[Xmca-l] Re: thoughts on Mathematics of Mathematics by Wolff-Michael Roth

Thu Apr 12 08:59:46 PDT 2018

Bill, Michael, and others

The problem with these pithy statements is that they do not define their
terms. For Vygotsky's "general genetic law" one needs to know what is meant
by a function, process, etc, and also an appreciation for different forms
of "internal": the internal of operationalisation, in which there is an
atrophy of supporting external signs that are replaced by internal signs,
contrasted with the internal dialogue often entailed in thought (though
granted internal dialogue may have its own externalised progenitors). For
Bruner's (Kay's summative) "doing with images makes symbols", one needs to
know what is meant by the full connotations of symbol. One might argue that
neither Vygotsky nor Bruner really knew with clarity what they respectively
meant by function and symbol (distinct from sign) -- it was part of their
exploration.

It is not that the "genetic law" is wrong per se, in my view, rather that
care needs to be taken in differentiating exactly what is being referred
to. In this view I see no contradiction between this law and the principles
of radical constructivism (which, to me, are rather obvious). The
clarification of inner dialogue, for instance, may be exemplified as a
dialogue between two perspectives that is no different (logically) between
a dialogue between two individuals, as exemplified by Pask's p-individual.
Hence in the realm of invention Vygotsky's genetic law may apply equally to
the "external" social plane as to the "internal" one. One needs to be clear
about what one means by internal-external and to heed the functional
possibilities from bootstrapping. This leads to a rejection of a naive
application of "all new psychological processes originating from outside",
but not from a sophisticated application.

Best,
Huw

On 12 April 2018 at 07:25, Bill Kerr <billkerr@gmail.com> wrote:

