Math student thinking
Components of math fluency - Answer Accuracy
Automaticity
Rate
Flexibility
Accuracy - Answer Getting the correct answer
Automaticity - Answer Selecting problem solving methods and performing computations
without requiring much time to think the processes through
Rate - Answer How quickly computations are made
Flexibility - Answer Being able to solve problems in more than one way and selecting
the most appropriate method
Mathematical reasoning - Answer Reasoning refers to students ability to hypothesize,
test their theories, and draw conclusions. Three main types:
Inductive
Deductive
Adaptive
Inductive reasoning - Answer Reasoning in which conclusions are based on observation
Deductive reasoning - Answer Reasoning in which conclusions are based on the logical
synthesis of prior knowledge of facts and truths
Adaptive reasoning - Answer The ability to think logically about the relationships
between concepts and to adapt when problems and situations change
Concrete model - Answer Use objects to demonstrate operations
Semi concrete model - Answer Use pictures (instead of actual objects) to demonstrate
operations
Semi abstract model - Answer Use a single symbol (such as an x or a tally mark) to
represent numbers of objects while performing operations
Abstract model - Answer Using numbers only to perform operations
Addition - Answer Modeled as "put together"
Subtraction - Answer Modeled as "take apart"
Array - Answer One way to model multiplication visually one factor is shown vertically
the other horizontally
2x4
Components of math fluency - Answer Accuracy
Automaticity
Rate
Flexibility
Accuracy - Answer Getting the correct answer
Automaticity - Answer Selecting problem solving methods and performing computations
without requiring much time to think the processes through
Rate - Answer How quickly computations are made
Flexibility - Answer Being able to solve problems in more than one way and selecting
the most appropriate method
Mathematical reasoning - Answer Reasoning refers to students ability to hypothesize,
test their theories, and draw conclusions. Three main types:
Inductive
Deductive
Adaptive
Inductive reasoning - Answer Reasoning in which conclusions are based on observation
Deductive reasoning - Answer Reasoning in which conclusions are based on the logical
synthesis of prior knowledge of facts and truths
Adaptive reasoning - Answer The ability to think logically about the relationships
between concepts and to adapt when problems and situations change
Concrete model - Answer Use objects to demonstrate operations
Semi concrete model - Answer Use pictures (instead of actual objects) to demonstrate
operations
Semi abstract model - Answer Use a single symbol (such as an x or a tally mark) to
represent numbers of objects while performing operations
Abstract model - Answer Using numbers only to perform operations
Addition - Answer Modeled as "put together"
Subtraction - Answer Modeled as "take apart"
Array - Answer One way to model multiplication visually one factor is shown vertically
the other horizontally
2x4
