Carl's Teaching Blog

A place to talk about teaching and learning

Author: Carl Oliver (Page 7 of 42)

CLOG: Thinking Classroom Intro and First Class

By

On November 16, 2018

In Classes, Clog, Uncategorized

Today I am about to get started on my Thinking Classroom experiment. I’m probably more nervous than I should be, so writing this will help. This post is to both organize my thoughts, and serve as a nice opening to a series of posts that I’ll write as this experiment unfolds. Today I am going to talk about what I’m going to try, but first I’ll recap how exactly this experiment came to be in the first place.

How this came to be

I was at the NCTM Regional in Kansas City, heading to an early morning shift at the #MTBOS booth, when the security guard informed me that the vendor area was closed. Naturally, I checked twitter, and saw a few tweets coming from a Peter Liljedahl session, so I headed over there to catch a little bit of the end. I proceeded to have my mind blown. Turns out the Thinking Classroom had dozens of great ideas behind it, and not just by the VNPS stuff:

 

Having a classroom built around thinking was my plan for years! 3 years ago, I stopped calling my classes algebra and started calling them Mathematical Thinking, to signal that this is going to be a different experience. Liljedahl’s research laid out a 10 point plan for making the class into the experience that I hoped to create, with research and charts to back it all up. The biggest headline of the 10 point plan was the Vertical Non-Permanent Surfaces, which I had piloted last year. The session gave me some ideas about notes, assessment, and how the teacher provides more problems for the students as the class progresses.

After the talk, I headed back to the booth and talked with Joel Bezaire who had also done some Thinking Classroom stuff in his school. He made it seem really realistic. He told me about Dry Erase Contact Paper, the kinds of problems he uses, the spreadsheet that randomizes kids, and some of the blog posts he used. He also helped me think of ways to make it work at my school, which is not traditional and I don’t have as much time with my kids who all have really different abilities. In another stroke of luck, Peter Liljedahl was doing a session around the corner at the infinity bar after I finished talking to Joel. He was super nice and answered my questions until well over his allotted time. I also was able to download a lot Dylan Kane’s Blog Posts about the thinking classroom before my plane home took to read on the flight home. The fact that all these stars aligned made it clear that the universe wanted me to try the thinking classroom this cycle.

Fast forward to this morning. Things seem pretty much set. First off I have students! 11 students signed up for my class for this cycle, and a few more will trickle in which is good. This means getting kids into groups won’t be too hard, and I can save some of the whiteboard paper I would have used for a class of 30. As each kid signed up I showed them this video from Alex Overwijk, and explained some big ideas. “We’re going to do group work, and we’re not doing a whole bunch of worksheets. Instead, we’re going to maximize how much time you spend in class thinking…” Once class actually starts, I’ll need to reiterate the main ethos of what the class is, while also getting them immediately working. In the past I usually started class with a speech about me, my syllabus and how great our time together will be, but this is always boring and dry. Instead I’m going to explain a little bit about what we are doing, use the randomizer, and then get into some visual patterns and some function notation.

_______________________________

Update: I taught the first class and it was pretty interesting. The class was small in number with 4 kids of 11 kids (there was really bad weather last night, so it’s possible that people couldn’t make it in). The small class size could have been a good thing since it lowered the chances for a wide scale revolt. I made this randomizer that is basically the one Joel Bezaire described, with some modifications for my small class size, unpredictable attendance. The scary thing that comes along with small class size is the lack of different kinds of thinking. What if the small groups only come up with a couple of answers? Today the class all went through the visual patterns and came up with a few different ways to solve it. In the future, it will be hard to ensure that all of the different kinds of thinking that need to be elicited will actually show up. Maybe I’ll have to write up imaginary group work and post it somewhere else in the room as a “shadow group.”

The math wasn’t that substantial today, but we did plow through it. All the kids say they liked it and thought it was a fun. I am not clear on how we will introduce precise mathematical vocabulary and notation. Function notation will be the first thing we’ll see how it goes. Maybe I can just roll it out!

What’s my role in the inevitable conversation about race in math education, and the #MTBoS?

