Mathematical Modeling

Another instructor asked me tonight to talk to him sometime about what made my mathematical modeling class a success.

Where to begin? Love your students, and believe they are capable.

Foster a classroom environment in which everyone is respected, respectful, and everyone’s goals are aligned.

Let students make choices about what they do. Then they will own the work more than if you choose for them.

Don’t be afraid to screw up. Some things will work, and some won’t. Some of the biggest screw-ups will have the most profound learning opportunities. For you and for them. Some of the “failed projects” taught students more than success at some canned exercise would have.

Praise them. Then praise some more. But you can’t do generic praise. You have to look and see the specific things they are doing that are worthy of your words.

Make things meaningful and relevant to them and their lives. But don’t simplify the hard stuff. Let them see the messy. That is what mathematical modeling is all about, the messy interface of mathematics and reality.

Make sure they understand what mathematical modeling *is*, and keep bringing that theme back into their work. Because if they don’t walk out of your class understanding what it *is*, what in the hell have you actually taught them?

Start by figuring out what you think they ought to know and learn from your class. Then design everything you do around those objectives.

Make assignments that you will be eager to grade. That will make your life easier, and their work more interesting. If you find it interesting, they will too.

Don’t be afraid to do something silly or fun because it is silly and fun, the Zombie Apocalypse has been a great modeling project for that reason.

Since it is your job to criticize, make it their job to praise. Make sure they point out to each other the good things they are doing.

Look for success, for creativity, for talent, for competence. And where you find it, nurture it. It won’t always be in those put-together students who always do well at everything. You will find amazing things in your mid-range students and even in your screw ups. Don’t waste those gifts.

Tell them about your failures. Tell them where you struggled. Make yourself a human being to them — let them learn from your mistakes. You don’t have to be right all the time, and you don’t have to have been right all the time. Understand where they are coming from and forgive yourself for those times when you demonstrated their faults.

And did I mention love them? Love them. Love them. And love yourself too. If you bring grace, dignity, integrity, humility and love into your classroom, you will have it returned to you.

Tears for Texas A&M

Dear Texas A&M,

I found myself crying on my bicycle ride home late tonight. I realized I was mourning the loss of our relationship, though it isn’t quite over yet. I can’t see a way forward. I haven’t been able to see a way forward for a while. You may have better days ahead of you, but I think they are going to be without me.

Since we are at the end, there are a few things I want to thank you for.

First, thank you for giving me care of your students. Every day, I have been honored to be in classrooms with them. Every semester, I have gotten to watch them grow in intellect, but more important, in spirit. I have watched these young people learn that they have the power to effect change in their lives.

Second, I want to thank you for what you’ve taught me about myself.

I wanted to teach, but I didn’t know how good I would be at it. I still don’t live up to my own standard most of the time, but I keep growing and getting better. I’ve been grateful for the Center for Teaching Effectiveness. For Wakonse South. For my superb Academic Professional Track Colleagues in Math. They embraced me when I was a visiting assistant professor. They welcomed me into their ranks three years later as a lecturer. They supported me when I went up for promotion. They helped me figure out how to write a syllabus, how to write exams, how to work the classroom computers. They’ve been generous with their notes, week-in-reviews and course materials. They’ve accepted and helped me lead when I’ve been asked to do that. They’ve given me many insights into better teaching.

I came to you thinking I didn’t really ever want to do math or programming again, but slowly, day by day, class by class, you’ve brought me back around to seeing my love for both. I find myself talking over and over again in class about the wonder of the material I teach. And I’ve found myself programming Project Euler problems in my spare time.

You helped me find mentors that have helped me to be able to pull my professional academic credentials together and see that they are worth something on the tenure-track market. If I hadn’t had these people to believe in me first, I would have had a hard time believing in myself. And they’ve been right. I am getting interviews. I may not be right for every school, but I have skills that are extremely valuable in the job market.

