Classroom poster with students names and mastered math facts

Shame in classrooms

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.

Classroom poster with students names and mastered math facts

Here not only is your math prowess public, but it’s linked to ice cream

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.


Our successful schools

School closings rally

School closings rally (Photo credit: chicagopublicmedia)

I have been thinking a lot lately about the failure of our schools, particularly with regard to mathematics. It’s impossible not to notice what a terrible job our schools and students are doing at math, particularly when I am reminded about it once every hour or so by my twitter feed. I got on this kick because of the latest way we’ve been flogging ourselves, the PISA (Programme for International Student Assessment) results. When you look at the US in the rankings of countries, you won’t believe where we stood. We were, well, average. I know that here in the US we think that we live in Lake Woebegon where everyone is above average, but being average is just, well, average. The sky isn’t falling and our scores didn’t drop alarmingly. We’re all OK.

What if we aren’t all terrible at math, and what if our schools aren’t letting our students down? What if our schools are doing an OK job of educating students? Are they doing the best job possible with each individual student? Not likely. Are they moving lots of students through the pipeline, teaching them to read, do math, write, understand politics, know something about history, and even giving them a little art, music, and physical education? Yes, we are doing all that and more.

Remember the 90s and how Baby Eistein and similar products brought us the mistaken idea that if it is good to parent your kids, then its even better to parent them really really really well? If parents do flashcards, teach their babies to sign, buy the right educational toys, and twist themselves into the right knots, we will raise a generation of kids that is uniquely poised to become super-geniuses. Except that none of it really works. Yes, when a child is hungry or neglected, or when a family is living too close to the edge to provide a normal environment for the child, then the child’s brain will be impacted in a negative way. Poverty really does hurt kids. But that doesn’t mean that environments that are excessively enriched will produce geniuses. More is better when you don’t have enough. But when you do have enough, more won’t continue to produce improvements in results.

The same is true of schools, of math education. We need to have schools that are good enough. Schools should be full of teachers that care about kids, that have some training in both subject areas and pedagogy. Schools should have the financial resources and leadership to support teachers and families. But schools don’t need some kind of huge overhaul. There is no magic bullet of ipads or entrepreneurship that is going to change our failing schools into amazingly successful schools. Sometimes it seems like we have found the answer. Like giving kids computers. Like unschooling or hackschooling. Like teaching kids to code. There are a lot of good ideas out there, but we can do them all and still not get better results. That’s because our schools are already doing OK, and thus any new idea we cram into our full educational system will replace something else that was already good for a lot of kids.

Yes, we should continually look to improve the way we educate kids. From where I sit, I see that we should particularly pay attention to how kids learn math, what math they need  to learn, what math they might want to learn, and how to creatively help kids get more of what they need and want while we still have them in this amazing system that seeks to help absolutely everyone to gain skills and knowledge. But we will get a lot farther in that enterprise when we acknowledge that we are trying to solve a problem that is really hard, and that the people who are at the front lines of our educational system — the teachers, support staff, parents, administrators, and higher-education faculty — are doing a lot of amazing things and having a lot of success already.

Math is jarring

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).

Writing a Paper and Asking People to Read It

Original image description from the Deutsche F...

(Photo credit: Wikipedia)

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.

Young couple with baby.

Young couple with baby. (Photo credit: Wikipedia)

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.)

Liberation Math: Penultimate Week

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:

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.

Who Benefits from Educational Intervention?

Last Monday in Liberation Math, the class, we had a great conversation about Logan LaPlante’s “hackschooling” TED talk. It’s a great talk, and I highly recommend checking it out. LaPlante is a winner and is doing great things with his education. He makes it all look easy, but extraordinary resources go into making his hackschooling education possible. His family skis a lot, which tells us that they have an income that makes that possible. He has an extensive network of opportunities, which means that his family is aware of the opportunities, that they are available to people like LaPlante, and they have the time and funding to allow him to access all of those opportunities.

LaPlante is a kid who is likely to be successful no matter what system he finds himself in — he’s charming and well connected. We can’t use him as a test case if we want to figure out if hackschooling is useful for a broad range of students because he is not a typical student, and he’s certainly not one of the millions of students struggling to successfully complete their education. Of course, it could be argued that if LaPlante was forced into a soul-crushing educational system that he might have begun to have difficulties. A bad education might have hurt LaPlante and decreased his chances at success in education and in life.

