Robert Hansen (RH) posted Jan 2, 2014 7:25 PM (http://mathforum.org/kb/message.jspa?messageID=9354490) - GSC's remarks interspersed: > > On Jan 1, 2014, at 8:30 PM, Anna Roys > <email@example.com> wrote: > > > Robert, > > > > Your definition seems to leave out the teacher... > > please consider the following: > > > > (2) Pedagogy - the art, science, or profession of > > teaching - retrieved from > > http://www.merriam-webster.com/dictionary/pedagogy > > > 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. > AHA! That crucial transitive relationship, "CONTRIBUTES TO"!!! > > 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. > And how does all of the above square up with your famous 'pedagogical philosophy'???
RH's famous 'pedagogical philosophy': "Children must be PUSHED to learn!" (math, or anything else) > > 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. > "INCLUDES", by the way, is also a very useful transitive, 'system relationship', which could help us come to understand 'system structure' to a pretty sizable extent. However, working with "INCLUDES" in a system demands that one has previously come to understand the 'system as a whole' earlier (to a fair extent, at least). This is most effectively accomplished by doing a little modeling with "CONTRIBUTES TO" to begin with (in its weakest manifestation of course, namely "MAY CONTRIBUTE TO" to start with). PERT Charts do not help in the early stages of working towards understanding of the system. > > > 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. > Limits, by the way, are generally "SURMOUNTED", not mitigated. (See below). > > > 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. > You are 100% correct. Interest could "CONTRIBUTE TO" development of available talent. Also, existing talent often could "CONTRIBUTE TO" interest to do the hard work needed to 'learn'. The two contributions above are slightly different from each other and are well worth studying in detail.
The simple and effective way to do the above (in fact, it's the ONLY way that I know works to enhance understanding) is to use Warfield's 'structural graphics' (more specifically the 'prose + structural graphics' [p+sg]) that I often recommend. We do this by inserting the two elements ('interest'; 'talent') into a dyad, and then 'systematically' developing, analysing and deepening (via 'synthesis') our understanding of the dyad. As earlier observed, it takes a little learning, and a fair amount of 'unlearning' to do this successfully - but all of this is, in fact, easy enough for any high school student to do. [It's easy when we work interactively]. > > When students have > initial interest in something it is usually genuine > and sincere. > Indeed. It is largely the task of the teacher to stimulate and nurture that interest. Unfortunately, the existing educational system(s) often lead to the stifling of that 'initial interest' - though many teachers do manage to overcome this deficiency of the system. > >But how well they progress (talent) will > affect that interest. It depends on what their > initial expectations were. > Nope. It largely depends on the ability of the teacher (in general within an incompetent system) to stimulate that initial interest. (Many teachers do manage to do this, despite system inadequacies - but it is a very difficult and often thankless understanding). > >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. > Ah, that famous PUSHING theory of RH's, no doubt? > > 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. > > Robert Hansen > In your last paragraph, do you at all understand just what you have written? Do you really mean that, if anything at all?
v. -gat?ed, -gat?ing. v.t. 1. to lessen in force or intensity; make less severe: to mitigate the harshness of a punishment. 2. to make milder or more gentle; mollify. v.i. 3. to become milder; lessen in severity. [1375?1425; < Latin m?tig?tus, past participle of m?tig?re to calm, soothe =m?t(is) mild + -ig?re (see fumigate)] mit?i?ga?ble (-g? b?l) adj. mit?i?gat`ed?ly, adv. mit`i?ga?tion, n. mit?i?ga`tive, mit?i?ga?to`ry (-g??t?r i, -?to?r i) adj. mit?i?ga`tor, n. usage: mitigate against (to weigh against) is widely regarded as an error. The actual phrase is militate against:This criticism in no way militates against your continuing the research. (The "?" in the above refer to 'accent' or 'separation' symbols in the original which the Math-teach editor does not translate exactly).
It is generally quite useful to understand what a word means before attempting to use it.
Your misuse of the word above leads the reader to question whether you know anything about what you have attempted to argue earlier.
GSC ("Still Shoveling! Not PUSHING!! Not GOADING!!!")