The following quote is from Thinking Fast and Thinking Slow:
"I propose a simple account of how we generate intuitive opinions on complex matters. If a satisfactory answer to a hard question is not found quickly, [the intuitive capacity] will find a related question that is easier and will answer it. I call the operation of answering one question in place of another substitution. I also adopt the following terms: the target question is the assessment you intend to produce; the heuristic question is the simpler question that you answer instead."
Not all errors involve some sort of substitution. Sometimes we avoid jumping to a conclusion, we grapple with the difficult problem, but we still make a substantive error. This is just one type of mathematical error.
Questions for homework:
- Do you agree with the author of this post?
- Are there other categories of mathematical error that you can identify?
- What can teachers do to effect the usage of heuristic questions by their students?
- Is this the sort of question the domain of psychologists? Of teachers? Of both?