Carl's Teaching Blog

A place to talk about teaching and learning

How it feels to give an ignite talk

This spring I gave a talk at the NCSM ignite session and here it is!  Below the video is how it felt through the process of making this talk happening.

Before the talk:

Going into the talk I was as rattled as I had ever been about doing anything.  I’ll give you a taste.  Here is an unedited snippet from my journal on the morning of the talk:

This talk is going to be fine.  I am in a safe space.  I am going to do my best, and the people are going to be appreciative.  It will look like I tried hard, and that is what matters.  It’s not my job to be perfect, I am trying to be as faithful as possible to the information and I will do that by delivering the presentation to the best of my ability.

Sounds a little like Stuart Smalley, right? Well don’t judge me until you’re in the same situation. These affirmations were what I needed to get out of the door and to the bus station to make it to Boston on time.  I had also just woken up from a pretty sleepless night.  The safe space imagery helped me shake off the late night/early morning visions of me messing up on the talk and every one looking at me like I tripped in the middle of a dance battle.  Sharing something with nearly 100 people is pretty scary, even if I regularly present information to nearly 100 students for a lot longer than 5 minutes.


In the conference room waiting to talk, there is a little bit of gallows humor, but not really a lot of fear.  As you see more and more people going up and giving their talks, starting with Annie and Max, you realize that the fears that you have about the talks and their outcomes really don’t matter because the audience is the most wonderful audience in the world.  It is as warm and accepting as the crowd at a summer camp talent show, or the shows around the holidays when all the little kids make everyone watch them sing by the mantle.  You wouldn’t believe it if you were in the room but the energy is amazingly supportive.  EVERYONE IS THERE TO SUPPORT YOU!

Getting up to talk your mind goes completely blank.  I whispered to Suzanne “I forgot everything.” who comforted me by saying.  “Everybody does, it’ll come back.”  She was kind of right.  I remembered through the talk what happened, but I don’t remember any of it now.  I think I got the laughs I wanted, there was conversation when I wanted, and people were quiet and thought when I wanted.  I finished with not only a weight off my shoulders but still slightly burdened by the mistakes I might have made.  “I didn’t plug twitter!”

A Little While After:

Once the talk has finished and the adrenaline is gone, the experience of the talk really inspires you.  When I finished running a Tough Mudder I remember getting injured and having to limp the last 20 miles to the finish line.  So much of that race was filled with dread and disdain, but once I crossed the finish line and met the rest of my team I couldn’t help but feel anything but pride and gratitude.  With the Ignite talk there was a similar feeling.  It was great to finish, and while people may nitpick pronunciations and powerpoint slides as they watch the video again, there was still nothing like being in front of such a large group of supportive people who wanted you to do well, and wanted to learn from what you had to say.

My talk:

So I have two videos below.  The first is cell phone footage of my self talking, the second is the video of the slides behind me.  Sync them up at the same time and it will feel like you were there!

Cell phone video of me talking:

Video of the slides (start this at :07):

The Powerpoint file of the slides for my talk is below, and you can also set this in motion by starting the slide show on the second slide.  It will run through the entire talk automatically:

Quick and Dirty Version

The whole idea of the talk is that there are a lot of changes that are hampered because certain people have what is called “competing commitments.”  These commitments compete against the change that you want to happen.  The example that I gave was that I wanted students to change and become better problem solvers, but I am committed to preventing students from having to struggle for long periods of time.  Unless I deal with my issue, I am never going to make that change happen. This talk is proposing that until we as a math community deal with all the collective commitments we are going to see numerous efforts to change, efforts with great promise and potential, fall flat because we are committed to keep things the same.  On an individual level, this change process could take place by examining what outcomes you assume these commitments are supposed to prevent like a scientist experimenting with a hypothesis.  Does it really make sense for me to always avoid students from struggling?  What if I experiemented with a lesson plan of “struggle” problems from a reputable source, like the Math forum?  Perhaps trying this experiment would be enough to stop my allegiance to that unproductive commitment.

Make sense?

I’m curious what kind of Changes, Fears/Commitments, Assumptions and Experiments the blogosphere has, so if you can think through this, please leave your thoughts at this link:

Here is the book that inspired the talk:

How the Way We Talk Can Change the Way We Work: Seven Languages for Transformation by Robert Kegan et al.
How the Way We Talk Can Change the Way We Work: Seven Languages for Transformation
by Robert Kegan et al.

This Week: Back to work

So this week was the first week teaching as a father! As excited as I am about fatherhood, I’m not yet going to try to flood the interwebs with pictures of my child. Well, maybe just this one.

Being a father is good, and perhaps I will write a post soon about what my early experiences made me think about math teaching. Our school district’s paternity leave policy, however, isn’t good. In fact it’s non-existent. In order to keep our lights on I’m back to work until the end of the year. Since NYC schools go DEEP into June. Seeing the year is far from over, I figured I could use the rest of the year to dive in with the blogging strategy I will use next fall

What I’m teaching this week

This week I have to pick up the pieces from my paternity leave. This has meant rushing through the two projects I have my two classes teaching right now.

