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Topic: From the Notices of the AMS
Replies: 71   Last Post: Jun 23, 2014 3:56 AM

 Messages: [ Previous | Next ]
 Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09
Re: From the Notices of the AMS
Posted: Jun 14, 2014 8:39 PM

On Jun 14, 2014, at 12:26 AM, GS Chandy <chandy.sag@gmail.com> wrote:

> I don't believe ANY subject or discipline under the sun has ever developed "coherently". While a subject or discipline is in its 'formative stages', the discipline itself as well as the methods of imparting knowledge about it are necessarily 'incoherent?.

Well, that goes against the observations of actual children learning arithmetic. The ones that excel *get* the coherence quite early. I am pretty sure that Joe is using the term *coherence* to mean a logical consistency in the subject. I remember a girl in my son?s kindergarten class that got the coherence, the method to the madness, in addition quite early. She was adding 2 digit numbers like a 3rd grader. Unfortunately, nothing came of this gift (she is still in my son?s classes) because the curriculum isn?t coherent, which I will explain shortly.

You can easily tell when a text book is working from a pedagogy of coherence. For example, the really old text books, 100 years or so old, go - One plus one is two, one plus two is three, and so on. They rely almost entirely on coherence and progress steadily through it. The newer-older textbooks, 30 to 50 years ago, retain that thread of coherence but also added more visceral relevance. Here are two apples, and here is another apple, now we have three apples. I think these offer a better balance than the much older books, but we can suppose that teachers 100 years ago added visceral relevance to their lesson plans when they desired. And I am using extreme examples to make a point, there are examples of visceral relevance in text books 100 years ago, though certainly, as printing technology advanced, the examples in textbooks became much better in later years. Another later development was spiraling.

The newest textbooks however have broken the subject into a collection of distinct topics which are no longer coherent. One week you are doing fractions and the next week you are doing integer subtraction. There is no continuity and without continuity it is impossible to have coherence. It is what I was harping about in third and fourth grade, and that Joe captured in the word *coherence*. I stopped harping because I gave up on the school?s version awhile back and have shifted to more at home work to give back the coherence the subject deserves.

The way this came about is complex and I can?t describe all that I have uncovered in the last 10 years in one post, but as more students attended school and took more classes in these subjects, more of them were not getting it, and the drift starts there. Education became very political and pedagogical theories that explained away differences became more popular than those that took them into account. A theory that promises that all students are good at math is acceptable and one that promises that only some are good at math is not. Even if some means a bright little girl in kindergarten. Talk about getting shafted twice. 50 years ago when some were allowed to be good at math, the little girl was not. Now she is not again because no one is allowed. And then there is the issue of money. Suppose you are selling OPMS like crazy, yet the results people are getting are no better than before. Worse even. Would that stop you from selling OPMS? Of course not. The only thing that sto!
ps anyone from selling anything is when people stop buying it. That is what an economy is. People selling things and people buying things. Colleges, schools, teachers and politicians will not stop doing any of this as long as it is economically viable, to themselves I mean, not to the parents or the students or the nation for that matter. Sure, bottled water is stupid, but as long as there is a market, why stop selling bottled water? The first rule of business, give the customer what they want, period.

But back to the topic of textbooks and pedagogy. Due to political pressures of equality and accountability, education was transformed from an exercise in coherence to an exercise in remediation. In the past, pedagogy and testing were quite separate. How you taught the subject was based on how the subject naturally flowed (coherence) and tests were only used to gauge how well the student did. Students not doing well could try harder or could try something else. Something else that they were possibly good at. For political reasons, this all changed. It was politically unacceptable that some kids were good at math and some not, especially when the issue of color or sex was involved. The new edict was that all kids are good at math and it is up to the schools to make that so and if they couldn?t make it so then it was the schools' and the teachers? fault. The schools in response had to refactor the curriculums and the tests. Even if they thought this was all hogwash, the custome!
r is always right, period.

