Spring Quarter Wrap-Up / Summer Kick-Off

Brief Remarks Encapsulating Spring Quarter

It’s hard to know how much disclosure is worthwhile here. For my own sake, I’m going to post a reminder to myself that this was the quarter I thought I was juggling everything like a champ only to have basically everyone in my life, in the same week, point out that I was only going through the motions of a world-class juggler. All the people, tasks, and things I thought I was juggling with such verve and style were lying on the ground around me.

There were basically endless ways to invest a few dozen hours this spring. That included interesting classes and projects at Stanford. It included the week I spent in Singapore learning from and working with ten of the world’s best math curriculum designers. It included speaking, workshops, and webinars. It included Graphing Stories, a project that seemed too fun not to pursue even though editing 160 stories cost me a pile of time during finals week.

I half-assed my way through much of it, convinced the entire time that I was owning all of it. In my first-year review, my advisers were rightly concerned about me, and about Stanford’s investment in me. I’m putting in a hectic pace this summer (see below) after which I need to sit down and take a machete to my calendar and day planner.

One outcome of the first year of grad school is that I became a faster, better writer. Blogging for years on an if-I-feel-like-it basis didn’t do much for my proficiency and speed at assembling an argument. Reading great writing daily (see below) and being asked to write a few thousand words about it every few weeks has done a lot of good for me. (I need to get faster at reading, though.)

The other outcome of this last year is that I’ve gone a long way to shed what Labaree (see below) calls the “normative view” of education. I’m less concerned with how I think things should be, with proving out my own pet theories, and more interested in accurately describing how they are. At the same time, other professors will insist that your pet theories are the reason why you were invited to doctoral study at Stanford. This is a tension I don’t expect to ever resolve. It’s a feature of grad school, not a bug.

The Sum Of My Research Interests

We submit a paper at the end of year two – a fun-sized research project, basically – that qualifies us for doctoral candidacy. The final project of the first year was a proposal for that study. My exact research question for that paper is this:

What teacher moves during a task’s launch lead to its productive implementation by the students?

Elaborating further, I taught a class a few weeks ago at my old high school. I popped in to say “hi” and wound up leading two activities for my old department head. In both cases, I had to launch the tasks. I set a scene and questioned the students about it to the point that I thought we were ready to work within it. With one problem, the task transitioned smoothly from launch to productive work. In the other, the task made a rocky transition. I find that moment of transition suspenseful, highly motivating, and worth some study.

Favorite Spring Quarter Papers

I read the last few pages of Augier & March five times, and the last paragraph, which features one of the most satisfying turns of a phrase I’ve read in grad school yet, a few more than that. I’d give a finger to be able to write a tenth as well as this team. (Rumor has it that March is the poet of the two. Reportedly, he rejects a syllabus for his Stanford business courses, assigning novels, poetry, and Homeric epics instead.) ¶ Berger & Stevenson wasn’t assigned but it’s valuable for anyone trying to carve out a living within education, but outside the classroom. ¶ Delpit explains why some minority parents prefer lecture and drill-oriented skill practice. ¶ Doyle & Carter describes the negotiation of a task between teacher and students better than anybody. This is high drama. You’re watching Ms. Dee start with a high-value academic task that her students negotiate down to nothing. ¶ Erlwanger’s piece was assigned as an example of research that has a) stood up over time and b) affected policy and practice in spite of its small sample size. ¶ The piece by Jackson, et al, isn’t available yet (though the author, herself, was extremely forthcoming) but it is the most forceful take on the task launch I’ve read yet. It comprises, like, 90% of the conceptual framework for my qualifying paper. ¶ Labaree’s proseminar course could basically be described in a single line: “why reform is hard to pull off.” Every time I read his stuff, I found myself thinking, “Oh so this is why Scott McLeod and Will Richardson are so angsty all the time.” His second piece describes the transition from teacher to researcher in a way that had all of us classroom expatriates nodding our heads grimly. ¶ The question no one seemed to be able to answer convincingly was “What is a conceptual framework, exactly, and how does it differ from a literature review?” Lester goes a long way, though.

Augier, Mie & March, James G. (2007). The pursuit of relevance in management education. California Management Review, 49(3) (Spring), 129-146.

Berger and Stevenson. K-12 entrepreneurship: slow entry, distant exit. Retrieved June 2007.

Lisa Delpit. (1995). The silenced dialogue. In Other people’s children (pp. 21-47). New York: New Press.

Doyle, W. & Carter, K. (1984). Academic tasks in classrooms. Curriculum Inquiry, 14(2), 129-149.

Erlwanger, S. (1973). Benny’s conception of rules and answers in IPI mathematics. Journal of Children’s Mathematical Behavior, 1(2), 7-26

Jackson, K. (2011). Investigating how setting up cognitively demanding tasks is related to the opportunities to learn in middle-grades mathematics classrooms.

