Explained Absence

In Middlebury College jargon, “explained absences” are distinct from “excused” ones.  My failure to keep up with this blog is due to a bunch of things, but the biggest reason is probably that my writing energies have been directed elsewhere.  I’ve written a chapter for a volume that will be put out by Springer-Verlag in cooperation with the Association for Women in Mathematics.  I’ve also continued to write for the “On Teaching and Learning Mathematics” blog from the American Mathematical Society.

My latest post for the AMS blog was a struggle, to be honest.  It’s hard to exhort people to DO something when it’s unclear what can be done.  Also, people different ideas about what is appropriate and useful, as one of the comments makes clear. Essentially I was struggling with the question of voice, and in particular how much I should tone it down for that blog as opposed to this one.

One enormous benefit of working on the AMS blog has been the chance to collaborate with four excellent writer/educators.  I’m particularly proud of the series we did on active learning, because I learned a lot working on it with them. We’re hoping to condense it into a different form for another publication.

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Various and Sundry

My original purpose in starting this blog was to keep track of interesting mathematics-related items.  I see that I have way too many browser windows open, so it must be time to share. First up is “I Love Math and I Hate the Fields Medal” by Cathy O’Neill.  As someone who missed out on truly collaborative mathematical work until after graduate school, I find the collaborator vs. lone genius question fascinating.  I saw Cathy’s wonderful talk on data journalism at the Joint Mathematics Meetings (JMM) in January, and I follow her blog. In a similar vein are two pieces from Evelyn Lamb, one for Scientific American and the other for the American Mathematical Society (AMS) Blog on Math Blogs. In reading the latter, I was particularly struck by Izabella Laba’s examination of the unspoken assumptions we make when discussing mathematics and gender. Continue reading

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The Sixth Sense for Multiplication (a reblog)

In this case, the drawings are great, as is the commentary. Lately I’ve been seeing headlines such as “Parents go Back to School with the Common Core” and “Teachers Teaching Math to Students and Their Parents”; I wonder about the vanilla extract analogy at the end of this post. Is it really too late for math-challenged parents? I’d like to say no, but then again I occasionally have college students with a poor grasp of these concepts. Of course it may be easier to hear “come see what math your kids are working with” than “your calculus problem is actually an arithmetic problem; you need to go back to fifth or sixth grade math.”

Math with Bad Drawings

 Or, Seeing Arrays (Less Cinematic Than Seeing Dead People, But More Useful)

This year, I’m teaching younger students than I’ve ever taught before. These guys are 11 and 12. They’re newer than iPods. They watched YouTube before they learned to read.

And so, instead of derivatives and arctangents, I find myself pondering more elemental ideas. Stuff I haven’t thought about in ages. Decimals. Perimeters. Rounding.

And most of all: Multiplication.

It’s dawning on me what a rich, complex idea multiplication is. It’s basic, but it isn’t easy. So many of the troubles that rattle and unsettle older students (factorization, square roots, compound fractions, etc.) can be traced back to a shaky foundation in this humble operation.

What’s so subtle about multiplication? Well, rather than just tell you, I’ll try to show you, by using a simple visualization of what it means to multiply.

Multiplication is making an array.


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5 reasons not to share that Common Core worksheet on Facebook

A former student just reminded me of this excellent post. Worth a re-read!

Overthinking my teaching

(NOTE: If you arrived here via Facebook, welcome. You may also be interested in the perspective of a middle school teacher, Mr. Aion. Click on through for more.)

You are browsing Facebook on a Sunday evening. Someone has shared a baffling piece of math homework that was sent home with their child. Accompanying commentary bemoans the current state and future trajectory of mathematics teaching and learning, and lays blame for this at the feet of the Common Core State Standards.

You are baffled by the worksheet too. You are about to click the Share button.

But here are five reasons that’s a bad idea.

1. Credentials are not a trump card.

Almost invariably, the parent who shares the worksheet cites a degree as a credential for the critique. “I have a Bachelor of Science in electronics engineering,” wrote the parent in the recent “Letter to Jack”.


The math…

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Effortful Teaching

In a recent post, Ilana Horn offers this food for much thought:

I still wonder if it’s possible to adequately capture teaching practice –– in the broad meaning of the word that I know my colleagues intend — through the specification of routine activities.

Once upon a time I had a student tell me, “I want to study enough so that I don’t have to think during the exam.”  I responded that my goal in writing each exam is to find out how students think; if they’re not thinking during the exam I haven’t written it well.  More broadly, one of my teaching objectives is to move students away from the misconception that mathematics is merely a set of routine activities, to be memorized and then mindlessly executed.

When we talk about the habits of mind that we want our students to develop, can we also consider what habits of mind we value in teachers?  For example, how might the CCSSM Standards for Mathematical Practice inform our thinking about the practice of teaching? (Stay with me here — I know this might be a stretch.)  Don’t we want teachers to “Use appropriate tools strategically” in their classrooms? This is what I see in the wonderful example of “contextuality” at the end of Ilana Horn’s post.  I wish I had a recipe for responding to calculus students with weak algebra skills, but each underprepared student is underprepared in his or her own way, and each set of students is different.  I’ve developed a toolbox through practice and reading and consultation with colleagues and so on, but in the end I have to decide which approaches to use and how, depending on the context, adjusting as I get more data.

When I was writing my latest post for the AMS blog, our excellent Editor-in-Chief Ben Braun suggested a few titles.  I used one of his suggestions there and another here (thanks, Ben!).  It’s not that methods and plans and instructional activities aren’t important; they are necessary. But they are not sufficient on their own, as I tried to argue in my contribution to a New York Times dialog on “scripted teaching.” As many have pointed out, a teacher makes many decisions in the course of a single day.  To suggest that all or even most of those decisions could be decided ahead of time is to misunderstand the complexity of the work.  Given that we (with the notable exception of, for example, some school board members in Colorado) want to help our students become critical thinkers and flexible problem-solvers, it seems worth considering how teachers manage to balance technique and improvisation in their approaches to the “cultivation of learning” problem.

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This week, the Vermont State Board of Education adopted a resolution on assessment and accountability.  I won’t try to summarize; what makes it so strong, in my view, is the careful and detailed development of the principles behind the resolution.  Please read the whole thing.

It’s probably just a coincidence (though Vermonters like to think our tiny state has an outsized influence on the nation), but today U.S. Education Secretary Arne Duncan announced that states could delay the use of test results in teachers’ performance reviews.  Not nearly what the Vermont board is suggesting, but perhaps it’s a start.

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Of Possible Interest

In case you missed it, the American Mathematical Society has a new blog, On Teaching and Learning Mathematics.  Full disclosure:  I’m one of the editors, but Ben Braun deserves the credit for getting it up and running.  My first post there will appear July 10. UPDATE:  my first post is here.

Here are a few things I’ve come across recently:

“Teaching Kids ‘Grit’ is All the Rage.  Here’s What’s Wrong With It.” by Jeffrey Aaron Snyder in The New Republic.

Why the Common Core Math Standards Should Make you Mad,” a YouTube video.

Yet another great post from Keith Devlin:  “The Power of Dots.”  This is in response to the front-page New York Times article about the Common Core math standards.  (Update:  my own letter to the Times is here.)

Correlation does not imply equality” by Cathy O’Neil, about the silliness of using “Value-Added Measures” (VAM) to evaluate teachers.  Oh, and here’s the American Statistical Association statement on this subject.

Anything to add?

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