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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.


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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