The refactoring started in earnest in the 1980?s. Gone right away was coherence. How can you continue to teach a subject as it naturally flows if only the students with innate abilities get it that way and your edict is that everyone gets it? How do you identify and remediate student failure in that model? Coherence had to be replaced with something tangible and it was replaced with conceptual pedagogy. Since all students weren?t getting the topic naturally, as it flows, and since the notion of *naturally* itself was no longer even allowed politically, the educationalists changed the subject from a flowing and coherent exercise into a non-flowing and explainable exercise. Focusing on concepts is different from the visceral relevance I mentioned earlier. Visceral relevance offers tangible examples of the coherence while conceptual pedagogy offers tangible examples in place of coherence. For example, a coherent student refers to the example of two apples and one apple as a tan!
gible example of what they already know and feel inside, that 2 + 1 is 3. A conceptual student on the other hand looks to the example of two apples and one apple to to know anything at all. It isn?t a visceral example of something they already know, it is in fact all they know. It is a substitute for coherence.

Also, another factor that I won?t belabor has to do with weaknesses with tests and very low cutoff scores.

I don?t rely on our system of education anymore and it seems that is true for most affluent parents. I will say that I was one of the longer holdouts though. I am proud of that, but the last few years of the realities of the global economy, our economy and the realization that I, a citizen, am often a minority at work, has made me realize the reality of the situation. Fortunately, I am able to fix it, easily, at home. And I know that other don?t have the same opportunity as me. I do get my hopes up though, when I see a new vocational school open, only to have them dashed again when the next paragraph reads ?To increase the number of girls" or ?To increase the number of students of color" or ?To increase the number of X?. How exactly and why exactly do you make a school do both? I mean, teach the subject well and increase the number of X? It seems that all you can do is create a school that teaches the subject well and encourage X to give it a shot. Just make more schools for!
all the paths and make them relevant to the economy and labor market and the students will choose. And more of them will be successful.

Bob Hansen

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Date Subject Author
6/2/14 Louis Talman
6/3/14 GS Chandy
6/3/14 GS Chandy
6/3/14 Joe Niederberger
6/3/14 Louis Talman
6/3/14 Joe Niederberger
6/4/14 GS Chandy
6/3/14 Joe Niederberger
6/3/14 GS Chandy
6/4/14 GS Chandy
6/4/14 GS Chandy
6/4/14 Joe Niederberger
6/4/14 Robert Hansen
6/4/14 GS Chandy
6/4/14 Robert Hansen
6/4/14 Joe Niederberger
6/7/14 GS Chandy
6/7/14 GS Chandy
6/7/14 GS Chandy
6/7/14 GS Chandy
6/12/14 Joe Niederberger
6/12/14 Robert Hansen
6/12/14 Robert Hansen
6/13/14 GS Chandy
6/13/14 Joe Niederberger
6/14/14 GS Chandy
6/14/14 Robert Hansen
6/14/14 GS Chandy
6/14/14 Joe Niederberger
6/14/14 Joe Niederberger
6/14/14 Joe Niederberger
6/14/14 GS Chandy
6/15/14 Bishop, Wayne
6/15/14 GS Chandy
6/15/14 Robert Hansen
6/15/14 GS Chandy
6/15/14 GS Chandy
6/16/14 GS Chandy
6/16/14 Robert Hansen
6/17/14 GS Chandy
6/17/14 Robert Hansen
6/21/14 Louis Talman
6/21/14 Robert Hansen
6/22/14 Bishop, Wayne
6/17/14 GS Chandy
6/17/14 GS Chandy
6/17/14 GS Chandy
6/18/14 GS Chandy
6/18/14 GS Chandy
6/18/14 Louis Talman
6/18/14 Robert Hansen
6/19/14 Louis Talman
6/19/14 Robert Hansen
6/19/14 Louis Talman
6/19/14 Robert Hansen
6/20/14 Louis Talman
6/18/14 GS Chandy
6/20/14 GS Chandy
6/19/14 Robert Hansen
6/19/14 Robert Hansen
6/20/14 Bishop, Wayne
6/20/14 Robert Hansen
6/21/14 Louis Talman
6/22/14 Bishop, Wayne
6/19/14 GS Chandy
6/20/14 GS Chandy
6/20/14 Robert Hansen
6/20/14 GS Chandy
6/21/14 GS Chandy
6/23/14 GS Chandy
6/21/14 GS Chandy
6/21/14 israeliteknight