Mathematical Correctness vs. Clarity of Writing

Objective: Students will be able to identify the difference between mathematical correctness and clarity of exposition.

Key Terms: Proof, notation, variable, convention, audience, correctness, clarity.

Timing: These lessons could be appropriate in classes where any students are gaining familiarity with proof writing, even if that only applies to a minority of students. Consider trying these exercises early in the semester but after you have introduced some content.

Lesson

Part I: Correctness vs. Clarity Group Discussion

  1. Consider this worksheet, Mathematical Correctness and Clarity of Writing, created by Margaret Beck. You may wish to modify the example it contains to better match the content of your course. 
  2. Put students in small groups. Ask them to spend a few minutes completing the activity on their own. Then give them additional time to discuss their work within their group.
  3. Ask each group to write their version of the sentence on the board, and discuss the results with the class. If none of the groups have come up with what you believe to be a successful sentence, share with the class how you would write the sentence. 

Part II: Proof Critique Exercise

  1. Consider this worksheet, Evaluating Proofs, created by Margaret Beck. You’ll need to remove the annotations for the instructor before distributing it to students. You may also wish to modify the example it contains to better match the content of your course. 
  2. Put students in small groups. Ask them to spend a few minutes completing the activity on their own. Then give them additional time to discuss their work within their group. You may wish to provide the students with a rubric, such as this one, created by Margaret Beck, that they can use to evaluate the proofs. 
  3. Ask the groups to share what they discussed.
  4. Expand upon and/or synthesize student comments, eg. at the board. Possibly also share and/or distribute the annotated version. 

Part III: Peer feedback of proofs using a rubric

  1. Ask students to bring in a current draft of a proof. 
  2. Put the students into groups of 2-3. Note that three can be better, because pairs don’t always work if one (or both) of the students doesn’t understand the material well. 
  3. Provide the students with a framework, such as this one created by Margaret Beck, to use to provide feedback to each other on the drafts of their proofs. You can consider suggesting that they use a rubric, such as this one created by Margaret Beck, to help frame their feedback. Note that this rubric separately addresses mathematical correctness and clarity of writing.