Short Answer
This category includes items on tests and homework.

You might be asked to give a definition of a word. Definitions should be memorized or, at least, very similar to the original. Remember: words that may be synonyms in everyday English often have different meanings in mathematics. Word and phrase placement is also critical in definitions; “for each x, there is a unique y” is not the same as “for a unique y, there is an x.”

You might be asked to provide an example or counterexample for a concept. You need to carefully state what the example or counterexample is and, this is the important part, what makes it an example or counterexample. For instance, if you are providing an example of a non-commutative operation, you need to say not just matrix multiplication but also provide two specific matrices A and B such that AB is not equal to BA.

The most common example of this type of writing is showing your work on or providing a solution to a particular problem. Different professors have different expectations for this, so be sure to ask if you don’t know what you are supposed to do. Generally, though, work should be in complete sentences. You should identify what strategies or methods you used and why you chose those strategies or methods. You should always answer “word problems” with a sentence, particularly when the numerical answer needs additional interpretation. Be sure to answer the questions that are asked.

Long Answer

These are typically quiz or exam questions, but they can show up on homework. Not only do you need correct grammar and sentence structure, but long answers tend to need correct paragraph structure and some organization as well.

The most common type of this assignment is to explain a concept or procedure in your own words. You can be a little freer with the language on these mini-essays than with definitions, but all mathematical vocabulary should still be used precisely. Even if the question does not specifically ask for them, you should provide specific examples and counterexamples to demonstrate your knowledge. You will also want to discuss properties, results, or rules associated with the concept or procedure.

Another type of this assignment is make connections between concepts or courses. Unless the professor tells you otherwise, these need to be written out in sentences and paragraphs rather than a list. Be sure to include as many connections, similarities, and differences that you can think of; this is especially important if you are given the question in advance.

Project or Program

Project and program assignments vary from course to course. Each assignment will come with its own set of requirements. As always, the writing should be in complete and correct sentences and paragraphs. The amount of writing for a project varies but it is usually at least one typed page.

General guidelines for this kind of writing:

• Follow the instructions.
• Respond to every prompt and answer every question.
• Provide an introduction: restate the problem and provide background information.
• Explain each step of the solution.
• Provide a conclusion: appropriately interpret the solution

Reaction Paper

These papers are assigned in MATH 353 and 480. They are approximately 2 to 3 pages long. They are different from most writing assignments.

These papers describe the student’s reactions to the material presented in the texts and the class discussions of that material. These papers are aimed at allowing the student to explore her feelings and thoughts about the class material. Although any mathematical content of these papers should be correct and the course material should be referenced, the papers are NOT "book reports" or summaries of the mathematical content of the material and discussion. They are supposed to be the student's reactions to the material and the discussion; potential reactions are continuing the discussion, arguing for or against opinions from discussion, making different connections between and among the articles, emotional or philosophical reactions to the material or discussion, and explaining how the material has changed your point of view.

Proof

Proofs are the most common and the most difficult kind of writing mathematics majors will do. Nearly every mathematics course will ask you to provide justification for mathematical statements and most will expect these justifications to be proofs.

Proofs in college courses must be written in sentence/paragraph form rather than the two-column statement/reason format that is common in high-school geometry classes. Although much of a proof will use mathematical symbols, you will need to include, at the very least, transitional and connecting words and phrases.

When writing up a proof, be sure to include the statement to be proved first. (The only exception to this rule is on an in-class test when the statement is already written.) You should indicate where the statement ends and the proof begins by starting a new paragraph with the word “Proof:” in front of it.

Always do a rough draft of a proof before writing the final copy (in-class tests are a possible exception). This makes reading it (and, hence, grading it) easier.

Formal Paper

“Formal papers” are papers that require information literacy skills. You will need to find sources of information about a topic (the library is a good place to start) and write a paper based on those sources. These papers are similar to the “term papers” or “research papers” written in other disciplines.

All formal papers in mathematics courses require the inclusion of mathematical content. Students should include mathematical symbols and equations into their documents through electronic means.

Mathematics has its own peculiar bibliographic reference format designed primarily for research papers rather than these formal papers. The department has decided that students may use either the APA or MLA format on the formal papers as long as the format is consistent within a paper. (Professors may have specific preferences.)

Requirements for every formal paper

• Thesis
• Preliminary work
• Meaningful title
• APA/MLA style
• Introduction
• Organization (paragraph, topic sentences, flow)
• Conclusion
• Use of technology (Equation editor)
• External sources

Additional requirements for specific assignments may include:

• Abstract
• Revisions after a conference with the instructor
• Works cited; works consulted
• Background information
• Peer evaluation

Portfolio

The mathematics portfolio is a requirement for MATH 480. Students provide samples of their mathematical work and write entries explaining why they chose the samples they did.

In addition, students are asked to provide a reflective statement on collaborative learning. This statement should represent the student’s understanding and appreciation of how the collaborative process works in mathematics. It is similar to a reaction paper.