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.


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.

Anger and Shame in my Teaching, a sort of anti-liberation-math

English: A metaphorical visualization of the w...

Photo credit: Wikipedia

Last week I wrote a post on another blog about being disappointed in students, which is something I struggle with and want to eradicate. Yesterday I realized that I had misnamed the problem. It’s not disappointment I struggle with, it’s anger. Anger isn’t a professional emotion as a teacher, and it makes me feel distant and disconnected with my students. My mission in life is connecting with students, so why would I repeatedly entertain an emotion that hurts my chances at living my dreams? And I do mean that I entertain the emotion of anger. I tolerate it, nurture it, and feed it. And I don’t just do it as a teacher. I do it with my kids, getting angry when I could be connecting. I do it with my spouse and my family, getting angry when they need me.

I have been studying shame for some time now, particularly shame around mathematics, which typically means shame around math in a school setting. Shame and anger frequently occur together, often in a cycle, so I should have suspected that my problem was really anger. Here is how it works, and how it connects to shame for me.

I ask students to do certain work and I have certain expectations of them and the work they do. I can do this because of the power that I have in the classroom. This is the power that I have over their grades, and the power that I have because they have been raised in a school culture of compulsion and obedience. When they do not do the work, or they do not meet my expectations, I feel that as a threat to my social self. I feel disrespected and I feel a version of shame because, in my eyes, the has student decided that my expectation was not important to them, and thus that I was not worthwhile. The work I ask for and expectations that I have are the clearest evidence of my relationship with the students, so when that is threatened, my relationship is threatened.

I respond to that feeling of shame by getting angry. Shame is an extremely uncomfortable emotion, so people will usually seek to cover it with another emotion, and anger is a popular choice. When I am angry, I can focus on the student as the problem, rather than the hurt, disconnection, or shame that I feel as the leader of the class. Furthermore, I can blame my feelings entirely on the students. The compulsory nature of education means that they should be doing what I say, and if they don’t, it is the students that are in the wrong, not me, the helpful teacher. And even worse than that, once I am angry, I don’t just want to let the problem slide, I want the students to know that I am right and they are wrong, to punish them and to have them accept that punishment as their rightful due.

Honestly, its a gross thing to admit to, and is the opposite of everything I want to be. I suspect that we all have this kind of shadow side, working against our dreams in the background even while we strive toward them in the foreground. I’m a good and caring teacher with a mission to connect with students — why would I keep this anger and meanness around? It’s my defense against being too vulnerable. I don’t want to look at what it means when students don’t do assignments, stop participating in class, or give up. Yes, sometimes it means that the students have things going on that don’t have anything to do with me. However, it can also mean that I am failing to build my relationships with the students and failing to find genuine ways to help them build power with and through math. It can mean that I don’t have real relationships with the students at all, only a dance with the students in which they carefully display certain signals in order to get the maximum grade with the minimum of effort. I’m responsible for that dance at least as much as they are, if not a little more. Why should they not be doing this when I have to admit to often falling back on my default job as a teacher, which is to compel students to do a certain series of tasks, to assess them on those tasks, and to assign them a letter grade that they take with them as a credential or a black mark. It can mean that I’m actually hurting them through my participation in a particularly oppressive subject within an oppressive educational system.

I sure want all of your thoughts on this one, whether you are a student, a teacher, or anyone who gets in the way of their own dreams and connections!

Disappointment and Hiding in the Classroom

I’ve been noticing lately my disappointment in students. I don’t want to feel disappointed in students. Honestly, I don’t want to feel disappointed in anyone. Who does? But you might argue that we have certain expectations for how the people around us will act, and that people don’t always meet those expectations. When they don’t, I am justified in feeling disappointed, at least provided that my expectations were reasonable. The trouble is that  disappointment is counterproductive, and for me it is part of an overall tendency I have to disconnect with people.

Let me look at this a little closer. I have certain expectations for my students. I set those out for the students by giving them specific assignments (“turn this worksheet in on Monday” or “write a blog post about your problem-solving process”), and I lay them out on the course syllabus by telling students to come to class, check their email regularly, participate, and so forth. There are also a collection of expectations that go unspoken by me. I expect that students will be thinking about what they need to do to prepare for upcoming exams, even if I don’t give them explicit assignments. I expect that students will ask for help and support when they don’t understand something after class. I expect that students will monitor what they do and don’t understand. I expect that students will give me their best work, and won’t piece together something at the last minute. I often say things which imply these expectations, but I’m not always explicit about them. Also notice that not all of these expectations are realistic.