Last, you’ve taught me that I am not a doormat; I will stand up for what is right. This past year has been so so hard for me, as I’ve watched things happen that I could not, with integrity, remain silent about. It has been terrifying to speak up. To continue to speak up. And to realize that speaking up required me to start looking elsewhere for employment. I am sad that a better conclusion wasn’t in the cards for us. And I’m angry with you for not having better to offer after all I’ve given to you. But the bottom line is that I am stronger for having lived through this. As angry as I am about what’s gone wrong, I cannot help but be grateful for the growth.

One concept that’s always been dear to my heart is the idea of Aggie Honor. As often as we have students violate our honor code, when you sit them down to talk about it, you can tell that being Aggies and embodying that honor means something to them. Honor means something profound to me too. Integrity. Willingness to do what is right even at a great personal cost. Willingness to speak up when I would prefer to remain silent. Unfortunately, I haven’t seen much honor in you lately, and that makes me sad. I believe you can do better, Texas A&M.

We are going to have some difficult discussions tomorrow. I don’t expect change to happen for me with you, though I hope it happens eventually. I hope, more than anything else, that you can find your way back to honor. To see yourself as I see you. To bring to our students our very best.

I hope you are up for it. I’m not sure I can keep believing in you for now, and that’s part of why I have to go. I know that it is through our darkest moments that we have the most profound break-throughs. I hope for one for me. I also hope for one for you.

With love, and profound sadness,

Dr. Jinx.

Assume nothing and open your heart to embrace the good

Dear Student 1,

We took you to brunch today, wanting to give you, if nothing else, another experience of two functional adults in your life who care about you and who are checking in with you to make sure everything is okay. Curious about your life and wishing you the best.

No, you aren’t going to pay for the meal when you are out with us. Pay it forward, to your kids if you have them. To some other struggling young person you encounter later in life. We can’t fix our pasts. We can’t fix your present. We can only try to give to you some of those things we wish we’d had back then, most especially some older adults who just like you and who are willing to go to bat for you.

We talked for a while about the future. My friend talked about finding a place to settle down; that was important to him. And me, what would I advise? I would advise you to expect nothing. It is nice to have a place where you are settled down, but you may not get that. Just when I’ve thought I’ve settled into a place, there has been a reason for me to leave it.

The biggest disappointments I have had are the things I always assumed I get, and didn’t. Assume nothing, except that life is going to be difficult. You will struggle, but you will find your path. It will be hard. That you can assume. Plan for adversity in the future so you can take care of yourself if the worst case happens. But don’t plan out the rest too much; allow yourself to walk through with open eyes and open arms for opportunities and people you will want to embrace.

And if you ever feel stuck and discouraged, try not to be afraid to change. Your worst moments will make your best stories — trust me on this — once they stop hurting you so much. You just have to get through them.

You can have a run of bad luck that goes on for months or years, but if you can just hang on, you can come out the other side.

And in the meantime, no matter what you do, no matter where you are, no matter where I am, if you need someone, please call. If you want to share some success, please call. Just keep my number handy for those moments, and know every time I will be glad to hear from you. I know I’m not your Mom. I’m not anyone’s Mom (that was one thing I wished for my future that I didn’t get). But if I can be your next best thing, I hope you know I’ll try my guts out for you.

With love,

Dr. Jinx (who hopes that word won’t freak you out)

(And, yes, I’m going to ask you and my male friend/partner in crime to lunch or something again in a few weeks and keep doing this until you are convinced that here we are and we mean it and we aren’t going anywhere.)

*****************

From Student 2:

Dr. Jinx,

I just wanted to take a moment to thank you for the amount of work you put into teaching us Linear Algebra.

Let me first say, this is in no way an attempt to “suck-up” or any such effort. My grade will be earned fairly regardless of any fallacious tactics to woo over a professor. 🙂

I just know how important it is to let those you contribute so much to your education know they are doing an excellent job. I feel I begin the homework and other assigned work with much more confidence and understanding of the material. This is highly due to the material you have provided (i.e. reading guided note taking, online notes from class for reference, posted solutions, and availability outside of class.) Take my absence from your office hours as a sign that you have taught well enough that there is no need for outside assistance.

