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Making Connections for Deep Learning

Explore different teaching strategies and promote metacognition through reflection and comparison in mathematics education. Gain insights from classroom examples and engage in round-robin discussions to deepen understanding and support student learning.

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Making Connections for Deep Learning

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  1. Reflecting on Practice: Making Connections that Support Learning Unit 3, Session 2 2016 Park City Mathematics Institute

  2. 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. Park City Mathematics Institute

  3. "Comparison can bring dimensions of variation of the concept or procedure to the learner's attention" Park City Mathematics Institute

  4. Gallery Walk Visit the posters, and using post-it notes leave: Compliments Comments Considerations Park City Mathematics Institute

  5. 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). Park City Mathematics Institute

  6. An 8th grade Japanese geometry classroom from the TIMSS video series Solve this on your own… Park City Mathematics Institute

  7. An 8th grade Japanese geometry classroom from the TIMSS video series • As you watch consider: What actions did the teacher take to promote metacognition? Park City Mathematics Institute

  8. 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? Park City Mathematics Institute

  9. What did you notice the teacher did to promote metacognition? Park City Mathematics Institute

  10. Park City Mathematics Institute

  11. 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) Park City Mathematics Institute

  12. 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 Park City Mathematics Institute

  13. A solution?? Park City Mathematics Institute

  14. Think about the two tasks (TIMSS angle task and mast problem).  -How are they similar?   -How are they different? Park City Mathematics Institute

  15. 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.  Park City Mathematics Institute

  16. References • Pintrich, Paul R. (2002)The Role of metacognitive knowledge in learning, teaching, and assessing. Theory into Practice, 41(4). 219-225. • Weimer, Maryellen.  (2012, November 19). Deep learning vs. surface learning: Getting students to understand the difference. Retrieved from the Teaching Professor Blog from http://www.facultyfocus.com/articles/teaching-professor-blog/deep-learning-vs-surface-learning-getting-students-to-understand-the-difference/. • 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, 177-195. Park City Mathematics Institute

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