One afternoon we listened to a lecture/powerpoint by Douglas Corey of Brigham Young University about comparisons of effective teachers at home and abroad. Toward the end of his talk, he seemed to have partaken of a generous serving of the edureformer kool aid and came across as anti-teacher or at least teacher-concern-dismissive, which obviously turned many people off. However I took away some notes about his research that struck me as important.

Based on classroom-level comparisons between different countries from the TIMSS video study, researchers found

- there is no single effective teaching method
- all high-achieving countries teach quite differently
- we can not judge a lesson's effectiveness by methods used, but rather
- effective lessons have deeper criteria in common he called "instructional principles"

- teacher content knowledge
- problem-solving
- students have to be working and thinking
- deeper explorations
- students making connections
- continuous assessment that informs instruction
- deliberate metacognition is part of instruction
- teacher believes all students can learn rigorous, conceptual mathematics
- students need to spend time thinking about math outside of class

**:**

*two*- "intellectual engagement" - the teacher has to get the kids thinking about a problem. Students have to
*struggle*. "Struggle" means students expend effort to make sense of math, to figure something out that is not immediately apparent. It does not mean needless frustration.

- "connection-making" - the focus of the teaching has to be on making connections. Connections don't come by accident but must be an explicit focus of planned instruction.

*plan and ask*connection-making questions and activities, but students mostly still end up

*doing procedures*. A big question I am still grappling with is how to design and deliver instruction so that the students are

*doing connections*. I have only vague notions about what that would even look like. I don't really know what to do with this yet beyond hang a sign on the bulletin board next to my desk at school that says "make the students do connections."