papers not printed, at least one showed up 1/2 an hour late. I didn’t hear the same quality of conversation; I got the feeling this class was more deer-in-the-headlights. I was getting frustrated with the lack of preparation. C’mon guys, we knew what was up for today.

What little I got to look over the papers, the second class’s stuff seemed weaker than the first.

After that, I had more than 10 customers in office hours, most needing tech support with something. Nothing to do but queue them up and go through it one by one. I felt like giving a big scold on starting sooner. I did scold a bit.

I ended the day exhausted, and tomorrow is back-to-back-to-back things to do. I need some time to grade and work. It ain’t gonna happen. Hopefully the weekend will save me. I’ll be frustrated, though, to spend another weekend at work.

Peer Review Tomorrow

We are doing our first peer review tomorrow. Rough drafts of the two-person dialog on mathematical modeling are due.

I feel unprepared for this. I’ve been reading about peer review and how you should prepare your students and instruct them. I haven’t. I don’t, for example, have examples of varying quality for them to look at, although I have a few posted on my website.

I spent a lot of today writing up worksheets to facilitate the peer review. It was hard to put this together! They will start with the premise that they haven’t (yet) taken this class. The dialog should explain to them what mathematical modeling is and the process of mathematical modeling.

  1. Do you have questions while reading? What are they?
  2. Can you identify the most confusing point or a confusing point? What is it?
  3. Can you identify a point that is well-explained in the dialog? What is it?

    Then we go on to the criteria we identified (in my most recent post).

  4. Is anything missing from the dialog? What is it?
  5. Comment on the organization. Are any of the items on this list done particularly well or poorly?
    • Does the writer introduce/motivate the topic?
    • Are ideas presented in a logical order?
    • Do the ideas flow, or are there abrupt transitions?
    • Are the two examples of mathematical models well integrated into the discussion and used to further the main ideas? Do the two examples seem “tacked on” at the end?
    • Is specialized vocabulary introduced and explained, then used consistently?
  6. Comment on the appearance: grammar, sentence structure, spelling, punctuation. Is this pretty good or does it need work?

It isn’t perfect, but I hope it is enough.

I am thinking about telling them the following story.

When I finished my dissertation, after defending my Ph.D., I wanted to submit my results for publication. I rewrote the dissertation into two articles. I asked my Ph.D. advisor to please read them and tell me what I needed to change before I sent them out. He had my things for a week or two. He never gave me any feedback. He told me to just send them. I did.

He was gone on sabbatical when the reviews came back some months later. I will never forget that day; the papers were rejected outright; the reviews were terrible. I still have them. I am not a strong enough person to go back and look at them now. The criticism was well-deserved, which made it worse. I felt small and stupid. Seven years of my life on that Ph.D.! It was years before I realized that some of the harsh words were probably not directed at me, but at my advisor. They all struck straight into my heart and self-esteem.

I went home and cried and cried and cried. When I finally managed to compose myself again, I put those papers away and I resolved to close that chapter of my life and move on. I was not a strong enough person to subject myself to that.

My advisor should have prevented that disaster. He set me up for failure. I asked him, appropriately, for feedback on my work. He was my advisor. That was his job.

It might have been hard to take his criticism, but it would have been infinitely easier to fix what he told me than to get my head chopped off by those strangers.

I eventually let my advisor talk me into trying again — with the understanding that there would be feedback from him and others this time — and at the price of having his name on the paper. To our my credit, those two papers got rewritten into one and accepted by that journal. As much vindication as I feel being able to tell you that fact, the vindication pales next to the strength of the remembered shame and pain of reading the reviews.

When I teach, I’m the reviewer. I am the lion you are sent in to the arena to fight. I put grades on papers, and I make comments. I’m the one who is going to rip you to shreds. Before you send our classmates in to fight with the lion (me), make sure you’ve given them as much help as you can to make sure that they won’t be torn to shreds.

It is easier to take criticism from our friends when the stakes are low, than it is to be told our work stinks when the stakes are high.

I wish I’d had a peer to consult with way back then.

Dear Students, do better for each other than my advisor did for me.

My head is spinning

The weather has been beautiful, and we had a day off yesterday. What did I do? I sat in my windowless office and updated websites and worked. I was really annoyed that I just didn’t get done until after dark. I missed out on the entire gorgeous day.

I’m realizing that I’m going to get 4 emails for every applicant we have for our REU program, each of which needs to be dealt with, replied to, filed. If we have 200 applicants, I will have 800 emails to deal with in the next month and a half … eeek.

Today in Mathematical Modeling we did a 2.5 minute free-write on our upcoming writing assignment (a dialog in which we explain what is mathematical modeling). This was mostly to make sure they’ve got something written down now; they are to have a complete rough draft done Thursday.

Then we did a shorter free-write on what are the most important things to get right on the assignment, i.e. identify the grading priorities:

  1. Follow the directions from the assignment and those given in-class; address all of the points you are supposed to address.
  2. Organize your writing so that you present material in a logical, well-thought out fashion.
  3. Write clearly, simply, concisely to explain each point well.
  4. Use good sentence structure.
  5. Spelling, grammar, punctuation, appearance.

Now if I just had a better grading plan for these to make the grading go fast when I get the final drafts. I’ve been reading about rubrics and other grading techniques, and I’ve been teaching this class for a year and a half now. I don’t have it figured out. Yet.

Advising, Teaching, Football

I had advising appointments with 4 students on academic probation today. My estimate is that 2 of them will get through the semester and continue, and 2 will end up in bigger trouble or no longer be in our department. I wish I could do something to help them, but the problem is they need to take the appropriate action. I can tell them to Just Do It, but they are the ones who have to do it. Maybe I give them a new idea; maybe I let them know someone cares. Maybe I do no good at all.