Project A: The Casino Carnival Project

Kids need to find the expected value for a carnival of their design where they need to make as much profit as possible off of the participants playing the game. This game is meant to model the role probability plays in designing a casino. There is plenty of variability with each of these ideas that should give the students a chance to each make a unique set of games of prizes. Kids calculate the expected value of various prizes and use it to calculate their total profit.

Project B: The “Coin Flip” Project

This project was an obvious copy of Dan Meyer’s Will It Hit The Hoop. I wanted to try a 3-Act kind of problem, as per my goal for this year, and also have kids to do shoulder some of the model building load. I showed them this video of me flipping a coin off of the end of a ruler but not quite landing and asked how they could know it was a quadratic, then guided them through making their own video. The day before my daughter was born I showed them how they could each flip their own coins and record it on an iPad and then find coordinates that track their flight by watching their video and analyzing the associated chart paper.

What I think happened with the subsitute teacher while I was on paternity leave was, well, very little. I realize that there are a lot of teacher moves and questioning that I do when launching projects, and I could probably benefit from taking time to think about what’s needed to teach a project and document it. This may be a summer project… In the mean time, let me know if you have any questions about these quickly describe projects in the comments below.

What I’m blogging this week

This week I plan to blog every day, just as I would if the school year were started. I have plenty of ideas on tap that I could blog about, but I definitely want to write about what happens as I try to finish these projects in a tight timeframe.

I also intend to make a concerted effort to comment on other peoples blogs. So many people out there are writing good stuff, but because I am on my phone, or on feedly, or am just busy, they won’t know that I appreciated their stuff. This week, and certainly going forward, I hope to change that. A comment a day may be a good goal. Anyone care to join me? Leave a comment below to start!

What I’m thinking this week

I’m going to end this post thinking about my former student Kalief Browder, whose life came to an untimely end. The kind of student that should be saved by our system was lost, largely because of this system. The fact that the bevy of resources afforded him later in life weren’t enough to overcome the damage done to him earlier is a sad reminder of the importance of each day with our students while they are young.

Visual Patterns First: Putting Together A New Quadratics Module

This cycle we’re focusing on Quadratic Equations.  The topic of quadratic equations has been a bit of a murky area in our transfer school.  We don’t necessarily have a scope and sequence, and teach a bunch of modules, and it seemed to me we weren’t giving fair treatment to Quadratic functions.  I had one project “The Function Field Guide” that covered the topic in brief details, but thought we could create a new module so kids could understand all the cool things about these functions.  Creating this module has been going good so far, so I figured it would be good to blog about the broad strokes behind it’s construction and roll out.

Visual focus from the beginning

I wanted students to understand the purpose for the quadratic equations centra distinction from the function that most stduents think of when they think of equation (linear functions of the y=mx+b variety) so I started by showing this pattern.  From this the students sat and thought about the pattern of growth in the table, and how they coudl represent it.  on one hand we saw that it was not going up by a regular amount, that “It was going up by odds” and on the other hand some one looking at the fact that it was a square could see that the area of square would be x*x.  We talked about this a lot over the first day.  I thought it was too much because the kids seemed bored, but I’m not sure if the connection between the two methods was understood.  THe kids seemed unsatisfied by not being able to tie their “odd” noticing to something concrete.  So we kept doing visual patterns at the beginning of every class varying between quadratic and linear, and after defining the terms the kids now have an added task with each visual pattern, (is it quadratic, or is it linear, or something else?).

The visual pattern Do Now activities I used on the first six weeks of the cycle

The visual pattern Do Now activities I used in the first six weeks of the cycle

Fixing potholes along the way

‘Fixing the potholes’ is a term coined by the East Side Community School teachers talk of the MSRI event (around 56:00).  The idea is basically to fill in pot holes on the way to new destinations, not tear up and repave roads without making any forward progress.  If you find engaging problems to inspire kids to understand higher mathematics, the kids will realize what areas they need to work on.  Then we tie their curiosity to the need to repair their old understandings, and provide the space for that “pothole-filling” as we pave the road into more interesting content.   I much prefer this to traditional review: teaching it the same as before, but faster and with less support.

Instead of starting with an introduction on graphing, equations, linear functions I decided to work situations into the class where we do the review along the way. So when we started off looking at these patterns and classified the idea of a quadratic pattern, I get a chance to review linear functions for the students who may not have been signed up for my linear module and can benefit from seeing it in a new light.

Begin with vertex format

In the past when I’ve taught quadratics I’ve taught standard form and factored form first, because kids are often familiar with the operation of going back and forth between those two.  This year I am starting with the f(x) = a(x + h)2 + k form of function because I think these are the kinds of functions kids will generate on their own when looking at visual patterns.  If I see patterns like the ones above, I am not going to think, “oh, it’s like that square function, but we have to add two to it first” or “oh, it’s like that square function but with an extra thing on the side.  If kids are comfortable making and using these this form, they can quickly translate it to a graph, and we can start to make sense of the graph from there.

