Response to the #MTBOS Challenge: Discover and describe (and validate!) some core ways to improve at teaching.

If teaching is improved, the improvement is the result of a teacher making changes in the classroom.  Perhaps policy, professional development, or standards inspired that change, but what matters is what happens in the classroom.  There are a number of levers that can be pulled to change what goes on in the classroom, and a quick list could include the following:

  • Content of printed or electronic teaching materials
  • Way the teaching materials are introduced and explored with students
  • Relationships the teacher has with students, and the students have between each other
  • The conversational norms  among students and the teacher about the material
  • The methods of formal and informal assessment
  • The messages students receive about assessment, learning and mathematics as a discipline

A teacher could come in to work and tweak any of those things tomorrow, and notice a difference with their students.  The next day the teacher can take the change they made yesterday, and how it differed from previous classes, and try another tweak.  Over a school year of tweaking their teaching, as well as noticing, and responding to the differences, the teacher could improve at teaching.  Teachers making adjustments in their class and learning from what changes is perhaps the only way changes in teaching practice.

Traditional ways of changing teacher practice

The traditional methods of changing teaching, such as PD,  attempt to create the catalyst that starts the teacher along a chain of reactions of tweaks that will lead to changed practice.  A one day PD gives teachers 3 examples of new lessons with the expectation that teachers will take those 3 lessons, use them, and question their current practices in positive ways.  The PD would then be a one-time catalyst of future growth.  Of course if the chain reaction dies out before the teachers leave the conference hall, then it will never have any intended effect, even if the teachers pantomime the 3 lessons and go back to business as usual next week.  This may not be the fault of the PD either, the teacher may be in the middle of working on some other part of their teaching, or have a different adult learning style.

In this traditional model, those in charge of improving teaching can only worry about the clarity and power of PD’s ability to inspire a change in the teacher, but cannot support the continual process of experimentation and noticing the difference.  What could be a new way to do it?

Supporting The Process

Blogging sounds like a perfect method towards supporting the process that teachers start in their own classroom. It provides a place to document the little changes they make  and also get feedback about those changes.  They can read about things that other people are doing in their classrooms they can learn new things to try in their room.  Thus, the blogosphere serves as a 24/7/365 set of ideas that can catalyze a chain reaction of teacher growth whenever the teacher needs it (as opposed to the 3 designated days on the district calendar).

There are certainly other ways to spark, support, and push the on-going teacher development process taking place inside their classrooms.  For people who aren’t interested in typing, there is a lot of value in talking about teaching with your peers.  A structured way to do this would be in a professional learning community and looking at different products of student learning through protocols.

Teachers reflections about their teaching are only as good as the information they have about it.  Having clear formal and informal assessment practices would allow them to have more information to base their next decisions on.  Other teachers have learned from having student surveys and feedback forms about their teaching.

Nothing is more important than doing something. There are also a number of specific technical things that can be done by teachers to improve a specific facet of their teaching.  I think part of what you’re asking in your tweet is how do we get people to improve their teaching when they might not want to otherwise.  We can package up a bundle of practices and air drop them into teachers lounges across the country, but it won’t make a difference unless teachers are actually trying them.  Actually trying means accepting the fact that constant change and growth in your practice is as much a part of a teacher’s life as having summers off.  (It’s not just teacher’s.  Surgeons, artists, scientists and many other professions have to hone their methods and explore new procedures


It all started when I was reading the Michigan State chapter of How To Build a Better Teacher on my way to work and I started getting all excited.  Since it was about my Alma Mater, and talked about the elementary school near my brother’s apartment, it was as if the fight song was playing in my head the whole time.  By the end of the Chapter, I was excited about really tearing into a problem with a class discussion.  Excited might not even be strong enough.  I was ready to run through a pedagogical wall.  When I was back at Michigan State we saw some of the footage of Magdalene Lampert and thought about how I always wanted to have a class discussion that could function like that, and assumed I’d have figure out in maybe my first 10 weeks of teaching.  The truth is, while I’m starting my 10th year, I still feel that I have a long way to go.

Why haven’t I got the class discussion figured out?  It’s rough having long deep conversations about math in my school, for the littany of reasons that one would expect (large classes, complex content, pacing concerns, classroom management, for starters), but in all honesty it’s probably me.  It’s probably that I just get satisfied too easily, and don’t try to push it.

But today’s class could be different for three reasons.

1)  I have small classes.  My class is only partially full because I’m holding spots for the kids who are going to be transfering from their school in a few weeks.  We always save spots for kids who report to their school in september and then decide to leave in october, and this year we are setting those students up with spaces in set aside classes.  Since I have a small group, and I have less pressure, it has led me to try more of this “Become a different teacher” Goal that Ihave for the year.

