Carl's Teaching Blog

A place to talk about teaching and learning

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Making Connections Across Math’s Changing Landscape

One of my co-workers was saying that she has no where to talk about what she is learning and how she is trying to grow as a teacher. She said that she is reading a lot of books, and trying a lot of things, but doesn’t have anyone to share it with or have a lot of time to process it. This was exactly the kind of thing that I talked about in my talk at #OAME2019 a month ago about why teachers need to connect online.

The basic premise of my talk was that teaching is constantly referenced in relation to the factory model which was the hottest economic opportunity as compulsory schooling went viral. Unfortunately, the factory model wants workers to follow the instructions to carryout precise and scripted movements to produce widgets, while schools need teachers who are able learn and grow in order to plan and implement innovative and dynamic lessons with students. The professional and emotional support that turn of the century factory workers need is vastly different than that for teachers. The kinds of support teachers need for this job may exists in patches, subject to grant funding or the shifts of political winds or under the eye of visionary administrators, but for many it doesn’t exist. Schools may make the shift, but the regulations and rules that allow schools to exist are essentially carved into stone and require loads of legal action for change. While it’s good that education’s importance is underscored by it’s inclusion in laws and regulations, it’s not good that people have to wait for change. Luckily we have the possibility to construct our own support network through the internet. We can write and share about things we are doing to learn and grow. By sharing we open ourselves up for feedback and perhaps provide writing that others can learn and grow from. 

Here are the slides from my talk:

It was great being in Ontario and giving this actual talk. Thanks to Sam Shah, Laura Wheeler, David Petro, Cal Armstrong and everyone else who was attended. If you were there, or if you weren’t and just think my slides are valuable let me know what you think in the comments. Better yet, let me know when you start sharing stuff on line!

Clog: Big questions to answer as I ask the #thinkingclassroom to dance again

Our school is beginning the 4th term. This means all new classes, all new kids and another fresh crack at the #ThinkingClassroom. I was debating about trying a different class this cycle, but the planning for this new class failed to materialize as I spent too much mental energy prepping for #NCTMSD2019. Repeating the class is important to me because the cycle ended in a way that felt unresolved.

A more deliberately comfortable classroom

Two very different students kids struggled from the beginning last cycle. It seemed like they didn’t know how to say they felt uncomfortable. My best guess was that the source of their discomfort could be one of three things:

  1. The whole VNPS routine
  2. Being in a math class in general
  3. Other things going on in their lives.

With the first two, a warm vibrant environment and lots of interesting math problems should be enough to win kids over. With the third, it seems like a larger effort for making the kids feel valued and competent would be useful. For the two students who struggled, their parents or their social worker made very clear that they had some other things going on in their lives, and no one had an easy answer for any of those things. Ultimately they both struggled with all 3 of those possibilities, and neither was able to gather enough momentum for the magic of the Thinking Classroom to have the same effect that other students were experiencing.

With more time, the discomfort may have gone away, but our block-scheduled, 8-week cycles made it hard for kids to really lock in. Instead students who aren’t excited to share or work with the group, a strong desire to ‘finish’ and get back to their seat, and frequent trips to the bathroom, college counselor, nurse, etc. One of these two kids stayed in the class a little more than the other, but they both struggled mightily on the final project. By the end of the last 8 weeks it was pretty clear that the uncomfortable students missed out on the practice of solving a lot problems, understanding the quadratic vertex form among other big mathematical ideas of the class, and a lot of the relationship building to support them as they finished the class. One of them scraped by and passed, the other did not.

Despite having the most positive experience I’ve had in years, I could only think about these kids as I looked to teach this class agian. They didn’t succeed with the math, which was disappointing, but they also didn’t succeed with this method. The primary reason I adopted the Thinking Classroom was to repair their negative relationship with math, but the last cycle seemed to just confirm that relationship. That doesn’t mean it didn’t work! I’m confident that I need to be more explicit about the kids relationship with math and look to find ways to help kids jump back in to the class despite their absences. I’ll hopefully be able to get some feedback on my improvements this time around as well as the student who failed last cycle signed up to take my class again.