The fact is that educational innovations and interventions work — nearly all of them work, which doesn’t mean that we should implement every educational fad. We spend a lot of money on educational “fixes” that don’t really change things very much, often at a high cost. And the impact of the intervention depends a great dean on the population you start with. Suppose we take 100 well-resourced students like LaPlante, 80% of whom were going to be successful without intervention. If we do an intervention with these students that shows a 25% rate of improving student outcomes, then we see the following:

100 students, 20% struggling, intervention helps 25% of students

You are a student in this group who is doing fine or better. Was it the intervention that made the difference for you? To calculate the probability that the intervention moved you from struggling to fine, given that you are a student doing fine or better, we have to take the number of students who are fine in the end but would have struggled (5 students), and divide by the total number of fine or better students (85 students). This gives a 6% chance that the intervention is what made the difference here. We have to provide this intervention to 20 students in order to move a single student from struggling to fine. If this is an expensive intervention, that may be impractical for the results that we get, but will be entirely worth it if you are that one students and you possess the resources for change

Now imagine a population of students that has far fewer resources and experiences greater struggles and a greater likelihood of failure. Let’s say this new population of students has only 20% who are going to be successful with no intervention. We’ll imagine the same intervention that helps 25% of students:

80% struggling, 25% intervention success rate

In this new situation, if you are a student doing fine or better, what is the likelihood that your performance is a result of the intervention? Here again, we take the number who were struggling and are now fine (20 students) and divide by the total number who are doing fine or better (40 students).  This gives a 50% chance that your positive outcome could be credited to the intervention, a big difference from the previous population of students! Here we need to provide the intervention to just 5 students to move a single student from struggling to fine, giving a much greater efficiency. Perhaps this hypothetical intervention now looks great, but if it is an expensive intervention, requiring a lot of human capital, we still may not be able to provide the intervention to a broad range of students who need it.

How effective does this intervention appear to be? If it is implemented with the first population, then 85 students are doing fine or better, so it appears to have an 85% success rate. But if the intervention is implemented with the second population, then just 40 students are doing fine or better by the end, so it appears to have a 40% success rate.

Population General Educational Intervention GraphBut of course I made up the numbers about the population and the effectiveness of the intervention out of my head! We can model the situation in general with a population in which F out of 100 students are fine and we implement an intervention which is I percent effective. In this general situation the success rate will be F+(100-F)*I/100, which we can graph F on the horizontal axis and I on the vertical axis, coloring each point in the plane with the success rate as below, where lighter colors means a higher success rate. You can see that both the base success rate in the population and the effectiveness of the intervention constrain the overall outcome. For very successful populations, nearly any intervention will appear to be successful, but not all interventions that “work” with a naturally successful population will work with a struggling population.  And for an intervention that is nearly 100% effective, you can achieve amazing things with nearly any population. The trouble, to my mind, is that there aren’t any interventions that are 90% effective or better. Even the best interventions are going to be unlikely to get much over the 25% mark. Of course you have to keep in mind that this entire scenario is simply a “toy model” — it’s not reasonable to measure effectiveness simply by reporting a percent or lump students into two categories of “struggling” or “fine.”

Educational success is not always easy to achieve. Interventions, even when successful, aren’t going to solve everyone’s problems. When we see amazing educational success, we need to ask ourselves who is successful and why they are successful. Our educational system holds out the idea of advancement for all, but the reality is often that the greatest advances are made by those who were already set up for success. I’m really trying to wrap my head around these things and connect them to other ideas, so I’d love to have your thoughts!

What is a Course?


maze (Photo credit: woodleywonderworks)

I can see the end of Liberation Math, the course. As we near the end, I want to both slow down to enjoy the last bit, and to ask “What next?” As I slow down, I start to ask myself this course actually is. Specifically, what is this course Liberation Math, but more broadly, what is a course in general? Is a course a collection of goals and outcomes that we meet in order to be successful at the course? Are courses stepping stones to a degree or a specialization? Are they administrative units that are collected in order to provide certification and signal productivity? Are courses events along a possibly transformational route to a degree? Do we need courses, or can education occur outside of them? Do courses help us focus, or do they constrain us, or do they do both?

I have a few readings and videos to share about courses and education.

From your point of view, what is a course? What are the benefits and drawbacks of the way our schooling is divided into these discrete units? What has this course been to all of us involved in it? What is the best way to wrap up the experience and move forward? Can we carry something with us that breaks out of the bounds of the class?