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by jltsiren 33 days ago
Hard problems introduce noise to the grades. A student who gets a hard problem right could be good or lucky. In order to grade the students properly, you need multiple problems of similar difficulty. If you have both ordinary and difficult problems in the exam, it's probably long enough that it should take the entire day.

Undergraduate exams tend to be short. Which means that a perfect grade should be interpreted as "meets the expectations".
1 comments
chongli 33 days ago
Which means that a perfect grade should be interpreted as "meets the expectations".

None of the mathematics exams I wrote during undergrad at Waterloo (as a math major) would fit that description. Nearly every single one of them had midterm grades with unimodal distributions centred below 70%, tending toward 60%. Typically, only 1-5 people in the class (of 100-200) would score a perfect grade. In upper year pure mathematics courses it was common to not have any perfect grades (in a class of about 20-30).

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jltsiren 33 days ago
Mathematics is notorious for exams like that. But if you look at the reasons why people fail to get a perfect grade at undergraduate level, it's almost always due to honest mistakes or because they didn't learn what they were supposed to learn.

In my experience, studying mathematics is a bit weird. If you are ready to learn a topic, it's probably the field where you can get top grades with the least effort. But if you can't learn something with reasonable effort, hard work is unlikely to help. Doing something else and trying again after a few months might help.

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chongli 32 days ago
If you are ready to learn a topic, it's probably the field where you can get top grades with the least effort.

Depends on your school. At my school, someone who was not super-talented in math but who works hard and is actually smart about studying is a 70s-80s student. The students who got 100s were basically IMO-level elite mathematics kids who were heavily recruited by the school and given full ride scholarships.

The course exams were essentially designed so that a "meets expectations" was a final grade of 65%. A grade of 100% is someone they were looking to recruit into research internships, grad school, and potentially a tenure-track position.

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