Years ago, I did some work to help students read mathematics textbooks. I gave a presentation on the material at an NCTM conference and wrote a piece for students that is still in use by the Harvard Bureau of Study Council. I was recently reminded of the work because of an email I received about it, so I’m going to be looking at making use of the work again and perhaps writing up something additional about it and getting the work out more broadly. It is based on the “click/clunk” method which is used in some reading methods in education.
I ran across a blog post by Brené Brown earlier today. In the post she relates some of the kurfluffle around her comments to Oprah Winfrey about teachers and shame (original video now hard to find — its the last clip on this page). This all happened at the end of September, so I’m late to the party, but I had a few thoughts about what happened here . To my mind, the biggest place where Brown goes wrong is when she says that shame is a classroom management tool used in schools. By calling shame a tool, she implied that the use of shame was conscious, and since her whole thing is talking about how bad shame is, that’s a pretty damning way to call teachers out as being bad for kids. That turned her comments into a public shaming of teachers. Brown didn’t intend to shame teachers, but that’s the sneaky way shame works — it’s everywhere, and it is hard to avoid.
Shame is certainly present in every classroom — it is a nearly ubiquitous emotion, so it happens in classrooms like it happens everywhere. For the moment, let’s try to avoid shaming the emotion of shame — shame and the threat of shame are intertwined with nearly every connection we have with other people. That’s not good or bad, it just is. When our relationships are working, we are able to use subtle clues about shame in ourselves and others to figure out how to navigate the relationships without alienating ourselves or other people. But an excessive weight of shame, or shame that calcifies in certain areas can break our relationships, causing disconnection and isolation. In classrooms, both students and teachers can feel shame, and that shame is a signal to us that our relationships are either fractured, or in danger of being fractured. Teachers feel it when they are disrespected by parents, administrators, and other teachers. Students feel it when they understand that they aren’t worthy of connection with classmates, teachers, and specialist because they aren’t good enough. We have to watch for signs of shame in other people, and use it as a sign of relationship danger. Relationships can be repaired and shame can be healed.
Teachers care about kids, that’s why they become teachers. They work hard every day to help kids succeed. They also face a job that is so difficult, so painful, so demanding of every resource they have. They do it without enough pay, and with a whole world watching to see where they are going to screw up first. In other words, teachers do their jobs in an environment that is a shame pressure cooker. When people are in that kind of pressure cooker, they will push their shame onto other people, and it is easiest to push shame onto weaker people. I do it as a teacher to my students, and I do it as a parent to my kids. I don’t do it because I’m a bad person, or because I am sitting around cackling and thinking up ways to torture students and children. I do it because I am human, and fallible, and, because, as Brown said in her mea culpa post “learning is vulnerable and classrooms are tender places.” We do need to raise awareness of the presence of shame in classrooms because awareness is really one of the only ways to combat shame. But we have to raise that awareness gently and carefully because any time we start to really see how shame operates in our lives it is easy to become overwhelmed.
I do think there are some institutional practices that increase students vulnerability to shame in schools. Particularly, I am thinking about public accountability in classrooms. In elementary math classes, you will sometimes find charts of times tables and other math facts, where you can see how each student is doing on proving their mastery. Short timed tests like “mad minute” are used in most elementary classrooms, and those are also a form of public accountability since all the students know who finishes on time and who doesn’t because they can look around and see everyone, including those kids that inevitably shouted out as soon as they were finished, before the timer rang, stopping the kid who still had half a page of problems left. Public accountability charts are also used for behavior management and in other subjects. For some kids, this is highly motivating. Students want to do well and the competitive spin of public results help spur them to work. But for other students, being at the bottom (or even in the middle) week after week is demoralizing and shaming. I think that in order to support all students, we need to have students set goals and chart their progress, but that this should be private. This won’t provide the competition that helps some students focus, but it will avoid the discouragement and feelings of shame and stupidity that other students experience.
We can’t change the fact that in every classroom, the students know where they stand in academic rankings. All of the students know who is at the highest reading level and who is still struggling to read beginning books. They all know who finishes the math assignments before everyone else and who never finishes. We humans are constantly comparing ourselves to others, and figuring out where and how we rank. But when those rankings are publicly displayed, their importance is reinforced, even if the teacher is telling the students verbally that effort and progress are the most important things. We need to put the rankings away and to consistently remind students that they need to look to themselves to measure progress. They need to be better able to handle fractions at the end of the unit than they were at the beginning. They don’t need to be better than another student, they need to be better than they used to be. We also need to talk to students about how we handle that terrible feeling we have when we realize that we aren’t doing as well at something as we wish we were. We need to talk with our kids about how to manage the pain when we find out we sang the wrong note, or messed up all the problems, or our drawing wasn’t selected for the prize, or we realize that our friends are all reading at a higher grade level than we are. If we avoid emphasizing rankings and do some explicit teaching around how to handle the emotions that arise when we fail or don’t do as well as we would like, then we give students the tools to navigate pressure and criticism without falling into a pit of shame. Most teachers already do a lot of work to combat shame, but connecting the dots on the impact and mechanisms of shame can help teachers better see what they are doing and how to do it effectively.
