[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]

[Ed Wall]

Philip

      To first comment on your note to Andy. The teacher was not necessarily interested in students' fluency with the operations (in fact she may have thought there were more than fluent). The first sentence of my story reads:

>Ms. Peña has, in previous years, noticed that her fourth graders, at times, struggle to make sense of multi-step word problems. Many seem confused about both the nature of the required operations—most usually, addition, subtraction, multiplication, or division—or the order in which these operations are to be applied.

    Second, we may see teaching mathematics (and see teaching teachers) differently (which is fine as I certainly do have all or even significant number of the answers - I am right now working on the questions). A story might be helpful:

A number of years ago I was asked to view an 'exemplarily' mathematics class for pre-service teachers taught by a mathematician (he had received a grant to design this special class). He began the class by clearly and succinctly introducing the mathematics  problem(s) to be considered and when all seemed to have a good idea what was to be done, the pre-service teachers - about five or six to a table - began talking and working. Students definitely seemed engaged, there was a lot of good discussion, and I think the teacher walked around a bit making comments and asking questions. The class ended and he asked me what I thought. I told him nicely it was among one of the worst taught classes I had ever seen (I did tell him why). Why do you think I said that? Student turns were certainly in the 90s.

Ed

On Oct 26, 2014, at  10:31 AM, White, Phillip wrote:

> 
> 
> as you wrote, Ed:
> 
>     " In the next section of the paper I take up a different math lesson with ostensibly the same purpose (i.e. making sense of 'word' problems). Some different things will show up which perhaps get me a little closer to a 'smallest' unit of analysis. It will, in a sense, be the 'kinds' of turns not the number of turns (although chidden will have more turns) that are interesting (or so I think - smile)."
> 
> clearly i did not express myself coherently, this this is exactly the point i was attempting to make - that it was the 'kinds' of turns, the action within the turn, that was of paramount importance.  i interpreted the teacher's turns as actions that the students could have been doing. which is why i noted that the teacher produced the greatest number of turns.  as a teacher of teachers i would have preferred to see the great majority of turns having been done by the students - preferably student to student responses.
> 
> and thanks for the smiles!  
> 
> phillip
>