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Saturday, July 30, 2011

Summer Learning, PCMI Edition: Deeper Criteria

This is a series of posts that are reflections from the Park City Mathematics Institute Secondary School Teachers Program.

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"
He asked us to predict the instructional features which must be present for students to learn with understanding. These were the guesses that my group brainstormed. If you want to play the home version of the game, take a moment to jot down what you think they are too.
  • 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
However researchers only found 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.
The struggle thing rang true for me. At some level I internalized that idea long ago. I'm still coming to terms with the connection-making point. The same concept was approached earlier by Gail Burrill with respect to the Common Core standards. She pointed out that in American classrooms, teachers can 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."