On Dec 31, 2013, at 10:48 PM, Louis Talman <firstname.lastname@example.org> wrote:
> Nor do I see why Robert might disagree, because---by his own admission---he's only interested in the "mathy" kids, who are certainly ready for this discussion in 8th grade.
Actually I was thinking high school, like Joe. But given the fact that textbook publishers have (due to market pressures) eradicated from their texts any mathematical treatment with even a hint of pedantry, this would be an impossible task for your typical school today. Granted, there are schools that are the exception, but the vast majority of students do not have access to those schools. And then the colleges cry because their students don?t possess formal thinking skills and can?t follow a lecture.
Even Devlin seems to have consciously avoided formal thinking in his nice little book on mathematical thinking.
Im not interested in mathy kids. I am interested in authentic math curriculums. I am interested in an authentic progression of sophistication in the student?s thinking.
Mathy kids are kids with some talent, any talent, for math. You teach them mathematics and they get it.
How am I to study authentic math curriculums without authentic math students?
> > The take-away from this discussion seems to be that Robert is interested in pedagogy only when it serves his purpose in discussions about how things "ought" to be.
That?s a bit circular. Given that I have been pursuing a single comprehensive theory of math pedagogy (how it ought to be) then it follows that I must believe that such a thing exists and it follows that this would be my theme. Maybe it?s how I use the word ?pedagogy? versus how you use it. I use it to describe the process that takes place as students successfully progress through levels of mathematical awareness. Don?t forget that I studied millions of test results, the world over, and they clearly show a progression that is the same for all students, regardless of all other factors. The only difference being how far each student makes it through the progression. That is pretty clear evidence of a progression.
Is the purpose of teaching mathematics to make it successfully through this progression or not?
When I expose fraudulent curriculums it is not about how they are teaching or in particular what they are teaching. It is what they claim to they are teaching. You show me gimmicks, semblances and frauds, then the James Randi in me comes out.
Have you ever thought that maybe many of these teachers are simply not well aware of the progression? That their own personal experience with and knowledge of the progression is shaky at best. And then, because of crazy proclamations like algebra-for-all and social promotion, they find themselves and their students in a state of perpetual remediation. How are they ever supposed to more fully develop a sense for the progression and become better teachers?
The progression doesn?t appear to be well taught in schools, but teachers with 5 years of experience in successful classes know about it. I don?t expect to convince people like Myers and Boaler, who trade their classrooms and students for 15 minutes of personal fame every chance they get. They are not even teachers. I don?t meant technically, I mean absolutely. And I am not holding my breath that this can put even a dent in the politics and fraud that defines education today. But, in spite of all of that, there still are many teachers and parents with genuine pedagogical motives who would greatly benefit from more insight into math pedagogy.