Robert Hansen posted Oct 1, 2010 2:00 PM: > GS, you often say that we should bring all the > stakeholders together and from this gathering will > emerge the answers we seek. Why does that make sense > to you? Wouldn't it make more sense to just look at > the top 20% of the students and do as they do? > Entirely valid questions - herewith some responses (unfortunately in pure prose which renders it difficult, if not impossible, to go very deep into the issue):
1. What the top 20% of the students actually do will show us something (not all) of what that 20% do to achieve success/ mastery / understanding of math. It will not much show us the way they overcome their difficulties or problems - which may be equally if not more important view developing effective strategies to overcome the difficulties faced in arriving at success/ mastery / understanding.
2. Looking at what those top 20% do may not much help to develop strategies to help the bottom 20% learn. I'm strongly of the view that these should NOT be ignored: it is entirely possible that several in those bottom 20% actually got turned off math by insensitive/ incompetent teaching in an earlier year.
I have my own example to point to for evidence: In the Indian equivalent of my 'freshman high-school year', I recall I was at the bottom of my class in math - mainly because I had been bored stiff the year before. My math teacher somehow sensed that I could do better and took some special pains with me. I don't quite recall exactly the details** of the strategy he used - but anyway, within 6 or so months he had successfully aroused my interest, after which I went to the top of my class in math. My interest in math continued after that, and I quickly learned trigonometry largely on my own, which then enabled me to go into calculus, long before calculus was ever even mentioned in class.
** I do recall that, because he knew that I read a lot, he gave me the book "Men of Mathematics" by E.T. Bell and I believe that must have been a major element in his strategy. But there was much else besides in his strategy.
3. It took a very special teacher to do that for me: I'd be interested to see if such strategies can develop right from within the system, even from teachers who may not be quite as special as that teacher was; I'd also be interested to see if a large number of teachers can become 'special teachers' like that one was. I believe this can be done.
4. I'm also certain that ability in math is far more common than is commonly realized - the teacher has to learn how to capture the student's interest and learn how to stimulate it strongly: this is not easy to do (though with Internet etc it is MUCH easier to do now than it was those days). That's why, in models of math-teaching-&- learning that I've posted here in several earlier messages, I've continuingly emphasized things like the Yoshimoto cube, George Hart's sculptures, and the like. I observe that Anna Roys has posted a very useful workout that discussed 'Math & Music' - which is probably a very good route to go for musically inclined students. My interest is to enable each teacher to develop a good strategy to stimulate each of his/her students. This will require a whole new thinking of what math is and how it should be 'taught-&-learned' - some small aspects of this thinking I have tried to show in those models I have posted.
5. Of course, there will be several who - even with this kind of OPMS workout - will not come to develop an interest in math: OK, but I claim that, if the educational system does not make this kind of effort possible for all students, it is not an effective educational system.
6. Likewise (just as it is necessary to take the bottom 20% of students into effective consideration, it is necessary to take into consideration the views of those with whom one may happen to disagree, even if one disagrees strongly with them: one never knows what wisdom may develop thereby - AND one also never knows what wisdom one may miss out on.
All of the above (and much more besides) becomes almost obvious if one were to write down elements, starting with simple responses to the 1st Trigger Question: "What, in your opinion, are the THINGS TO DO in order to accomplish ....?" and then develop Interpretive Structural Models (ISMs) and Field Representations (FRs) from them and then an OPMS for a worthwhile Mission - ANY Mission to start with, after which one could attempt an OPMS for a truly ambitious Mission like "To develop an effective math educational system for ----". (I had embarked, some years go, on such a Mission for India. Only now am I beginning to get interest from a few teachers. The Mission will actually take of when I get some real teachers (and their students) ACTIVELY involved in creating their own models for the Mission.
Basically, in each case, one would convince oneself through the models one develops for himself/herself. Without the kind of model development that I am discussing (unfortunately here only in prose!), I could go on for a 100 pages in prose and I still would be unable to convince anyone of the points I am making.
Anyone who embarks on this kind of development of his/her ideas will then discover that one steadily develops (over time) a deeper and deeper understanding of the issue under consideration. This happens for EVERY Mission one takes up.
And what is remarkable is that one never needs to spend more than 10-15 minutes a day in doing 'OPMS-work', though one might certainly spend a lot more time DOING any single one of the elements in the OPMS.
For instance, I have a workshop coming up for an organizational group early next month. It took me no longer than 2-3 minutes to write up a couple of appropriate elements for that workshop, and to integrate them into my ongoing OPMS. There is one element there stating: "To develop an appropriate presentation that would interest participants from Organization ABC". As stated, integrating that element (along with a couple of others) into my ongoing OPMS took me no longer than 2-3 minutes: but I've already worked for about 3 hours on developing that presentation and I anticipate that it will take me many more hours before I am reasonably satisfied with it.