Expect to see a high score earned on my first Exam!

Thank you!

Dear Student 2,

You had no way of knowing what I’d be doing today. I was out on my bike and started to have an anxiety attack. I cut the ride somewhat short to get back home for some medication, and along with the medication I found your note.

Thank you for helping to lift me out of that funk of self-doubt, where I am afraid that everything in the world is wrong and me along with it. I wonder sometimes how many of you are hating me for teaching a hard class, even though I know an easy one won’t serve you well in the future. I feel guilty for all the times I’ve had to be gone this semester. For struggling to find time to give you. For not working further ahead, taking each day as it comes, doing what I can, and hoping it is enough. For not being able to give you a better big picture of this wondrous subject we are learning. For not having time enough to explain all the examples, and resorting to the advice that you read them in the book.

Because there it is, at the end of the day, if you are enjoying learning, I know what I’ve done has mattered. I can’t make math into a video game (at least, I haven’t figured out how yet), but at the same time, it shouldn’t be torture. Little puzzles to figure out, one after another.

Thank you for your thanks. Today it meant the world to me. And I did print out what you said, cut it out, and tack it onto the bulletin board by my desk.

And, for darn sure, you better ace that exam.

Sincerely,

Dr. Jinx

On Being Angry

For the past few days, I have been angry. I have been wronged. I have been afraid. I have been treated unjustly. And so, I have been angry.

Here’s the thing. I don’t like being angry. I don’t like myself when I am angry. I don’t want to continue to be angry. At the same time, that I am angry means there are problems to be solved, and things to be fixed. My anger helps me to do that.

Can I find a better way?

What would a better way be?

Is there a path to peace with those who wrong you? With those who do wrong knowingly?

What if I was the teacher, and these were my students doing wrong? How would that change things?

I get angry with students, frustrated, tired. But one thing that’s different when I am dealing with students: in these young people, almost without exception, no matter how bad the behavior may be, I am always trying to see through to the possibility that they can do right and grow into honorable, kind, productive human beings. In my interactions with them, I want them to see themselves as those honorable, kind, productive human beings. Or, with the possibility of becoming those honorable, kind, productive human beings. Whatever bad behavior I am called upon to address: it is their behavior; it is not their identity. I want to leave them with that image of themselves as greater, rather than lesser. I open up my heart as wide as I can so that they can see themselves as I can see them, full of promise, hope, possibility, honor.

You may have made a mess. But you are not a mess. You have all the potential that you need to be someone worthy and worthwhile. You get to decide what you do next and how you handle this. Choose well.

Can I do this with a 60 year old department chair too? Can I even try to see this from where he’s at? There is the world he knows well, the world he’s lived in, and the things he’s been taught because of his position. There is a major assumption of privilege. An ignorance of the day-to-day lives of those who report to him. Ignorance of the careers of those who require his good judgment and wisdom in handling our concerns. Perhaps he knows nothing of this. Never considered it to be important. Never saw the people in front of him as human beings, with ambitions and motivation just like him.

Is there the possibility of growth, honor, better in the future?

Of course there is a possibility for growth, honor, and better in the future. There may have been too much bad for me to want to remain for the long term. But can I uphold honor while advocating for fairness, can I be peaceful when addressing wrongs? Can I be courageous in facing those with more power than I have and, armed with little besides my integrity, be a force for good?

That is the standard I set for myself. To let go of the anger. To arm myself with integrity. To see the good and to help others see it. To allow myself to walk away where there is nothing to be gained or when too much has been lost, but to open the doors wide to change for the better where change is possible.

Little lost letter

I send a holiday letter to my Aunt Em (one of Dad’s oldest friends), even though I don’t hear back. She must the same age he is, 86 or so? Her husband died about 15 years ago; on a day Dad was visiting me. I may never forgive that boyfriend for not waking me up from the nap I was taking when that call came in. That was Dad’s best friend, and he sat there, stunned and alone in his grief while I slept. That boyfriend was clueless.

