Benchmark 2A: The Nature of Mathematics - Patterns and Relationships
(grades 9-12, page 29)
 
  • Mathematics is the study of patterns or relationships, whereas natural science is concerned only with those patterns that are relevant to the observable world. Although mathematics began long ago in practical problems, it soon focused on abstractions from the material world, and then on even more abstract relationships among those abstractions. (1 of 4)
    • Standard 4-3 page 146, Grades 9-12
    Use and value the connections among mathematical topics

    Standard 4-3 page 146, Grades 9-12
    Use and value the connections between mathematics and other disciplines
  • As in other sciences, simplicity is one of the highest values in mathematics. Some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived. (2 of 4)
    • Standard 2-6 page 140, Grades 9-12
    Appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas
  • Theories and applications in mathematical work influence each other. Sometimes a practical problem leads to the development of new mathematical theories; often mathematics developed for its own sake turns out to have practical applications. (3 of 4)
    • Standard 4-3 page 146, Grades 9-12
    Use and value the connections among mathematical topics

    Standard 4-3 page 146, Grades 9-12
    Use and value the connections between mathematics and other disciplines
  • New mathematics continues to be invented, and connections between different parts of mathematics continue to be found. (4 of 4)
    • Standard 4-3 page 146, Grades 9-12
    Use and value the connections among mathematical topics