Principles of Mathematical Writing
What is Writing in Mathematics?
Objective: Students will be able to recognize mathematical writing as writing, even though it may look different from the writing they have done in other courses. In addition, they will be able to recognize commonalities between mathematical writing and more general writing, such as the use of complete sentences and the use of nouns and verbs, even if the nouns and verbs are sometimes represented by symbols. Moreover, students will recognize the varied genres of mathematical writing, including pen-and-paper calculations, proofs, exposition, and coding, and recognize various audiences that mathematics can be written for, including the general public, students, and experts in the field. Finally, and perhaps most importantly, students will recognize that mathematical writing can serve not only to communicate ideas, but also to clarify the thinking of the writer.
Key Terms: Genre, audience.
Timing: These lessons could be particularly appropriate in lower-division courses, or any course where students are learning or broadening their idea of what comprises mathematical writing.
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Conventions in Mathematical Writing
Objective: Students will be able to recognize and utilize a variety of conventions used in mathematical writing.
Key Terms: Convention, audience, discipline, stylistic choice.
Timing: These lessons could be particularly appropriate in any course where students are learning to think of mathematical work as writing.
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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.
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Writing Precisely with Quantifiers
Objective: Within the context of quantifiers, students will be able to identify the details in their writing that affect the mathematical meaning of a sentence, and the details in their writing that are less consequential in determining the overall success of the proof.
Key Terms: Proof, notation, variable, correctness, quantifier.
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.
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