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Blanton & Kaput modify the Christmas carol The Twelve Days of Christmas for an algebraic reasoning task befitting the season:

How many gifts did your true love receive on each day? If the song was titled “The Twenty-Five Days of Christmas,” how many gifts would your true love receive on the twenty-fifth day? How many total gifts did she or he receive on the first two days? The first three days? The first four days? How many gifts did she or he receive on all twelve days?

“The X Days of Christmas.” I like it.

November Remainders

Hi again. It was a busy November. I spoke at the three NCTM regional conferences, keynoting two of them. That plus the Thanksgiving holiday, some family fun, some preschool volunteer work, and some forward progress on my dissertation has left blogging somewhere around eleventh place on the to-do list.

All of that makes your blogging more useful to me than ever. Please keep posting your interesting classroom anecdotes.

Here are all the blogs I subscribed to during November 2014:

Great Classroom Action


Coral Connor’s students created 3D chalk charts to demonstrate their understanding of trig functions:

As a showcase entry we spent several lessons developing the Maths of perspective drawings of representations of comparisons between Australia and the mission countries- income, death rates, life expectancy etc, and finished by creating chalk drawings around the school for all to see.

Malke Rosenfeld assigned the Hundred-Face Challenge – make a face using Cuisenaire Rods that up to 100 – and you should really click through to her gallery of student work:

Some kids just made awesome faces. Me: “Hmmm…that looks like it’s more than 100. What are you going to do?” Kid: “I guess we’ll take off the hair.”

One of my favorite aspects of Bob Lochel’s statistics blogging is how cannily he turns his students into interesting data sets for their own analysis:

Both classes gave me strange looks. But with instructions to answer as best they could, the students played along and provided data. Did you note the subtle differences between the two question sets?

Jonathan Claydon shows us how to cobble together a document camera using nothing more than a top of the line Mac and iPad.

Malcolm Swan, on how to begin a lesson:

Every lesson should begin by getting [students] to articulate something about what they already understand or know about something or their initial ideas. So you try and uncover where they’re starting from and make that explicit. And then when they start working on an activity, you try to confront them with things that really make them stop.

And it might be that you can do this by sitting kids together if they’ve got opposing points of views. So you get conflict between students as well as within. So you get the conflict which comes within, when you say, “I believe this, but I get that and they don’t agree.” Or you get conflict between students when they just have fundamental disagreements, when there’s a really nice mathematical argument going on. And they really do want to know and have it resolved. And the teacher’s role is to try to build a bit of tension, if you like, to try and get them to reason their way through it.

And I find the more students reason and engage like that then they can get quite emotional. But when they get through it, they remember the stuff really well. So it’s worth it.

October Remainders

Awesome Internetting from the last month.

New Blog Subscriptions

  • I met Nicholas Patey at a workshop in San Bernardino. He wrote up a summary of some of our work that made him seem like a solid addition to my network.
  • I added Amy Roediger to my blogroll (my short list of must-reads) because more than most bloggers I read she has an intuitive sense of how to create a cognitive conflict in a class. (See: two sets of ten pennies that weigh different amounts. WHAT?!)
  • I subscribed to Dani Quinn. My subscription list skews heavily towards North American males and she helps shake me out of both bubbles. She also wrote a post about her motivations for teaching math I found resonant.
  • In her most recent post, Leslie Myint wrote, “Apathy is the cancer of today’s classroom.” Subscribed.

New Twitter Follows

  • I met Chris Duran in Palm Springs. Liked his vibe.
  • Leah Temes plunked herself down at my empty breakfast table in Portland last month and started saying interesting things. Then she told me I should follow her on Twitter with the promise of more interesting things there. With only two tweets in the last week, though, I’m getting antsy.
  • I subscribed to Peg Cagle because she understands the concerns of Internet-enabled math teachers and she also understand the politics that concern the NCTM board of directors.

Press Clippings

  • I was interviewed for the New York Daily News about PhotoMath, which at one point in Fall 2014 was going to be the end of math teaching.
  • An interview with some kind of education-related Spanish-language blog.


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