Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Writing (and presentations) of nonmajors

This list from the JMM 2013 Minicourse Teaching and Assessing Mathematical Communication characterizes effective writing (and presentations) of nonmajors. The first version is a transcription of the brainstorming notes from the minicourse.  The second version is in more freely edited paragraph form.

Lightly edited notes

Mathematical accuracy

• identify “thinking process”
• understands the modeling process (e.g., makes assumptions; defines consequences)
• accurate use of terminology/conventions
• correct and consistent use of notations and symbology
• in word problems, variables (quantities) are defined unambiguously
• definitions are precise
• the conclusion is clear and unambiguous
• reasoning (logical/mathematical/quantitative) is correct
• when theorems are applied, shows how all premises are met
• shows how definitions apply

Format for effective communication

• Well organized with a start, support, and conclusions; Presentation is organized around the logic of the problem; organized ideas flow logically; algorithmic process is shown in a logical and organized way; organized on page; it is easy to find info
• Sentences are complete, grammatically correct, and logically sound, and spelling is correct.
• objective (when applicable)
• tonally consistent: writer has in mind a specific mathematical level when writing
• for presentations: presenter articulates and looks at audience

Content for effective communication

• Multiple communication modes are used–words, graphics, models, etc., so the explanation can reach all members of the target audience.
• Appropriate use of graphics (diagrams, charts, graphs)
• Good choice of examples for concepts/definitions; Well illustrated (good examples) to promote understanding of concepts.
• Well motivated to capture interest (why does the reader/listener want to know this?)
• The problem is explained, not just the answer, so an uninformed reader understands the whole picture.
• Set up correctly (variables defined; problem introduced)
• Assumptions are clearly stated

Form appropriate for audience

• clear
• thorough yet elegant
• complete–including all details necessary for audience understanding
• succinct
• deliberate word choice
• appropriate balance of words and symbols: words are used to explain and/or motivate that which is demonstrated with symbols.

Content appropriate for audience

• Content is pitched appropriately to the target audience; for example, definitions as appropriate; choice to use technical language or not as appropriate
• Addresses the understanding level and questions of the audience
• Tone is enthusiastic to keep the reader interested
• Interesting/engaging (e.g., choice of examples, choice of presentation style, writing voice)
• Gives a story of the human experience in the problem, either their own or something out of history.
• Respectful of the audience. e.g., for group work, constuctive group-work skills, participating and listening to & encouraging other participants; for presentations, well prepared.

Characteristics not categorized

• Achieves intended or desired goal
• Demonstrating self-reflection/metacognition
• Confidence

More freely edited paragraph form

Content is mathematically correct and complete.

Reasoning is correct and is clearly communicated to readers; for example, when a model is created, the text clearly identifies assumptions and considers their consequences, and when a theorem is applied, the text indicates how all premises are met, how definitions apply, and how these lead to a clearly identified, unambiguous conclusion. Notation, conventions, and terminology are used correctly and consistently. Anything new is defined precisely; for example, in word problems, variables (quantities) are defined unambiguously. The paper answers the assignment.

Writing is crafted to convey content effectively

The paper is carefully organized so the structure of the reasoning is clear and information is easy to find. For example, the organization matches the logic of the problem, starting by introducing the problem, flowing along logical lines through the supporting arguments, and ending with conclusions. The structure is communicated to readers (e.g., via guiding text, page formatting, and text formatting). Sentences are complete, grammatically correct, and logically sound, and spelling is correct. The paper targets a consistent audience and is appropriately objective. Similarly, for presentations, audio and visuals are crafted to convey content effectively; for example, the presenter articulates well and looks at the audience, and handwriting/slides are legible.

Content is designed to guide audience to understanding

As needed throughout the paper, motivation and context are provided to help the audience understand the big picture and follow reasoning; for example, the paper begins by eliciting audience interest in the problem and building audience understanding of the problem and, throughout the paper, groundwork is provided as needed (e.g., concepts are introduced, definitions are precise, assumptions are clearly stated). Multiple communication modes are used–words, examples, visuals, models, etc.–so the explanation can reach all members of the target audience. Each example and visual (e.g., diagram, chart, graph) is designed carefully to achieve particular objectives (e.g., help readers to understand an important point, concept, or definition).

Writing is carefully crafted for the audience.

The text is succinct, deliberately worded, and elegant while facilitating audience understanding. For example, all details necessary for audience understanding are included and words are used to explain and/or motivate that which is demonstrated with symbols, but unnecessary details and wordiness are omitted. Tone, level of detail, and correctness inspire reader confidence in the author.

Content is carefully designed for the audience

The content is designed to meet the target audience’s needs and desires as readers. For example,

• the content is crafted to be interesting and engaging for the target audience, for example through the use of a lively or enthusiastic tone, interesting examples, thought-provoking questions, or human stories
• helpful meta-cognitive commentary is included as appropriate, for example to help readers think about the problem or to help readers see connections within the paper or to their own experiences and knowledge from other contexts.
• the audience is treated with respect (e.g., tone is collegial rather than authoritative; writing and presentations are carefully revised; in group work, the student participates and encourages others to participate).
• definitions are provided (only) as needed, technical language is used (only) when doing so aids audience understanding, and audience questions are anticipated and addressed