A year ago, I got a “this person has moved to this address” and my letter was returned, but I saved the address. I sent another one this year, somewhere up in Wisconsin. I don’t expect to hear back, but if she’s still alive — and her mother lived to 100-something — I want her to know that I think of her still, and fondly.

I got a letter from one of her sons tonight. My letter was received and enjoyed. She’s got dementia, like Dad does, and is living in a facility in Chicagoland, so maybe I will go visit her the next time I go see my Dad, if her son gives me the address.

Sometimes love is in the little things that you aren’t convinced really matter at the time you do them. The little things that would be so easy to skip. Just another holiday letter; I’m not even sure I have the right address. You just do them anyway and hope. Sometimes those letters make it, not to where you sent them, but to where they needed to go. They gave someone a smile, maybe only a brief one, but that’s all you could really expect to do.

Are you ready to sign up for this?

Contrary to my worries, that last interview went smashingly well. I still think there will be some financial issues to discuss, but I think there is a good chance they will get resolved satisfactorily.

I really liked the people. Knowing I do geocaching, someone put GPS coordinates on the schedule sheet, and then question 8 during the Search Committee Panel Interview (that’s supposed to be the scary one; it wasn’t):

Some of your research appears to involve zombies. Would the University be expected to provide you with zombies, and, if so, how much risk is there in housing such creatures locally?

We all had a laugh, and I mentioned that maybe we could persuade the students to get a game of Humans vs. Zombies going. Then we can harvest the data to do some modeling. I did harvest some data from the local game, but I never had time to do any real analysis with it.

But one thing is bothering me tonight. The town. It’s small. 18,000 people. Okay, less than 2 hours from a major city, if the pass is clear, and not too far from a somewhat larger community (100,000).

But here rears my fear of being alone, forever (well, until I die). Look at that ugly head on it. And would I be choosing that for myself if I moved there?

I remind myself that I didn’t exactly date much when I lived in Austin. Maybe I’ve even done more dating in my current smallish town (pop ~120,000-200,000 in the area). The most dating I’ve done is when I was on one of the internet sites, and that was eye-opening. Not in a good way. But definitely eye opening. I’m not at all sure I want to do that again.

I know it is also true that I could move to New York City and spend the rest of my life alone, but this feels like I am asking for it. Am I? Am I just in a funk feeling sorry for myself?

If I’m in a funk, there I am tonight. All I can do is continue with the interviews and get more information about the places. One step at a time, and try to trust that an answer will become clear. It may not be the answer. It may not be a good answer for very long. But it will be an answer, and that is all we get in this world.

You are enough

Dear Student,

You almost walked out on a Team Exercise today because you weren’t prepared, and you didn’t want to freeload. I admire that, but I asked you to stay and to learn, because the point of the Team Exercise isn’t the grade; it’s to help the members of the team to better understand the lesson.

At some point we will all walk in unprepared, and have to ask our team to help us out. That’s why some of the hard stuff is Team Stuff, rather than individual. Because I think that having you work together will cause more learning than if I just preach it at you.

I still felt terrible because you did today. And I questioned myself and what I was doing.

I talked to you for while late this afternoon, and there are other things going on in your life. This class isn’t easy for you, and logistics lately have been difficult. I get the feeling there are other things too. You apologized to me, but no apology is necessary. This is my job. I am here to try to help you learn. I know that other things get in the way. I know how they get in the way. I’ve lived that. I just wish you knew it too. You are worthy of being here. Worthy of my effort. Worthy of the help from your team. Worthy of being taken seriously. Worthy of help. Maybe worthy of better than I am capable of giving you.

I know that you are the type of person who wants to be the one to help others. If another came to you unprepared, or unable to get something, or struggling, you’d be proud to be the person to help them out. You’d treat all their problems with loving kindness. That loving kindness that you’d so easily give to someone else is the loving kindness I want you to give yourself right now.

Just hang in there. Just keep trying. And seeing the high level of frustration and pain I saw in your face today, just in case, I want to say: if there comes a point where you realize or decide that this is not for you, I want you to know that is okay too. You are still worthy and worthwhile. Sometimes it feels like we are deep in a dark tunnel with no way to climb out. And I can’t even tell you how to get out, except that you have to just keep at it.