If a student doesn’t meet these expectations, I get cranky. In between classes, if I am expecting work and participation from students that I don’t see, I start to worry, and to run my “disappointment tape.” Typically it involves me getting frustrated and making up a lot of things that I imagine to be happening with the students. I imagine them as uninterested in the course, not dedicated, not hard-working, wanting to get away with not doing work, not caring about thinking deeply, not caring about interacting with me or other students. Yes, there’s some really ugly stuff hiding in there. The thing is that I don’t know that any of that is really happening. Mostly, I think what is happening with me is that I want this connection with students, and most of what I have to connect with is their work. When the work isn’t there, I feel rejected. I imagine the students pulling away from me, and I rush to pull away from them first, by getting “disappointed” in them. Most of the time, I can get back my connection with the students simply by being around them — it is the time in between classes that provides a space for these feelings to grow.

Students don’t always do what we teachers what them to do. In fact, people in general don’t always do what other people what them to do. So we get anxious about our relationships and our standing with other people. In school, this means teachers get frustrated with and disappointed in students. What do students do? Students learn to hide from the disappointment of teachers. They hide and they lie so they can save themselves from the consequences of expectations unmet. Students hide so that they’re grades aren’t in jeopardy and they hide so that they can maintain positive relationships with the powerful people that are important to them. Students get into a habit of hiding, so that it seems as natural as breathing. I remember it well from the last time I was a student — doing work I wasn’t proud of and hoping it would slip by without notice, making up excuses for doing work late or stretching excuses that were technically true but not really accurate, trying to look good in order to get away with things. As a teacher, I know that students are doing these things, but I ignore it, acting as if students are going to meet all of my expectations, and then getting disappointed when they don’t. Because I am required to assign grades to students, I maintain and perpetuate the fiction that grades mean something objective, when the reality is that they’re just a somewhat arbitrary record of how well a student met my somewhat arbitrary standards about a somewhat arbitrary collection of activities and topics.

What if I stopped doing this? It’s hard to imagine. Could I stop having expectations of students? What would happen to me and to the students if I did? What if I kept having my expectations, but was more honest about the fact that I know students won’t always meet them? What’s so bad about the students not meeting them anyways? Could I keep the expectations, but let go of the disappointment, simply connecting with students about what happened and deciding what to do next? Could I let my students be honest with me about the unrealistic nature of my expectations and with what really happens for them in a class? Could I let students formulate their own expectations, help them to make those expectations realistic, and then help them to live up to those expectations? Could I create a classroom environment in which I helped my students evaluate themselves? Wouldn’t this cause the very foundation of objective and rational subjects like math and science crumble because students would start writing expressive poetry about how math makes them feel and giving themselves an A++ on every assignment?


Woman with hands in air

Showing Work in Mathematics

Last week, Karen Young stopped by this blog and made a comment that led to a great discussion that has taught me a lot, so I decided to pull it out and capture it in this post. First, she said in the first comment on this post:

As a kid I could do math in my head, doing basic mathematics without using a calculator or pencil (when I do laps I still do fractions in my head). Every test, there were marks off for not showing my work. If I answered a question on the board I had to show my work. Well sometimes I couldn’t do that because my brain “knew” the answer.

I replied to that point (and yes, I edited a typo in my original comment):

I really think your point about showing work is interesting — I know that the curricula used in my area are all about showing work, often showing multiple methods. I can get that we want students to be able to communicate their thinking, but can we do that without making it drudgery?

To which Karen made a response that really blew my mind:

Angela, when did we decide, as educators, that we had to show work in math? My grandfather was an accountant and brilliant with figures but he did them in his head. That is how I did math when I was young. Having to show it actually made me have to rethink my answer, leading me to doubt my accuracy, which lead to me “showing my work” and making more mistakes. Math was intuitive, almost instinctive prior to that point. Now it is something I fumble over, except when I am swimming laps and almost in a trance. Why is intuition in learning a bad thing?