By

On October 28, 2018

In Philosophy

First off, I’ve experienced the #MTBoS as a very welcoming place. Its certainly very white, but I’m used to that. At three I moved to an entirely white neighborhood, was the only black student in my class through 5 years of elementary school, and I went to primarily white MS, HS and Colleges (MSU, Harvard & Columbia). I can count the number of black males in my undergrad math education classes on my thumbs. When I reflect on how I made it this far, luck is the main answer. A slight turn of events could have led me to a trajectory that is out of this profession, or towards incarceration, or left me dead. A busted tail light and a cop with a mean streak could have easily ended my life because those are the values our country espouses, but I was lucky. My parents were also lucky, and wanted to risk giving their kid an education in a good school in the suburbs. Because of all this luck I became a math teacher and an assistant principal, and have become very comfortable with learning in primarily white spaces along the way.

In most of these spaces, conversations about race is avoided, or serves to further existing beliefs. When it comes up it feels like you are simultaneously on trial, the expert witness, and the lawyer presenting the case to a jury that you may need to ask for help later or just tension friends with. One day in middle school Dexter Adams was saying to a rapt audience about how his parents drove through Detroit and heard gun shots. I spend the night at my Grandma’s once a month, and I know that those sounds were probably fireworks or cars backfiring. After some deliberation, I remember deciding it wasn’t worth it to reply. It’s anxiety provoking.

It’s even more anxiety provoking in college where you’re trying to sub-consciously prove you’re not the affirmative-action case that people seem to think you are. Speaking out is a 3-ring circus. If you’re making a point or sharing your experiences, be sure to 1) get the point across, lest they miss it and go out and ruin kids lives, 2) be positive enough to ensure they won’t hate you for challenging their long-held beliefs, only to wind up a partner on a project later, and 3) be entertaining enough that they can’t exercise the privilege of checking out. It’s hard to do even if you have great teachers and classmates, which I’ve been lucky to have. It’s still hard to garner the emotional energy to have these conversations in my primarily white school now, where I swear everyone is on the same page.

https://twitter.com/crstn85/status/1055269644586704896

I was introduced to the #MTBoS through friends I had met that I wanted to keep in touch with. In posting and sharing the things that I wanted to work on, mainly PBL and PrBL, I was able to quickly find a number of people with great ideas, abundant resources and welcoming positive energy. Despite everyone’s different contexts and perspectives, everyone is willing to chip in because we are all fighting this larger, asynchronous, guerrilla war against traditional math education. Conversations about race, social justice, the whiteness present in math education have come up over time and they are handled well. When they happen, the conversations do a good job of unearthing the experiences facing us #MTBoSers, and the populations we serve, as we all navigate the systemic injustices that emerge in our classrooms. Maybe some of the conversations are successful because they result in people understanding someone else’s perspective, or further one or two people’s thinking about something. Along the way some people get upset, unfollow people, and send tweets to let everyone know they are checking out, “I came here for math, but what you’re posting now scares me…” But the conversation keeps moving forward. Forward towards giving all kids a meaningful math education sanitized of the white male privilege that has been baked in through so many years.

There is nothing wrong about saying the #MTBoS is a community that started with lots of white people. That is a result of the system that we live in. If all the math programs, and all the teacher programs are primarily white, it follows that math education twitter will also be primarily white. The danger is whether we don’t questing the role that whiteness plays in determining the culture of math that students experience. Math has been a vehicle that reproduces societal inequalities while being billed as meritocratic and immune from biases. If the #MTBoS set out on the journey of reshaping our students’ math experiences it was certainly only a matter of time before they must deal with the latent white male privilege. This is now complicated because, the #MTBoS, and math education, is primarily white.

In looking at the #MTBoS’s whiteness the most important question to me is: “Can this primarily white group of math educators effectively practice anti-racism?” I don’t know the answer to that question, but I’d argue a serious consideration of this question would further the conversation than the “Why aren’t there more educators of color?” The second question is kind like asking “Why is the Canary dead?” while the first question is like asking “How do we get out of this deadly coal mine?” White Privilege is a large intractable villain that’s buried deep beneath our society like those tunnels in Stranger Things. Fighting it is going to be forever and take our whole lives, and that of our kids. Focusing on easily measured successes like the number of POC may trick people into thinking that the battle is a finite one, when it’s really an infinite one. It’s a battle that will require lots of persistence and collaboration, much like long battle that currently being waged by the #MTBoS against the traditional math system. Traditional math education is part of what is currently impeding many POC from becoming math teachers, so it is no surprise that there aren’t many who could immediately join the #MTBoS in this fight. “Can this group of mostly white kids take on this big insidious monster that no one even sees, knowing that we might not look like the people who should be facing it?” Just like in Stranger Things, it may not be the perfect team, but it may have to be the perfect team.

