Right answer, incorrect solution

I'm curious to hear from the folks at Brilliant.org what fraction of submitted solutions are seriously flawed or incorrect. This past week was the first I was invited to submit solutions, and it forced me to notice when I took steps I couldn't fully justify. It would be interesting to see what the general gap is between a solver's intuition and his/her rigor, whether this changes with level, and whether it is different for math vs. physics.

#Math #QuestionsOrSuggestionsForBrilliant

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Comments

It heavily depends on the question. For the straight-forward questions, the percentage of correct solution tends to be extremely high, especially since we only solicit solutions from correct numerical answers, and students only submit solutions when they are certain of what they are writing.

However, there are questions in which the 'obvious' step is false, and students apply a simplistic logic. 2 questions come to mind from the Jan 14 set. In Number of Divisors, every solution made the fatal error of assuming that the smallest value of $N$ must result from the smallest value of $A$ , which must result from the smallest value of $B$ , so on and so forth. However, while this logic is flawed, few students were able to spot the error in their thinking.

The other example is Product of Values of Roots, where students forget that in taking square roots they need to be clear about the positive and negative possibilities, which could result in wrong solutions as in the Proof that -1 = 1. While lots of students could see the fallacy in the blog proof and quickly criticize it, they fail to see the error of their own thinking just because they think they had the solution.

Calvin Lin Staff - 8 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$