2. Reflecting on Practice: Making Connections that Support Learning
Unit 3, Session 2
2016
Reflecting on Practice
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3. Park City Mathematics Institute
Reading Reflection
Round Robin
Share either your surprise or your significant insight
Round Robin Instructions
At your tables, go around the table with each person offering a thought.
Without discussion, continue around the table round robin until no one has new ideas to offer. Then open the table to general thoughts.
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"Comparison can bring dimensions of variation of the concept or procedure to the learner's attention"
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5. Park City Mathematics Institute
Gallery Walk
Visit the posters, and using post-it notes leave:
Compliments
Comments
Considerations
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6. Park City Mathematics Institute
Different procedures can be compared for their advantages and disadvantages. Such discussions in the classroom can deepen students’ understanding and skill.
(How People Learn, p. 221).
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7. An 8th grade Japanese geometry classroom from the TIMSS video series
Solve this on your own…
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8. An 8th grade Japanese geometry classroom from the TIMSS video series
As you watch consider:
What actions did the teacher take to promote metacognition?
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9. Park City Mathematics Institute
Flip to the back of the handout and look at the student work. The teacher had students then design their own problems changing the condition just a bit, some of which were then displayed on the board and compared to the original.
What would you want to have students compare/contrast?
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What did you notice the teacher did to promote metacognition?
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11. Park City Mathematics Institute
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12. Park City Mathematics Institute
Metacognition
“Students who know about the different kinds of strategies for learning, thinking, and problem solving will be more likely to use them” (Pintrich, 2002, p. 222), notice the students must “know about” these strategies, not just practice them.  As Zohar and David (2009) explain, there must be a “conscious meta-strategic level of H[igher] O[rder] T[hinking]” (p. 179)
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13. Park City Mathematics Institute
The mast problem
A sailboat has two masts. One is 5 m tall, the other 12 m tall, and they are 24 m apart. They must be secured to the same location using one length of rigging. What is the least amount of rigging that can be used?
Diagram to explain “masts” and “rigging” … does not show specific situation
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A solution??
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Think about the two tasks (TIMSS angle task and mast problem). -How are they similar? -How are they different?
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16. What examples from our work in reflecting on practice might fit :
1. Comparing how different problems can be solved with the same method 
Example: Choosing examples for the Cover Up Method  
2. Comparing problems involving different contexts but the same mathematical structure 
Example: Triangular Numbers 
3. 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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17. Park City Mathematics Institute
References
Pintrich, Paul R. (2002)The Role of metacognitive knowledge in learning, teaching, and assessing. Theory into Practice, 41(4)
Weimer, Maryellen.  (2012, November 19). Deep learning vs. surface learning: Getting students to understand the difference. Retrieved from the Teaching Professor Blog from
Zohar, Anat, and David, Adi Ben. (2009). Paving a clear path in a thick forest: a conceptual analysis of a metacognitive component. Metacognition Learning, 4,
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