She further expands this in a later comment:

We always remember how to tie our shoe because of motor memory, so if we’ve created a motor memory (or song memory) through the physical teaching of math, doesn’t that link remain? Especially if we exercise it everyday? At some point, if we approach a subject in the wrong way, I think we can break the ” old link” in the brain, by creating the new “show your work” path. And do the two conflict? In my case, yes. I am intuitive by nature and am used to my brain making what appears to be sudden connections but I am in fact just allowing it free rein to make associations that lead to “aha’ moments.

So, why do we ask student to show their work in math? Here are some reasons I came up with (if you have more reasons  or more interpretation of these reasons, please lay them out in the comments):

  • We believe that explaining the mathematics is an integral part of understanding the mathematics. That is, just as Karen says, we mistrust intuition. After this conversation with Karen, I think that this mistrust may be wrong-headed. I’ve known plenty of students that could see answers that they couldn’t fully explain, and I think it is patronizing of me to not believe in their understanding simply because they can’t walk me through a solution step-by-step in a way that I expect their mathematical learning should have trained them to do.I see both my own 6-year-old and a fourth grader I tutor working with the TERC Investigations curriculum which asks them to draw out solutions to problems (for the first grader) and to show two different methods for a problem (for the fourth grader). These both seem like they might artificially interfere with a student’s process. You should of course draw out solutions to a problem, but only if that’s the way you solve the problem — if you count on your fingers or see the answer in your head, the drawing step is artificial, meaningless, and can possibly get in the way of your own method. And you should explore different methods for doing, say, three-digit addition so that you can understand the process and settle on a method for yourself that is actually meaningful, but why would you need to show two different methods for the same problem simultaneously? (And see Karen’s comment below this — if you were comparing answers with a peer you would get exposure to multiple methods for the same problem in a more authentic way.)
  • Some problems are complex enough that they require record-keeping. This might be careful recording of useful data, recording results and methods so that the problem can be tackled again after a break without losing momentum, or writing an explanation to be shared with others. Asking students to show work even on less complex problems may help to train them to do this kind of recording so they have it available as they problems they are going to tackle get more intense. I think this is actually a good reason to show work, and the question for me becomes whether we can do this kind of training in an authentic way that still honors intuition (which is really just deep, non-verbal understanding), but helps students gain facility with communicating.
  • We don’t trust that the students are really doing the work we set out for them, or we don’t trust that they are using the methods we want them to use. This could be because we think the students are cheating or because we think they are using techniques or technology that we don’t want them to use on the problem. I have been noticing lately when I make choices as a teacher because I don’t trust students. It is more often than I would have thought, and I want to find a way to stop and increase my trust of students.
  • As instructors, we want a window on students’ thinking in order to help them. If we only have an answer, and that answer is wrong, then we don’t know anything about where the student went wrong — it could be as simple as an error in what numbers were used, but it could be a misunderstanding about the mathematical concepts. This is, I think, another good reason for having students show work, but it is really only needed if students are struggling.

I laid out these reasons for Karen, more or less, as part of the comment thread then asked:

How do we support student intuition and still help them to develop record-keeping and communication skills that will serve them well as problems get more complex? And if we are having them “show work” to help develop those kind of skills can we make sure that it is authentic, not made up after the real work is done to satisfy requirements?

Karen answered:

When we look at teaching math we are, in a sense, trying to develop two skills within math once the basic math foundations are in place. The ability to edit numerically (see your mistakes) and to be able to reason mathematically (knowledge, logic and intuition). This is predicated on the foundation being strong (but we both know sometimes it isn’t.) In English, I have had many students who have a wonderful writing style, a true “voice”, but their grammatical skills are terrible. I have always counseled them to keep writing and find themselves a good editor. Not every student can see their mistakes, which is why we have groups share papers to help proof at all grade levels. So why can you not have math conversations and math proofing shared between students? If sharing is how we build knowledge and understanding this would help support student math learning and math intuition.

I think this is a great suggestion, and a profound one in mathematics. If students are in conversation with each other, then communicating mathematics and showing a record of your work become authentic tasks that allow you exchange ideas with other people.

Thanks, Karen, for the great conversation! If you have any thoughts about your own experiences with showing work or asking students to show work, or if you have thoughts about why students should (or shouldn’t) be asked to show work, chime in!

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.