If all of this ladder of abstraction material has seemed soft, fuzzy, and opinionated so far, I’ll offer up my summer project, A Literature Review of the Process and Product of Abstraction. Feel free to add comments or questions in the margins. I’ll try to get in there and chop it up with you. If you have written more than a handful of literature reviews yourself, I’d be grateful for your feedback on the format.
That video has me explaining the research from my qualifying paper, which is the culmination of a grad student’s second year at Stanford’s School of Education. It qualifies you, in the eyes of your advisers, to take on the much larger research project they call a dissertation.
I showed two groups of students an image of a water tank. One group saw all the information and abstraction relevant to the question, “How long will it take to fill?” The other group just saw the question, “How long will it take to fill?” and had to request the information and develop the abstractions themselves. If you’re remotely aware of this blog’s obsessions, you can guess the research questions I asked about that experiment. (Watch the video!) Perhaps the most surprising outcome of the experiment (to me) was that the higher-achieving math students in the study really disliked not having all the information and abstractions in front of them.
If you’d like to read the paper, you can feel free. If you have some commentary or criticism that’d profit us here, you’re welcome to the comments.
A few other notes about the qualifying paper, my second year of grad school, and my next year of grad school:
Stanford gives great feedback. The school of education has several schools within it. My school, Curriculum and Teacher Education, does a great job preparing its students for the qualifying paper. In the spring of your first year, you take an introductory course. In the fall of your second year, you take a doctoral seminar that builds to a proposal for the qualifier. In my particular case, I had a qualifying committee that was generous with feedback when I needed it. I also developed the study while taking a course with Alan Schoenfeld at UC Berkeley. So my ideas and writing had as many as eight sets of eyes on them, as needed. (And that’s just faculty. My student-friends gave great feedback also.) That’s amazing and, from my understanding, kind of rare in doctoral programs. That criticism was occasionally contradictory, however, which required a certain discernment I haven’t really developed yet.
The criticism I remember most vividly: a) my weak review of the literature, b) the sense that I wasn’t really taking myself anywhere new with the study, and c) a claim about equity that had me reaching beyond my data.
Great classes I took.
- Accelerated programming in C++. I had no business in an accelerated course in anything related to programming but I had a scheduling conflict and they weren’t putting the standard class online. It nearly ate me alive but spat me out a better programmer and granted me a great deal of sympathy for students who felt like idiots in classes that I taught.
- Analysis of Social Interaction. With Ray McDermott, if that name means anything to you. If it doesn’t, read “Can We Afford Theories of Learning?“, which begins, “If American culture were an Internet, the domain name “learning” would be owned outright by the testing services that use it to feed the yearnings of parents and their schoolchildren.” So a great quarter, basically.
- Qualitative Analysis, with Pam Grossman (one of my advisers) and Sam Wineburg, who have taught together for decades, dating back to their time together at the University of Washington. Put these items under the heading “exceeded expectations”: a) the four assignments, b) the syllabus, c) their respect for our time.
- Directed Research, for practical reasons. Make sure you write that one down, class of 2016-2017. There’s no excuse not to max out your units.
Papers I flagged as being particularly worthwhile.
- Berman, P. & McLaughlin, M. (1979). An exploratory study of school district adaptation.
- Brown, JS. & Burton, RR. (1978). Diagnostic models for procedural bugs in basic mathematical skills.
- Cohen, D. (1990). A revolution in one classroom: The case of Mrs. Oublier.
- Egan, K. (1999). Education’s three old ideas, and a better idea.
- Geertz, C. (1972). Deep play: notes on the Balinese cockfight.
- Lareau, A. (2000). Common problems in field work: A personal essay.
- Pollak, H., Albers, D. & Thibodeux, M. (1984). A conversation with Henry Pollak.
- Schoenfeld, A. (2011). A modest proposal.
- Schoenfeld, A. (1998). Making mathematics and making pasta: From cookbook procedures to really cooking.
- Small, M. (2009). ‘How many cases do I need?’: On science and the logic of case selection in field-based research.
- Tyler, R. (1950). Basic principles of curriculum and instruction.
What I’ll be doing my third year.
I have this image in my head from a movie from my childhood that I’ve forgotten. A man stands with one foot on each of two rowboats that are side-by-side. It seems like a good, fun idea at first but then the boats start to drift apart. His weight bears down on both boats, pushing them farther and faster apart until he falls in the water and we laugh.
