This is the post I’ll re-read when I want to remember my five years at Stanford’s Graduate School of Education.

Why Grad School

My first year at Stanford was almost my last. A talk I had given right before I arrived at Stanford rolled past one million views. That opened up a lot of opportunities outside of Stanford, very few of which I declined. During what was supposed to be a perfunctory first-year review, my advisers invited me, with as much grace as I could expect of them, to leave Stanford, to return when I had more focus. I stuck around but I think all of us knew then I wasn’t really cut out for R1 university work. Still, I figured I’d work with teachers in a preservice program somewhere and a doctorate wouldn’t hurt my employment odds.

Two years later, just before my dissertation proposal was due, I received a job offer that was really too perfect to pass up, from people who didn’t care whether or not I had a graduate degree. They were nice enough to allow me to defer that offer until this summer.

All of this is to say, I had every incentive to walk, to join the ranks of the ABD. Here’s why I stayed, why I’d do it again even though my new employers don’t care about the letters after my name, and why I’d recommend graduate study to anybody who can make the logistics work: developing, proposing, studying, analyzing, and writing a dissertation works every single mental muscle you have and forces you to develop a dozen new ones. It’s the academic centathlon. I know how to ask more precise questions and how to better interrogate my prior assumptions about those questions. I know many more techniques for collecting data and statistical techniques for answering questions about those data. I know how to automate aspects of that data analysis through scripting. My writing is stronger now. My presentation skills are more polished. My thinking about mathematics education is more developed now, though still a work in progress.

It’s certainly possible to develop all of those muscles separately, without the extra overhead of a dissertation. (Michael Pershan seems to be making a go of it on Twitter, with Ilana Horn as his principle adviser.) But tying them all together in the service of this enormous project was uniquely satisfying.

Technology

If you’re thinking about grad school, take advantage of your tools:

Papers to manage references. Dropbox to sync them across machines. iAnnotate PDF to read and mark them up on an iPad. Google Scholar for everything. Scrivener for writing anything with more than five headings. Google Docs for writing anything else. I couldn’t survive grad school without those six tools.

Google Tasks for scheduling to-do’s. Boomerang for scheduling emails. I couldn’t survive professional life without those two tools.

The Last Five Years

• Wrote two books.
• Foster parented three kids.
• Buried my dad.
• Traveled around the world with my wife.
• Learned from the best.
• Collaborated with great people on interesting projects.
• Traveled to a bunch of states and several countries, meeting basically all of you at one point or another.
• Keynoted a couple of big-ish conferences.

Opportunity Cost

• Never presented at AERA, PME, or ICMI.
• Never attended AERA, PME, or ICMI.
• Never gave a poster talk.
• Never gave an academic presentation of any kind until my dissertation defense.
• Never taught a course.
• Never TA’d a course.
• Never supervised any of the promising new teachers in Stanford’s teacher prep program.
• Never connected with the people in my research group as much or as often as I would have liked.
• Attended only a small fraction of the lunch talks and job talks and colloquia and dissertation defenses from the great thinkers passing through Stanford.
• Heard “Oh — do you still go here?” way too often.

Gratitude

• You guys. I thanked you all in my dissertation’s front matter and I’ll thank you here. The difference between a happy and sad graduate school experience often cuts on whether or not you like to write. In our conversations here, you guys made me, if not a great writer, someone who likes to write. As much as some of you drive me crazy, our back-and-forths made my arguments sharper and easier to defend in the dissertation. There was also that time that I asked on Twitter for help piloting assessment items in your classes and dozens of you helped me out. You have no idea what that kind of support is worth to a grad student around here.
• I never got sick of my dissertation. I didn’t enjoy some of the logistics of its data collection. I didn’t always have the time I wanted to work on it. But I never got tired of it, which is some kind of gift.
• Michael Pershan. My codes needed interrater reliability, the stuff that says, “Someone else can reliably see the world how I see the world, whether or not that’s the right way to see the world.” I hired Pershan onto my research team (doubling the size of my research team) when my time was crunched. He coded a bunch of data as fast as I needed and also changed “how I see the world” in some important ways.
• Desmos. I had some of the area’s best computer engineers and designers building my dissertation intervention. I got very lucky there.
• Jo Boaler. Jo was my principal adviser for all but my first year of grad school. There were a lot of great reasons to ask for her mentorship, but one of the best is that I never had to hide from her my lack of ambition for a tenure-track research job. As those ambitions faded, a lot of advisers in her position would have waitlisted me, focusing their efforts (rationally) on students who stood a chance to carry their research agenda forward. She invested more in my work than I had any reason to expect and I’ll always be grateful for that.

