Adding
It Up page 129-131
Adaptive reasoning refers to the capacity to think logically about the relationships among
concepts and situations. Such reasoning is correct and valid, stems from
careful consideration of alternatives, and includes knowledge of how to justify
the conclusions. In mathematics, adaptive reasoning is the glue that holds everything
together, the lodestar that guides learning. One uses it to navigate through the many facts,
procedures, concepts, and solution methods and to see that they all fit
together in some way, that they make sense. In mathematics, deductive reasoning
is used to settle disputes and disagreements. Answers are right because they
follow from some agreed-upon assumptions through series of logical steps. Students
who disagree about a mathematical answer need not rely on checking with the
teacher, collecting opinions from their classmates, or gathering data from
outside the classroom. In principle, they need only check that their reasoning
is valid.
Research
suggests that students are able to display reasoning ability when three
conditions are met: They have a
sufficient knowledge base, the task is understandable and motivating, and the
context is familiar and comfortable.37
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