As someone who doesn’t participate much in conversations around race on #MTBoS or on the internet, here are three things that I think should be considered by anyone:

1) We are all from really different contexts. Conversations are happening across a number of racial, political, geographical contexts, making it difficult to provide the necessary backstory to go along with what is going on at their school.

2) The work is messy. It’s hard to know whether a social justice lesson that worked in one context won’t get you a visit to the superintendent’s office in another district. And it’s hard to know what to say when the student who beamed during that lesson divulges that they overheard the n-word in the teacher’s lounge yesterday.

3) This is people’s jobs. We are all professionals, most people’s real names and institutions are stated. Most people don’t know how to have conversations and feel like they are assured to be safe when a parent, or a student, or a superintendent might see what you’re posting.

So it’s hard to engage in a conversation that crosses many contexts, about work that is hard in nature, on a platform that poses actual risk. All of those problems get amplified when you are a person of color and talking about race in a primarily white space. Does the person reading this tweet really understand the way I experience race in my context? Am I confident that the solution I tried with my kids will work in other people’s classrooms (and not cause unintentional harm)? Am I being viewed differently than the white parties in this conversation, and could that change the way I am viewed professionally? As someone fully aware of the thin sliver of luck separating my trajectory from so many others, I worry about that luck running out every time I open my mouth.

For me personally to be involved in a conversation about race I’d need 3 things. The number 2 thing I need is what I’ll call a brave space. A teacher I know shared an article with me after her school had some tough conversations about race at their school meeting. The article (which I can email) basically says that the idea of a safe space is a myth, as safety is usually preserved for the majority culture. This is more or less what a grad school program director told me as they defended a white student who offended the people of color in one of my grad classes. Race was born out of violence and it’ll probably take some violent conversations to face it, so a promise of safety could serve to stymie whatever could come out of the conversation. The 3rd thing I’d need is the same thing I’ve always gotten from #MTBoS, and that is constant support and positive energy. The likes, and the retweets of people who you might not be following yet may be the 1st thing that needs to happen. The 1st thing I need to happen is to not have my baby daughter having a 103 fever, and my other daughter not insist that I show her spiderman videos whenever my laptop is open. I’ve wanted to get on #ClearTheAir, or respond to some of the email chains that I’ve been on, but there just isn’t enough time, or at least not yet. Maybe after October.

Clog: Number talks for high schoolers

By

On October 25, 2018

In Uncategorized

For the past 3 cycles I’ve tried to start my class with a 5 minute Number Sense routine for my class. These have most often been number talks in format. I have come up with a few number talks trying to get at mathematical ideas that I think are worth reviewing with my kids. They have been somewhat successful, some kids really get into it, others roll their eyes, but on the whole it has been pretty positive.

The idea behind the number talks was to give the kids some way to build confidence around concepts with number, operations and proportional reasoning each day. The talks themselves are the little powerpoint openers that I put on the screen and go through each day. Here is an example (and a folder with a bunch of them):

Before the routine each day I remind kids that the talks are about thinking building up the kind of number sense they will need in order to be successful in school and in regular life. We use the “thumb” method to indicate that they have thought of something, and once the thumbs have all come up I’ll showcase individual ways that students thought about the problem. I’m trying to get better at not injecting my strategies because it has turned into a “Carl on stage” routine a few times by mistake. Then we go on to the next problem and during the awkward moment while we wait for thumbs to come up we end up, I’ll point to some of the strategies that other people have used to solve the earlier problems.

I’m keeping with them despite some struggles. A few students don’t seem to engage and almost seem like they are waiting me out. Waiting longer eats into the lesson, and talking to those students or looking at those students seem to kill the class culture, so I worry about that. One idea may be to have some kind of number talks related to the topic at hand, in addition to being about earlier math topics. That might help validate the activity for students.

