You need some mathematical model. The bell curve emerges as a sum of many things. For example you have many genes that can contribute to higher intelligence, so it’s a question of how many times the coin of fate had landed the right way, and the result is approximately the sum of the contributions.
Now if we assume that school just adds some knowledge to children—even if we assume that each child gets a random amount of knowledge, but it’s a random amount independent on the starting value—the result is still a bell curve.
If we had a model assuming that school e.g. doubles each child’s knowledge, that would increase the gaps, but it would still be a bell curve (only twice as wide).
However, if we assume that each child gets a random multiplier by school, let’s say, everyone’s starting knowledge is multiplied by a random number between 5 and 20, then the result is no longer a bell curve.
Basically, bell curve × bell curve ≠ bell curve, but instead (assuming all numbers are positive) it is asymmetric, with longer right side. Imagine {1, 2} multiplied by {1, 2}, you get {1, 2, 2, 4}, with the 4 far away from the center.
If this were true, your expect grades/scotes to not be a uniform gaussian. You’d expect the middle to be slightly lower than expected.
Also, you’d expect crossover events (below-average to above-average or vise versa) to be less common than chance would predict.
Why? Links appreciated.
You need some mathematical model. The bell curve emerges as a sum of many things. For example you have many genes that can contribute to higher intelligence, so it’s a question of how many times the coin of fate had landed the right way, and the result is approximately the sum of the contributions.
Now if we assume that school just adds some knowledge to children—even if we assume that each child gets a random amount of knowledge, but it’s a random amount independent on the starting value—the result is still a bell curve.
If we had a model assuming that school e.g. doubles each child’s knowledge, that would increase the gaps, but it would still be a bell curve (only twice as wide).
However, if we assume that each child gets a random multiplier by school, let’s say, everyone’s starting knowledge is multiplied by a random number between 5 and 20, then the result is no longer a bell curve.
Basically, bell curve × bell curve ≠ bell curve, but instead (assuming all numbers are positive) it is asymmetric, with longer right side. Imagine {1, 2} multiplied by {1, 2}, you get {1, 2, 2, 4}, with the 4 far away from the center.
If depends a lot on which model you choose.