Carl's Teaching Blog

A place to talk about teaching and learning

#NCTM Regionals Stats Trumps Hate – Slides and Ideas

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 AtlasNPR Article about it

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

“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.

Watching this Home-made gushers video might remind you of a good STEM project

August days are good for planning the next school year, and binge watching episodes out of procrastination. I’m convinced Bon Appétit’s Gourmet makes” show helps you accomplish both. The fast-paced ~15 min episodes  are excellent for binge walking, but also are ideal models of an inquiry-based STEM design challenges. In watching ALL of the episodes while waiting for toddlers to go to sleep, I couldn’t help thinking that each is a good example of a design challenge, the challenge being how do you use regular kitchen ingredients and techniques to recreate classic junk foods like Oreos, Gushers, and Kit Kats.

The show follows the pastry chef Claire as she goes through an arc that look like a STEAM Inquiry. Specifically, it seems to line up with Stanford Design School’s 5 basic modes of design thinking Empathize – Define – Ideate – Prototype – Test. The first step empathize happens as they ask other people who work in the test Kitchen about the product they are duplicating. Claire asks “what kind of things do I need to do to make a copy of this?” and “What kind of things should I do to improve on this?” It’s almost like a notice wonder about the challenge, but in partners. This helps clarify what the finished product looks like, and establishes that chef can go to the other person later in the show to see if their final product meets that expectation. Maybe a process like this could be used in class to help kids determine their own rubric for the challenge. It also tranforms the people giving feedback into helpful judges as they give feedback as progress along the way.

Next Claire moves to other ways of gathering information.She reads the ingredients, she looks at stuff on amazon, she reads other recipes, and she watches commercials. She does all of this to come up with an approach that she can take to the challenge. This helps her get to the Define and Ideate steps, and then you see her describe what her first prototype will look like. What is nice about this is that the research is well-defined and has a fixed end point and is kept separate from being on-going and paralyzing, and the actual prototyping has to get done away from the internet while she is actually cooking stuff. What is also good is that she is making decisions and keeping track along the way, not necessarily following a recipe, which might be a good thing for students to do when they are solving a problem.

Then the show follows her as she struggles to make the different parts of that episodes dessert. After a quick montage she has something that she can eat, a Prototype she can Test. As she eats it, she can test how good it works. Since she is in a room with a bunch of people!

This made me think about a classroom full of kids, and how the kids use each other as sources of feedback while they are trying out the different prototypes they are developing to finish their design challenge. Because the students would have already given feedback in the Empathize phase. Maybe there could even be some graphic organizers that are created to ensure that these kinds of exchanges happen. On the show the exchanges often are the moments where the Claire both finds out that she isn’t there yet, and also finds out what direction to go in next. Creating these kinds of exchanges are the ones that I’m the most excited about trying in the fall.

Finally at the end, when they have satisfied the goals at the beginning of the challenge Claire declares victory. The show ends with her reading the recipe, and thus presenting the result of their work in a way that someone else can use it. I think a lot of times with projects kids get the project finished, but don’t think through how they can present it.

The show isn’t perfect (i.e. glaring lack of diversity), but it seems like good inspiration for the summer planning, or late summer binge watching. What are good projects that you could use this process?

My Reflections on Reimagining High School Math at #TMC18 #rehsmath

I was super lucky to do the Reimagining High School Math morning session with Sadie Estrella. This session first came to be with a conversation on the eve of the TMC deadline.

We spent the next 20 minutes polishing up a draft proposal. A few weeks later we found out we were accepted and we started planning.

As we started to plan we had one overarching goal: to have people leave prepared to DO something. Reaching that goal meant a few things would have to happen. Participants would have to talk honestly about their schools or districts and what needed to be reimagined there. Everyone’s school is different, and we’d find it impossible to predict what changes were needed in each school. Schools are also full of people, and any change is going to involve getting people on board. This meant that we wanted people to practice the experience of pitching their idea at TMC before they go home while thinking about all of their social dynamics.

We started planning early to get an idea of how to make this unstructured session happen. In trying to build a session around ideas that we don’t know, it’s kind of like trying to plan a meal for Chopped without knowing what the secret ingredient will be. We did a couple of twitter chats ahead of time, just so we could harvest some ideas from people in the #MTBoS. The more we talked with other people, however, the more it became clear that we couldn’t really gather enough information to pretend to be the experts about any of the possible ideas. My list of potential ideas went from 5 to 15 to 50+. It was clear that we couldn’t expect to narrow the focus to a central idea like de-tracking, for example.  Instead we focused on giving people lots of time to think about their situation and their idea, and how they can go about making change there while we’d do our best to help them feel supported.

On the first day we did an affinity mapping activity with post-it notes. Our group used as many post-its as they could to answer the question above, and then we moved them all around into groups afterwards. We took pictures of these and put them on this google doc:

TWITTER STORM GOOGLE DOC

We called it a twitter storm because we wanted twitter to help us brainstorm resources. If you look in there you will see each of the clusters and then some relevant resources below it.

On day 2 people thought about their school and the ideas that would make the most difference there. The next day everyone wrote out descriptions of their idea and took turns giving each other feedback. Ideas were as a varied as we’d expected. Everyone had a different idea for their school which reflected their different backgrounds (private, public, urban, rural, etc). A thread emerged connecting the ideas. Each idea was just the first step towards some larger cultural change. The larger change that everyone wanted was some different. Maybe a shift away from forcing everyone towards calculus, or a shift towards more collaboration, or a space for teachers to do more risk-taking. These cultural shifts echoed the conversations we have on twitter and in a number of places about how math education should change. It was probably predictable that larger culture change was beneath the surface of each idea, just as it was predictable that the ideas would be unpredictable. However these unique, unpredictable ideas created by each individual represented a realistic set of first steps towards the kind of larger math changes that fill all of our imaginations.

