Yes We Can!(notate)
Problem Solving Journals and the Standards for Mathematical Practice Stephanie Hironaka, Daniel Moscoe, Hector Nieves
Problem-solving journals are a tool to support student growth in the standards for mathematical practices, and can serve as a jumping-off point for exciting conversations about math. This PL shows one method for incorporating problem-solving journals at the middle school level. We also consider structures for student self-assessment and reflection.
What we do:
Students are encouraged to follow these Standards for Mathematical Practice:
Don’t give up
Mathematize the problem
Make a supported conjecture
Construct a model
Search for patterns
Simplify the problem
How we do it:
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.
Why it works:
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.
Research:
"Students are more likely to employ specific metacognitive strategies when teachers intentionally incorporate these strategies into instruction.""
Pintrich, P. R. (2002). The role of metacognitive knowledge in learning, teaching, and assessing. Theory into practice, 41(4), 219-225.
"After metacognitive training, lower achieving students demonstrated especially large gains in metacognitive and problem-solving skills."
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.
"Structured journaling is one effective means of metacognitive training."
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.
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