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by cube13 5239 days ago
This is the exact attitude that the blog post is saying is wrong. For mathematics, computers are tools. Computers don't create the answers, they assist the user in finding the answer. They're time-saving and error checking devices, which are useful after the student learns the concepts inside and out. They are not supposed to solve the problems directly.

>>"Explain whether 4/3 or 3/4 is closer to 1, and how you know."

>I am not familiar with the domain, but dont we have some automatic theorem-proving tools? This would look like a perfect use case to me.

Theorem proving tools would work if the students wrote their answers in a format that the tool would work in. In this case, it would be a natural language proof instead of a formal proof, which simply isn't possible to parse right now. Perhaps it will be in the future.
2 comments
nickolai 5239 days ago
> What does a student learn from this? They're learning the tool, not the process of solving the problem.

They will learn the process if the tool is only used behind the scenes to validate their answer

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cube13 5239 days ago
I misread your post, and did a ninja edit. Sorry about that!
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ori_b 5239 days ago
> Theorem proving tools would work if the students wrote their answers in a format that the tool would work in.

Theorem proving tools would work if you were writing formal proofs. At the level he's talking about, students are not writing formal proofs -- they're writing explanations.

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gbhn 5239 days ago
Right. It seems to me that the despair is that it is very hard, from knowledge like "student checked box B in this test, which was correct" to deduce "student actually understands the concept".

Perhaps a partial solution to this problem can be found in... wait for it... programming! That is, it is really hard to write a program to find general answers to problems unless you understand the basic idea. This definitely doesn't work for everything, but I wonder how big the domain is where this is a really good way to mechanically assess understanding, and whether the language that'd be required would itself become a bigger component of the measure than what you're trying to assess -- mathematical reasoning.

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