Building tent posts with reflective writing

So my way of thinking about this unit is kind of like building this series of mathematical tent posts, like a circus tent.  We get the main ones up, then all the little side posts and supports.  A the end of the unit, we’ll have created a place where kids can play around or build something cool.  The tent posts I’m planning will be the big thought for the week, and we’ll do it every Friday.  I’ll keep these big ideas on chart paper some where in the room to keep referring to through the week.  I’ll also ask kids to write about it, as well as create an example.

This tent post is pretty good so far.  The first big thought was what distinguishes a linear relationship from a quadratic relationship.  Last week was the shifts of the parabola and the connection to the vertex format.  Next week will probably involve either a further exploration of the parabola graph, the general function of the parabola, or maybe both.

Searching for the final project

My plan is to end up with a final modeling project. I have done a few things before, but I’m hoping I can find something better.  Since the last thing we will cover will involve the factored form and finding zeros as an important component.  Projectile motion makes a lot of sense, but that will involve a lot of physics.  I doubt I will have enough time to teach physics with understanding and I refuse to end this unit by telling kids “Here’s this function, don’t worry if you don’t understand it, just plug your numbers in.”

If you have any ideas for a good ending project, let me know in the comments!

Clog: “I don’t know, like a million?!?”

Over the weekend I was excited to attend my first baby class.  As a teacher, watching others teach triggers an unrealistic urge to by hypercritical. My wife is also a teacher so we left for lunch shocked at how much of the teacher’s time was spent talking at the unhelpful Powerpoint. She basically talked the whole time, constantly referring to the stuff we had to “get thorough”.  We had all sorts of pedagogical wisecracks about the experience while we ate at this greek restaurant that seemed a lot like Chipotle, and I thought about that lunch today in class.

Today’s class did not begin how I would have liked.  Unable to find a star wars themed Estimation180 kind of task, and unable to make one that would only appeal to fan boy trivia geeks(e.g. “Estimate the number of parsecs needed for the Millenium Falcon to complete the Kessel Run?”) Chipotle popped back in to my mind. The menu specifically.  Since we were talking about combinations and permutations, I thought let’s make an estimate of all of the things that are possible to order at Chipotle.  I gave them a menu that had all of the meals and proteins, and asked them to be specific about what they were taking into consideration.  I gave kids this menu that showed the meat and the menu choices.  To avoid over-scaffolding, I didn’t mention all of the sides, in hopes that the kids would think of the sides on their own.

Lots of kids immediately noticed that there would be more to it than the options listed, but they all seemed to shrink in the face of such a number.  I had a lot of exchanges where the kid would say ” Oh, that’s like a million?!?” as if they were comically startled to think of a number that big.  I would ask them to try and use the multiplication rule to take it into account.   Instead they would get overwhelemed and settled for 24 (four meals, 6 proteins), which would be the safe choice.

 I wanted to show them all of the other possibilities that it seemed most people were scared to explore. At the board I walked through the rest of the possible meal options, one at a time.  “What are the choices for beans? Brown and black?” Ok, that’s 2 more, so multiply by 2″ in as engaging a manner as I could.  At the end we multiplied it out and got something like 516,094, allowing kids to have two kinds of meet, any of the salsas, and also getting an optional extra tortilla on the side.

Yes, I am fully aware that this sounds like I’m defending a teacher led call and response.  I felt the full irony of me doing pretty much what our birthing class instructor was doing over the weekend. At that moment, with the do now almost over I genuinely wanted to see what we could up with, it’s hard to turn that off. At the same time, kids were watching me do math and sort of cheering along.  The argument could be made that this diversion was not really valuable.

What I think makes this valuable is that I am making explicit the process that one has to go through in order to both think through a problem, and really justify their thinking.  This process is important, and now I can refer back to this component of the lessons when I want to explain to students how to think through and justify their reasoning with similar problems, and I can assess this I provide an opportunity for them to do a similar type of counting on their own in the future.

The view of San Francisco Bay from the steps of MSRI.

MSRI 2015 – A national math education conference focusing on developmental ed

This year there was a pretty spectacular conference in the hills of Berkeley California that brought a number of people who are involved in Developmental Math including Deborah Ball, Bill McCallum, Hyman Bass, but mixed among them were some lesser known names including Gregory Larnell, and a scene stealing group of high school math teachers from NYC.

The Mathematical Sciences Research Institute (MSRI) is a magical place in the hills above the University of Berkeley near the Lawrence Hall of Science.  It’s home to a group of academic researchers who work on their research from the inside of a beautiful complex, largely funded by MFA creator Jim Simons, which plays hosts to a number of national conferences with various focus on a yearly basis.  The annual Critical Issues in Math Education meeting was held in March and had the focus of “developmental mathematics at two- and four-year colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels.”

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