2) The content is perfect.  Today’s lesson was talking about representation, and connections, and how they should be represented in a math project.  In all honesty we could have done whatever I want because I don’t have to dig in to the course until October’s influx of new Students.  This lesson today was designed to get students comfortable with the NCTM process standards, so they can understand how they will get graded.

3)  I started slow, but I am going to finish fast.  I was as pumped about it as Apollos Hester, and the motivation was going to take me over the top.  Today is the day.  We are having the discussion.

We started the class talking about estimation as we always have, then we focused on two problems.

The first was a “5th test” problem, where there had been 4 test previously and what would need to be scored on the 5th in order to reach a certain average.  The 4 tests were 98, 96, 97, and 89, and they needed to find out what score the 5th one should be in order to get a 95.  What students got stuck on was the fact that the 4 tests actually averaged out to 95 on their own.  It was strange how much of the class was confused because the number 95 was the same number they were starting with, and the same number they needed.  All of a sudden, we were doing it, we were having a conversation about what this means, and it was pretty natural.  The students understood that if a test lower than 95 was scored, and a test higher than 95 was scored, it would lower and raise the average, so it followed that the number 95 would be the only one to maintain the average on the final test.  I guided them through this proof, and it wound up the students all writing my logic as the explanation for the problem.


The conversation about the first problem didn’t lead to the rich mathematical discussion that I wanted, but I still had the Skittle problem.  Roger has 2520 skittles, how many would he get if he had to divide them among 2, 3, 4, 5, 6 or more people.  There was too much here to not have all the students get engaged, and we can have the students develop the function during the conversation.  We are DOING this!


The class worked silently at first, and I circulated to gather the students’ various responses.  The goal of this problem was to think about representation, and we had talked earlier about how graphs, tables and equations were all great representation, so I took note of these things as they popped up around the room.  One student tried graphing, so I had him make a neater graph on graph paper to show up under the document camera.  Another girl who said she hates math on the first day made a table out to 10, so I had her write it up on the board.  I was setting the stage for a pretty dope conversation.


We got started.  I asked kids “What are the ways they could represent this?” The table was already up there, everyone agreed with the numbers, the graph was an obvious choice, and I put the student’s graph on the document camera.  We had a diversion about the graph, where asked them about what they thought the graph would do, and I put a couple of extra points on Walters graph that we knew from Janice’s table.  Seemed like a good time to talk about asymptotic behavior.


Then I asked if anyone had represented it as an equation.  Shaking heads.  I asked everyone to think quietly about an equation and then we were going to construct the equation based on each others thinking.  I was amped.  After 5 minutes I wrote everyone’s equation on the board.  I asked Janice, she said “S = 2520 + P.”  This seemed like addition infatuation, when people think it should be addition just because.  We could totally break down why that operation isn’t important.  I didn’t say any of this, I just quietly moved on to the next student.  Roger, gave me “S/P = X.” This seems like we could quickly touch on which variables are important here, and what variables even mean.  Next, Clyde said he didn’t know, and Walter said “S = x.”


Is it weird that I was excited about having a bunch of “wrong” answers on the board?  I was about to launch into one of those conversations about math where the kids talk about what they were thinking, and defend their points against what other kids proposed, and develop conjectures when all of a sudden Clyde says:

“Is it s = 2520/p?”

And my response was:

“Oh, That’s right.”

WHY DID I SAY THAT!!?!?!?!!!?????  The blood left my face as the impact of that statement reverberated through the class.  My reflexive affirming of Clyde’s statement triggered a cascade of verbatim copying across the class.  Once they all had the “Answer,” I might as well have been teaching Charlie Brown, as the rest of the students begin focusing on packing their bags.  Before I had time to recover, Walter reminded that class had already ended, and filed out of class with rest of class past the board full of answers that I had accidentally confirmed as “wrong”.  Everyone filed past me as I lamented another opportunity lost.  Hopefully they still learned something.  I guess I still have a lot of learning to do, and a lot of bad habits to break.


Have you found ways to improve in this area?

This Week: 3-day week. (Not a typo)

This week’s three day week, due to NYC’s observance of Rosh Hashanah, has been an interesting one for me.  It serves as an adjustment period away from the almost full time scheduling that I was doing up until last Friday, and the full teaching load, and department coordinatorship that ramps up next week.  Here’s what I’m doing with my short breather.

