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  1. High Leverage Practices

  2. Developing Teachers’ Capacity to Reflect on and Learn From Teaching Peg Smith University of Pittsburgh Teachers Development Group Leadership Seminar on Mathematics Professional Development February 11, 2009

  3. What is Reflection? • A piece of installation art by Shane Cooper • A song by progressive rock band Tool • An online card game • An episode of Power Rangers:SPD • A map that transforms an object into its mirror image • It is a conscious mental and usually purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul.

  4. What is Reflection? • A piece of installation art by Shane Cooper • A song by progressive rock band Tool • An online card game • An episode of Power Rangers:SPD • A map that transforms an object into its mirror image • It is a conscious mental and usually purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul.

  5. What is Reflection? A piece of installation art by Shane Cooper A song by progressive rock band Tool An online card game An episode of Power Rangers:SPD A map that transforms an object into its mirror image It is a conscious mental and usually purposive process relying on thinking, reasoning, and examining one's own actions and interactions in the classroom and how those actions are affecting students’ learning.

  6. Why Reflect? • Teachers do not learn from unexamined practice (Dewey, 1938). • Research suggests that reflecting on teaching can lead to improvements in practice (e.g., Hart, 1991; Smith, 2000; Wood,Cobb, Yackel, & Dillon, 1991) • Cultivating a habit of systematic and deliberate reflection may hold the key to improving one’s teaching as well as sustaining lifelong professional development (e.g., Stein & Smith, 1998; NCTM, 2000)

  7. Reflection -- A Starting Point Reflection, although necessary, is not sufficient for transformative teaching. Teachers must also be willing and able to acknowledgeproblems that may be revealed as a result of the reflective process. Moreover, they must explore the reasons for the acknowledged problems, consider more plausible alternatives, and eventually change their thinking and subsequent action in the classroom. Artzt and Armour-Thomas (2002, p.7)

  8. Learning to Reflect • Challenge: • What should a teacher focus her attention on? • Supported By: • Using frameworks as lenses through which to “notice” key aspects of classroom instruction • Creating records of teaching practice (e.g., videotape, audiotape, collect student work) that document what occurred and can be used for more in-depth analysis

  9. Teacher Prompts for Noticing • What is important here? • Can I understand what is happening here? • What is this a case of? Sherin & Van Es, 2003, p.92

  10. Catherine Evan’s Vignette Read the vignette of Catherine Evan’s class (see yellow handout) What do you notice?

  11. What you might have noticed… • Students presented at the overhead • Students could connect verbal descriptions and visual diagrams of the train • Students were able to find the perimeter of any train sequence given the train number • Student saw that the task could be solved more than one way and that both ways generated the same answer • Students were engaged throughout the lesson

  12. What you might have noticed… Only one student contributed a solution Students responded in unison but it is not clear what students other than Angela really understood about the problem The mathematical potential of the task was not realized -- there was no explicit discussion about variables, rate of change, or any other mathematical ideas, and there was no attempt to express a generalization either verbally or symbolically

  13. Catherine Evan’s Initial Reflection The lesson was all I could have asked from the kids! They found the perimeters of the trains and where even making progress on finding generalizations…the kids were very proud of themselves, I think, and so was I!

  14. Catherine’s Reflection Several Weeks Later Unfortunately, the lesson contained too much whole-group teacher questioning and students’ explaining and not enough time for students to stretch and discover independently/collaboratively. I made the lesson safe for kids -- no fail -- which was my goal at the time. I now think I need to let them go though the frustration that goes with problem solving. The lesson probably wouldn’t have looked as smooth, but I think it would have stretched the kids more. I am at a different point in my thinking than I was at the time of the lesson.

  15. Framing What You Notice • Task Analysis Guide (green) • Mathematics Task Framework • Factors Maintenance and Decline (green) • Question Types (pink)

  16. Framing What You Notice Task Analysis Guide (green) Mathematics Task Framework Factors Maintenance and Decline (green) Question Types (pink)

  17. Framing What You Notice Task Analysis Guide (green) Mathematics Task Framework Factors Maintenance and Decline (green) Question Types (pink)

  18. Sequence of Activity • Help teachers’ learn to notice important events in someone else’s classroom • Provide teachers’ with lenses through which to view instruction (i.e., frameworks, protocols, rubrics) • Have teachers’ create records of their own teaching on which to reflect(i.e., collecting student work, videotaping, audiotaping, or photographing) • Encourage teachers tocritically analyze the records they have created through a particular lens

  19. Karen Zigmond • Preservice teacher enrolled in a methods course • Assignment • record and transcribe a 10-minute segment of a class discussion • analyze the questions asked focusing on four of the Boaler and Humphries question types (1, 3, 4, and 5) • Consider what students responses to the questions tell you about what students understand • Lesson focused on the Inclines problem (blue)

  20. What Karen Noticed • She asked a variety of different questions types • Type 1 questions (e.g., lines 5, 35, 51) • Type 3 questions (e.g., lines 17, 33) • Type 4 questions (e.g., lines 12, 27) • She didn’t make sure students really understood the different approaches or explanations • … I am not sure that all students understand why this method (used by group 2) works in getting an equivalent answer for the height. I did ask if there were any questions about their method and if it worked [lines 21-22], but did not really force students to think about it based on just those questions. • I asked “Does this make sense?” [line 40] but relied on head nods alone to supply the answer.

  21. Karen Reflects Several Weeks Later Actually taking the time to sit down and analyze my questions was very eye-opening in both a good and bad way. I was able to recognize my strengths and weaknesses in terms of the type of questions I ask my students… I’ve noticed that planning these questions has become easier and I’m also asking some on the spot that just come naturally. I’ve already been able to notice a difference in the amount of effort my students put into their answers.

  22. Conclusion • Noticing, analyzing and reflecting on classroom events is critical to teachers growth over time • These are skills that teachers can learn and improve over time • Frameworks are powerful tools that can draw teachers’ attention to particular features of instruction that matter

  23. Teaching need to be parsed into a set of core practices Professional education could then focus its efforts on developing teachers’ ability to engage in such practices Grossman & McDonald, 2008 Core Practices