I ran across this video yesterday, by a math major, taking about other people’s reactions to learning that she is a math major.
I particularly like the analogy around 1:15 where she is talking about the jarring nature of switching from ordinary conversation to math. She likens it to being asked mid-conversation to compose a poem in Russian when you don’t know Russian. I think that is a lovely analogy. She notes that math feels this way when you are not used to it, and sometimes even when you are used to it.
I think this is an apt analogy, because academic math comes out of left field for most people. In math class, it isn’t that weird to have someone tell you:
The track at Made Up School is one mile long and features semi-circular ends connected by straight lines. Find the area enclosed by the track as a function of the radius of the semicircles. What dimensions allow the maximum area to be enclosed by such a track?
Say what? What does it look like? If the track is there already, how can we change it? Why are we doing this? And sometimes things get even worse:
If line segment BD is a perpendicular bisector of line segment AC, prove that triangle ABC is isosceles.
It just makes your brain hurt due to the sheer number of technical terms, and I have no sense whatsoever of this being a meaningful task that there would be a human reason for being able to do.
Notice that this is very different from other subjects that we study in school. In history, you might be asked:
In 1938, British Prime Minister Neville Chamberlain chose to adopt a policy of appeasement toward Hitler’s aggression against Czechoslovakia. What did this mean? (from this list of sample questions)
There may be some confusing terms in here. Maybe I’m not totally sure what a Prime Minister is, or who Chamberlain was, or where Czechoslovakia was in 1938, but I can get the sense of the question and have some idea of why I might want to be able to answer it, namely because I want to understand how the international world works.
Same with a thick subject like physics:
A battery is connected to a light bulb with copper wire to complete a circuit. The bulb immediately lights. Why?
Whoa, that’s intense. You are asking how a battery works. It may seem like a hard thing to understand or explain, but I can see why I would want to try an answer it — because I want to know how the world of electricity works.
I am not suggesting that there is no point to learning “higher” mathematics beyond arithmetic, but I am suggesting that those reasons can be obscure and subtle. We learn mathematics past basic computation because we want to understand the world, but it is an understanding of the world of thought, the world of algorithm, the world of logic, the world of abstraction. It is not the “real world” that we are seeking to understand, although higher mathematics often does have applications in the real world. Instead it is a fantasy world in which we ask “what if” and try to find a way to get consistent results. It is a world that is jarring precisely because it is so headily academic and is tethered to everyday concerns like a balloon that may slip away.
I think that if we all realized that we currently have enough math to understand our worlds, we’d all be a lot happier. The math most of us use in life is more straight-forward than it is portrayed in school, and you may, right now, be as good at it as you need to be. Or you may find that you have some math-related problems in your real life that always frustrate you. That might be because they are really hard problems, and would be hard even for someone with advanced mathematical training. For instance, if you want to figure out a system of bonuses for your employees that reward certain types of job performance, then you probably will want to use some math, but the problem won’t be simple, and math will only be one part of the solution.
I also love the end of the video above where Sarah emphasizes practice, and the fact that mathematical skills can be developed. Absolutely true. You probably already have most of the math skills that you need, and if you need more, practice is a good way to get more. Of course, one of the big troubles that I see is that K-16 math classes don’t give people skills they will need after school, and it is actually quite hard to find needed and useful math skills if you aren’t in a STEM field (see, for instance, Audrey Watters on the difficulty of learning to code).
Last week I had a paper published in the journal Rationality and Society, “Division of Labor in Child Care: A Game-Theoretic Approach” . You might like the paper — it’s pretty interesting actually. But the first thing that’s interesting about this paper is that it did not occur to me to announce it here. For heavens sake, why not? My excuse is that I assume (erroneously) that you might be interested in my thoughts on education, but not in my thoughts on applied mathematics. Really that doesn’t even make any sense, and it’s not the real reason. I hope that you will find something in this paper that gets you thinking. In the paper I use game theory, a theory from mathematics and economics, to model an imagined situation in which two parents are caring for a child. The model itself is like taking the whole complex story of how real parents live and work with small children at home, and taking most of the story out, leaving just one aspect of the situation intact, in order to see what mathematics might say about how such parents would behave. The paper provides a great example of using mathematics to explore human relationships and building models of the real world in mathematics. It shows off what math is best at — abstraction and simplification. Writing it allowed me to explore sociology, gender, and economics, and it could provide a window on those vistas for all of you as well. I want everyone to read it that is interested in math education, applications in math, gender, and parenting.
