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The following ten recommendations are quoted from "Communicating Mathematics: Useful Ideas from Computer Science" by C. Wells..


1. In elementary exposition, explain a basic concept by giving a specification of the concept---a carefully written description of the interaction of the object with other mathematical objects.

2. Teachers and authors of textbooks should make the distinction between syntax and semantics explicit.

3. Introduce informal parsing of mathematical expressions as a learning tool.

4. Make explicit the allowable syntax for statements about a type of object.

5. Encourage students to begin proving a theorem by replacing (some or all of) the words that have definitions with the text of their definitions.

6. Transmit your mental representation of concepts whenever you can, but also give proofs as explicit logical calculations when appropriate, because that provides the student with a second way to deal with the problem and provides him or her with the tools to carry out similar proofs.

7. Give explicit rules of inference for concepts when they are introduced.

8. Use the concepts of type and polymorphism explicitly to help students to understand and avoid the traps of type confusion.

9. Expect conceptual understanding at the appropriate level from all students in any course, and test them on it.

10. Describe and name the common kinds of mistakes students make.


  • Communicating Mathematics: Useful Ideas from Computer Science
  • Author(s): Charles Wells
  • Source: The American Mathematical Monthly, Vol. 102, No. 5 (May, 1995), pp. 397-408
  • Published by: Mathematical Association of America
  • Stable URL:
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