Intuition for regression to the norm So for regression to the norm it says if someone has a high score on a test (relative to the average) then they are likely to score lower and lower on each following test? This seems very counter intuitive. 
 A: As with all probability problems the setup is very important, perhaps you heard of the problem of 3 coin flips, if we know 2 of them are heads what is the probability the third is heads? Which has probability 1/4 This is because the third coin to fall heads is not fixed. 
Likewise consider if you were to pick a high score from the class. For any given person they are much more likely to be picked if they did relatively well for themselves on the test rather than relatively poorly (with respect to their own average). Another way of thinking about this is consider a class with 10001 people 10000 average 70 on tests which we call group B and 1 that averages 90 which we call group A. You pick a paper with grade 80 is it more likely it came from group A or B?. Of course B is the natural answer which means that this person is likely to score lower than 80 on the next test.
A: It's usually called regression to the mean in my experience
(and you will get a lot more relevant hits from the math.stackexchange 
"search" box if you use that term rather than "regression to the norm").
Looking only at the sequence of scores earned by a single individual, the only
regression to the mean you are likely to see (other than the obvious effects of
gaining or losing skills over time) is regression to that individual's own mean score.
A very bright student might tend to score two standard deviations above the 
population mean (which I'll abbreviate as $+2\sigma$), but (depending on the test) 
they might occasionally score $+2.5\sigma$ (on a good day) or $+1.5\sigma$ (on a bad day). 
Having gotten what is (for them) a much-better-than-usual or much-worse-than-usual score
one time, the next time they take the test they are likely to get something
closer to their usual score.
Looking at the entire population, however, the group of students who scored
$+2.5\sigma$ on any given day will contain a larger percentage of students who
tend to score $+2\sigma$ but who had a good day
than students who tend to score $+3\sigma$ but who had a bad day,
simply because $+3\sigma$ students are much rarer.
Hence when you retest you will likely see that among all the students who scored
$+2.5\sigma$ on the first test, the majority will score worse on the retest.
But you will also have a new crop of students (a different set of individuals)
who score $+2.5\sigma$ on the retest just because they are more alert than usual
or simply got lucky that day.
A: Suppose every day I take a $12$ question multiple choice test where each question has $4$ possible answers, and I always choose my answer randomly.  On average, I should expect to get $3$ correct answers per test.   So, for example, getting $9$ or more correct answers is unlikely.
Suppose when I took the test yesterday, I got $9$ correct answers.  Is it still unlikely that today, when I retake the test, I get $9$ or more correct answers?

Edit: If the assumption that the student guesses randomly bothers you, consider the following formulation:  I take an $n$ question test each day, and answer each question correctly with probability $p$ (perhaps reflecting that there is some probability that I focused on certain types of questions over others, or that I forgot some definition, or $\ldots$, etc.).   On average, I should expect to answer $np$ problems correctly on each test.
Now, suppose I answer $n$ problems correctly on the first such test.  What is the probability that I do worse on the next test?  We can compute
$$\operatorname{Pr}[\text{score} < n] = 1 - \operatorname{Pr}[\text{score} = n]$$
$$= 1 - (1-p)^n$$
So, for $p < 1 - 2^{-n}$, 
$$\operatorname{Pr}[\text{score} < n] > \frac{1}{2} > \operatorname{Pr}[\text{score} = n]$$
and I'm more likely than not to score worse on the next test.
Put another way: if, without changing my study habits or understanding the material any better, I suddenly score much higher than usual on a test, then I probably just got really lucky.  Since I don't usually get really lucky (otherwise, it wouldn't be called luck), I should expect to score something closer to average (lower) next time.
A: They would score lower and lower, and then higher and higher, and then lower and lower, etc. such that the mean is realized over large $n$. If a higher score is indicative of some real improvement in the student's average ability (as you suggest) you would need to alter the mean to reflect this. 