So why didn’t I think to announce it here? Because I don’t want you to know that I want you to read it. I want this paper to be read without having to take the risk of actually asking people to read it. It is embarrassing to release something you created out into the world. Asking you to read this makes me imagine you reading it, thinking about it, and judging it. That puts me in the realm of self-conscious emotions — embarrassment, pride, shame, guilt. I can imagine lots of reasons why you might find the paper lacking, and being able to produce quality work is important to me, hence the potential exists for me to feel shame. So I am caught in the middle between two desires that pull me in opposite directions. On the one hand, I should ask a lot of people to read the paper, and hopefully some of them will, and some will even talk to me about it. But I should also bury the work and never mention it to anyone. Best is if you just stumble across it in a journal, and email me to tell me how much you like it and what kind of interesting conversations it spawned in your family or in your classrooms; then I never have to imagine you reading it with a frown on your face. But that’s not going to happen, so I decided to share it with all of you in the hopes that you will read it and talk about it with me and with other people. (And FYI, in case you are wondering why I would say all of this,
I find that being honest and open about my fear, especially fear of shame, allows me to manage that fear. I still feel exposed, but when everyone know about that feeling I can more easily manage it since I don’t have to hide it.)
In Liberation Math, the class, the students and I are wrapping up the semester by writing and writing some more. Students are (slowly) getting content up on a website the class has organized, and over the next couple of weeks our writings will be collected into the form of print zines focusing on different topics.
On Monday, we welcomed Shaunalynn Duffy, from Sprout & Co, who talked to us about what she does with Sprout and her educational vision. The topics ranged from science to math to music. As Shaunalynn said, the mission of Sprout is to turn science into a cultural experience, and that idea resonated with many of us in the class.
I have a few interesting readings, groups, and events along the themes of community, culture, education, and liberation:
- There is a conference happening this Saturday at the Harvard Graduate School of Education on alternatives to compulsory education. The conference is free, but they are asking people to register in advance. I would be great if someone connected with the class could go, report back to the rest of us, and even make some connections!
- On May 17-18th, there is a free conference for educators, students, and others focusing on building a social justice movement in education (Boston-area Educators for Social Justice conference). From their website, the purpose of the conference includes “develop youth leadership and youth voice in education” and “build a movement for liberatory education that combines the visions of youth, communities, families, and teachers.” Sounds great! I’m giving a talk on liberation mathematics Saturday the 18th at 10am. I’d love to see some of you there.
- Take a look at this essay about the need for storytelling in science, “instead of worrying about teaching students every fact about cell biology, why not embrace the stories of cellular biology and teach students to think like biologists.”
- Readers who were in class saw the video of me playing drums with my band at Ladies Rock Camp Boston. You can read more about my thoughts on LRCB and how it connects for me to empowering and liberatory education in this post, and if you scroll to the bottom you can find a link to that video! There is an interview with the founders of Girls Rock Camp Boston, Hilken Mancini and Nora Allen-Wiles, in the Boston Hassle.
Next Monday in class, we will:
- Watch a couple of videos focusing on teaching math concepts, and have a couple of live shares
- Get a flavor of some art from graduating seniors whose show got moved due to the events in the Boston area last Friday
- Finalize our written works, pulling the whole semester together! This means that you should all be finishing up your writing this week!
You should also work on a summary account of this class as your final blog post (of course, you are welcome to continue your blog even after the end of the semester). Take a look back through what you have written. Look over your original memory that you shared, and think about if anything has changed (or not changed!) about how you view that memory, or how you view yourself in relation to mathematics. Ultimately, what has this class meant to you? This final piece will be due on your blogs by 5/9 (that’s the thursday after our “final exam”) so that I have a chance to read them over before I have to close out the books on this semester.
Today and tomorrow, I’m trying to get people to fill in this sentence: “Math is [fill in here].” Feel free to give your own answer in the comments below or on twitter. Once I get the blank filled in, I’m trying to prompt people to ask why or probe a little deeper. In part, this is preparation for a talk tomorrow that is on the liberation math class. The class discussed what we should do last week, and most of us liked the idea of creating a taste of the experience of the class. So we’ll talk about what math is, why it is that way, get people to contribute some brief memories and talk about what themes and stories we notice, and then talk about hidden curriculum and how we are working to reclaim power, starting with having people ask questions about pictures drawn from http://www.101qs.com/. It will be fun!
The talk will be on Wednesday, 3/27 from 3:45-4:45, in Cambridge, MA (porter square) at 1815 Mass Ave, upstairs in room 2-078.
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.
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?”