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

[Bill Kerr]

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.
> >
>