Some new tweaks

To launch the thinking classroom, I decided to spend more time trying to explain the model to students. Today I decided to spend more time explaining why we are going to learn this way, and even made a space for talking about the class and it’s structure on the note sheet.

This time the note sheet will be different as well. I am going to make it a daily point to collect notes, and some kind of feedback about the class, and then get in the habit of the responding to what students say. Opening a space for conversation with kids will be good, and I can try to download them towards some positive note-taking habits so they don’t have to learn the hard way. The notes will hopefully be for them, but hopefully they will also be a space for students to let me know if the class isn’t working for them and where I can suggest strategies other than leaving class.

We teach 90 minute classes, which is too long to do VNPS all class, so I will break the class up into different acitivities. Today I took the chance to do a proper icebreaker in the middle of class. This gave a chance for everyone to get to know each other. We did a speed dating activity, which would be about half way down this powerpoint, after which kids worked in groups based on who they partnered with in the activity.

Going forward I’m going to ask the kids to read about math and what their thoughts are. I’m going to give them my ignite talk, make clear that we are taking time to play with math, and ask them to write about the research about some of the Thinking Classroom ideas (VRG, VNPS, etc) as it’s always good to include some literacy, and it may help the kids who are uncomfortable find more reason to engage.

Open questions

As this first class ended, I’m realizing that many parts of the thinking classroom work is still a work in progress. Here are some questions I still have.

I am pretty unresolved about how to deal with kids who are uncomfortable, or who may have anxiety or other conditions. How do I get those kids who are uncomfortable to be involved and invested?

It also seems like however the groups share out, the male students end up dominating the conversation and the ideas. How can I structure the tasks, and the class time to make the female students feel empowered?

The Thinking Classroom structure gives a lot of opportunity for the teacher to tailor activities for each of the students at the different boards. In trying to help any student in my class, there is space for me to provide scaffolding in real time that can support or push students as needed. It’s a great idea, but… How do I actually use my questioning and my question-answering to make sure all student are staying in flow?

Lastly, I think my struggles with the last class was that I assumed that this new approach to teaching would create a new classroom culture, like uploading a fresh new operating system on to the computer. In reality, the thinking classroom is really like an app and the larger operating system is what the kids and I think math class really is. If I am not doing the work of deliberately creating the environment, communicating expectations, and building relationships, I’ll basically be allowing all those old ideas and mindsets about math remain operating in the background. It’s like trying to upload the newest version of photoshop on an old Compaq that is running Windows ME. So I need to upgrade my classroom culture. How do can I change the culture of my class in order to help the students change their relationship with math?

All of this is going to have to be pretty difficult to do given my school and everything that comes with it (8 week classes, kids who are uncomfortable with math, project based classroom). I’d love any ideas you might have, feel free to leave any thoughts you have in the comments!

Ignite afterthoughts

I did an ignite talk yesterday!

It was pretty scary. Having to speak in front of that many people, getting introduced by Matt Larson, having to come after all of these people you respect and not getting to control when your slides change. It’s impossible to just not think about the people. If you’re doing one of these, begin by choosing an idea that keeps you up at night. Make sure it’s a good one. You will definitely be nervous, no idea can fix that, but knowing that you are about to say something important will help you push forward. Especially if it is something that needs to be heard, and that won’t get heard any other way. I had a bunch of ideas which boiled down to the talk above, but I thought it would write a little extra about what I might have said if I had more time.

Initially the graph below was going to be my first slide but it’s too complicated. It’d take 3 slides at least to explain what google ngram is (a search of words and phrases in all the books that google has analyzed since 1800), I realized that this might eat too much time to include, but it’s still really interesting;

This graph shows how often the term ‘mathematics test’ appeared in books published in english over the last 200 years. ‘Mathematics test’, and similar terms like ‘math test’, ‘arithmetic test’, and ‘math assessment’ all seem to be non-existent until the mid-1920’s, implying that math tests weren’t part of school math education earlier. This means the engineers who built the railroads, engineered clocks, and laid out cities, were probably taught math without seeing a published ‘mathematics test’. The mathematicians before that time did their work with no one insisting they score a certain percentile on a collection of multiple choice items. It’s quite a contrast to the measuring stick mentality where math is only the test. If the only reason to take math is to prepare for the test that assures successful passage on to the next level, then we’ve turned this beautiful subject into Candy Crush.