Jackson, K. (2009). The social construction of youth and mathematics: The case of a fifth-grade classroom. In D.B. Martin (Ed.), Mathematics teaching, learning, and liberation in the lives of black children (pp. 175-199). New York: Routledge.

Labaree, D. (2003). The peculiar problems of preparing educational researchers. Educational Researcher, 32(4), 13-22.

Labaree, D. (1997). Public good, private goods: The American struggle over educational goals. American Educational Research Journal, 34(1) (Spring), 39-81.

Lester, F. (2009). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. ZDM, 37(6), 67-85.

Schoenfeld, A. (1988). When good teaching leads to bad results: The disasters of ‘well-taught’ mathematics courses. Educational Psychologist, 23(2), 145-166.

Stein, MK., Grover, B., Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.

Turner, Ralph. (2000/1960). Sponsored and contest mobility and the school system. In Arum, R. & Beattie, I (eds.). The structure of schooling (pp. 22-35). Mountain View: Mayfield.

Webb, N., Franke, M., De, T., Chan, A., Freund, D., Shein, P., Melkonian, D. (2009). ‘Explain to your partner’: teachers’ instructional practices and students’ dialogue in small groups. Cambridge Journal of Education, 39(1), 49-70.

Music For Final Exams

James Blake.

Spring Speaking & Workshops

I’ll be in ten states doing ten workshops and keynotes this summer. Three of those are still open for registration. Details here.

  1. Grand Forks, ND. June 13-14. Grand Forks Education Center.
  2. Beaufort, SC. June 21. Beaufort County Summer Institute.
  3. Bowling Green, KY. June 22-23. Green River Regional Educational Cooperative.
  4. Richmond VA. June 24. MathScience Innovation Center.
  5. New York City, NY. June 27. Math for America.
  6. Grapevine, TX. July 19. Conference for the Advancement of Mathematics Teaching.
  7. Orlando, FL. July 28-29. NCTM High School Institute.
  8. Washington, DC. July 31. Siemens STEM Academy.
  9. Atlanta, GA. August 2-5. The Lovett School.
  10. Mountain View, CA. September 10. The Perplexity Session.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Joe Henderson

    June 27, 2011 - 2:50 pm -

    Where to begin?

    (In a good way this time)

    1. Get used to the tension of being pulled in a million directions. Wait until the thought/reality of having children enters the picture. That’s prioritized things greatly for me.

    2. Very interesting RQ. I immediately think of power dynamics and the quality of the student/teacher relationship when I read it. I recommend nexus analysis as your lens toward getting at that answer.

    3. Thanks for the reads. Regarding your Labaree link, check this out at as well: http://www.amazon.com/Tinkering-toward-Utopia-Century-Public/dp/0674892836

    3a. Regarding how to do all the reading. I’ve found that it’s physically impossible. Learn what can be read at a surficial level and adjust accordingly. I don’t really understand a paper until the 3rd time around, but that’s only for the stellar works that prove germane to my own research.

    4. Regarding your Lester-related question, check out Cresswell and know that you’re right where you should be with this question: http://www.amazon.com/Research-Design-Qualitative-Quantitative-Approaches/dp/0761924426

    5. What’s the climatic impact of all that travel?

  2. Awesome research question! Can’t wait to read your paper when available. My guess is that some of the best “moves” will be dripping with teacher creativity, that some argue comes naturally to the teacher but others argue can be acquired or learned through thoughtful preparation and the ability to make small spontaneous revisions as the lesson unfolds.

    Reading the book “Little Bets” by Peter Sims that explores how small revisions can produce big results. Thought-enriching so far. I’m trying to apply it to my own teaching.

  3. Who are these curriculum designers in Singapore and is their work on the web? Would love to see it.

    And . . .
    I will never complain about being spread thin again. I hope one of those white points end up in the central part of this great country one day.

  4. Joe: 5. What’s the climatic impact of all that travel?

    Fer Pete’s sake ….

    Daniel: Who are these curriculum designers in Singapore and is their work on the web? Would love to see it.

    Malcolm Swan, Hugh Burkhardt, Charles Lovitt, Peng Yee Lee, Michal Yerushlmy, Jan De Lange, Ian Lowe, and some others. Especially Swan and Burkhardt, though, out at the Shell Centre. Their work there is really difficult to pry out in the open, unfortunately, though this link gets you close and we featured Swan’s work previously here.

  5. Joe Henderson

    June 28, 2011 - 9:39 am -

    Heh. Just wondering… Those are the types of research questions that I ask.

    But seriously though, keep up the good work.

  6. Dan,

    Thanks for the reading and the music tips. Love James Blake and just read the Schoenfeld article last week. It had been sitting on my desk for months. I just read something that you might find valuable.
    Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education 35(4), 258-291.

