
Re: Why do so many of us hate math?
Posted:
Jul 4, 2014 11:16 AM



On Thu, Jul 3, 2014 at 9:43 PM, Joe Niederberger <niederberger@comcast.net> 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 robograder.
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 oneonone 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 K16 classroom.
I find this an interesting way of teaching and it's what online schools tend to allow in principle: a private bubble for each student without "peer pressure" to "keep up" with some cohort. On the other hand, there's the pressure to have skills and find a niche in the job market. People come to our school already motivated to learn SQL or JavaScript or whatever.
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.
Example:
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.
http://mathforum.org/kb/message.jspa?messageID=9450041
Kirby

