Saturday, February 07, 2004

Grades for Loan

The Marginal Revolution provides this entry:

Loan markets in grades
Tyler Cowen

A school in China is allowing students who don't do well in tests to borrow a few extra marks as long as they pay them back with interest.

The scheme was recently introduced by Penglai Road No 2 Primary School in the Huangpu District of Shanghai, reports Xinhua.

Students who do poorly on a test can ask their teachers to lend them a few points to improve their grade, but twice as many points must be paid back on the next test, assuming they achieve a better mark.

If they don't, interest on the loan continues to run at 100% per test until it is paid off.

It is reported that about 40% of students at the school have taken out such loans.

The fact that people are willing to borrow points is entirely an artifact of the grading system. If the system awarded a letter grade based solely upon the total accumulated points at the end of the semester you would never need or want to borrow them, as doing so would only lower your total number of points.

This is different then the incentive to borrow in the real world, because there you can use the funds borrowed to produce something that hopefully provides enough return to cover cost of borrowing plus something for the risk and effort undertaken. In the regime where grades are only assigned at the end of the semester based upon the total points earned there is no incentive to borrow earlier in the semester, since you can not use those points to generate a positive return. It would simply be a matter of shifting the earning of the points from later in the semester to earlier and it would come at a cost.

What makes this possible is the censoring that happens when mapping the points earned on an exam into a less sensitive measurement scale, such as letter grades. Say you receive 88 points out of 100 on an exam which maps to a B, but is only 2 points shy of an A/B. Borrowing those 2 points, which only represents about a 2.3% improvement in the total number of points, but a 16.7% increase in letter grade (assuming a 4.0 scale). On the next test you will be expected to pay back 4 points, which may not even lower the letter grade on that exam.

Anyhow, you could figure out how often, or in which cases you'd want to borrow points. It would depend primarily on the interval between grades, the smaller the interval, the more likely the large interest payments will lower future letter grades. The wider the intervals between grades, the more censoring that goes on and the larger the incentive to borrow points from future tests. However, I'm pretty sure that the intervals at the Chinese schools aren't wide enough to justify 40% of the students borrowing against future grades. It is likely more evidence of students overestimating their abilities.

This is why I do not assign intermediate letter grades, since you could have a student get the same final letter grade as someone who has actually earned more points, or even worse they may get a higher letter grade than someone who has earned more points.

90-100 A
80-89 B
70-79 C
60-69 D
59 and below F

Adam gets the following scores on his 2 exams
90, 80,
Eve gets the following:
99, 89

Averaging the assigned letter grades gives them both something between an A and B, whereas averaging the number of points and then mapping that into the letter grade gives Adam a solid B and Eve a solid A.

What if Adam earned 90 and 20, which would average to a C if censored by exam, or an F if done based upon total points. Whereas if Eve earned 79 and 59 would give her a D if based upon censoring and a D if based upon total points. Of course it would better to never sensor into a letter grade and instead report only the total points earned, the total possible points and maybe the class rank.

The original article is here.

Keywords: Grades

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