So that’s that. On to the next thing.

Title

Functionary: Learning to Communicate Mathematically in Online Environments

Bloggy Abstract

I took a collection of recommendations from researchers in the fields of online education and mathematics education and asked our friends at Desmos to tie them all together in a digital middle-school math lesson. These recommendations had never been synthesized before. We piloted and iterated that lesson for a year. I then tested that Desmos lesson against a typical online math lesson (lecture-based instruction followed by recall exercises) in a pretest-posttest design. Both conditions learned. The Desmos lesson learned more. (Read the technical abstract.)

Mixed Media

You’re welcome to watch this 90-second summary, watch my defense, read it if you have a few minutes, or eventually use it with your students.

Process Notes

True story: I wrote it with you, the reader of math blogs, in mind.

That is to say, it’s awfully tempting in grad school to lard up your writing with jargon as some kind of shield against criticism. (If your critics can’t understand your writing, they probably can’t criticize it and if you’re lucky they’ll think that’s their fault.) Instead I tried to write as conversationally as possible with as much precision and clarity as I could manage. This didn’t always work. Occasionally, my advisers would chide me for being “too chatty.” That was helpful. Then I stocked my committee with four of my favorite writers from Stanford’s Graduate School of Education and let the chips fall.

Everything from my methods section and beyond gets fairly technical, but if you’re looking for a review of online education and the language of mathematics, I think the early chapters offer a readable summary of important research.

David Pimm:

We name things for reference, and hopefully for ease of reference, to draw attention to the thing named. But naming also classifies and hence causes us to look at the named thing in particular ways, the chosen symbol stressing some and ignoring other attributes of the named object. Naming something gives us power over it, particularly in algebra, as we can transform and combine expressions involving the unknown — to find out more about it (p. 127).

This is the strongest case for algebra. Your ability to speak, think, and use variable notation makes you powerful — particularly when you interact with computers. But how often do students think of variables in math class and feel powerful? Those experiences aren’t simple to devise.

I read Pimm’s excellent book over the holiday in preparation for my dissertation proposal. I’ve pulled out several pages worth of quotes and supplemented them with a) my analysis and b) some details about my upcoming study. Comments are turned on in the Google doc, so let’s talk about it.

Featured Comments

David Lloyd:

Perhaps using words as the descriptor (“number of songs”) instead of using X (as in “Let x = the number of songs on Dave’s iPod”) would be a step in the right direction? The same level of rigor without the confusion of what X equals.

Galen:

How often do students name their own variables?

Dina Strasser isn’t and wishes she was:

In June of this year, I turned down the most prestigious scholarship for doctoral work that my local, nationally recognized university had to offer. It was as generous as you could hope for: full tuition, opportunities for stipends and grants. The gracious professors there, and others who helped me with my applications, spent hours of their own time walking me through the process, writing recommendations; they said, to wit, you were born to be a Ph.D. And I knew it, because I had figured that out for myself in third grade. It was the only lifelong dream I have ever had.

Paul Franz was and now isn’t:

So why give up the prospect of a cushy professorship for an uncertain career as an entertainer and artist? Because being a PhD student has made me miserable, and because I would rather be true to myself and take a chance at pursuing my actual passions than pursue a path which I know ends in unhappiness and cynicism.

Paul was a member of my grad program here at Stanford. Dina is the Terrence Malick of ELA bloggers. Both are thoughtful writers and you’ll find lots to learn from about life and work from both their pieces.