Reflection, Feedback, and Revision in Mathematical Writing

Metacognition

Objective: Students will develop a greater awareness and understanding of their own thought processes.

Key Terms: Metacognition. Process.

Timing: These activities can be utilized at any time throughout the course.

Identity and Belonging

Objective: Students will have the opportunity to identify and name their personal strengths, goals, and/or fears within the context of their work as mathematicians.

Key Terms: Identity. Belonging. Representation.

Timing: These activities could work best if given at the beginning of the semester, both to help set the tone for the course and to help students feel comfortable in the course during the entire semester.

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Peer Feedback on Student Writing

Objective: By utilizing peer feedback of student writing, students are able to receive more feedback than if they were only receiving feedback from the instructor alone. Moreover, they will benefit from seeing examples of their peers’ writing and by having to articulate what they feel is and is not successful about the writing that they themselves are evaluating.

Key Terms: Feedback. Mathematical Correctness. Clarify of Exposition. Notation. Terminology.

Timing: The timing of these lessons depends on the content and nature of the course. For example, if they are being utilized for peer feedback on proof writing in a course where students are learning to write proofs for the first time, then they are best used a few weeks into the semester, once students have had some time to get used to the notions of proof and proof writing.

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Revision and Portfolios

Objective: Students will have an opportunity to revise, and possibly also showcase, their previous work, to arrive at pieces that they feel represent their best work. They will also have an opportunity to reflect on what has gone well in their work so far and what could be improved upon.

Key Terms: Revision, reflection, early/final draft, portfolio.

Timing: Revisions and portfolios could be utilized periodically throughout the semester, or less often, depending on instructor preferences.

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