On Jul 9, 2014, at 11:11 AM, Joe Niederberger <firstname.lastname@example.org> wrote:
> I think the recog/recall distinction helps understand what's the common thread among these various complaints: a confusion between understanding something and being able to explain it, and of course in this context that means explain it in the "Approved" way. > They are taking conceptual understanding, which is a very delicate and private sort of thing, and trying to regiment it and make into a drill that everyone does the same way in lock step.
They are confusing conceptual understanding with formal thinking, something that young and mentally immature children are incapable of. Asking them to *explain* things is not going to work as it might when asking more mentally mature high school students to explain things. Thus, the result ends up to be rote with rote like approved answers. The only way to establish *knowing* at this age is by *doing*, not *explaining*. I am not saying that having discussions around explaining isn?t useful, just too early to be tested in this manner.
> > > Once you really "get" a new concept, it doesn't do much good to do it over and over. Once you realize that a grid of dots helps explain what 3x5 is, its over. Doing 10 more pictures with dots doesn't do anything but make people weary and disgusted.
I agree, but we need to be clear about why there is so much repetition to begin with. Connecting multiplication with grids of dots is going to take more than one pass and connecting multiplication with pictures of dots requires a multitude of realizations. All of this will require many pictures and then there is some minimum number of pictures required (in a test) to ensure fluency. I see two types of weariness. Type A when the student doesn?t get it and becomes weary of trying and failing and type B when the student does get it and becomes bored of the exercise. I haven?t found students to be bored with the exercise at 10 pictures. At 100 for sure. It may be that whether the student is getting it or not, there is a magic number of repetitions that will no longer cause any improvement, at least for that siting, and will cause boredom in both cases.