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Defining Mathematics Education *REDUCED*

Defining Mathematics Education

The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.

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Good teaching

A variety of learning experiences reinforces the big ideas associated with the development of mental computation.

Fluency and flexibility in thinking are critical to developing effective mental computation skills. Developing fluency requires an ability to recall facts as well as an understanding of number properties. Flexibility is recognition of the demands of a problem and the selection of the best strategy for the numbers involved.

Effective assessment is a window to students' number sense and can expose learning issues such as a reliance on counting.

Many key ideas have been collected under three areas:

  • addition and subtraction
  • multiplication and division
  • combined operations.

Everyday problems might require several steps using different operations.

Using contexts that are meaningful to students as opposed to using 'naked numbers' can assist students to make connections and see relationships between numbers. Contexts can be real or imaginary.

Addition and subtraction

Addition and subtraction are two of the four arithmetic operations that are used in mental calculation.

Multiplication and division

Good teaching of mental calculation of multiplication and division uses physical models and a variety of learning experiences including games, everyday contexts and opportunities for students to build connections.

Combined operations

Addition, subtraction, multiplication and division are binary operations, meaning it is only possible to calculate with a pair of numbers at a time. Many everyday problems require a sequence of calculations, sometimes involving different operations.