{"id":8411,"date":"2025-08-26T15:55:47","date_gmt":"2025-08-26T19:55:47","guid":{"rendered":"https:\/\/www.bu.edu\/teaching-writing\/?page_id=8411"},"modified":"2025-09-03T15:32:11","modified_gmt":"2025-09-03T19:32:11","slug":"mathematical-correctness-vs-clarity-of-writing","status":"publish","type":"page","link":"https:\/\/www.bu.edu\/teaching-writing\/teaching-writing-at-bu\/writing-in-the-disciplines\/teaching-writing-in-math-and-statistics\/math-resources\/principles-of-mathematical-writing\/mathematical-correctness-vs-clarity-of-writing\/","title":{"rendered":"Mathematical Correctness vs. Clarity of Writing"},"content":{"rendered":"

Objective:<\/b> Students will be able to identify the difference between mathematical correctness and clarity of exposition.<\/span><\/p>\n

Key Terms:<\/b> Proof, notation, variable, convention, audience, correctness, clarity.<\/span><\/p>\n

Timing:<\/b> 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.<\/span><\/p>\n

Conceptual Framework<\/h6>
If a proof is not mathematically correct it cannot claim to be a successful proof of the stated result. However, if a proof is mathematically correct but just very difficult to read, the writer can still legitimately claim to have proven the result. Helping students understand this distinction can help them create a more targeted revision process for themselves, and help them process and understand any feedback they receive on their writing. For example, a student may want to first focus on mathematical correctness, with minimal (if any) concern for clarity of writing. Then, once they feel confident in the mathematical correctness, they can move on to working on the clarity of their writing. Moreover, students who are more confident with the material can focus primarily on the clarity of their writing, even if they do not need to place as much effort on the mathematical correctness.\u00a0<\/span><\/p>\n

The separation of these two ideas can also help students think about different genres of writing. For example, in more informal settings, such as personal scratch work or board work during an oral exam, perhaps only mathematical correctness is relevant. But for formal writing, the writer must consider the needs of the intended audience and make sure the argument will be clear from the reader’s perspective.\u00a0<\/span><\/p>\n

<\/div>\n<\/div>\n<\/p>\n

Lesson<\/b><\/h2>\n

Part I: Correctness vs. Clarity Group Discussion<\/span><\/p>\n

    \n
  1. Consider<\/strong> this worksheet, <\/span>Mathematical Correctness and Clarity of Writing<\/span><\/a>, created by Margaret Beck. You may wish to modify the example it contains to better match the content of your course.\u00a0<\/span><\/li>\n
  2. Put students in small groups<\/strong>. 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.<\/span><\/li>\n
  3. Ask each group<\/strong> 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.\u00a0<\/span><\/li>\n<\/ol>\n

    Part II: Proof Critique Exercise<\/span><\/p>\n

      \n
    1. Consider<\/strong> this worksheet, <\/span>Evaluating Proofs<\/span><\/a>, 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.\u00a0<\/span><\/li>\n
    2. Put students in small groups<\/strong>. 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, <\/span>such as this one<\/span><\/a>, created by Margaret Beck, that they can use to evaluate the proofs.\u00a0<\/span><\/li>\n
    3. Ask the groups<\/strong> to share what they discussed.<\/span><\/li>\n
    4. Expand upon and\/or synthesize<\/strong> student comments, eg. at the board. Possibly also share and\/or distribute the annotated version.\u00a0<\/span><\/li>\n<\/ol>\n

      Part III: Peer feedback of proofs using a rubric<\/span><\/p>\n

        \n
      1. Ask students<\/strong> to bring in a current draft of a proof.\u00a0<\/span><\/li>\n
      2. Put the students into groups<\/strong> 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.\u00a0<\/span><\/li>\n
      3. Provide the students with a framework<\/strong>, <\/span>such as this one<\/span><\/a> 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, <\/span>such as this one<\/span><\/a> created by Margaret Beck, to help frame their feedback. Note that this rubric separately addresses mathematical correctness and clarity of writing.\u00a0<\/span><\/li>\n<\/ol>\n

        Variations and Follow-Ups<\/h6>
        There are many variations on peer feedback<\/a> that you could utilize.<\/span>\u00a0For additional practice in evaluating proofs, you could suggest that students ask a generative AI to prove something, and then evaluate that proof for themselves, perhaps using a rubric you provide. You could also provide the students with a published proof (e.g. from a textbook, or possibly from a research article if the course is sufficiently advanced or the proof is not too involved), and ask them to evaluate that proof.\u00a0<\/span><\/p>\n

        <\/div>\n<\/div>\n<\/p>\n

        Further Reading<\/h6>
        Consider giving your students example proofs to read, e.g. from a textbook, or possibly from a research article if the course is sufficiently advanced or the proof is not too involved. Many students are not in the habit of actually reading mathematics writing, because many students can be successful in courses, particularly lower level ones, without opening the textbook, except possibly to look up their homework problems. And even if they do read their textbooks, not all textbooks are well-written. Having good models of mathematical writing is essential to being able to write well, so providing students with such models can often be helpful. Imagine trying to write a short story without ever having read one before. That would be very difficult, right?<\/span><\/p>\n

        <\/div>\n<\/div>\n<\/p>\n","protected":false},"excerpt":{"rendered":"

        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 […]<\/p>\n","protected":false},"author":15811,"featured_media":0,"parent":8454,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/pages\/8411"}],"collection":[{"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/users\/15811"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/comments?post=8411"}],"version-history":[{"count":3,"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/pages\/8411\/revisions"}],"predecessor-version":[{"id":8709,"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/pages\/8411\/revisions\/8709"}],"up":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/pages\/8454"}],"wp:attachment":[{"href":"https:\/\/www.bu.edu\/teaching-writing\/wp-json\/wp\/v2\/media?parent=8411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}