One boat is christened “Grad School” and the other is “The Other Stuff.” The thing I can do to help myself right here is tie several cords from one to the other, committing myself to projects, papers, and talks that are researchable or that will, at least, inform my research. I just don’t have the time for a long stay in grad school but I may not have the skill to get a dissertation done quickly either.
So for the third year:
- I’m still designing tasks for and consulting with publishers in the US and elsewhere.
- I’ll be facilitating some workshops and speaking at some conferences.
- I’ll be taking the winter quarter off to work with The Shell Centre in the UK. (Did you guys know they pilot their tasks five times before they release them. What new questions do they ask in each new pilot? Let’s find out this winter, okay?)
- I’d like to submit a dissertation proposal at the end of this school year. Vegas oddsmakers are frowning at that one, though.
- I’ve taken the required major coursework for the education doctorate but I need to complete several more courses in my minor emphasis in computer science. I’ll be taking as many of those as I can this next year, online as much as possible. As I narrow in on a proposal, I’ll take some appropriate methods courses also. (ie. if I plan to run an experiment, then something in experimental methods.)
- I’ll continue to develop 101questions into the tool I need to be.
Of course, all of this has been and will be more fun with you guys tagging along, chirping comments and critiques at me as we go.
2012 Sep 13. Elaine Watson posts some thoughtful commentary on my qualifier.
What would you do with a doctorate degree that you are not already doing?
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. (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
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.
- Grand Forks, ND. June 13-14. Grand Forks Education Center.
- Beaufort, SC. June 21. Beaufort County Summer Institute.
- Bowling Green, KY. June 22-23. Green River Regional Educational Cooperative.
- Richmond VA. June 24. MathScience Innovation Center.
- New York City, NY. June 27. Math for America.
- Grapevine, TX. July 19. Conference for the Advancement of Mathematics Teaching.
- Orlando, FL. July 28-29. NCTM High School Institute.
- Washington, DC. July 31. Siemens STEM Academy.
- Atlanta, GA. August 2-5. The Lovett School.
- Mountain View, CA. September 10. The Perplexity Session.
Brief Remarks Encapsulating Winter Quarter
- Mentorship. This is new: I switched emphases from teacher education to math education. I’m retaining Pam Grossman (my current adviser in teacher education) but adding Jo Boaler (who is the math education professor at Stanford) to the Team Dan Meyer, Ph.D. roster. The education of new teachers and development of current teachers is still wildly fascinating to me, but I am asked with growing frequency to speak to and write for and work with math educators. I know enough about what I don’t know to know that I need to study up and work out some blind spots in my vision if I’m going to be effective in any of those roles.
- Temptation. The private sector extended several invitations my way last quarter to leave Stanford — to cut a corner, basically, and go straight to work. Some of those invitations were easier to turn down than others. In every case, though, I was grateful for the opportunity to remind myself again of the reasons I committed to this difficult, frequently humbling work.
- Music. I tend to wear out the grooves on a single record during finals week each quarter, playing the same songs over and over and over until they become useful white noise. Fall quarter it was Mumford and Sons. Winter quarter it was the soundtrack to The Social Network by Trent Reznor and Atticus Ross. Anyway.
Notes on last quarter’s classes:
- Statistical Methods in Education. Key skill: analyze regression tables like this one for meaning. Prof. Stevens said in fall quarter he loves the moment when an author drops the tables in a paper because up until that point we’re just bobbing along with the author’s narrative. But the table tells its own stories.
- Proseminar. One of my colleagues said it pretty well: “In any given week of proseminar, two thirds of the class simply don’t give a damn.” Which is to say the wonks don’t really care much about the pedagogy and the teachers don’t care much for policy and the social theorists have an entirely separate set of interests.
- Casual Learning Technologies. This was a mixed bag. The field is really, really new (James Gee, the discipline’s flag-bearer, is a linguist by training who got interested in gaming all of six years ago) and has a lot of room to grow. Which is to say, I wasn’t dazzled by the literature. Remind me to post my group’s final project, though. That was fun.
