Liberation Math Week 7: Easy Now

I have a tendency to make things hard, and I wonder if you have the same issue.

Almost everyone in an academic environment gets behind at some point during the semester. I have watched students do this for years. Typically a student starts to get behind, feels bad about themselves, and the bad feeling makes it hard to work and the student falls further behind. After an episode like this, a student will often come to me apologetically, promising to do better, and telling me about how they are going to get caught up soon and will keep up after that. The trouble with that is that it rarely happens. I think it’s a bit like how dieting causes weight gain. For the most part, we all want to do well when we take a class, and when our actions run counter to that goal, then something is going on. Maybe we really don’t want to engage with the course, and so we avoid the work because we don’t want to do it. Maybe we have more on our plate that we can handle, so we start letting go of things, coping with feeling overwhelmed through avoidance. Maybe we feel bad when we do work for the course because we don’t think our work is good enough, so we avoid possible failure by avoiding the work. I do each and every one of these, and more. We all do, because we are only human.

The Fables of Aesop

We all know we’re supposed to be the ant, right? (Photo credit: dierken).  Currently listening to Easy Now by Edie Carey 

I think we actually use our tendency to get angry at and disappointed with ourselves to give us an excuse to do even more avoiding. Sure, you may be letting yourself down, but if you feel really awful about it, then that gives you a little distraction from the fact that you really do have a dream or a goal and your actions are hurting that dream. We can’t get out of the hole by feeling really awful, or by making a vow that now we are going to be perfect and we will never fall behind again (that’s making promises that our future self doesn’t want to keep any more than our present self does). There’s really only one way out: Take one step. Taking an action that points your feet in the right direction, an action that gets you moving, that’s the only way out. Any one real action right now can make things better.

I’m talking about this as if it’s a student problem, and it’s not. Everyone does this, and we all deal with it in different ways. I deal by staying really busy and pushing myself hard. Then when I get overwhelmed I have an excuse to throw up my hands and give up since there’s not enough time to really set things right. If it is true that the only way through is to take the next step, then maybe I should make the next step easy, rather than hard, which is my natural inclination. In fact, I’ve decided to let everything be easy. Ironically, that’s not easy to do. It runs counter to what I’ve been taught in my years of school and what I’ve taught my students since I graduated and became a “source of knowledge” (note to readers: use an ironic tone in your mind when reading that last phrase). We all know that the secret to success is hard work and that “practice makes perfect.” Particularly in math, I have always believed that lots of practicing is absolutely essential if you want to do math. The trouble is that I’m starting to think it’s a bit more complicated that that.

In K-18 education, we have students practice by giving them homework, and there are arguments both that homework is “good for kids” and homework is “bad for kids” with research about the impact of homework on achievement (grades, test scores) backing up the different sides. But is achievement what we really care about? In K-18 we care about grades and tests because grades and tests will serve as a signal to future schools and employers that they should pick us for their team. If we can get the right GPA, degree, or test score,  the promise is that we can have something that we want in to future (like a great job), so achievement is something we care about when we think about the future.

But what about our current selves? Do we really have to wait to a diploma or degree to have what we want in life? Sometimes the answer is “yes” — for instance, if a master’s degree will get you a promotion and raise, then you really want that marker of achievement, and that may be enough of a goal to sustain you along the way. But for many of us the game of grades and tests is stressful, scary, unpleasant, and hard, even if it is necessary. Many of us need something to care about something besides achievement in order to make it through all of those difficult tasks, to make things a bit easier. We also arguably need to care about something other than achievement in order to make our school experiences truly transformational. So, if its not achievement that turns our cranks, then what is the point of homework, practicing, and all that hard work? If we have an authentic purpose, aside from achievement maybe we don’t have to slog through the drudgery. For instance, if you want to launch a rocket, you might need to test out configurations and do hundreds of calculations, but its not practice and it doesn’t have to be hard. True, it may take time, your path to that rocket launch may not be direct, and you may sometimes be very frustrated, but you don’t have to drive yourself forward, convinced that if you don’t keep your nose to the grindstone, you’ll never get there. Some of your best ideas will come when you distract yourself and take time for play, and you can have faith in your dream and keep taking that next step.

As a teacher, when I worry that my students aren’t “getting it,” my inclination is to do to my students just what I do to myself: push harder. I do the same thing to my kids; when things aren’t going well I make more demands, thinking that pressure is really what they need (that, and lectures too). I do the same thing to myself — when I feel that I am “behind” or that I want to be doing something more or different, I remind myself that I’m lazy and that I really need to push myself hard if I want to have my dreams. After all, I did watch three TV shows last night rather than working on this blog post.