What’s worse about this graph is the historical backdrop of the increase in mathematics testing. America was still unsure how all the recently freed slaves were going to integrate in society. At the same time racial hierarchies based on pseudo-science were being adopted by some as a way to reorganize society. This is also around the time that the eugenics movement was gaining prominence. Some of these tests were popular because they affirmed people’s beliefs that some races were better than others. Go read about the guy who made the SAT. These tests have a legacy of assigning privilege to certain racial groups, while making claims to be objective. Tests are probably better now, but given this legacy, and the outcomes, maybe it’s time to explore the idea that the tests might be the problem. However, there is a lot to unpack in the history of testing, and I only had 5 minutes to do this ignite so the ngram got scratched.

Pedagogy has also changed a lot since then. When I looked around for resources about why certainly been influenced by testing, and also by the need for matehematicians to outfit cold war defense contactors. The “traditional” or “Skill and drill” way of teaching that results is pretty sad. Paul Lockhart a lot about this in lockharts lament. It was long enough that it could be an ignite by itself, but just read the first bit if you haven’t.

Download (PDF, 391KB)

If I had more time I’d talk about the compound benefits of cutlurally relevant teaching. Learners need to connect new information to the world around them. The brain learns through connection, not isolation. It’s literally a huge mesh of neurons and learning connects those neurons or strengthens those connections. If we are actively connecting the math part of the brain, to student’s culture and identity, when they are going to be more likely to think about math outside of the classroom. So if we can get kids to think about fractions when they are making empanadads or california rolls or bratwurst, they are more likely to master the concept than if they only think about it on test prep worksheets.

The idea of homework is really popular, We talk about flipping the classroom, but if we want kids to engage in mathematical thinking when they aren’t in our classrooms we should start by telling them connect math to things that they are already doing. Ask students to talk to the elders in their community about the math they use and bring that back in the classroom. Have students think about recursion when they go to get braids Put their world to work for mathematical thinking. This could be a whole other talk too. but I didn’t really have enough time.

Bethany Lockhart’s Shadowcon talk really connected with me especially the part about facing your fear. After her talk I worked her hashtag onto one of my slides.

Changing the way we talk about tests, bringing beauty, culture, and kids identities into the classroom is scary. To make progress we all have to face our own fears around these topics, often alone. Facing their fears and making a bold move is the only way to move past the problems caused by the measuring stuck mentality and the lack of culturally relevant teaching. Being scared will have to take a back seat to moving forward if we are going to change the way we think about math. Of course, I don’t know the right scary thing is for each person. People need to figure out what things are just outside of their zone of proximal development and do that, particularly in the form of CRP, particularly as it relates to changing kids relationship with math, andparticularly with changing the testing culture. What I would have loved to gone into more in my talk, and what I think Bethany did beautifully, was letting people know that the teachers are the ones to take risks and try new

One more thing. #mathphoto18 was useful in coming up with the pictures that were used to visualize real world math connections. @erricklee did a great job facilitating that last year and I hope #mathphoto19 will be even better. Thanks to the following for taking the pictures that helped me make this talk: @alfgoralo, @MrsNewell22, @MNmMath, @carodumas29, @nadine1osborne, @debboden, @pinn,@ccampbel14,@mr_davis_math, @sagold, @BonnieUMontana, @wmukluk, @TheErickLee

My Biggest Current Hope For Math Education

Insight struck twice in our living room a couple weeks ago as my daughter was teaching herself the Peppa Pig theme song, with some help from us. We played it for her, and put some stickers on the keys to help her, but it took a long time for her to actually start playing it in sequence. When she was actually learning this she would sort of work away quietly, until she hit a point where she needed a break. Then she would get really silly, blow raspberries or joking around. After about 4 or 5 rounds of tunnel-vision followed by silliness, she eventually had the song mastered. I was left thinking about what her learning style might mean for her future schooling, as it seems to be quite similar to mine.

