Chapter 9: Monitoring Mathematical Comprehension (BMC Book Study)

Students need to understand that a breakdown in mathematical comprehension is not a sign of failure; rather it is a part of the learning process. When students monitor their mathematical understanding, they call upon the full spectrum of comprehension strategies (273). It is our job as teachers to make sure students realize the importance of being aware when their understanding breaks down. To help students recognize when there is a breakdown in comprehension, Laney Sammons offers this list of signs:
  • Your internal voice is not interacting mathematically with the concept or problem.
  • Your mind wonders away from the mathematical task at hand.
  • You are unable to visualize the mathematical concept or problem.
  • You are unable to recall the details of a math idea or problem.
  • You cannot answer questions asked to clarify meaning. (259)
How do we help students gain the confidence and skills necessary to rethink and switch strategies for a fresh start when there is a breakdown in mathematical understanding? Students need some fix-up strategies in their mathematical toolbox.
  • ask questions
  • connect to other mathematical concepts
  • draw a picture
  • use manipulatives
  • make inferences
  • pause/refocus
  • reread/rethink
  • collaborate with a peer
Check out this earlier post to read about this strategy: Need a Hand? Try This! I have used this tool in the classroom.

Bottom line...students need to monitor and KNOW WHEN THEY KNOW and KNOW WHEN THEY DON'T KNOW. Is it a "HUH?" moment? or a light bulb moment? (263) The Color-Code Metacognition Math Stretch (266) reminds me of the red, yellow, and green buckets I use in my classroom as a Ticket Out the Door.

After a lesson or at the end of class, students can put their names on a slip of paper in the colored bucket that best reflects their understanding of the day's lesson. Red: I need help. Yellow: I am getting there. Green: Got it! Another way I have used these buckets is to give students a problem to do as a Ticket Out the Door where they record their responses on an index card. After solving the problem, they place it in the bucket that best reflects how they feel about the problem. This can be used as a quick formative tool to identify which students may need additional help and which students are ready to move on. The buckets allow students to metacognitively reflect on their own personal understanding. The data from the buckets should be used in conjunction with teacher observation.

Chapter 7: Determining Importance
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