- EDUC325C — Proseminar. David Labaree, Francisco Ramirez. Required. Labaree, in his initial remarks to the class: “You may have heard this course features too much reading, too much writing, that the criticism is too harsh, and our opinion of schools is too pessimistic. It’s all true.” (Labaree has written a few books of note.)
- EDUC359F — Research in Mathematics Education. Jo Boaler. Elective.
- EDUC424 — Introduction to Research in Curriculum and Teacher Education. Hilda Borko. Required.
Winter Quarter #GradSkool Tweets
- Yes, this is #gradskool and, yes, Angry Birds is on the syllabus. http://yfrog.com/gzqghxsj 6 Jan
- Today’s #gradskool throw-down: Who won in US schools and universities — Dewey or Thorndike? Great discussion. Lots of nuance. 18 Jan
- Stats prof, reading the room: “I don’t know how to make this more lively. I really don’t know how to make this more lively.” #gradskool 23 Feb
- Carol Dweck is speaking. I am listening. #gradskool yfrog.com/h4l7mjoj 8 Mar
- Dweck has no slides. She’s four-feet tall, sitting on a table, feet dangling beneath her, positively /owning/ the room. #gradskool 8 Mar
- Five rows from Michelle Rhee. An unlikely mix of education and business grad students in the building. yfrog.com/h0wo8yhj 11 Mar
- Rhee: “What we did definitely made people unhappy.” She literally seems to believe that diplomacy and efficacy are mutually exclusive. 11 Mar
- Rhee: “Is there a less controversial way to do controversial things? I don’t know the answer to that.” 11 Mar
- Rhee: “Chris Christie? I love him. He’s a Republican and I’m a Democrat. It’s not obvious we’d get along so well.” Seriously? 11 Mar
- Rhee: “I worry about people going into the job with longevity as one of the goals. I’m not a big believer in longevity.” 11 Mar
- GSB student: “Did you really eat a bee?” Rhee: “I did eat a bee.” Way to pitch her a fastball, Chuck. 11 Mar
- These moguls were the most out of place contingent at the Rhee Q&A. Good luck finding the executive washroom, fellas. yfrog.com/gzz8vdcj 11 Mar
Michelle Rhee followed me on Twitter the next day. So look out, right?
Favorite Winter Quarter Papers
- Brown. Physical science and an assessment of the in-service workshop as an effective means of influencing the teacher verbal role behavior of guided discovery/inquiry. (1972)
- Engaging schools: Fostering high school students’ motivation to learn. The National Academies Press (2003) pp. 31-59
- Gee. Good video games and good learning. Phi Kappa Phi Forum (2005) vol. 85 (2) pp. 33
- Glazerman et al. Evaluating teachers: The important role of value-added. (2010) pp. 1-13
- Nash. Fostering moral conversations in the college classroom. Journal on Excellence in College Teaching (1996) vol. 7 (1) pp. 83-106
- Wineburg. Crazy for history. Journal of American History (2004) vol. 90 (4) pp. 1401-1414
I spent a few weeks of my winter quarter trying to make sense of the PBL / anti-PBL scrum of 06/07. Those papers are below, in chronological order, with a closing paper pitched specifically at math educators.
- Kirschner et al. Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist (2006) vol. 41 (2) pp. 75-86
- Hmelo-Silver et al. Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist (2007) vol. 42 (2) pp. 99-107
- Kuhn. Is direct instruction an answer to the right question?. Educational Psychologist (2007) vol. 42 (2) pp. 109-113
- Schmidt et al. Problem-based learning is compatible with human cognitive architecture: Commentary on Kirschner, Sweller, and Clark (2006). Educational Psychologist (2007) vol. 42 (2) pp. 91-97
- Sweller et al. Why minimally guided teaching techniques do not work: A reply to commentaries. Educational Psychologist (2007) vol. 42 (2) pp. 115-121
- Sweller et al. Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Journal of the American Mathematical Society (2010) vol. 57 (10) pp. 1303-1304
Spring Speaking & Workshops
Brief Encapsulating Remarks
- Academic writing is hard, especially if you’ve grown accustomed for the last five years to posting whatever random 450 words pass through your head at a given moment. Writing even something as basic as a literature review was like trying to run a marathon on sixteen tabs of Benadryl.
- Too many units. Someone on the welcome weekend panel — none of us can remember who it was — told us all to max out our units. Never again.
