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Unit 3, Session 32016

Reflecting on Practice: Making Connections that Support Learning

Reflecting on Practice Park City Mathematics Institute 2

“Metacognitive functioning is also facilitated by shifting from a focus of right or wrong to a more detailed focus on ‘debugging’ a wrong answer, that is, finding where the error is, why it is an error, and correcting it” (How Students Learn: Mathematics in the Classroom, p. 239).

Reflecting on Practice Park City Mathematics Institute 3

Using Comparison1. Comparing how different problems can be solved with the same method

Example: Choosing examples for the Cover Up Method2. Comparing problems involving different contexts but the same mathematical structure

Example: Triangular Numbers3. Different problems in same context solved with different methods

Example: Equation of a line, choosing most appropriate strategy (Star approach)

4. Comparing different approaches to the same problem.Example: Mast problem & Japanese angle task

5. Comparing correct and incorrect solutions to the same problem.

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Research on learning algebra: Making links to the classroom

1988 NCTM Yearbook on Algebra: Common Mistakes in Algebra (Marquis, 1988)

a2 b5 = (ab)7 (x+4)2 = x2+ 16

x+y y x r x+rx+z = z y + s = y+s

x+y - 3(z+w) = x+y - 3z+wIf (2-z) < 4, then z < -2

6http://tube.geogebra.org/m/1418605

Instructional Goal: Students recognize that a line of symmetry with certain properties in a triangle produces an isosceles triangle.

What does dynamic geometry bring to helping students think about errors?

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Highlighting Errors

As you watch the video, reflect on what evidence of metacognition you see.

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• What evidence of metacognition did you see in the video?

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Highlighting Errors

• What evidence of metacognition did you see in the video?

• What norms did Leah create to establish a class culture of learning from mistakes?

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Highlighting Errors

Students correcting “error exemplary” work

As you watch the video, reflect on what evidence of metacognition you see

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• What evidence of metacognition did you see in the video?

• What norms did Susie create to establish a class culture of learning from mistakes?

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"Finding the part that is wrong and understanding why it is wrong can be a powerful aid to understanding and promotes metacognitive competencies"(How Students Learn Mathematics, p. 224)

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In your table groups.

What are some additional strategies that you have found successful in your own classroom?

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In your table groups.

What are some additional strategies that you have found successful in your own classroom?• Grindelwald - http://bit.ly/pcmi16ropg• St. Moritz - http://bit.ly/pcmi16ropsm• Davos - http://bit.ly/pcmi16ropd

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Journal:Itisimportantthatwearemetacognitive aslearners&practitioners ourselves. HowhaveyourthoughtsaboutyourownpracticechangedsincestartingPCMI?

ExitTicket:IfwehadonemoreweekatRoP,whatare3thingsthatyouwouldwantustofocuson?

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