#NCTM Regionals Stats Trumps Hate – Slides and Ideas

By

On October 5, 2018

In Conference Talks

Here are the slides from the talk. Thanks to the people who decided to be with me instead of seeing all those other awesome people who were presenting at the same time slot.

At the end of the talk we all brainstormed a few more ideas which are in the presentation, but I thought I would also post here:

Upshot New York Times

What’s going on with this graph

Gapminder  ted talk

Dollar Street

Spurious Correlations

Opportunity Atlas – NPR Article about it

Problem-Solving, Theory-Buliding and Collaboration: How I stopped sucking

By

On August 30, 2018

In Blog philosophy, Conversations, Philosophy

“Let them do it.” This was the constant mantra that Joe a retired NYC math teacher turned math coach repeated often to me during the classroom management struggles of my third year. At the time I was hoping to write material relevant to my South Bronx classroom by pulling from a different textbooks and 2007-era Google searches. Joe followed a similar routine when he made material to teach his East Harlem population using whatever people used in the early 90s. He quickly noticed something off about my tasks that I wouldn’t realize until after a few months working together. My efforts to control student behavior had seeped into a lot of the work that I had them do. Students weren’t doing the work of solving real problems, or making real connections with their prior math knowledge.  Instead they were walking down these narrow pathways of my own thinking. That’s exactly what I thought would help them, but in reality, I was doing them harm.
My teaching moves were as constricting as my curriculum, but I thought that this was necessary. My student population posed a lot of behavior and academic challenges. Changing the focus from my thinking to their thinking allowed me to stop worrying about their math levels or 8th grade scores and instead on how to build off the last lesson so kids really learn. When kids made mistakes, I typically told them what to do as clear and fast as possible. Joe, as politely as he could, shut that down.  Instead he’d ask me to start a conversation up at the front of the class to dissect the student error. He once said: “MAKE SURE THAT YOU NEVER, NEVER, NEVER GIVE AN ANSWER AND DON’T COMMENT ON ANY WRONG ANSWERS. Students will learn more from wrong answers that they discover themselves than they will if you tell them.” This is a quote from one of his emails, with his emphasis by the way. He continues, “They have been trained to look to the teacher to verify their answers and we want them to start depending on their own evidence for confirmation.” It was weird realizing that I was playing into this pyramid scheme of answer-getting, with the kids’ help, and preventing them from building their own critical thinking skills in the process. In trying to keep order, and keep my administrator from seeing chaos spill into the hallway, I played the answer giver that kids seemed to want, not the math teacher they needed.
To get students to do the kind of work they needed to build their thinking skills, I needed new tasks and new practices. One task Joe gave me that I still use today is Tina’s quilt squares. This task was, open, visual and had exactly the kind of thinking my kids needed to do. The old Carl would have totally strangled the joy  out of this. Taking his advice, I “let the kids do it.” The class was as quiet as any of my lectures as they all worked to find pattern. Some kids approached the task by actually drawing out each stage of the pattern. Others probed the tables for patterns in search of a larger explanation. These two types of student thinking were so interesting that I tried to validate both of them at the necessary end of class discussion and it became very clear which people should be presenting, and what I should, and shouldn’t, say about their thinking.
I thought about Joe, and my early years of teaching when I read The Two Cultures of Mathematics that Michael Pershan passed along. The paper’s author describes a tension among mathematicians among people who align with one of two statements:
(i) The point of solving problems is to understand mathematics better.
(ii) The point of understanding mathematics is to become better able to solve problems.
This creates a useful distinction of two kinds of math doers, the theory-builders and the problem-solvers. My first years was a time where I was torn between needing my students to become problem-solvers and wanting them to be theory builders. I was so focused on helping the students solve problems like being on the test, that I didn’t have time to let them really build the theory, so I figured I could do it for them with my awesome worksheets. The two styles seemed to be avenues for the kinds of approaches that students could work on and the kind of thinking that students could show in their student work. Looking back on it now, it was clear that I really didn’t understand what it meant for students to be problem-solving, theory-building, or doing mathematics in the first place.
The theory-building and problem solving avenues are different flavors of “Doing mathematics.” According to the Task Analysis Rubric by Stein et al., tasks are considered “Doing mathematics” if they:
  1. Require complex and non-algorithmic thinking.
  2. Require students to explore and understand the nature of mathematical concepts, processes or relationships.
