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.


Liberation Math Week 1: Welcome!

Welcome to the first week of Liberation Math. Over the next 13 weeks, we are going to explore mathematical identities, the way that those identities are constructed, and how mathematics and math education interact with our culture. During this course, we will be collectively unpacking our ideas about the doing and learning of mathematics, and talking back to those ideas and imagine other possibilities. My goal is to create a community of people that develops a critical consciousness about mathematical identity and the place of mathematics both in our lives and in the world, which will allow us to move from reacting to structures outside of ourselves to being empowered actors who create our own identities. Participants will also work on mathematical problems that grow out of contexts that we identify as interesting, as well as mathematical problems that are abstracted (as is much of school mathematics), and that work will inform our developing and shifting perspectives on mathematical identity and the place of mathematics in our world. Anyone is welcome to participate, so feel free to read, comment, question, or argue!

Picture from the Ethnomathematics Institute Kalaupapa, Molokai in Summer 2011 (credit: http://goo.gl/3H2bf)

Picture from the Ethnomathematics Institute Kalaupapa, Molokai in Summer 2011 (credit: http://goo.gl/3H2bf)

You can start by reading some short pieces critical of math education. These are interesting to read together since the solutions proposed are so divergent:

This class is really a research collective — we’re researching ourselves and our memories in order to understand mathematical identity and culture, using a research method known as memory-work. Everyone is invited to write a mathematical memory and post it via this form or through a post on a blog or other venue (just provide a link in the comments, or post link to twitter with hashtag #liberationmath). The important thing is to write the memory under a pseudonym (to create some distance), to be as detailed as possible (don’t leave out anything, even what seems unimportant, and to write one memory, not a string of events or biography. We’re looking for the raw memory, rather than how you interpreting it (for more information about this, see the Haug reference below). We’ll be collectively identifying similarities and differences, themes, what seems to be missing, and what our writing says about who we are. That conversation will begin next Monday. To read more about the memory work method, check out the following three articles. The first talks about mathematics specifically, the second is by Frigga Haug, the woman who developed the method, and the third is a paper by a research collective of adult learners that used the method in a class.

What do you think about math and it’s place in our culture? What kinds of memories (good or bad) do you have of mathematics? Leave a comment below! Anyone who is going to be posting about Liberation Math, please leave a link to your blog and/or twitter account below — I’ll be compiling the links on the sidebar.

(Lesley Students who are enrolled in the course, make sure you cover all of the assignments in the course outline under Week 1 — it’s a big week, so I recommend starting early!)

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Join Us for Liberation Math (it’s a class and a community!)

Liberation Math, the course, starts next week. We’re going to be doing a wide variety of readings and critical reflection about mathematics education, and we would love to engage and interact with you (yes, you). You can see my outline for the class here — everything is in flux and the participants will have a big influence on what we actually do, especially in the second half of the semester.

One of the things I want to do with Liberation Math is to give a voice to people who wrestle with mathematics, especially those who feel like their voice doesn’t belong in a conversation about math or math education. I want to hear the voices saying that something doesn’t fit about math, that math is oppressive, that math has no relationship to people’s lives, that math education doesn’t fit their needs, that something is broken. That means I need your story of wrestling with mathematics, no matter what form that struggle has taken. You could write your story in any medium you want. Comment on this post with your story. Tweet it with the hashtag #liberationmath. Fill out the form at the top of the page to “Add Your Voice.” Write a post with your story and give a pingback or tweet your post with #liberationmath hashtag. Do a story on Cowbird. You get the idea.

Starting next week, I’ll be posting readings and conversation starters each Monday. These should give you something to wrestle with and talk back to. By Friday, notes will be posted from the in-person class that might provide further fodder for discussion and reflection. By early Monday morning, there will be a roundup posted about the activity of the week, including, perhaps, some of your ideas and thoughts.
(P.S. For those of you in #etmooc, I’m looking at ways to grow my students PLNs and using this course as a tool for social change. Anyone have ideas about more ways to do that?)