I didn’t have the exact right words to say to you. I can only hope that the ones I had were enough to plant this idea, for it to grow and blossom later. You are enough. Just as you are. Deserving of respect and love and help. If you can’t trust yourself to judge that, I hope you can trust me.

Sincerely,

Dr. Jinx

Lunch

One of my students last semester told me he was working 50 hours a week to support himself and go to school. Adding 13 hours of coursework on to that, which means an ideal 39 hours of homework, I calculated he would be working 92 hours a week. Plus transportation to and from. Which is a life without relief or rest or relaxation. It is nothing but work and work and work and sleep. There are some people that can handle that, but productivity studies snort at that. All it does is wear you out.

I did the math with him and told him most people can’t handle that pace. Can you find a better job, or make do on fewer hours?

My student indicated his parents weren’t helping with college expenses. I can smell a story in things like that. I’m from a dysfunctional family that was threatening to cut me off while I was in college. Family crap is hard to take, and he sounded like he had a truckload full.

Now I’m a busybody and a meddler, but there are boundaries that you have to really watch with current students. I kept a weather eye on that one, considering my next move. I thought about asking him (and an adult male friend/colleague who is also dedicated to the well-being of our local college students) out to lunch sometime over the holidays, but I bailed on that idea at seeing some lack of effort reflected in the grades in my class. Maybe that was unfair considering the pressures he was under. I have a principle to hold back a little until I see the effort going in.

But, he showed up in my office earlier this spring semester. I extended the invitation to lunch. I brought my friend along, someone comfortable with uncomfortable truths, who also comes from a background of dysfunction. I allowed myself to pry a little.

Fair is fair, if you are going to pry, you better give the other person a way out, and agree that they can ask you to answer first. My friend and I answered first. Then we got a long story that I am sure wasn’t even the half of it.

It is amazing the things that 15, 16, 19 year-olds have dumped on them by their parents. We know there’s nothing we can do to fix it, but we try our best to provide this one with two functioning (if imperfect) adults who are willing to help watch his back and who are willing to receive that phone call when things are tough. “There’s a lot we can’t solve, but one thing we can do is make sure you get a warm meal and someone to listen.” And if there are bigger problems that seem overwhelming, we’d like you to call us rather than taking on the world alone. Every young person needs an older adult person at their back to help navigate. Every young person needs an older adult person who thinks they are worthy and worthwhile.

That was one part of my work today. Probably the most important part. I can look back at my past, and I can’t help the younger me-that-was. I can help this one. This is how we make peace with our past and all the darkness we’ve gone through. You can’t pay yourself back for those times. You can only pay it forward to some one else, and let those you help do the same.

The other side?

Since I wrote and published Half-Assed, a mild case of concern has set in. Was I fair? Did I see it from the other side? What have I missed? One known cognitive bias is that we tend to rate experiences not on their overall happiness, but on their peak intensities (good or bad) and on how they end. And that relationship surely had a painful and unpleasant end, which certainly has colored my view of all of it.[1]

Another aspect of my thinking is from watching the video at the Representation Project, about judging men and their maleness. Men are supposed to be the fixers in the relationship, and they are supposed to do a good job of it. When one fails to do so, whether through sloppiness or lack of knowledge, we are (meaning I am) quick to judge.

What if he opened up the electric plug, and understood generally how it worked, but couldn’t quickly come up with a way to shorten the wires and strip the plastic coating? He could have asked — I would have had a suggestion — but men aren’t supposed to ask. There are numerous “How to Repair It” books around the house, all of which I purchased.

What if his access to the resources was reduced, not really knowing the books were there, since those were mine and not his. Unable to ask, because guys don’t ask. Not conscientious enough to really care about doing it right. “I put it back together, and it works, even though it is ugly and doesn’t look right. Good enough. And I don’t really like this vacuum anyhow, partially because I didn’t pick it out and partially because I just don’t like vacuuming (who does?), so maybe we should get a new one.”