What I’m teaching this week:

I currently have about ten students enrolled in a class called mathematical thinking, and we have been doing a variety of different tasks including Dan Meyers meatballs, and an almost daily dose of estimation 180.  In order to capture their thinking I plan to have our first of for reflections this cycle, the last of which will be their final project.  The reflections I have done in the past feel to the students almost like a bookkeeping task.  I’ll tell them “you’re just writing about work you already did,” and some grown about having to write sentences, while others dive into the task while adding thought to what they did.  I’ll tweak my prompts for this year, and perhaps…

What I’m blogging this week:

…I’ll write a blog post about how the new reflection prompts go over with my students.  In addition to this task I have a few posts sitting in drafts, and in my head, that didn’t get out because of my unsustainable and somewhat unbalanced approach to scheduling the students (and I might write some about that, too).

What I’m thinking this week:

I’m thinking a lot about what I’ve read in the book “How to build a better teacher” and the sections about Deborah Ball and Magdalene Lampert’s teaching at Spartan Village elementary school.   When I was a student at Michigan State, Deborah Ball had left for U of M, but Magdalene Lampert was still there and I even “borrowed” a copy of her book “Teaching Problems and The Problems Of Teaching,” but I always kicked myself that I didn’t learn enough about “That Kind Of Teaching” during my time there.  Now that the ideas are getting brought back to life, so has a desire to return to my college aspirations (the teaching aspirations, not the drinking or the fashion sense).

This Week: Emerging From The [Metaphor for 'work']

Ok, so want to hear something weird about this school year.  I’ve been going to school for every day that wasn’t a holiday since the week I got back from my honeymoon (August 15th).  That means I’ve been working for a month when half of that was supposed to be vacation.  For many of the past two weeks of the school year, I haven’t even gotten home before 7, some days I’ve gotten home at 10, and one day after helping my wife’s school we got home at 12:30.  The weirdest thing about that?  I’ve only taught two (two!) classes so far this year.   I have developed an acumen of sorts for putting spreadsheets together, and using those spreadsheets to upload schedules.  Our school has wildly unique schedules for each student, so I have been helping out a lot with that.  Since our school is also running a rolling admissions situation, they are going to let in a group on October 1st, and I am going to pick up my teaching load with that group.

Since this year started, it’s been pretty dark and lonely for me and my spreadsheets, and I don’t think I should wait for it to end so that I can get back to my passions.  For the next two weeks I decided to pick up one class, to help with some of the school overflow so now I can talk about teaching and learning!

What I’m teaching this week

This week I am teaching problem solving for my “Mathematical Thinking” class.  I aim to work on the curriculum that I did last fall.  One thing I am surely going to do is work in more estimation. One question I had today was “How many flourescent light bulbs are there in the school?”  Last friday I asked “If I turned 33 on Sept 1st, when will I be 1/3 of century old?”  I like doing the big problems, but I think I am going to work on having a big discussion as a group about them.

What I’m blogging this week

Something.  I’m going to try to emerge from my excel tabs and write something.  Baby steps.

What I’m thinking this week

This week I’m wondering what is the thing I’m missing.  I always watch basketball players and think “If you just get a 3-point shot” or “If you just get a left-handed layup”, as if a couple hours in the gym would make them an all-star.  Assuming that it’s more or less true, what’s the thing that I’m missing?  I think it’s having productive, amazing, Magdalene-Lampert-esque classroom discussions, but I don’t know exactly how to get into the “gym” and work on that.

Read books?  Moderate other people’s subway conversations?  Do Squats?


With issues of race arise I always wonder, “should I talk about it?”.  Typically, my willingness to talk about it is less than other people’s willingness to talk, and is rarely matched by people’s ability to objectively listen.

When I arrived back from honeymoon to the images of life in #Ferguson after the murder of Mike Brown I was so unaware of American Politics that I needed to get caught up, and the highly polarized media reports and shifting stories made that task difficult.  As the facebook/twitter/etc. conversation steered away from this one incident and towards the larger topic of race in America, and people began connecting what happened to incidents in their life.  Somewhere between reading this post about privilege and watching John Stewart’s coverage of Fox news’s coverage it got stuck in my head that I need to write something about this incident, and what it means for our country.    But it was hard to figure it out, one, because of the confusing nature of the incident, but mostly because of the role of race in America.

Race is to defined as differing sub-species of people, but in America, race usually refers to our social system.  From before the country there was a need to associate citizenship, with race, with being White specifically.  Owning land, and wealth was important, as was being male, but being white was always really important for early Americans.  More important, were our national ideals of freedom and liberty, and so the flawed ideas about race led to a number of social movements to direct our country out of this flawed way of thinking.   Fast forward to the legal mandates that followed the civil rights movement, and you’ll notice a country rapidly distancing itself from it’s past.