> ps. Addition to this comment from me above:
> Papert's framing of the turtle as an "object to think with" and
> incidentally also Bruner's similar conception of "doing with images makes
> symbols" do represent a learning theory which combines the kinesthenic with
> the visual with the symbolic. Does that gel with your learning theory? From
> my reading it does partly but you would be chary about the symbolic part,
> I'm not sure.
>
> On page 49, FN 31 Michael cites 2 papers about the emergence of signs from
> hands on science. This seems to me to be compatible with Bruner's approach
> which he summed up with the slogan "doing with images makes symbols" and
> also with Seymour's "object to think with" even though he didn't spell out
> the signs when he said that.
>
> My speculation here (to be shot down probably); Michael Roth's theory and
> Papert / Bruner theory cover the same ground and reach similar conclusions
> but they have different names
>
>
> On Thu, Apr 12, 2018 at 11:12 AM, Bill Kerr <billkerr@gmail.com> wrote:
>
> > hi Michael,
> >
> > > not so much "socially constructed."
> >
> > ok, sorry for incorrect summary of your ideas, I guess the construction
> is
> > so hard wired into me that I didn't notice the misrepresentation
> >
> > > before there was culture, before we used tools, where
> > were those tools for constructing anything of the likes that
> > constructivists say that we use to construct?
> >
> > Well, the hand is a tool and Engels essay "The part played by labour in
> > the transition from ape to man" is one you would know about.
> >
> > > eclecticism
> >
> > Thanks for the Leontev reference. I have read a bit and will read some
> > more before commenting.
> >
> > The reason I'm eclectic is because I read the various learning theories
> > and find some bits are useful for my teaching practice while other bits
> are
> > not. I'm very impressed by your book in its effort to develop what I
> call a
> > unified learning theory but it doesn't cover all the bases for me to be
> > fully persuaded.
> >
> > Also some of the critiques you make, eg. of constructivism, don't match
> my
> > understanding of what they stand for. The critiques in your book are
> > directed at radical constructivism (von Glasersfeld) and Piaget /
> > Inhelder. When I read pp 51-53 of your book it didn't sound like the
> Piaget
> > that has circulated in and out of Australian schools in the 1980s when
> > Piaget became the preferred flavour of the decade and science curricula
> > were developed around his ideas.
> >
> > Specifically you say that constructivists argue that: (I've *bolded* the
> > bits where your understanding of Piaget is different to mine)
> > "the individual mind is ... *informationally closed* to the surrounding
> > world" (51)
> > "In a constructivist account, she (Melissa) might be said to *incorrectly
> > 'interpret'* the object ..." (51)
> > "As Piaget, modern day constructivists often characterize children's
> > knowing *negatively: as lack, deficit ... or deviance* ..." (52)
> > "In the constructivist literature , we can frequently read that
> *misconceptions
> > ... have to be eradicated* (53)
> >
> > Piaget's best known observation were about conservation, the tall and
> wide
> > glasses, and I've never heard children's responses described as
> incorrect,
> > deficit or misconception but always as a stage that children have to pass
> > through. It always seemed me that Piaget respected and understood the
> > child's different view of the world.
> >
> > The version of constructivism that I am most familiar with was called
> > constructionism by Seymour Papert, which combines the internal
> > constructivism with an external construction. (Papert did spend some time
> > working with Piaget). This had real life application in the development
> of
> > logo-LEGO which evolved into Mindstorms LEGO. The idea was that kids
> would
> > build things out there and make those things do stuff with the logo
> > programming language and this would change/develop their minds inside.
> >
> > I'm not saying that Papert's constructionism was without difficulty due
> to
> > the fundamental idealist nature of constructivism but nevertheless I have
> > found it very useful in thinking about how kids learn.
> >
> > Papert described the logo turtle as "an object to think with" and tapped
> > into Freud's idea of body syntonic to describe the process. eg. how do
> you
> > draw a square? The teacher pretends to be a robot and asks the students
> to
> > direct him / her to draw a square.
> > Student: "walk forward"
> > Teacher: robot doesn't understand walk but he does understand forward
> > Student: forward
> > Teacher: How far?
> > Student: forward 50
> > etc. etc.
> > This leads to development of concepts of directed motion, angles (right
> > 90) and iteration. Once the square is drawn the teacher goes back and
> asks
> > students to identify which parts are repeated, and the code eventually
> > becomes repeat 4[fd 50 rt 90]
> >
> > Papert's framing of the turtle as an "object to think with" and
> > incidentally also Bruner's similar conception of "doing with images makes
> > symbols" do represent a learning theory which combines the kinesthenic
> with
> > the visual with the symbolic. Does that gel with your learning theory?
> From
> > my reading it does partly but you would be chary about the symbolic part,
> > I'm not sure.
> >
> > (my initial comment did mention what I see as a tendency to deny the
> > internal and I intend to post more later on that issue. Repeating what I
> > said then "Moreover internal representations or schemas seem to be denied
> > because that would be a capitulation to dualism, emphasising brain / mind
> > activity whereas the real deal is an integrated thinking body")
> >
> >  It was because of the idealist nature of constructivism /
> constructionism
> > that I became more critical of it over time and delved more into other
> > learning theories. I wrote about this back in 2008 when there was some
> > discussion about constructivism in the one laptop per child movement.
> I'll
> > put some links here for completion and my own convenience
> > https://billkerr2.blogspot.com.au/2008/08/towards-
> > fingernail-definition-of.html
> >
> > The funny thing was that each new learning theory I looked at offered
> > something useful to me as a practicing teacher. I won't go into more
> detail
> > at this point, there is enough here already for discussion.
> >
> >
> >
> >
> > On Wed, Apr 11, 2018 at 9:27 PM, Wolff-Michael Roth <
> > wolffmichael.roth@gmail.com> wrote:
> >
> >> Hi Bill,
> >> it is not so much "socially constructed." My key point in the book is
> that
> >> it is social BEFORE there can be any construction. It is social, and
> this
> >> is where I refer to a Vygotsky that has not been taken up, because
> "every
> >> higher psychological function ... was a social relation between two
> >> people." That is, in this specific case, mathematics is social, was the
> >> relation between two people before you see it in individuals...
> >>
> >> I think the construction metaphor breaks down when you look at our
> species
> >> becoming human. So before there was culture, before we used tools, where
> >> were those tools for constructing anything of the likes that
> >> constructivists say that we use to construct? How can a hominid
> construct
> >> "meaning" of the branch as tool to start digging for roots or fishing
> for
> >> termites? And how do they construct meaning of the first sound-words
> when
> >> they do not have a system that would serve as material and tool for
> >> building anything like "meaning?"
> >>
> >> So yes, a learning theory has to be able to explain learning from before
> >> culture (phylogenesis), before language and meaning (ontogenesis).
> >>
> >> And about eclecticism---I think we would be a step further if we
> listened
> >> to and pondered A.N. Leont'ev's complaint about the "eclectic soup
> >> [eklekticheskoj pokhlebke] ... each to his own recipe" that
> psychologists
> >> are trying to cook (in his foreword to *Activity. Consciousness.
> >> Personality*).
> >>
> >> Cheers,
> >> Michael
> >>
> >> On Tue, Apr 10, 2018 at 7:15 PM, Bill Kerr <billkerr@gmail.com> wrote:
> >>
> >> > One interpretation of Vygotsky (Wolff-Michael Roth) argues that all
> >> > knowledge is socially constructed and that ethnomethodology, paying
> >> > detailed attention in the now, is the best or only way of detecting
> and
> >> > evaluating what is going on . Human activity can’t be reduced to
> >> individual
> >> > actions. Anything individual originates in the social, be it words,
> >> > mathematics or by implication computer science (mentioned not in the
> >> > original but because it is a current interest of mine). Moreover
> >> internal
> >> > representations or schemas seem to be denied because that would be a
> >> > capitulation to dualism, emphasising brain / mind activity whereas the
> >> real
> >> > deal is an integrated thinking body.
> >> >
> >> > This world view is critical of other learning theories be they
> >> > behaviourist, cognitivist, enactivist or constructivist.
> >> >
> >> > The question that I want to explore here is the pragmatic one of
> whether
> >> > and how learning theory (an abstraction) makes a difference in
> practice,
> >> > for busy, hard working (usually overworked) teachers. An alternative
> >> > epistemology/ies which might appeal more in practice to real teachers
> >> under
> >> > pressure is an eclectic one centred around the issue of “what works”.
> >> >
> >> > I believe I am better read on learning theory than most teachers. See
> >> > http://learningevolves.wikispaces.com/learning%20theories
> >> >
> >> > Up until now I've developed an eclectic / pragmatic approach to
> putting
> >> > learning theory into practice. Take something from Seymour Papert's
> >> > constructionism, something from Dan Willingham's cognitivism,
> something
> >> > from Dan Dennett's behaviourism, something from Andy Clarke’s
> enactivism
> >> > and roll them altogether in an eclectic mix. The authors in this list
> >> could
> >> > be multiplied. My underlying belief was that it was not possible to
> >> develop
> >> > a unified learning theory, that human learning was too complex for
> >> that. As
> >> > Marvin Minsky once said in 'Society of Mind', "the trick is there is
> no
> >> > trick", I think meaning no overarching way in which human's learn.
> >> >
> >> > One big surprise in reading Wolff-Michael Roth is his serious attempt
> to
> >> > put an end to such eclectism and develop what appears to be a unfied
> >> > learning theory.
> >> >
> >>
> >
> >
>