What if I stopped doing this? What if when I feel really bad about what I’m not doing, I think back to my big goal, remind myself that the work really is easy and pleasurable, and just get myself to engage for 15 minutes and then take my TV break? What if instead of lecturing and threatening my kids, I remind them of how great they really are at the things I’m wanting them to do? And in the classroom, what if I point out to my students what they are doing well and find a way to increase my connection to them, believing for them that it is going to be easy to re-engage with the class and get over the obstacles in their path? No, none of these would be perfect solutions, but expecting things to be perfect never really gets me anywhere.

My questions for all of you: Why do teachers have students do work outside of class? That is, what is the purpose of practicing the math concept, reading the article, writing the paper, or whatever else we are asking students to do in K-18 classrooms? Is the work we assign the most effective way to reach our goals? Is the solution to difficulty to work harder? Do you believe that you should work harder? What do you do when you “get behind?”


Week 6: Difficult Feelings and Getting Curious

This week in class, we worked together on using a google spreadsheet to find the amount of money in Fry’s account when he started with $0.93 and left the account for 1000 years. Spreadsheets take time to learn to use, but they give you a lot of power to do repetitive tasks. You can do non-mathematical things with them as well. For instance here’s a blog post about things a  literature professor does with a spreadsheet, and even a short music video created with a spreadsheet.  and even a music video in spreadsheets (no, I have no idea how they did this!)

We also worked with calculating interest by converting a percent to a decimal, and then multiplying by the principal (the balance in the account). This video covers this procedure (I like the guy who did this video a lot, and he has lots of videos about math in the real world). We did this in a google spreadsheet in class (feel free to open this up and tinker with it, or go to File->Make a Copy and create a copy for yourself). I have a challenge out to everyone to try to create (1) a spreadsheet that will show your balance over time for a savings plan in which you deposit $50 a month and early no interest, and (2) a spreadsheet of the same situation, but with in interest rate of 1% per year. Feel free to post a link to your spreadsheet with a solution, or describing where you are getting stuck (you’ll need to go to File->Share to make the spreadsheet publicly viewable).

Difficulty and Curiosity

What I really want to examine this week is difficulty. I taught two classes on Monday, this Liberation Math class and another class on Math, Art, and Design. I felt bad after each class, and that’s usually a good signal to me that something is happening that I should be paying attention to. In Math, Art, and Design, I felt like students weren’t interested in or connected with what we were doing together in class. In Liberation Math, I felt like the class was a bit frozen, and like I was floating out there alone. At the end of the day, I worried about the classes and my teaching, wondering if it was something that I did or if there was something going on with the students, and spinning out lots of possible scenarios. This morning, I finally remembered remembered that feeling bad and worrying doesn’t actually help anything, and that the proper response to things going badly is actually curiosity.

As I have blogged a bit about before, I think a lot of hiding and dishonesty goes on in a classroom setting. Teachers often hide their true motivations from their students, and they hide the emotions they have while they are teaching. Part of this seems entirely as it should be — it’s not my students’ responsibility to take care of me emotionally, and although I try to be open about my struggles as a teacher, I am careful to deal with my difficult emotions on my own before I bring them out into the light for examination. On the other hand, I think we teachers do our students a disservice when we pretend that we are free of emotion, especially since those emotions have a way of leaking out even if we think we are clamping down on them. Students also pretend a lot of different things in order to get by in a class — they may pretend to like a class, to like a teacher, to understand things that they don’t get, to have studied more than they did, or to have done work that they didn’t do.

The trouble with all this pretending is that we misunderstand each other. We teachers are not all that good at reading students. As Andy Hargreaves says in “The Emotional Practice of Teaching” (p. 839), “Teachers frequently misconstrue their students’ exuberance for hostility, bored compliance for studious commitment, embarrassment for stubbornness and silent respect for sullen resistance. This misunderstandings seriously interfere with teachers’ ability to help their students learn.” I recently ran across another paper by Hargreaves (here) that may draw out this issue even more usefully. Plenty of potential also exists for students to misread teachers, and when I look at students that are struggling in a class, I often feel like I see them writhing under my steely glare, when really I just mean to give them a look of reassurance.

This is why I say the proper response to feeling bad about a classroom experience is to get curious. I have such a limited view of the classroom and there so so much going on at any one time that I actually have no idea what is actually happening for the students. It may be I was having a bad day and the difficulties were all in my mind. It might be there was something I was doing that was decreasing the safety and connection for the students, who responded by protecting themselves. It could be that the students are feeling their own collection of difficult emotions about their performance in and connection to the class. It could be that I engaged students in a difficult task that decreased their sense of safety in the class. It could simply be that it is almost spring break and everyone is simply tired and overwhelmed.