MOOCs as a Liberatory Project

I’ve been reading Elizabeth Ellsworth’s article “Why doesn’t this feel empowering? Working through the repressive myths of critical pedagogy.” This paper is about Ellsworth’s experiences teaching a course called “Media and Anti-Racist Pedagogies” in 1988 at UW-Madison. Ellsworth says, about the role of dialogue in critical education, “Through dialogue, a classroom can be made into a public sphere, a locus of citizenship in which ‘students and teachers can engage with the process of deliberation and discussion aimed at advancing the public welfare in accordance with fundamental moral judgments and principles…Dialogue is offered as a pedagogical strategy for constructing these learning conditions, and consists of ground rules for classroom interactions using language.'” (Ellsworth, 1989, p. 314) The rules she cites include equal opportunity to speak, tolerance of ideas, and logical critical inquiry, which leads to a a goal of unification within diversity. But given the power dynamics of our society, our classrooms, and the multiplicity of perspectives, the dialogue described is, for Ellsworth both unattainable and undesirable. As Ellsworth says, “I expected that we would be able to ensure all members a safe place to speak, equal opportunity to speak, and equal power in influencing decisionmaking…It was only at the end of the semester that I and the students recognized that had had given this myth the power to divert our attention and classroom practices away from what we needed to be doing. Acting as if our classroom were a safe space in which democratic dialogue was possible and happening did not make it so” (Ellsworth, 1989, p. 315).

Ellsworth found that the class was not, in fact, providing a safe-enough space for students to truly dialogue. She cites reasons like fear of exposure and vulnerability and memories of old experiences — without naming it, she cites the presence of shame in the classroom (one of my research interests). But Ellsworth nails the problem/solution as going beyond shame. No individual student, no affinity group, and no course has a complete “narrative of its oppressions,” so the entire educational project is unknowable. In Ellsworth’s case, her class could not know if a particilar anti-racist action would undercut other groups, or even their own group. The enterprise of liberation is complex, chaotic, and unknowable, and we must “build a kind of social and educational interdependency that recognizes differences as ‘different strenglths’ and as ‘forces for change.'” (Ellsworth, 1989, p. 319)

What kind of educational practices are possible when we confront the true unknowability and incompleteness of our pedagogies, when even as we come together we lack the knowledge necessary to answer basic questions of survival and justice? As Ellsworth asks, “What kind of educational project could redefine ‘knowing’ so that it no longer describes the activities of those in power ‘who started to speak, to speak alone and for everyone else, on behalf of everyone else.'” (Ellsworth, 1989, p. 321) To me, a question then becomes can a constructivist MOOC, moocified course, or personal learning network do exactly what Ellsworth is calling us to do? How can we be sure that these projects will really bring out the new voices instead of just brining us the voices that have already spoken?

Ellsworth describes the process in her class: “Our classroom was the site of dispersed, shifting, and contradictory contexts of knowing that coalesced differently in different moments of student/professor speech, action, and emotion. This situation meant that individuals and affinity groups constantly had to change strategies and priorities of resistance against oppressive ways of knowing and being known.” Our educational mechanisms need to allow us to move fluidly between sameness and difference, in a way that “cannot be predicted, prescribed, or understood beforehand by any theoretical framework or methodological practice…[A] practice grounded in the unknowable is profoundly contextual (historical) and interdependent (social).” (Ellsworth, 1989, p. 322)

Connected Learning

Indeed, a connectivist MOOC or similar structure may be uniquely poised to answer Ellsworth’s call. A foundational analogy is that of Rhizomatic learning, and the power of networks in creating knowledge. As Dave Cormier says in a post on rhizomatic education, “If a given bit of information is recognized as useful to the community or proves itself able to do something, it can be counted as knowledge. The community, then, has the power to create knowledge within a given context and leave that knowledge as a new node connected to the rest of the network. Indeed, the members themselves will connect the node to the larger network. Most people are members of several communities—acting as core members in some, carrying more weight and engaging more extensively in the discussion, while offering more casual contributions in others, reaping knowledge from more involved members.”So we have the freedom and flexibility to grapple with the unknowable, and to move flexibly around sameness and difference.

But what happens when networks do not provide spaces that are safe enough to bring out all voices, and when the “unity” of the network comes at the cost of erasing the voice of individuals and groups. On the one hand, the internet and social sharing provide a wonderful equalizer that allows us to connect on what certainly appears to be an equal playing field. But there are no equal playing fields, and in living in a fantasy world of equality of access and power, do we do ourselves a disservice? Is it the community that is able to create knowledge, or is it the thought-leaders in the community? The social networks on which MOOCs and personal learning networks are based obey a clear power law, which means that in fact a few voices dominate the conversation. How can we ensure that connected learning is a liberationist exercise and doesn’t self-organize us all into exactly the same power structures we had before with regard to education?