People left preparing plans to meet with teachers at their schools, or to start online initiatives, or to create math jams where teachers could get to know each other. The last idea already happened:

Every person had a different way to get people back home to start to think differently about high school math, and I’m excited to hear what happens with them. I’m also excited to help more people think about the change that needs to happen in their school/district some in the future.

Here are our slides:

https://docs.google.com/presentation/d/1yNv-NDBBZy9UR4CIws1AgxXv7DjzfN3DWAsWeuWYTOY/edit#slide=id.g3d745c0250_0_0

 

Three big things that make me scrap my admin posts. Scary relationships, word salad, and the minutiae trap.

3 years ago I became an assistant principal at my school. While I am still a teacher of one class each cycle, my main focus is on leading the math team and the support staff and also overseeing the programming and scheduling for the school. It sucks writing about admin stuff for a lot of the reasons that makes blogging challenging for anyone. Last year I tried to do more blogging about admin stuff but ended up hiding most of those posts somewhere else because they didn’t feel right. There are 3 specific things that has made it hard for me to blog about my admin work like I blogged about my teaching.

Relationships are hard to write about safely

Relationships are key to any kind of school effort, but writing about staff relationships is rarely appropriate. As we talk about school change, the conversation quickly talks about what people think about the change, or what people think about other people, or what people me. If any of those relationships are keeping you up at night, how do you get the ideas out on your blog that all your co-workers know about? When I wrote about students I used pseudonyms and changed details Those tricks don’t seem to apply as it’s too easy to figure out. Even if I try to mask the name, one would have to guess which of the 8 teachers I’m talking about, as opposed to which of the 90 students I taught that day. A potential staff slip up is more dangerous than with my students. My relationship with those 8 people will go on a lot longer than the kids who I probably won’t see after this year. Longer relationships are longer, and full of complex, tangled details. It’s hard to fully describe the full picture of a co-worker relationship while trying to tell a story of why today was a success, or why the meeting went terribly wrong. I could ask the co-worker if they mind that I write about them, but that isn’t really fair. As their administrator, they would probably feel like they have to go along with what I’m saying, and potentially harbor discomfort.

Vagueness of leadership writing

Writing about education leadership is pathologically vague. Tweets I’ve seen from administrators always sound kind of feel like word salad of educational jargon. A lot of these school leader tweets have this feel (which I am in no way meaning trying to hate on, btw.) I’m guessing she is trying to both describe a pattern she has noticed over interactions with a bunch of teachers and abstracting in order to get something across in tweet form. She can’t go too into detail about where this arose from or how it plays it out in her school, because teaching probably looks totally different at her school. Administrators work with systems and structures that are as unique as their fingerprints, and there just isn’t the time to explain all the necessary relevant items when you have something to get across. Instead the ideas have to extracted from the actual situation that happened, and written as an abstract life lesson that people can maybe apply to their life. I’ve noticed this in leadership books and a lot of other things. Stuff is pretty vague.

I’ve noticed it in own writing too. Last year I had to have a mediation with a couple of staff members and afterwards I wanted to write about it. If it was a conflict between students I could approach a blog post like this: it like “XXXXX and YYYYY had a conflict around ZZZZZZ. We used this protocol, it went pretty well!” I would be able to provide details about who X and Y are, and I can also point to where the task is online that they were working on. As an administrator working with adults, I can’t give too many details about X and Y without divulging their identities, and probably breaking their trust and ruining the relationships we talked about a couple paragraphs ago. Furthermore, Z is a task that really only makes sense at my school, which would require a whole separate blog post to explain, and my actually get us in trouble if fully detailed. So instead I wrote this post on my other admin blog. I instead use a metaphor about icebergs, I posted this a good week or two after the event so people can’t guess who I’m talking about, and it isn’t even clear what I did or why a protocol would be helpful in doing that. It’s super vague. Why go through the trouble of thinking out a reflection to wind up with something that feels as substantitve as soggy shredded wheat?

The Minutiae Trap

Given all of this, it’s easy to want to reflect on a lot of the stuff you can write about. Spreadsheets, compliance, budget allocations. These things are nice and sanitized, self-explanatory, and because they are so concrete they are easy to write about. They are also boring and dangerous. So Megan Roberts did a really good job of illustrating the dangers in a story I’m not sure I have permission to get into details with…but I can vaguely describe it. She was an assistant principal, and she was focused on a lot of these technical aspects. Programming, compliance, getting things done. Her colleague was more interested in building relationships, setting the tone and other “touchy-feely stuff”. Megan felt like she was doing more of the leadership work on her admin team. Then 9/11 happened. In the face of that crisis the school didn’t a leader to check boxes. It needed someone who could connect with everyone personally and let them know everything is going to be ok. It was clear to Megan that leaderships is more than just checking boxes, doing the spreadsheets and other things. The trap you can fall into with admin stuff is thinking that the things that are detached from everyone, and that fit into nice clear boxes which people can understand are the things that are important. This minutiae is not the leadership that the school needs when an emergency comes, but that kind of stuff involves the messy human relationships and the weird institutional quirks at your school that are hard to write about with any clarity.

So what am I trying to do?

I guess I’m trying to figure out how to not be the minutiae guy and have real relationships with people, people who I can’t blog about without being vague. Umm… Oh and there’s all that minutiae stuff that I do want to write about, just without falling into to the trap of thinking that’s all there is to this job. Any ideas on how to do this? Any bloggers out there doing it? Let me know in the comments.

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