I have a few students in mind that I want to personally connect with, but I thought I’d also throw it out to all of you. What do you think it was? Some of you were in one of these classes and might have an idea of it felt on the ground. Others of you have been students in many other classes and have felt the rise and fall in the mood of a class. As a student, what have you noticed that either increases or decreases your sense of connection to a class, your classmates, or a teacher? What shuts you down? What increases your safety? What makes it more likely that you’ll talk in the class?

P.S. I’ve cooked up a few tasks for this week for those of you participating in the Liberation Math class. Anyone can check them out and play along, particularly if you are interested in a discussion of the positives and negatives of group work.

Emotional Cycle of Teaching

I’m now in the second week of classes, and today I noticed how much my emotions have been fluctuating over the last week. I’ve experienced excitement, tension, anxiety/worry, happiness, connection, and isolation. For me, what primarily drives these emotions is how connected I feel and how exposed I feel. As I gear up for a class, I think about what I want to do and what the students might want and my anxiety and excitement both go up. I want the class to go well, and I manage the anxiety around that by preparing. Sometimes my preparation is great, and sometimes I over-prepare, repeatedly messing with my plans and making them more elaborate or complicated than they need to be. Essentially, the anxiety is about exposure and vulnerability. Teaching leaves you very vulnerable and we all deal with that vulnerability in different ways. The more I can just be OK with the vulnerability, the better things tend to go because when I do that I leave plenty of room for the students. When I get to tense and over-prepare, I tend to shut the students out, trying to control everything about the class. There’s a sweet spot to preparation, where I feel safe enough, but let myself be vulnerable enough to the students to make real connections. It’s often a hard spot for me to reach!

During class, my emotions all depend on what I get back from the students. If I’m getting a lot back from the students, I feel connected and less exposed, so I relax and take more risks. When I get less back from students, I talk more and feel more exposed and anxious. I want to focus this semester on watching the students more, no matter my mood, setting aside whatever anxiety I feel to really see what they are doing. It’s harder than it sounds, at least for me.

After a class, I tend to get a dip where I worry about both my performance and the students performance. What did they get out of the class? Are we moving in the right direction? Here I find that minute responses can help, because at least I have information from students and for me data is often an antidote to anxiety and that feeling of exposure. Even better is real conversations with students directly after class, and I want to make more of those happen. Checking in with students after class can lead to a great dialogue and a chance to offer support. I also feel relief after teaching — another class is over and I don’t have to start that cycle planning, execution, and evaluation for another couple of days.

Math Exams

I gave exams this week, which means that both my students and I are in emotional turmoil. My calculus students struggled to complete the exam in time, which isn’t typically true of my exams, so I need to compare this year’s exam to last year’s. I did have a worry as I was writing it that it was a little long, and I should have listened to my gut! The exam I gave in abstract algebra didn’t seem too long for the students, but I know students struggled. Now I have to grade all of the accumulated exams and have the usual emotional baggage. I feel disappointed in myself and in the students. I doubt myself. I question my fitness for teaching. I get angry at the students for not trying harder, and I even get angry at them for making mistakes. I feel hopeless about the class and about the possibility of any forward progress at all. Dreary and gross stuff that I really don’t even want to admit.

Exams are a situation of artificial pressure. Exams are weak on authentic importance. These exams are only important because I will use it to write down grades for the students. The grades are important to me because they give me a way to assess my class and the students in it, determining whether individual students and the class as a whole met the objectives of the course. The grades are important to the students because they want good grades in order to stay in school, keep scholarships, look good to others, be attractive to employers, and meet requirements of a program or major. Note that none of those things involve student learning. What I want to do in my life is to help students understand and use mathematics, to be powerful with math. A test can only do that as an accidental outcome. A test might help me to assess if I have helped students, but the only way for a test to help with learning is if the pressure of the test helps students to put forth more effort, or if, when faced with a bad test outcome students make a change in their learning habits or approach.

But I have seen first hand what happens when students aren’t having tests — the majority of them don’t push themselves to work. Maybe students are addicted to tests, and thus we are all addicted to this unpleasant experience. Maybe I’m addicted to tests because I have developed too few other methods for helping students to motivate themselves. In any case, I don’t know what to do about it, so I keep giving tests.

