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Correctly Executed Procedures
Do not mean a student understands what s/he is doing
Students often cannot read or explain the numeric value of their correct answers
Careless Errors
can reflect lack of understanding of the process being used
can be a positive sign of allocating resources to meaning rather than procedure
are often more systematic than random
Problem Solving
often not problem solving, just learned strategies matched with standard "problems"
Real Problems have never been solved before, that's what makes them problems
Conceptual problems falsely attributed to visual functions
i.e., writing 21 as 12
failure to keep digits aligned while computing
Conceptual issues possibly reflective of visuo/integrative functions
appreciation of 3-dimensional space
number intuition
interest in novel problems
intolerance of memorized algorithms
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