[IAEP] reconstructed maths

Bill Kerr billkerr at gmail.com
Wed Jul 23 09:20:24 EDT 2008

On Wed, Jul 23, 2008 at 2:35 AM, Albert Cahalan <acahalan at gmail.com> wrote:

> On Mon, Jul 21, 2008 at 10:08 PM, Bill Kerr <billkerr at gmail.com> wrote:
> > On Thu, Jul 17, 2008 at 7:16 PM, Albert Cahalan <acahalan at gmail.com>
> wrote:
> > misunderstandings and misrepresentations aside, I'd raise this point
> > in response - your assumption is that a large scale study is more
> > important than the individual research and findings of one person
> >
> > I don't see why this assumption should necessarily be true - ie.
> > historically it has been shown many times that lone individuals or
> > small groups have turned out to be correct and the predominant or
> > mainstream way of doing things has eventually been displaced - that
> > is the nature of scientific revolutions
> I agree, but this doesn't help constructionism one bit. If anything,
> constructionism is the predominant or mainstream way of doing things
> in teacher's colleges. Don't compare "large scale study" against
> "lone individuals or small groups"; this is apples and oranges.
> Compare "large scale study" against the complete lack of evidence
> that constructionism works in real classrooms with real teachers
> and real students.

I can reply to that directly from my experience as a teacher in an education
system (south australia)

In our system the official curriculum guidelines are based on "social
constructivism". When the C__ word was promoted by the system I worked in I
was surprised, astonished actually. I had been using aspects of Papert's
constructionism (but not in exclusion to other approaches, by any means) in
the classroom for some years before this.

What I subsequently discovered was that the official "social constructivist"
curriculum was nonsense. What sort of nonsense? Fuzzy nonsense that
attempted to turn maths,science and IT into sociology type subjects. I can
add  more detail but no need here because we seem to be in agreement on this
point. And yes, this curriculum is generally seen as a time consuming
distraction from the real work of teachers, by teachers.

> There are numerous smaller and less formal studies in support of
> non-constructionist methods. Typically an underperforming school
> will switch methods (new leadership or parents nearly rioting) and
> the math performance will go way up.
> I found neither size of study in support of constructionism.
> Constructionist web sites are totally quiet on this issue.
> I thought this to be odd. After all, if you have such a great
> idea, surely you'd gather evidence in support of it. I was left
> with an uneasy feeling about the whole thing. I then stumbled
> across the opposition while researching something else, and woah!
> I see real evidence! It's really refreshing to see solid numbers.
> There are studies both large and small. The largest one is of
> course most impressive, being the biggest educational study ever,
> but there is no lack of smaller and less formal ones.

My website is not quiet on this issue.

For example, I did at one stage have a crisis in confidence where I thought
a method I was using successfully was more in line with "instructionism"
than "constructionism". So, I thought this through and analysed it:

Also I have seen other studies that provide some evidence of the success of
constructionist approaches. The best example I think is Idit Harel's study,
written up as a book, Children Designers. This had control group, summative
tests etc. as well as a very detailed descriptive account and individual
studies of child development. But there are others, I can dig up cite other
references if you want.

> it could be that whole systems have been built and maintained for
> > generations on principles of direct instruction - that various
> > challenges to this have arisen and been trialled, some good,
> > some not so good - but throughout this process the predominant
> > form of teaching has remained direct instruction
> >
> > it seems to me that in a system that has evolved in that way, that
> > due to forces of inertia and group think mainstream studies would
> > tend to show that mainstream ways of doing things are the "best way"
> Project Follow Through's data was analysed by two independent groups.
> Since math was the topic (a favorite for constructionists), there was
> little room for interpretation: did the students learn math?
> > Piaget did many studies and wrote many books and papers based on
> > the study of 3 children - that does not in itself make him wrong.
> > He might be wrong but I can see many advantages of doing in depth
> > studies based on a small group.
> That's an interesting prototype, but nearly any teaching method
> will work great in a tutoring environment with a fanatical teacher.
> The next appropriate step is to try it out in a full classroom, then
> in several classrooms with typical grade school teachers. Much more
> than that has been done for constructionism already, and it failed.
> When you have a proven failure, you need to stop.

I'd replace your word "fanatical" with informed here - really, it's a
question of whether the teacher has an informed view about knowledge
development in the child. And part of my argument here is that such a view
can only come from small scale in depth studies (Piaget type) - it can't
come from large scale studies.

I can see where you are coming from - my efforts to teach other teachers
about the approaches I use have not been very successful, in the main. A
little success but not much. But the issue I have raised with you is that
Papert's constructionism can work very well but it is also "advanced" and
requires the teacher to take a lot of new things on board. So, I acknowledge
you have raised an important practical point - how can we make
constructionism scale? But that doesn't mean that your theoretical position
(constructionism as an approach doesn't work) is correct.

> > I would like to discuss this issue more, just raising it here in
> > simple form --> minority views are not wrong because they are
> > minority views
> Right, they are wrong just because they are **WRONG**. :-)
> Remember that constructionism is, at least in the teaching
> colleges, the majority view. You probably won't graduate
> unless you at least pay lip service to it. It's a political
> correctness of the teaching profession. (one of many...)

I agree that the political correctness of soft sociological reform of
maths, science, IT is a real problem and this is often promoted using the
label of "constructivism".

In broad terms my view is that educational reform is pretty much politicised
and stuck because we have two opposing camps which could be categorised as
"back to basics through direct instruction" and "fuzzy sociological type
reform sometimes labelled as constructivism" hurling insults at each other.
Nevertheless, I think real educational reform is required and could be
possible if we can move past this stuckness.

- Bill
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