pedagogy - how mathematical awareness builds in a student, any student.
Point noted Anne, but -
When I say ?how? in my definition, I am implying any and all factors that contribute to the awareness. This certainly includes teachers and teaching.
My definition of pedagogy is probably broader than the common version. In my view, pedagogy must study both the teacher and the student, at the same time. A successful outcome involves both. And pedagogy (my version) can involve just the student, learning on their own. It involves all conscious effort to raise the student's awareness of a subject, beyond what it would be without any conscious effort. That effort can come from the teacher, the student, and other participants, like the parents. Generally, especially in grade school, we attribute most of that effort to the teacher. But as the student matures intellectually, more and more of it falls on them. While my focus of study is on that effort, I also recognize that there are other factors that affect the outcome, like the quality of the student?s home life. I call these other factors the environment.
In my view, the student is mostly the limiting factor. I am not saying that teachers are secondary, only that we can control for the teacher, by selecting the teachers we want to teach, but we cannot control for the student.
> QUESTION: Shouldn't the goal more than just having a mathematical awareness? > > Extending..... > > (3) Perception - the way you think about or understand someone or something - retrieved from http://www.merriam-webster.com/dictionary > > (4) Conception - the capacity, function, or process of forming or understanding ideas or abstractions or their symbols - retrieved from http://www.merriam-webster.com/dictionary > > I think words (3) and (4) fit better.
Awareness includes those two words and probably two dozen more.:) I keep things a bit looser because it doesn?t lock me in.
> I am most interested in these two words, as I struggle to parse what it really means to "learn" and how learning occurs. I would assert that learning happens within each learner's mind, depending on his or her engagement in the content. ( I am considering how much is filtered out while students are being exposed to the content.)
I agree. Engagement is the student?s conscious effort. Obviously, there are things teachers can do to improve the student?s conscious effort. But the (pedagogical) quality of the student?s conscious effort has limits that are outside of the student?s and the teacher?s control. The goal of teaching is not to overcome those limits, just to reach them.
Note, disabilities are not necessarily limits, because they can often be mitigated. The limit is what remains after the mitigation.
> I would suggest that learning cannot happen without students' desire to learn and that whatever any pedagogy may offer is nearly useless without student motivation to spark the learning.
Talent and interest. I used to debate whether these are the same thing, but after a lot of consideration, i am convinced they are not. When students have initial interest in something it is usually genuine and sincere. But how well they progress (talent) will affect that interest. It depends on what their initial expectations were. This is where I realized that interest and talent were not as dependent as I once thought. It isn?t that we are only interested in things we are good at (my previous thought). It is that we are interested in things that we are good enough at. Unfortunately, most students do not have interest in school. If it were up to them, most of them would not go to school. Fortunately, this lack of interest can be mitigated. We (parents and teachers) are able to coerce them into going to school and feigning interest anyways. In doing so, we hope that the interest becomes genuine and sincere, and to some extent, it often does, but not in every subject.
For my purposes, from a pedagogical point of view, Interest can be mitigated. Talent cannot.