On Thu, Jul 3, 2014 at 9:43 PM, Joe Niederberger <email@example.com> wrote:
> >I'd change the focus a bit and ask if "machine grading" of mathematics is > OK. > > Is grading of mathematics OK? > Who grades mathematics? > Mathematicians, of course. > What would the consensus be? > > Cheers, > Joe N >
Actually, just to clarify how my school works: we don't "grade" in the traditional sense of letter grades.
Rather, a student turns in work and is then coached / coaxed / referred to readings etc. if the work does not meet all the criteria or even if it presents a perfect "practice moment" in some way. I.E. each student just keeps improving the work until in passes. That can take multiple drafts of any given Python or C# program, or multiple reworkings of a math problem.
In both cases, there's the immediate feedback of an interpreter (e.g. Python, Mathematica), mixed with the slower feedback of a human, not a robo-grader.
As a result, if two students sign up the same day for a Calculus course, one might finish in three weeks, another in ten.
They're not obligated to work at the same rate. There's no "cohort", no "classmates". It's one-on-one with the mentor, and the feedback is to you privately, not to you in front of a group.
There's no turning back quizzes with As on some Bs on others, with some students publicly outed a Cs and below. There's no public shaming, which is almost a definition of the typical brick and mortar K-16 classroom.
Is what I teach mathematics? As I mentioned earlier, we have an exercise where we repurpose the multiplication operator * to serve as a composition operator, such that two functions might be composed using a Composable class, a type students are then asked to add to, to make "powering" possible.
def f(x): return x + 2 def g(x): return x * 2
c0, c1 = Composable(f), Composable(g) newc = c0 * c1 result = newc(10) # x 2 then + 2
result should be 22. Then c1 ** 4 (powering), thanks to student work, would give c1 * c1 * c1 * c1 e.g. (c1 ** 4)(10) = ((((10 * 2) * 2) * 2) * 2) = 160.