Julianne’s focus was as intense as her silliness and she shifted back and forth between the two so quickly, it seemed like they were both part of her problem solving process. This could be a headache for her future teachers. As an elementary schooler, she might be the student who tells jokes, distracts their friends, and gets notes home about behavior, but can answer the questions and tear through the worksheets. It’ll be hard to find success in a skill and drill class. Ideally she would be in a class focused on solving rich problems, explaining big ideas, and collaboration may keep her too busy to get in silly mode, or channel that energy towards something productive. Any teacher who can embrace her learning process and not make Julianne feel like an outcast would be good. Most teachers don’t tolerate a lot of silliness, preferring to punish the student or push them out of class until they get in line. Hopefully, Julianne’s future teacher will focus on creating a teaching environment that funnels Julianne’s focus and silliness, along with the energy that the other students bring, through activities that give students room to explore their curiosity.

There are three big things that give me a lot of hope that Julianne will find the right teacher. One is the internet’s growing collection of math activities, instructional routines, and curricula that speak to a variety of learners. Everyday more lesson ideas are posted on the #MTBoS and around the web for teachers to find. Another source of hope is the increased agency that teachers are given from their administrators, curriculum writers, and school districts. In NYC, teachers are expected to have rich discussions, facilitate group work, and customize or supplement lessons using their discretion. All of this would be unthinkable when I was in school. Lastly, because teachers have materials, and agency, they can make decisions that affirm the identities of their students, prevent the marginalization of students, and seek to disrupt systems of oppression and microaggressions at play in their school. Based on ideas happening on Twitter, with curriculum, and in my district, it seems like the focus on how identity affects the classroom will be at the forefront, going forward. This makes me very optimistic for what my daughter’s teacher will be able to accomplish.

My daughter, a biracial girl, will be treated differently in Brooklyn than me, the only black student in my suburban Detroit 5th grade. We learn similarly, so it may be useful to compare one of my school experiences where a teacher writhed my identity. Of course, the teachers of my classes, and her classes would have to make different choices because of the different culture of the school and our different identities.

I HATED social studies from the beginning of 5th grade. Mr Brownbear, along with my other teachers, sent me to the office so often I thought it was my assigned seat. One day, we took turns drawing little slips of paper from an envelope, each with names for our colonial explorers research project. My turn came, and the teacher pulled me aside with the same tone that I hear before I’d get a pink slip. I wasn’t in trouble  He didn’t let me draw from the same envelope as everyone else, instead giving me a handwritten slip he’d been saving for me. It read “Jean Baptiste Point du Sable.” I learned he was the founder of Chicago, and also a Black man.

Mr Brown Bear validated my identity and it made an unforgettable impact on me and probably on his teaching as well. Mr Brownbear must have made some changes too. He must have looked critically at the materials he was going to teach, and used his agency to change the task to reach the dual goals of satisfying the content and validating my identity. I’d had issues around being the only Black student in my grade which were probably well known among the teachers, so it was pretty clear that he was using his discretion as an attempt to expand the discussion around a unit that would otherwise be dominated by Whiteness. The fact that I’m still talking about shows that teachers who can make these kinds of choices can be impactful. I just wish I could do more than hope that my daughter’s teacher will exercise their discretion in similar ways.

My daughter in the kitchen this week and me at age 5 or so.

Looking to validate kids identities, racial and ethnic backgrounds, gender, languages, should be a natural part of planning for teachers today. With a preponderance of activities, technology, and more ways than ever to collaborate, this  work will soon become a necessity for teachers. The right choice could also alter the focus/silliness ratio for kids like me for weeks, even years. My experience with Mr Brownbear was in a social studies, and I can’t recall any similarly affirming experiences from math. Math was very abstract, rarely relevant, and often with timed tests that made me really hate the subject. My math teacher wouldn’t have the palette of options for affirming kids identities, making math culturally relevant, and eliminating the negative effects of status that will be available to my daughter’s teacher.

