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Yes We Can!(notate) Problem Solving Journals and the Standards for Mathematical Practice

Yes We Can!(notate) Problem Solving Journals and the Standards for Mathematical Practice. Stephanie Hironaka, Daniel Moscoe, and Hector Nieves. What do students do when they encounter unfamiliar or complex problems?. Unskillful student responses to challenge. Guessing

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Yes We Can!(notate) Problem Solving Journals and the Standards for Mathematical Practice

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  1. Yes We Can!(notate) Problem Solving Journals and the Standards for Mathematical Practice Stephanie Hironaka, Daniel Moscoe, and Hector Nieves Park City Mathematics Institute

  2. What do students do when they encounter unfamiliar or complex problems? Park City Mathematics Institute

  3. Unskillful student responses to challenge • Guessing • Asystematic/disorganized engagement • Waiting for the answer Conundrum Camel Park City Mathematics Institute

  4. Skillful responses to challenge The Standards for Mathematical Practice (SMPs) • Don’t give up! • Mathematize the problem! • Make a supported conjecture! • Construct a model! • Search for patterns! • Simplify the problem! Competent Camel

  5. Our main point When students identify the SMPs in their own and others’ work, they: • Begin to deploy them systematically; • Come to see themselves as skillful, adventurous, and invested in mathematics; • Become more sophisticated learners.

  6. Support from research • Students are more likely to employ specific metacognitive strategies when teachers intentionally incorporate these strategies into instruction (Pintrich 2002) P C M Ibex

  7. Support from research • After metacognitive training, lower achieving students demonstrated especially large gains in metacognitive and problem-solving skills (Pennequin et al. 2010) Rabbit

  8. Support from research • Structured journaling is one effective means of metacognitive training (Smith et al 2007). Journaling Yak

  9. Annotated problem-solving journals • Students spend dedicated time journaling on rich problems pursuing progress/solutions. • Students pause for metacognitive review: where in your work do you demonstrate SMPs? Label your work and explain your labeling. Note: We will start the year focused on 3 SMPs and include more as the year proceeds.

  10. Example and Key Elements STRUCTURE: I am trying to look for patterns, through the steady increase in rectangle width and height. [SMP7] These annotations encourage neatness, organization, structure, as well as having a reference for future use. The student sees that they already employ valuable metacognitive strategies.

  11. Another Example MODEL: After looking at tons of rectangles, I used math symbols to try and solve the problem algebraically. I also started to draw a graph to see if there were other connections. [SMP4] The student (possibly) identifies opportunities to make further progress.

  12. Student guide

  13. Student guide

  14. Next steps/open questions • How can we include a peer critique or sharing component? • How can we use journaling to intentionally support students’ developing positive identities as mathematicians? • How does this practice differ between middle school and high school?

  15. Try it! How’d it go? • Let us know at dmoscoe@gmail.com Affirming Alpaca

  16. References Pintrich, P. R. (2002). The role of metacognitive knowledge in learning, teaching, and assessing. Theory into practice, 41(4), 219-225.Http://dx.doi.org/10.1207/s15430421tip4104_3 Pennequin, V., Sorel, O., Nanty, I., & Fontaine, R. (2010). Metacognition and low achievement in mathematics: The effect of training in the use of metacognitive skills to solve mathematical word problems. Thinking & Reasoning, 16(3), 198-220. Smith, K. S., Rook, J. E., & Smith, T. W. (2007). Increasing student engagement using effective and metacognitive writing strategies in content areas. Preventing School Failure: Alternative Education for Children and Youth, 51(3), 43-48. Park City Mathematics Institute

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