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Courses as Maps or Incendiary Devices

math atheistWhen I was an undergraduate and a graduate student, I used to hate taking classes. Classes were generally mind-numbingly boring. When I was doing graduate coursework, I played a game of hangman during class in which I got to put in a new body part every time a certain number of minutes passed. It wasn’t that I hated education. I loved getting the kind of gold stars school gives you, certainly, but I also loved working, thinking, and solving problems. Homework was never boring. It was sometimes aggravating, and I remember wishing that one of my professors would be jailed for the semester because his homework frustrated me so. But I have always enjoyed working on problems, whether those problems were mathematical or theoretical.

So, honestly, it’s a little surprising now that I just signed up for my second course of the new year. I started the year with #moocmooc, and I can’t even remember why I signed up. I had started reading Hybrid Pedagogy and some of the ideas were getting me fired up. Suddenly I was in a course, but one where I got to skip all of the boring parts. Instead, I got to have some amazing conversations about pedagogy, open learning, and the educational system. Now I’m signed up for #etmooc (Hi #etmooc-ers!) because it is clear to me that if I want to liberate people with and through mathematics on a big scale, I’m going to have to figure out how to make intense, disruptive, and connected learning happen through technology.

In a #digped discussion that was part of #moocmooc last week, the idea of a course as a container was discussed. You can read this Storify to get a feel for part of the discussion. I think that most of my courses are actually routes on a map. In them, guide my students to some pre-defined learning outcomes, and I tend to take students on paths that I have walked before, in the hopes that I can be the best guide possible. I’m helping them to explore a terrain and create a map of that terrain, and I do that by guiding them along the path I laid out and pointing out particular features of the landscape. Honestly I have always hated the kind of course I teach, and I feel guilty when I teach it, because I know I’m teaching the wrong way.

Like many mathematicians, I privilege mathematics as problem-solving over mathematics as quantitative literacy. I started my life as a teacher firmly in the constructivist movement, taking as my bible the NCTM standards of 1989. But I’ve been teaching in some form now for over 25 years. I understand the job of teaching much less now that I did then, since it is a complex job, and everything I learn shows me anew how impossible the task is and how inept I am at it. In those 25 years, again and again I have learned that most students don’t actually want constructivism, at least not a pure form of constructivism. Most students want to be helped and guided. Students want some assurance that they are doing the right thing, and learning the right thing.

I have been reading “Why Doesn’t This Feel Empowering? Working through the Repressive Myths of Critical Pedagogy” by Elizabeth Ellsworth. It’s a thick paper and I’m not through even close to the whole thing, but I’m struck by this quote: “Strategies such as student empowerment and dialogue give the illusion of equality while in fact leaving the authoritarian nature of the teacher/student relationship entact” (p. 306). I feel this way about problem-based learning and constructivism in my classroom — they give the illusion of allowing the student to construct meaning, but really reinforce the power structure that allows me to dominate the class and inculcate my students. Constructivism appears to stand against the rote, oppressive recitation of mathematics as Betty Johnston calls it:

To learn every day that it is normal that mathematical knowledge is externally given and monitored, that patterns reflect no reality, that a quest for a certain kind of understanding hinders success, that everyday practices are quantified and regulated by a vast array of indices, is to experience mathematics as a profoundly decontextualized discourse that could refer to anything and for most people refers to nothing. It is to experience mathematization as the ordered daily training in the normality of heteronomy.

But constructivist classrooms are just putting a small bandaid on the overriding oppressive and compulsory nature of mathematics education. I can’t change dynamics in my classroom by flipping a problem-based learning switch. Students simply experience that as more oppression. And when I try to push in onto them as a style of teaching and learning that they hate because it is is “good for them,” then that’s me violating the trust that the students place in me.