Julianne’s teacher will have a lot more agency, and a lot more materials, so her education will be great and she will love math…right? Despite all that’s possible, this future teacher’s discretion will determine what my daughter’s math class feels like. Maybe they will discern that Julianne’s silliness is disrupting the others and kick her out of class. Maybe the teacher will find a way to modify a lesson that affirms my daughter’s identity. The teacher’s discretion will have a great impact in a student feeling confident among their peers, and feeling confident as a mathematician. What’s scary is that it’s hard to know how it will affect the class. What’s even scarier is that the teacher may not know either. The use of discretion will be influenced by the implicit biases that the teacher may not even be aware that they hold. Deborah Ball, whose 2018 AERA talk influenced a lot of my thinking. In the talk she dissects a short clip of her teaching to illustrate the way she used her discretion to support the class seeing black girl brilliance. It is a great clip that everyone should find the time to watch. The increased attention that all of this is getting from the research community and on twitter makes me hopeful. I’m hopeful that maybe the people in the research community and on twitter can start to create a conversation about students’ identities and how they can be validated as they are learning math. Especially if they are kids who can be a little silly.

Clog: Launching the #ThinkingClassroom again

So my thinking classroom may have just given the best math class interactions I’ve ever had. More on that later. First let me get up to speed with this experiment.

Last cycle I had a good experience with the Thinking Classroom. I’ve written a few blog posts about it, including one about my plans, another about my awesome and excessive randomizer, and another about kids taking notes. The experiment ended in January because the marking period closed, but I decided to reboot it with a new kids on a different schedule. It’s really great having a second chance to go over the norms with a fresh group and get more practice on-boarding them. Having a bank of problems to use is an added bonus. So far, we have been doing  visual patterns, including my new favorite visual pattern lesson for VNPS, which I could write a whole other post about. (Actually, I’ll just write it now. This lesson has lots of patterns, you can cut them up into strips and give different linear and quadratic patterns to different kids. Give them to different groups and then have them walk around and check out the patterns that the other kids worked on). My classes on this schedule are an hour and a half long, and the VNPS seemed like it would be too long for that, so I have been doing Desmos activities in the remaining time. As the class comes to an end I’ll have kids work on using Desmos to make models of data that is important to them.

Today we used a different shell center problem and it just kept on giving. I showed the kids this prompt and asked them to think about how many would be int 30cm x 30cm and the 40cm x 40 cm and an equation.

The kids ended up doing a lot of thinking, including two students who weren’t here for the first cycle. Two of the three groups got to an equation after 45 minutes, but one group defined the 20cm case as n=1, while the other made an equation where n=20. This was led to a great conversation that we have been having about equivalence, but also about this thread of what I guess I would call “Mathematician’s License,” (like “poetic license”) One of the groups was trying to convince themselves that they had done it wrong, and I had to stop them and say “You made an equation the describes this situation, and that group did as well, and they aren’t the same. That’s ok. In fact, that’s what mathematicians do!”

All the groups seemed only 80 percent clear on the problems, so I made an extension question. I asked the kids about the 20cm x 30cm rectangle and they were all able to think about an equation, and no one’s equations were the same. The two groups from above actually tried solving it using the other groups value for n! It was great to see ideas spreading around the classroom. All the kids were supposed to sit down to work on the Desmos activity, but those two groups kept lingering around their boards. One group had a functional equation and they kept working on the ways to ‘simplify’ it. The other group was struggling a little with their equation, because they wanted to figure out how to write it so that it could apply to rectangles of any size!!!! I was shocked that a kid would even ask that. I told him that we would probably need some multivariable equation to try and figure that out and he was like “are we going to do that this cycle.” What!?!!? I had to restrain myself from not nerding out because we needed to get to work on the Desmos activity. I’ll say this is the first time I’ve ever had a student linger around and do more math, let alone ask me to do more. I think it shows that the kids have built up a lot of confidence and ownership in the first 4 days of the class.

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