I have an advantage of sorts in that I’m a female. I’m not supposed to know how to fix things. I know I can generally learn from a set of instructions, and so I provided myself with sets of instructions. I’m conscientious, which you might call anal-retentive if you are mad at me. If I am going to do a job, and I can do it right, I get stubborn and I will do it right. I’m experienced. I’ve been living alone and I’ve owned a house for over a decade. If something breaks, I’m the first line of defense for fixing it. I might not have started out as confident or competent, but it grows.

And as for the rest, it is one thing to have an attitude or opinion of really valuing communication in a relationship, but it is another thing to know how to do it. How would you learn when your parents never do such a thing? When your previous girlfriend made it impossible to do such a thing? How would you know how to deal with someone who tells you up-front what she needs and wants? Would that be a good thing or a threat? Maybe someone more confident would have been able to make more of it. But maybe this just wasn’t him. Not even when I was the one who was putting forth the effort and trying.

It’s that thing about responsibility. You can’t ever really give someone responsibility. The other person has to take it. You can give all you want, but if the other person doesn’t take, it doesn’t matter.

“What else could I have done,” is the question I am always asking myself. I don’t have an answer, and I don’t think I ever will. A relationship, a good relationship, requires two capable, responsible, willing, and invested partners. I am not sure I had that. I am pretty sure of my own investment, even though there were times I had a hard time holding it together. I know what I was willing to do. The one thing I saw clearly at the end was that if it was going to get better, he had to make the move, to make the commitment toward that happening. It wasn’t there. I think it had been missing in all the earlier conversations we’d had. Maybe it wasn’t neglect. Maybe it wasn’t not caring. Maybe it was just not knowing how or not being confident enough to try.

But once again, here we are. There it is. It is my job to make peace with this. I hope that I am; I hope you can see I am trying; one slow step at a time.

1. For more information on this, I read Daniel Kahneman’s Thinking Fast and Slow. For a discussion on experienced vs. remembered well-being see page 4 of this NYTimes article for a discussion on duration-neglect and the peak-end rule.↩

Half-assed

I fixed the plug on the vacuum today. It’s been broken for a while, and I know who last fixed it. I think I remember an “oh, this is so hard, we may need to get a new one,” at the time.

Let’s just say that repair was half-assed. Which means, I took a look at it when I went to fix it and I thought, “Seriously, this is the best you could do? It would have taken 5 more minutes to do a quality job here, and you couldn’t bother?”

The cord was pulling out of the plug. You could see the insulation exposed. This wasn’t actually harmful, but to my mind, annoying.

How do you fix such a thing? Since the plug had already been replaced once by a professional — before the repair mentioned above — I had to remove two screws on the plug, taking it apart. Inside I found the electrical cable, stripped, with a white and a black plastic coated copper wire exposed with some fiberglass or similar insulation. What needs to be done? Loosen two more screws, removing the wire from the plug. Shorten the white and black wire sufficiently so that the cord is snug in the plug. Remove the outer plastic coating, exposing the copper inner wire. Screw this back in to the plug, making sure we get white on the correct side and black on the correct side. Screw the plug back together. Voila, done. It took about 10-15 minutes.

The repair represents that relationship for me. Half-assed. I know my patience and pleasant personality were getting burned off at the end, but sometimes it just strikes me as I look back at all the big and little things that got neglected. I don’t think I am easily in a half-in/half-out state in a relationship. If I am in it, I am in it. I give my heart, and I do my best to fix things. I get stumped sometimes, if talking isn’t helping. I brought up the problems, but even I had to disconnect after a while of non-response.

“What the hell were you doing?” I want to shout. Nothing? Expecting me to figure out how to make you happy and to do all the work to make it so?

And should I be surprised at the ending? After all, it’s easier to go buy a new vacuum than to spend 15 quality minutes fixing the electric plug. Except that, actually, it is easier and faster to spend 15 quality minutes fixing the electric plug.

I remember the beginning too, the connection, and connection is rare. To think it perished to a half-assed general lack of effort. That just makes me angry. But there it is.