Critiquing your analysis
Critiquing while solving the problem
Most investigations switch modes back and forth several times between
analysis and critique:
- Analysis: Try something.
- Critique: Evaluate the success of what you tried, and think of
intermediate questions whose answers might help your pursuit.
- Analysis: Try something else.
- etc.
Occasionally your critique will include taking stock of all you've done so
far, as you try to get ideas of what to do next.
Critiquing a solution
Mathematical work shouldn't cease after a problem is solved. You need to
critique your work again:
- Check details until you are confident in each step of your reasoning.
- See if your solution uses all of the data.
- Assess the reasonableness of your solution, especially if you're
modeling. If the mathematical solution doesn't translate back into a good
solution for the original problem, then your mathematical model may not be
capturing all of the
important aspects of the original problem.
- Make sure your general solution applies to particular cases.
Going beyong doing homework
As an investigator, you do further critiques:
- See if there's another, perhaps simpler or more elegant, solution.
- Assess your overall progress in the investigation.
- Very importantly, pose extension problems.
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