- Blogiversity. I was talking to Jo Boaler last night (name drop!) and she admitted she didn’t really get the whole blogging thing. I said I didn’t really get the whole peer-reviewed journal thing. Then I recommended blogging in two ways. First, I showed her the time I asked you to help me identify a core practice of teaching and you came through with 100 (mostly) measured responses. Second, I showed her our ongoing soon-to-end-I-swear investigation of pseudocontext. I’m sure it would’ve taken me many months more to come up with my working definition of pseudocontext had you all not come through with so many examples.
I’m putting in the minimum this quarter, units-wise:
- EDUC250B – Statistical Methods in Education. Eric Bettinger. Required.
- EDUC325B – Proseminar. Hilda Borko, Brigid Barron. Required.
- EDUC396X/176X – Casual Learning Technologies. Shelley Goldman. With an emphasis on iPhone apps in education. This one’s candy. Here’s the syllabus.
Fall Quarter #GradSkool Tweets
- Heroic student in seminar: “Are these articles purposefully obtuse?” #gradskool 4:13 PM Sep 30th, 2010
- In CS section taught by a soph. 10 yrs younger than me. I love watching
non-pros teach. This kid is a natural. Great questioning. #gradskool 5:48 PM Oct 1th, 2010
- Over a career, it’s possible to align yourself to an incentive and status
structure that will strike laypeople as totally insane. #gradskool 6:48 PM Oct 1th, 2010
- Struggling to write like a human being. #gradskool 9:31 PM Oct 3rd, 2010
- Pigeons: Central Park :: Bicyclists : College. Fearless pests. #gradskool 5:36 PM Oct 12th, 2010
- “Known-answer question” is the awesomest term I learned in #gradskool last week. As in, “My kids hate when I ask known-answer questions.” 8:03 PM Oct 16th, 2010
- “By the time you see a paper in a journal, the field has moved on.” (Loeb, 2010, lecture). #gradskool 8:27 PM Oct 22nd, 2010
- The proseminar professors are bickering over the definition of a “literature review.” I love when they get going like this. #gradskool 5:27 PM Nov 9th, 2010
- Jo Boaler is subbing in my professional pedagogy class. Freak out! #gradskool http://j.mp/d7ybma 10:26 PM Nov 10th, 2010
- Critiquing the professor’s book in class, referring to him in the third person. Weird. #gradskool http://j.mp/cCmA3x 6:35 PM Nov 11th, 2010
- Stats HW. Find the formula. Identify the variables. Plug ’em in. Weird being on the other side of this arrangement. #gradskool 5:42 AM Nov 12th, 2010
These are the ones I gave my highest rating in my aggregator.
- Carrel. Does Professor Quality Matter? Evidence from Random Assignment of Students to Professors. NBER Working Paper No. 14081. National Bureau of Economic Research (2008)
- Gamoran Sherin and Van Es. Effects of Video Club Participation on Teachers’ Professional Vision. Journal of Teacher Education (2008) vol. 60 (1) pp. 20-37
- Rothstein et al. Grading education: Getting accountability right. (2008)
- Nelson et al. A culture of collaborative inquiry: Learning to develop and support professional learning communities. The Teachers College Record (2008) vol. 110 (6) pp. 1269-1303
- Hiebert et al. A knowledge base for the teaching profession: What would it look like and how can we get one?. Educational researcher (2002) vol. 31 (5) pp. 3
- Lewis and Tsuchida. A lesson is like a swiftly flowing river. American Educator (1998) vol. 22 (4) pp. 12–17
- Grossman et al. Toward a theory of teacher community. Teachers College Record (2001) vol. 103 (6) pp. 942-1012
- Barnes et al. Teaching and the case method: Text, cases, and readings. (1994)
- Grossman et al. Teaching practice: A cross-professional perspective. The Teachers College Record (2009) vol. 111 (9) pp. 2055-2100
Winter Speaking & Workshops
- Doha, Qatar. January 28-29. Near East South Asia Council of Overseas Schools.
- Naperville, IL. February 25. DuPage Valley Mathematics Conference.
- San Diego, CA. March 7. California Charter Schools Conference.
- Calgary, Canada. March 21. Calgary Regional Consortium.
- Edmonton, Canada. March 22. Edmonton Regional Learning Consortium.