The paper seems to be about unifying mathematics education research. Parts are a bit open to debate (especially arguments concerning the 'nature' of mathematics) and Ernest tends to somewhat gloss over this. However that is not relevant and you are correct Ernest does, among other things, put forth a unit of analysis for mathematics teaching which, as he admits is simplified for the purposes of the paper; i.e. the usual triad of teacher, student, and text (which is hardly unique to Ernest as he notes). At this point I have a question that I've been pondering about concerning such triads and their elaborations (and this goes back in a sense to things Schwab said elsewhere - the Schwab he quotes in the beginning of his paper) and, as he quotes you heavily, I will ask you: If this triad is indeed a prototype of mathematics teaching (i.e. posses all the basic characteristics of the whole), what makes this a prototype of mathematics teaching and not a prototype of, say, the teaching of reading? This is not a spurious question since, as a mathematics educator (of the type that Ernest wishes to unify - smile), I often find myself needing to help elementary school teachers realize there are actually substantial and observable differences (and substantial similarities) between teaching reading and teaching mathematics and, for sundry reasons, they tend to favor something like the former and cause their students some anguish in the learning of mathematics as time passes. Hmm, I guess I am asking whether the unit of the analysis can, in effect, be the 'world' or should it be, so to speak, among the 'minimum' relevant prototypes. It seems that it would be somewhat worthless otherwise (again similarities are important).
On Oct 23, 2014, at 3:57 PM, Andy Blunden wrote:
Paul Ernest has a position on the unit of analysis for mathematics teaching:
Julian Williams wrote:
Now I feel we are nearly together, here. There is no 'final' form even of simple arithmetic, because it is (as social practices are) continually evolving.
Just one more step then: our conversation with the 7 year old child about the truth of 7plus 4 equals 10 is a part of this social practice, and contributes to it....? The event involved in this Perezhivanie here involves a situation that is created by the joint activity of the child with us?
Peg: Germ cell for the social practice of mathematics... I wonder if there is a problem with Davydov's approach, in that it requires a specification of the final form of the mathematics to be learnt (a closed curriculum). But let me try: One candidate might be the 'reasoned justification for a mathematical use/application to our project' ... Implies meaningful verbal thought/interaction, and collective mathematical activity with others. Not sure how this works to define your curriculum content etc.
On 23 Oct 2014, at 16:28, "Peg Griffin" <Peg.Griffin@att.net> wrote:
And thus the importance of finding a good germ cell for mathematics pedagogy
-- because a germ cell can "grow with" and "grow" the current "social
practice of mathematics." Whether someone agrees with the choice of germ
cell made by Davidov (or anyone else), a germ cell needs to be identified,
justified and relied on to generate curriculum content and practice, right?