[jjaredsimpson]

Does this article say anything more profound than, "If you roll 10 dice, you'll expect a score of 35, however any pair of rolls which sum to 35 are unlikely to be similar."

All the worst students will be very similar and all the best students will be very similar because the number of available states is low. Average students are all unique in their average-ness.

Am I missing some subtle statistical understanding that the toy example doesn't capture?

[jimhefferon]

I think the article's contention is that on-the-ground teachers expect that two people coming out of a high school Algebra II with C+'s are similar. (Certainly that is my working hypothesis.) The article argues that it ain't so.

[sanderjd]

That's interesting that it's your working hypothesis! I have never thought grades correlated very well with anything at all. It's interesting to hear from someone who does not intuitively view it that way.

[jjaredsimpson]

The sets of dice which have equal sums will often have different constituent values.

[jimhefferon]

The article's contention is that on-the-ground teachers expect that two people coming out of a high school Algebra II with C+'s are similar.

[arjun810]

This is exactly what we think is a fairly common attitude -- thanks for stating it so clearly! It has ramifications both within a single class and when you think about how prerequisite and dependent classes are structured.

[jimhefferon]

How do you think it could be done differently? Student need to be judged for who moves ahead. That is, I have people in Calc I and I have to decide who moves on to Calc II. I can't send the next instructor a poset of their competence. I cannot require that everyone be competent at everything. I wonder what is your proposal?

[pmiller2]

You are missing that students have multiple dimensions they can be compared on.

[jjaredsimpson]

The dimensions are the dice.