Mathematical Flexibility is the ability to maintain and shift among multiple representations of numbers and between problem-solving strategies in an adaptive manner. Students can use Mathematical Flexibility to better understand mathematical concepts and more adaptively use strategies to find solutions to math problems.
Main Ideas
There are two key types of Mathematical Flexibility:
- Representational flexibility supports students in thinking about number and relationships in different ways. For example, a fraction may be represented as a numerical ratio, a place on a number line, or a slice of a pie, while a simple function may be represented using a table, a verbal statement, or an equation. Being able to represent mathematical concepts in multiple ways supports conceptual understanding and allows students to see the deeper similarities among math problems.
- Procedural flexibility supports students in considering different strategies when solving a problem. Not only do students need to be able to solve problems quickly and accurately, they also need to make strategy choices in an adaptive manner. Procedural flexibility allows students to shift away from more cumbersome procedures to use more efficient problem-solving strategies given the content or context (e.g., dividing both sides of an equation by a constant as a first vs. a last step in the problem), which improves speed and supports greater accuracy in mathematical thinking and problem solving.
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