One graph. Ten minutes. An important conversation.

At the beginning of class I showed this to my students:

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They came up with lots of interesting things.

  • There are three variables
  • They are functions
  • They are different colors
  • The units are millions and years
  • The scale for the millions is by 500,000’s and for years is decades
  • The domain of all 3 functions is 1920 to 2010
  • The range is 0 to 2.5 million
  • All of the functions are positive over their domain
  • The average rate of change for the red graph from 1920 to 2010 is positive
  • The average rate of change for the light purple graph from 1920 to 2010 is close to zero
  • The greatest average rate of change for all functions appears to occur from 1980 to 2000.

Then I asked them to predict what the graph was about. Most felt it detailed some sort of economic situation. Or population. Then came the reveal:

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They were shocked. We talked about possible causes for this situation, like the school-to-prison pipeline and the privatization of the prisons. More eyebrows raised. I brought up the question of what the racial breakdown of the prison system might look like. It was an important conversation.

And then we moved on to the regularly scheduled program: the lesson.

That was this week. While this class opener wasn’t directly tied to work that we’ve been doing in algebra 2 and was relatively brief, I felt compelled to have this conversation with my kids. This summer I began thinking about how to deepen the connections between social issues and math. Since I suck at projects, I thought about making these connections in smaller, bite-sized ways — comparable to problems found on a typical NYS Regents exam. In an ideal world, I would find (and write some) problems around social issues that are directly tied to the algebra 2 curriculum and discuss them with students. But this is really, really hard. Factoring by grouping doesn’t exactly lend itself to talking about racial inequities.

I was upfront with them. I said that its hard for me to relate some of the mathematics we learn to their daily lives, but we can do it in other ways. I told them that it was my responsibility to help you see how math can you uncover your world. Graphs are one way.

Through this graph of incarcerated Americans, I’ve myself learned that periodically presenting an interesting graph or data can be another way to build in time for important discussions around social justice and empowering students through math — even if the discussion isn’t wrapped up in a “problem” or directly tied to what we’re studying. This is not unlike What’s Going On in this Graph from the NY Times.

 

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Student as author and critic of mathematics

I’m hoping to improve my students’ journal writing experiences this year. After learning about problem-based journal writing from the work of Joseph Mellor and Carmel Schettino, last year I created/stole a fancy handoutrubric, and told the kids to go write.

I was hopeful for more, but the kids ended up only writing one journal entry. This is totally a result of me assigning in the late in the year, yeah, but mainly because I was too lazy to actually read through them all. I pitifully underestimated how long it would take to read what was essentially 120 essays. English and history teachers out there, I can now finally appreciate your workload. I feel for you.

Fast forward to this year. I’m ready to step my game up. I’m primed to better position my kiddos as authors of mathematics. I tweaked the handout, rubric, and my introductory talk with kids about writing and why it is important — even in math class. Through the journals, they will be formally reflecting and thinking about their own mathematical thinking in a deep-ish sort of way. Just like with the Mathography, I’m pretty sure they’ve never done this before.

One of the key differences this year is that instead of me being the authority figure on providing feedback and grades (and putting this onus on myself for reading ALL those journals), I am forming six editorial boards in each class. Each board will be a yearlong grouping of students who will peer-review the journals.

I got this idea after I read The Art of Problem Posing by Stephen I. Brown and Marion I. Walter this summer. After they’re turned in, I will distribute 4-6 journals to each editorial board, who will use the rubric to do a blind-review (I will remove all names of journals) to discuss, assess, critique, and give feedback on the mathematical writing of the authors. I will have final say on all marks, but I will fully expect integrity, honesty, and fairness from the boards. And by reading through and analyzing so many of their classmates journals, I hope that their own mathematical writing gets better over the course of the year.

