Benchmark 2C: The Nature of Mathematics - Mathematical Inquiry
(grades 9-12, page 38)
  • Some work in mathematics is much like a game mathematicians choose an interesting set of rules and then play according to those rules to see what can happen. The more interesting the results, the better. The only limit on the set of rules is that they should not contradict one another. (1 of 2)
  • Standard 5-4 page 150, Grades 9-12
    Appreciate the power of mathematical abstraction and symbolism
  • Much of the work of mathematicians involves a modeling cycle, which consists of there steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. If the match is not considered good enough, a new round of abstraction and manipulation may begin. The actual thinking need not go through these processes in logical order but may shift from one to another in any order. (2 of 2)
  • Standard 1-4 page 137, Grades 9-12
    Apply the process of mathematical modeling to real-world problem situations

    Standard 4-2 page 146, Grades 9-12
    Relate procedures in one representation to procedures in an equivalent representation