Then something happened.  I’m not sure what it was, but the achievement gap stopped shrinking, the number of high school graduates flattened out, and a lot of the progress stopped progressing. Perhaps it is related, but a great deal of young black males began getting incarcerated perhaps having to do with overly aggressive sentencing rules.  It appeared, and still does, that the nation has started regressing towards the pre-civil-rights-era social norms. The story of the black person on the rise, living the Cosby-esque middle class family life, never really disappeared.  But, it does have to compete in the nation’s eye with the black person as a threat.  The fact that these two story lines are competing at all conjures up a short-sighted America, wrestling between the promise of social change promised half a century ago, and the troubling, deep-seated, racial beliefs impressed on the country from the early colonial days.

Mike Brown’s few remaining moments tell the story of this struggle for America.  Mike Brown was a recent high school graduate, headed to college, and perhaps a successful life as his family expected of him down the road.  Certainly America wants this story to happen.  This is the kind of story that I want to help play out, as we all would.  At the same time, there is the competing story about Mike Brown, the 18 year old who, to the officer’s knowledge, was walking in the middle of the street in defiance of the town’s laws.  The idea here is that young black teens could head down a road towards crime, perhaps violent, and need to be punished immediately and severly.  This is a story that I also see as an educator and that troubles me.  The “avoiding crime” story of telling a student what not to do, and punishing them accordingly doesn’t coincide with any kind of education model for people.  People get motivated about where they are headed, not where they shouldn’t go. Surely both stories need to get taken into consideration when talking to students, but we seem to be emphasizing the latter and are thus putting the former in jeopardy.

We’re conflicted about whether our nation wants to nurture our young black males in our schools, or punish them in our prisons.  Our politicians who emphasize the allure of lower crime rates but not school equity are perhaps why so many black students in certain neighborhoods get stopped by the cops, but not nearly enough of them graduate high school.  This problem, then, is not just for people in these neighborhoods to consider, but for every member of the country who is voting.  When we vote on our anti-crime bills, or our state’s prison-building bond initiatives, we’re deciding what we as a country should emphasize.  Perhaps, if Ferguson didn’t have so much money to spent on surplus army equipment, they would have had to put more effort into maintaining better community relations.  Perhaps if that money was spent on programs to engage teenagers, Mike Brown would have had something better to do.  If we don’t like what our public institutions are doing, it is up to us to change them.

The emphasis on cracking down on teen crime also implies that such harsh treatment will be effective.  When we impose a consequence on a kid before we have a conversation with them, especially when that consequence is meant to “teach them a lesson”, what are we really teaching them?  As an educator, I put a lot of work into planning lessons, and the best ones usually don’t result in kids learning stuff.  When people choose to impose harsh punishments on kids to “teach them a lesson” it is quite an insult to the word lesson.  Swerving your police car and waving a gun at someone might not teach them a lesson, or at least not whatever lesson that you are intending to teach.  If they are supposed to be thinking about how they need to respect traffic rules, that might not be what is understood, what might be understood is that you don’t value them as a person, and they should react out of fear and anger.  I was at a school once where a 6th grader was getting arrested.  Parading middle-schoolers through their class and their school in handcuffs might not be teaching them to avoid crime, it might just be teaching them to not trust their teachers and that they can’t feel safe at school.

Ultimately, it is up to us to choose which narrative of young black males we want to emphasize.  If officer Wilson chose to emphasize how important and valuable it would be to have a 6’4″ black male attending college in a couple months he may have thought that it isn’t worth shooting all 6 of those bullets, maybe he could have not used any weapon at all, and perhaps have talked to him about why he was in street.  If Brown was the starting left end of the local football team, would he be approached the same way?  Would he have a different emphasis if he was stopping a police officer’s son?  Mike Brown could have been example to the community of what happens if you do everything right, but instead the officer decided that the best example to make of him would be that of a corpse, perhaps so his friends could “learn the lesson.”

The sad part of this incident to me isn’t necessarily the treatment of the protestors (which is a whole other conversation), but the fact that the Mike Brown, the potential criminal, was deemed more important Mike Brown, the potential college student.  We’re setting dangerous precedent by saying the value of a young Black person’s life is measured by how threatened they make another person feel, and a Mike Brown court case seems like it will offer more support for this idea.  This makes a statement about the worth of Black people that seems to echo the “punishment without trial“, or even the 3/5ths clause in the constitution, and is evidence of a continuing slide backwards. It might be a scary time for U.S. race relations.  Let’s hope it’s scary enough that we all decide to move forward.  Deciding what to emphasize, and what not to emphasize, is an easy first step.