I’m really hopeful that they’ll get to write four journals over the course of the year. What’s really cool is that after each round of submissions, each editorial board will select one journal that they read to be published at the end of the year. By “published,” I mean featured in a compilation that I will print out in a little booklet in the spring. It’ll look and feel professional…like this one that I came across at TMCNYC this past summer from Ramon Garcia who teaches at Borough of Manhattan Community College Adult Learning Center:

By the end of the year, I want every student to get at least one journal entry published.

I’m not 100% confident in any of this, but I am very excited. At a minimum, I know it can’t be any worse than last year!

 

bp

 

Why am I all about chalk and t-shirts this summer?

I need to let this out of the bag.

This summer, I have had two things on my mind more than they probably should be:

  1. using sidewalk chalk
  2. buying t-shirts

Why? Hang on.

First here’s some of what I’ve done with the chalk:

And these are the t-shirts that I have bought:

Through both the chalk and shirts, I’ve found myself publicly advocating for math like I never have. Obviously, I’ve always been a proponent of math in my classroom, but now through what I subtly wear and create on the pavement in my neighborhood (and around my school), I’ve found myself attempting to transfer this passion more broadly…to the general public.

With the awakening of my social conscience during these last few years, I am more mindful of the damaging stereotypes and inequities that exist in and around the culture of learning math. Far too many people in society are put off with math as being a cold, lonely subject that is reserved for the elite. The reasons for this vary, but, as a math teacher, I think I am really coming to grips with the responsibility I have in reversing this trend, even if most of my effort goes unnoticed. There’s something bubbling up inside me to find and create small, practical ways to promote math as an accessible, friendly science…that go beyond the scope of my classroom.

It’s a very steep mountain to climb, but the hope with both the sidewalk math and my new t-shirts is to promote equity, access, and exposure to math in unique ways and to spark meaningful conversations about math (potentially with perfect strangers). Along with this comes helping to shift the mindset of how other people (young and old) view learning math and their own mathematical value.

I’d like to think it has worked…as both the chalk and shirts have elicited reactions from people I’ve encountered this summer. Two other teachers even liked my t-shirt so much that I went ahead and got them one. I guess that’s a good thing.

Come to think of it, this is really no different from Sara VanDerWerf’s call for math teachers to identify themselves evangelists.

 

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It’s complicated

I’m not a big TV person, but I can get down with some Wheel of Fortune. It’s pretty fun to watch and Vanna and Pat are seemingly ageless…which blows my mind.

But as much as I like the show, this puzzle from last night’s episode bothered me:

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They didn’t choose English, social studies, or computer science. No, they mindfully chose math (and physics) to associate with “complicated.” This is exactly the sort of damaging groupthink that fosters fear, anxiety, and stereotype threat of mathematics in my students (and society) and makes my job so dang hard. We can be better than this Wheel. C’mon now.

 

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Example analysis from DeltaMath

With so much problem-based learning happening this year, I’ve been mixing in plenty of algebra by example-esque problems. They work really well because they get kids to analyze math work on their own and then use it to solve a similar problem.

I’ve been writing some of these problems from scratch (horribly), but DeltaMath has shown up on the scene and helped out in unexpected ways. At the beginning of the year, I originally intended for DeltaMath to be a review of the problems/topics we learned in class. I assign them one big assignment that’s due the day before the next exam and they do it over time as we explore ideas in class.

That’s happening, yes, But what I’ve found is that the kids are also using the DeltaMath to learn the new ideas by means of the examples, not just review them. They’re independently leaning on their own analysis of DeltaMath examples to learn rather than on me to hand-hold them through examples in class. Independent learners, yay!!

The result is that someone regularly comes to class saying “…on DeltaMath I learned that…,” when presenting a problem we’re discussing in class – even when its an introductory problem on a topic. And, more often than not, this opens the door for a complete student-led class discussion around the problem.

For example, take this “Factor by Grouping Six Terms” problem that I assigned earlier in the year:

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When they click the “Show Example” on the top, a worked-out example appears:

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Students can even filter through different types of examples of the same problem by clicking “Next Example.”

 

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