  7. Monty Zukowski

    June 28, 2011 - 10:16 am -

    You seemed to be doing an author by author takeaway from your favorite papers but you left out Schoenfeld, Stein, Turner, and Webb. Copy and paste error?

  8. @Jim: thanks for the recommendation.

    @Monty, in the past I haven’t done those recaps at all. In the interest of time, I rattled off a few thoughts as they came but nothing stuck out from those four except a strong positive association and a high rating in my research aggregator.

  9. These wrap-ups are always great reads.

    There were a number of educators debating the relative merits of Sal Khan’s pedagogy on Twitter, say a few weeks or a month ago. Dan was cast in the middle of it as elder statesman.

    He did what he does, and well. But while the dialogue was impassioned, it wasn’t terribly interesting. We get it at this point. Khan Academy’s polarizing, there’s some good but it’s not the future of ed, who cares. Oh and he uses Wikipedia who cares.

    Then the tone started to shift. Weirdly, the conversation became less about Khan and more about how to ‘market’ good pedagogy. One teacher insisted that research showed his method of teaching as the most effective.

    Dan mentioned that ‘research doesn’t go viral,’ and that we needed to start playing offense. I take it that ‘we’ meant his cadre of innovative educators, bloggers, and consultants.

    I wonder what the definition of ‘offense’ is, though.

    The vast majority of questions we have about teaching- smaller things like how to teach linear equations, bigger things like how to integrate procedural and conceptual knowledge- have almost all been researched. Some down to their essence.

    An understandable knock on research is that it’s divisive more than conclusive. As a teacher, I often felt this way. It also seemed a little heavy on “double blind triple blind a priori z quotient correlation control group table quotient z score type” vocabulary. It seemed too wrapped up in the science and not enough in the art of the thing.

    So I cowboyed on and built my own stuff.

    But in doing so, I ignored a lot of practical suggestions and sound advice. Look at the dozen or so studies posted above. All make profound insights about teaching. It’s not always unresolved fracas and intellectual vanity.

    Research won’t ever go viral. But if it did, or could, how would that change the way classrooms look?

  10. I wanted to say that I really appreciated your candor about the uncomfortable slamming shut of the gap between your own experience of certainty that you were seamlessly juggling a million flaming chainsaws with ease versus the opinions of those who lived in your orbit during your juggling experience. Those gap-closing moments are a bitch. For me, it’s that “Wile E. Coyote” moment when my awareness of my situation catches up with its reality. And that’s usually what happens about two nanoseconds before I blink twice at the camera, gulp, and get slammed against the canyon bottom by Lady Gravity.

    What was most valuable about this reflection for me was your implicit reminder of how grounding it is to reflect while one is “in process.” The times when I am too busy to reflect are *exactly* the moments when I most need to stop, sit down, and reflect on what is going on and what I am missing.

    That kind of reflection is way different than academic writing, but is very useful in its own anchoring way.

    Thank you for reminding me that, when I am *least* inclined to sit down and reflect, *that* is exactly the signal that I am overdue for doing so.

    – Elizabeth (aka @cheesemonkeysf on Twitter)

  11. Thanks for the reading material. Doyle’s article and the two axes of Ambiguity versus Risk (and what points on that graph mean) has me thinking about all of the things that I do. I can add that to my Complexity versus Rigor graph. Strong stuff.

    I also wonder what happens if you unhitch Risk from Grades…

    BTW, thanks for the Shell Centre link. The “Red Book” is one of my favorites and a reason that I can’t wait to see what becomes of the Graphing Stories project.

  12. Thanks for the pointer to the Berger & Stevenson paper – best thing I’ve ever read on ed-entrepreneurship! I am currently evangelizing the hell out of your Perplexity session to the math teachers at my school, to see if I can convince one of them to make the trip, so I can experience it vicariously.

  13. Thanks for the list of papers. I also enjoyed reading Labaree, although we read his “Peculiar Problems” paper as one of our very first readings at the beginning of the year. Sobering, indeed. We also read Erlwanger’s “Benny” – it’s pretty amazing to think that rarely did it occur to math ed researchers prior to that paper/era to actually *talk* to a child and write about it. On the other hand, I wonder if that paper has had undue influence, inspiring researchers to do less-necessary qualitative work when quantitative studies might have proven more useful.

    I see Jan de Lange was on your list of designers you experienced in Singapore. You might consider attending (caution, shameless plug ahead) the Realistic Math Education conference this fall at CU-Boulder. Jan and many others from the Freudenthal Institute presented at the last conference, and I believe Doug Clements will be at this year’s conference, which will focus on the design and use of learning progressions in math ed. See http://fius.org/ for details.

  14. Somewhat tangential, so please allow the intent to ask one, what I perceive to be, unasked question. Is the goal in mathematics education to teach mathematics or teach children? If it is both, is can it “respect” both?