Basically I’m damned if I do and damned if I don’t — I can’t teach rote recitation in good conscience, but neither can I teach a constructivist problem-based curriculum without my student’s consent. So what do I do? I think the type of course I need to teach more is like an incendiary device than a map, but one that’s delivered with love and connection, and one in which I give the students a map, point out the landmine on the map, and as them to go over and step on it. I need to find a way disrupt both the students and myself, because we are all wrong about what we can and should do with mathematics. I need to get them to give voice to the righteous and unspeakable rage and shame that they have bound up with mathematics. We need to blow up the whole project of mathematics learning together, and then maybe I can find a way to listen to them and we can all start asking and answering the right questions. That brings me (finally) back around to the role of technology, which I see as giving my students power to create new narratives publicly, narratives that have the potential to disrupt education beyond the confines of my class.

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Reading: Grading Student Writing by Peter Elbow

On the recommendation of Jesse Stommel, I’m reading this paper about grading student writing by Peter Elbow, and I’m trying to figure out what it might say about my own grading practices. First, let me say that that the problems of grading writing may be qualitatively different that the problems of grading mathematics. Mathematics has this wonderful and horrible right/wrong duality in it, and it is often set up as an objective arbiter. Emotions and opinions don’t come into mathematics grading, because how can they? It is always true that 2+2=4, and it is never true that 2+2=0 (except of course if you are working mod 4, but that’s just me being an obnoxious mathematician). I suppose that is the true truth if you are either machine grading, or are grading with no “partial credit.” But that is almost never true for me, because I don’t think that the most important thing about a solution on an exam or in homework is the final answer. The process is far more important, and gives me more clues about what the student is thinking and what they have learned. Add to that the fact that I typically give projects and other more subjective assignments for at least part of a student’s grade, and the situation gets quite muddled. And of course I accumulate a large list of quantitative measures during a semester and combine them together in an arbitrary way that I determine at the beginning of the semester, with each grade making up a certain percent of the final grade. All of that is the say: mea culpa, I may need a better theoretical framework here.

Right away the paper grabs me, then with the discussion of the difficulty and unreliability of grading, and even more with the wall it puts up between teacher and student. As Elbow says on the first page, “Students resent the grades we give or haggle over them and, in general, see us as people they have to deceive and hide from rather than people they want to take into their confidence.” I’m in, but what do I do?

Elbow recommends using minimal grades, like pass/fail or strong/satisfactory/weak. He recommends this for low stakes writing, and I could see it working perfectly for low-stakes assignments. In fact, I rarely grade homework. Most is graded on completion only, or if I actually want to provide feedback I use a 0-2 or a 0-3 scale. But really, maybe the words work better (only what do I write in my gradebook?). Elbow says that we can judiciously increase the number of levels in higher-stakes situations if we want, still without resorting to the eight levels of the traditional letter grades with pluses and minuses. Honestly for a test, this would be harder for me than what I already do. I tend to grade student work on each problem using a rough rubric that tells me how many points to give what kind of work — I might subtract points for certain kinds of errors, or give a certain number of points if the student made a correct start to a problem. So when grading is done, I have a bunch of number to add up, and presto, I have a grade! And arguably that grade gives me an idea of how well they were able to demonstrate their knowledge on that particular test. Moving to a more fuzzy system would be more work for me, but I can still see some advantages. I would likely still grade in much the same way, but I’d have a less fiddliness over the small numbers of points, with all questions being strong/satisfactory/weak. Then I have to think of a way to get the exam assessment overall.

Elbow can help here again, and maybe help with my poor Excel gradebook. He suggests to look at all of the grades in aggregate. Say you have a lot of low-stakes grades. Doing “satisfactory” on all of those might be a B, and then looking at the smaller numbers of higher-stakes pieces could pull that B up or down. Being a math person, that screams out to me to make up a formula, and you again get into the whole problem with grades. Wouldn’t a narrative evaluation simply be better and more nuanced, allowing me to say to a student “You did great with all of the lower-stakes pieces, but once the stakes were raised, you struggled to show your competence and understanding.” Then the student and I could both think about why that was. Perhaps the higher-stakes assignments required putting more concepts together, or maybe the pressure negatively impacted the student’s ability to think and communicate clearly.