  3. Demand self-monitoring or self-regulation of one’s own cognitive processes.
  4. Require students to access relevant knowledge and experiences and make appropriate use of them in working through the task.
  5. Require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions.
  6. Require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required.
The kinds of tasks that can fit into “Doing Math” could be either theory-building or problem solving, and possibly both. Tina’s quilt square was my first example of such a task, and seeing it first hand changed the rest of my teaching career. Students were doing complex thinking, analyzing the result, using multiple solutions. The kind of tasks I was doing before Joe would fall under the task guides memorization and procedures without connections, with little focus on making connections or, well, anything in that “Doing Math” category.
Before Joe, I spent hours doing the theory-building, and the problem solving for my kids. I then packaged up my results in a way that would help students easily retrace my steps. They didn’t see how these steps are useful, as they didn’t approach a real problem. They didn’t see how these steps could be built from prior understanding, as we only talked about theory superficially. All my efforts were going towards weren’t going towards making good future mathematicians, but good retracers. It stayed that way because any thoughts about doing things differently would throw my pacing off. It wasn’t until Joe’s frank meetings, and All-Caps emails, that I realized my current style had to change.
The whole point in going to teach on the east coast was to change the world with my teaching. Helping kids learn math seemed like the best path towards that goal because it could improve their test scores and make them eligible for higher education opportunities. Yet, I was lying to myself when I thought that it was enough for my class to do well on tests. My failed first test of calculus was proof that kids who do well on tests can still struggle at the next level. The right goal would be to make kids mathematicians. To help them actually learn how to solve big problems and make the connections needed to build theories. The application of those skills lies beyond just the math classroom, but can be actually used to think about tackling larger social problems and skills. The only way to get to my larger goal would be to not just teach Tina’s Quilt Squares the way Joe did, but to change my own thinking about my profession so I could make my own tasks to give to my future mathematicians.
After Joe, I sought to approach the the task of teaching my classes as my kids approached the task of learning algebra. I approached it like a problem-solver, looking to try and solve lots of little problems while simultaneously looking to connect big ideas and make sense of things like a theory-builder. Just like my students began to learn from each other and work things out in conversations, I began to talk with Joe and later other educators which helped me develop my practice. This was before I found the #MTBoS or joined NCTM or MFA, so this took a lot of time. Luckily Joe, and my Principal allowed to approach the task of improving as a teacher without having to retracing some steps or memorize some procedures, as it is probably the reason I’m spending another fall preparing to teach.
* * * * *
In writing this piece, I read W.T. Gowers 2000 article about The Two Cultures of Mathematics, of which I understood about 65%. I do know that is not about K-12 schools and what goes on there, but is actually a bit of a call two action about two cultures that exist among people in the field of mathematics. The prominent theory-builders belong to a culture that studies the fashionable ideas which are at the center of that field, while problem-solvers work around the periphery. This distinction reminded me a lot of math education. It feels like there is a prominent culture of around that approaches things in the old ways, like in this recent pro-memorization NYT article. Meanwhile the world seems to ignore ideas that come from problem-solvers working around the periphery in classrooms like Joe working with me.
The problem-solvers Gowers describes, who were creating the field of combinatorics, could actually benefit the theory-builders with their unique ways to solve problems. Technological advances would allow for major advances in combinatorics and math as a whole as the two cultures learned to collaborate and move the field forward. Hopefully writing this story of what happened in a cramped South Bronx classroom, might describe a different approach to how to improve teaching and learning. And hopefully the larger conference that it is a part of could promote the kind of collaboration across the world of mathematics education that has been seen among the problem-solvers and theory-builders of mathematics.

Page 7 of 42

← Previous

Next →

Recent Blog Posts

How envisioning the future helped us work together
As I write this we are all waiting for the results of the election. For me I’m trying to do something between waiting with bated breath for cnn.com to update. While I wait I will extend a little 3 day streak for blogging in the month on November. The thing that I keep thinking about […]

Pages

Latest on Twitter

Categories

Powered by WordPress & Theme by Anders Norén