Being Dissapointed and the Fractal Nature of School

We’re getting toward midterms and spring break at my college, which means that I’m wrestling with disappointment. This week, I’m disappointed that so many students are missing class. And I’m disappointed in the energy they are putting behind their work. Being disappointed really sucks. I immediately personalize it (“They hate me”) and then get incredulous (“Don’t they realize how hard I’m working for them? Don’t they realize that when they do lackluster work and don’t even show up that it hurts all of us?”) and then I get mad and mean (“I’ll get them back when their grades reflect their poor effort!”). I’m not proud of going from hurt to bewildered to hostile, but I’m only human and I can’t separate my feelings so easily from my job as an educator (as I wrote about a few weeks ago). Midterm time always feels like the end of the honeymoon to me. I realize that they aren’t the perfect enthusiastic students that I wanted, and they realize that I’m not the teacher that will make math easy or effortless. I have to remind myself that there are problems that I can’t solve for students, and that many of them have nothing whatsoever to do with me. I think back to what I was like as a college student and remember that I skipped classes like I was allergic to them and once wrote out the lyrics to a Beastie Boys song because I had no idea how to start answering any of the questions on a calculus exam. I turned out OK (although I did fail calculus) and they will too.

What I was really wanting to write about today is how as teachers our struggles are the same as our students’ struggles. You know what I want as a teacher? I want to know how to be successful. I want to know what tricks I have to do and what buttons I need to press in order to have students that are creative, competent, and successful. I want to know the best way to teach every topic and the right way to respond to student difficulties. I want to know an easy way of telling if I’m doing the right thing in the classroom. I get really frustrated when I look for those answers and they aren’t out there, and I also get frustrated when the answers are out there, but the methods proposed don’t work for me. I get easily overwhelmed by the enormity of the problem of how to be a good teacher.

You know what my students want? They want to know the tricks and methods that will make them competent and successful. They want to know the right way to do every problem. They want an easy way to tell if they are “doing it right.” They get frustrated when they can’t find that kind of structure, and they get frustrated when the methods they find don’t have any meaning or don’t work for them. They want sample solutions for every possible problem. They get overwhelmed by the enormity of the subjects I am teaching them and the difficulty of finding a path through those subjects.

And you know what my administration wants? They want to know the tricks to making a school that produces bright and capable alumni that go on to graduate school or successful careers. They want to know the right way to structure majors and general education to meet those goals in a cost-effective manner. They want an easy method to assess students and faculty so they know if the school is “doing it right.” They get frustrated when faculty screw up their plans  — they’re looking for simple solutions that are quick to implement everyone gets overwhelmed by the enormity of the task of providing students with a quality post-secondary education.

So we’re all doing the same thing, just at different scales. Kind of fractal, really, which is nice since I’m teaching students about fractals right now in Math, Art, and Design.

What does it mean when students don’t do the assignment?

For today’s calculus class, I had the students read about average rates of change in the textbook and answer some questions on the reading. Most students did the reading. A few students did not. I expected this, but it is still difficult. One of the difficulties is around how to proceed with a lesson which some students are prepared for and others are not, but I want to leave that difficulty aside for the moment. The difficulty that is interesting to me right now is my interpretation of the students’ actions (or lack thereof).

This summer I read a great article — “The Emotional Practice of Teaching” by Andy Hargreaves. One of the things Hargreaves talks about in the article is emotional misunderstandings (p. 839):

Teachers frequently misconstrue their students’ exuberance for hostility, bored compliance for studious commitment, embarrassment for stubbornness and silent respect for sullen resistance. This misunderstandings seriously interefere with teachers’ ability to help their students learn.

When I have students that don’t do assignments, I leap to any of a number of conclusions. I go to that old standby of teachers everywhere — the students are lazy and want to be spoon-fed the material. Or this one — the students just don’t want to think for themselves. I go to the favorite of math teachers — the students just aren’t interested in learning math (so I guess I’m going to have to do all of the work around here).

After I had lots of these feelings in class today, I realized that I was feeling crappy about my students and about myself. So I decided I needed to write something about my feelings down here — after all, that’s why I’m blogging this semester — to give myself a way to process the emotions of teaching and a way to reflect on the relationships I am forming with students. And what I realize through this reflection is that I’m making a lot of assumptions that may be wrong — I don’t know why some students didn’t do the reading. I didn’t ask. What if I tried to find out rather than making assumptions? Digging down to the real reasons students fail to do assignments isn’t likely to be an easy task, because we all love to give nice excuses for things rather than being honest, but perhaps its a task worth attempting.

It is at least worth noting that my assumptions about why students don’t complete assignments paint them in a bad light and don’t point toward my own culpability. Maybe the reading assignment I gave was harder than the students were prepared for. Maybe it was too easy and thus boring. Maybe I didn’t give them any real reason to do the assignment aside from the fact that I’m grading it. Maybe the assignment was a complete waste of their time. Those reasons are potentially just as valid as the conclusions I came to, but they are less appealing to me as they point to my own flaws rather than the flaws of my students. I’m not proud of it, but there it is.

I’m not sure where to go with this next, but I think that I at least need to be communicating the purpose of assignments to the students, and I also need to solicit their feedback about assignments (are they at the right level of difficulty? do they seem designed to increase understanding?).