I’ve been attending Mathematical Biology this semester with an eye toward teaching it in the future. It’s quite the contrast with my own classes. You walk in before class starts and everyone is sitting there in silence (myself included). Then the instructor starts talking. He’s interrupted with an occasional question from me and a rare question from one of the students. Then we wrap up and head to lunch, back to our offices, home.

My priority is to get my students talking. Talk! Meet each other. Ask me questions! Don’t sit there like lumps. You are not lumps. Let’s try putting some of ourselves into the material and see how that goes.

That said, he’s put more math on the board this past week than I did. And will continue to do so. I want my students doing the math more than I want me showing them the math. I will show some, they will do. Hopefully they will learn and absorb.

More embarassing news for Notre Dame and their football program. I was pretty outraged to read about the Lizzy Seeburg case and how it was handled several months ago. Now we can look at that case in contrast to the one of Manti T’eo and his fake girlfriend.

NPR article: More Tears For Notre Dame’s ‘Fake Tragedy’ Than A Real Girl’s Death?

I’ve heard the argument that football players are protected everywhere, and this happens everywhere. It may be true. But it sure as hell doesn’t make it right. Why is football such a sacred cow that we continue to put up with these institutionalized abuses?

Sometimes you can tell I’m from the University of Chicago where football was banned from 1940-1962, because the president of the university sought to emphasize academics over athletics. [Wikipedia on the U of C] That always makes me proud of my Alma Mater!

Dear Madam and, “We are now going to talk about sex.”

I collect the applications from our Research Experiences for Undergraduates program.

The most recent starts out, “Dear Madam.” I am annoyed. I made sure that my title, Dr., and name was given clearly on the web page with application instructions. Send to Dr. So-and-so at this address.

Use my proper academic title. Why is this so hard?


One of my students was falling asleep in class today. Fortunately, we were discussing a mathematical model for a rabbit population, and so I could truthfully say, “We are now going to talk about sex.” That did the trick.

Can you guess who formulated this model? Here are the assumptions:

  1. We start with one pair of baby rabbits, 1 male, 1 female.
  2. Rabbits take 1 month to reach sexual maturity.
    (We were discussing the previous step as the student’s eyes closed.)
  3. As soon as rabbits reach sexual maturity they mate. The female gives birth to a male, female pair the next month, and every month thereafter.
  4. Rabbits never die. At least not for the duration of this modeling scenario.

So how many rabbits are there?

  • The first month, there is one pair of rabbits.
  • The second month, the rabbits reach maturity and mate. There is still one pair of rabbits.
  • The third month, the rabbits give birth to another pair and get pregnant again. There are two pairs of rabbits.
  • The fourth month, the first pair gives birth again, and the first two pairs get pregnant. There are three pairs of rabbits.
  • The fifth month, the first two pairs give birth, and the third pair gets pregnant for the first time. There are five pairs of rabbits.
  • As you can see, each month the number of births we get equals the number of rabbits 2 months back. We add that to the rabbits we had in the previous month. So the number of rabbits equals the sum of the preceding two numbers.

Can you identify who created this mathematical model and when it was created?
One option to check your answer, and
here is a second option to check your answer.

Tell them what they did right.

What’s the most important thing to tell my students tomorrow? Duh. I need to tell them what they did right on the first day. The introductions were awesome. I picked up more names than I expected too. I like that they embraced meeting someone new. They participated. I gave everyone (including those late) a participation point for the day.

In the early part of the semester, I’m mostly working on tools for success. Getting students participating in class and talking to each other and me. Getting students using LaTeX and Matlab and feeling somewhat comfortable with these. Getting students comfortable with asking for help, because they won’t be able to solve every LaTeX or Matlab problem on their own…and then we have to understand the mathematical concepts of what we are doing and know how to explain them in writing.

I generally do a fine job with that.

I often don’t do a good job of getting them to look at the many interesting examples of mathematical models. I have many articles linked up on the course home page, most are to popular press and general interest articles, so they tend toward fun to read and non-technical.

I don’t do a good job of getting students brainstorming what they might like to do for their final projects. In fact, I need to put some guidelines about this somewhere on my website!

I’ve thought about doing brainstorming in class about final projects, but I haven’t done it. We might start by brainstorming what we might like to do, or, if we have absolutely no idea, we could brainstorm on what are some important problems facing the world today. From there we can brainstorm on how math might help, how to get started, where to start. A few easy steps might yield an interesting result. Or not. If not, will I have wasted that much time?

Some potential side benefits even if it is a mostly failed experiment: maybe I will spark some interest or get them thinking about how math is applied somewhere. Maybe someone will do a Google search that they wouldn’t have otherwise done and learn something. Maybe someone will read an article or watch a video that they otherwise wouldn’t have … and learn something. Any of those would be a nice outcome. And those are all plausible outcomes.

I think the 1 minute brainstorm/just scribble ideas down storm is a good one. I am wondering how to better use it for class. We did a lot of this on Tuesday!

I looked back over my first class day information. I think I was only missing 1-2 students from either class. I think my numbers absent from the first class were on the pessimistic side. I probably counted 13-14 students right at the beginning of class, so I didn’t account for the late ones. I also think a few students who didn’t show up for the first day dropped.

Two students from the 9:35 am class have come to visit me. No one from the 2:20 class yet. Students get a small number of points for this on the first assignment. Points for what you probably should do anyway, like attendance points. I figure I will see a lot more students tomorrow/next week.

I will, at minimum, go for a walk tonight. Part of me wants a run, but it is getting later, the repairperson is still here, and the later it gets the more motivation I lose.

I should go into the office and put some things away there, too. That one is more dubious than the run!