Elbow advocates for portfolios, which I think are a good idea, but I have only occasionally used. He also discusses the use of contracts for grading, which I think I last encountered in high school. I could see contracts being a way of being up-front in my manipulation of students, as Elbow suggests. In doing so, I could clearly spell out my expectations for behaviors associated a passing grade. My only question there is what happens if the student has all of the behaviors associated with passing, but still doesn’t learn the material? What if they still can’t do any math? Honestly, I don’t think that really happens, at least not if I choose the right behaviors. But I worry about whether I have a clear leg to stand on if criticized for this kind of grading practice. Is it “rigorous enough?” Don’t I want students to come out of the class with some products, rather than just a process and effort? I think what I am struggling with is the student that just does the motions as they go through my class, appearing to really engage without really engaging. I suppose that such students pass through my classes all of the time, and there is no fool-proof method for bending them to my will and forcing them to engage in the ways that I desire. And when I put it that way, perhaps there shouldn’t be. Maybe the real problem is in trying to manipulate students into doing what I want them to do at all.

SJSA Grade Six -  The Year I Rebelled

Photo credit: Michael 1952

Elbow also suggests being explicit about criteria. I tend to have rubrics when I grade project work that spell out what I am looking for, and Elbow’s minimal grading would make this easier and less rigid. I could also give criteria on exam problems, or I could split up into multiple criteria. In a calculus class exam problem I might be looking for the method of solution, setting up the solution in a reasonable way, and executing that method including getting algebra correct. I could be clear about each of these criteria and evaluate each problem on each criteria.

Part of what makes grading hard is being the person that holds the power of judgment, and that’s just part of being a teacher. The power is mine to hold and negotiate, since I have to write down a letter grade at the end of the semester. I want to use student assessments in a way that is helpful to the students, and to determine letter grades in a way that doesn’t create excessive distance between me and the student, or between me and the task of judgement. Honestly, right now I use my grading system as a very long arm that allows me to avoid the uncomfortable position of judge. I don’t really determine the grades — a lot of numbers determine the grades, and I have very little to do with it. I can hide behind those numbers. I can even advocate for and advise students about how to beat those numbers, ignoring the fact that I’m the one writing down that letter grade. Once again, it all comes down to the relationships in my classroom and how I navigate them and engage with the students, and I can see that I have some work to do here.

Two Mathematics

Take an equilateral triangle and cut it into t...

Take an equilateral triangle and cut it into three similar parts, just two of which are congruent (Photo credit: fdecomite)

Yesterday, I was sitting in a talk at the Joint Math Meetings, and someone made the comment that the Common Core State Standards to not support quantitative literacy. The comment hooked something in me. Was it true? How might the CCSS fail to support quantitative literacy? What is quantitative literacy anyway? And what does the CCSS support, if not quantitative literacy. I actually haven’t yet gotten familiar enough with the CCSS to answer most of those questions, but I have an answer congealing in my mind anyway. There are two worlds of mathematics.

On the one hand, mathematics is about a love of figuring out problems, and puzzles. It’s about thinking abstractly, putting things together, and taking them about. Mathematics is an abstract intellectual exercise that is a joyful romp through problems, exploration, and mind-bending puzzles. This is the mathematics that mathematicians love. It’s the mathematics of Martin Gardner and the Museum of Mathematics.

On the other hand, mathematics is about understanding and being able to use the quantitative and geometric information that infuses our lives. It’s about being able to interpret basic statistics, make predictions, and pin down relationships between variables. Its about understanding risk, stripping complex information down to basics, and making comparisons. This is the mathematics of quantitative literacy and the mathematics of science.

Mathematicians want people to learn to love the first kind of mathematics. We see the fun, the beauty, and the power of mathematics for mathematics sake, and we want to share it with the world. We also believe that understanding this kind of mathematics will lead naturally to quantitative literacy, without any additional effort needed. But many people want the second kind of mathematics, and are not interested in the first. People want mathematics to be concrete and useful, to serve the world — otherwise what is the point? It is the first kind of mathematics that people see as irrelevant an obtuse. Do I need to convince them that it is not, that it is, in fact, wonderfully fun and beautiful? Or can I be convinced that their experience is authentic, and that they may not actually need that first kind of mathematics at all?

So I wonder — does the CCSS privilege the first kind of mathematics over the other? What kind of math does more traditional K-12 schooling privilege? Does learning the first kind of mathematics lead to understanding the second? Are they inextricably linked?