# Jim Stigler

Because the book that I was reading in my last post mentioned stark differences between Japanese and American instruction. I decided to watch this talk given by Jim Stigler earlier this year, and took some notes:

Jim teaches mathematics, but not at community college level, so his background is university education. Studies below are more remedial level, outside his core experience.

- Focus on cross-cultural work, and culture differences
- K-12 TIMMS, study teaching, do video survey, 8th grade math class
- random sample, get data on average teaching
- teaching is a cultural activity. Huge differences across culture, small difference within culture. Very pervasive, and constraining. Even with autonomy, they choose to teach with same technique.
- American teacher demonstrates how to solve problem, then students practice. Japanese present class with problem that students don’t know how to solve. Students are confused, challenged, agonized. Then students share approaches, and discuss.
- Teachers don’t goto teaching school, so they repeat how their own teachers did it.
- Culture diff: We think it is unfair to expect students to do something they haven’t been shown before. We are very, very uncomfortable to watch someone struggle or be challenged.
- Very hard to change cultural activity. Students/parents will go on strike. Have to break the ‘natural order of things’.

- devolpmental mathematics
- Japanese do better on international tests, because of their instruction. Not innate abilities.
- But there is no one way, because other countries do very well too, but employ different techniques.
- not even focus on ‘real-world’ problems increase understanding. Same with ‘group-work’.
- Something else at issue: quality and enthusiasm. Techer creates effective learning environment regardless of teaching methodology.
- Japanese teach area of triangle: give students sheets of many different kinds of triangles, no measurements or dotted-lines for height. Ask: come up with a way to get the area that will work for all of these triangles. Can cut, fold, rotate, etc.
- No real pattern in these learning approaches. Amer teacher gets uncomfortable, and gives the formula away. Cultural change difficult.
- In US. no teachers that presented a making connection problem followed through, always turned it into a procedure problem.
- two features connected with higher performance
- struggle. have to actually work at it. desirable difficulties.
- making connections: explicit relationship between problem (real-world) and procudure (math concepts).

- fast, fun, exciting: think you understand, but bad when measured.
- hard, sticky, no fun: hate the experience, but good when measured.

- Hong Kong has many procedure problems. So it’s not the quantity of making connections lessons that counts. Just need some.
- We handle variability across schools: low-achieving students in different school than high-achieving. Japan, large school, variability occurs within classroom. Don’t track ability.
- To measure all the angles in a pentagon, and notice you always get same answer, is not a struggle approach. Instead measure, 3, 4, 5, predict 6-sided. then try derive the formula. explain why the formula works. Can you always divide polygon into triangles?
- Watch the TIMSS videos
- Interviews at community college (students that failed a placement test)
- students view math as whole bunch of rules to be memorized. Don’t think that it’s something that can be figured with analysis, or that there are reasons behind the rules.
- When asking conceptual (non-standard) questions, got remarkably low correct answers. Regardless of student placement (even the better placed students didn’t get it, at the same rate) Don’t know what it means to multiply by a fraction.

- clear principles to develop instruction
- Don’t get to high achieveing, but starting with procedure. Must integrate concepts all the way.
- Try stats class, in case these students auto-shutdown in normal math class.
- Add 3rd bullet to learning strategy: Practice. but not repitition. deliberate practice, something differs with each problem instance, so have to refigure, reinforce neural paths.
- stat and math proficiency, flexible and stable knowledge understand concepts, procedure stragegies, productive disposition (belief can figure out answer).
- primary drivers: struggle, make connection, practice.
- need instructional resources to create these learning opportunities. need students that are prepared to engage (esp if have history of failure). need teachers that can implement, flexible, creative.
- lesson design: try to implement struggle by starting with rich problems. helps to start with struggle. try to change cultural routine.
- conception flow: figure out how to ask questions. see polygon example above. Why does this work? is assumption always valid?
- practice not repitive. It’s analysis.

- questions, comments.
- Feels like disservice to directly challenge and watch students struggle. unfair to ask students to solve problem they’ve never seen before. Teachers supposed to dispense knowledge. Image of newton and apple: understanding supposed to happen quickly; easy to fake: “Oh! I get it.” Teacher has to have resolve not to continue unless students actually gets it. Must require engagement.
- clear about struggle: have clear problem. it must be useful interesting question. problem directed by goal, struggle must be making direct progress toward solution. must believe that the struggle will pay off.
- Japan: socialize students to understand that learning is about suffering. vs America: engagement is entertainment. Students: Jap 90% think study hard is way to success, America 90% think getting good teacher.
- Are there materials that will prevent teacher from regressing to old behavior/technique. Have exams that are really tough on concepts, integrative of procedures. Test must be aligned with the goal of instruction.
- One teacher allowed students to bring in sheet of whatever they wanted: then they stopped complaining about it being memorization.

- Summary:
- Struggle to learn. But it pays off.
- Make conceptual connections. The procedure/formula comes from analysis.
- Practice, but not repetition.