[IAEP] educational brew

[Costello, Rob R]

Indeed...I agree Albert 

I think working out that sequence, its dependencies, and lesson
resources,  would be a great goal 

The only practical issue with this is it takes so much time ...that I
still can't see its that likely here or in any educational system
...the discipline and time (and money) resources to slow down enough to
do the architecture (working out the sequence and implementing it) for
that sort of approach properly is the issue ...so everything tends to be
done in a more fragmented way 

Its like a reset is needed - take half a dozen maths and IT types and
deconstruct maths learning sequences and curriculum resources like this
(over say a year) (there are various research based maths continua and
sequences that would make this possible) ...then take a few dedicated
programmers who could implement all this into a lesson framework that
kept track of pathways and progress

If it could be done, I think this would be a very useful resource - 80%
of the game in my view

I also think we need some more open ended tools - etoys, Scratch, Logo,
geogebra, like- for exploring and building models ...and maybe
illustrating and playing with concepts from the 'makefile sequence' -
20% of the game

All this is loosely on the radar in some commercial places, but still
perhaps not as deeply reset as is needed, and its not open source

I'd also like to see the maths content get more computer inflected  -
not just use computers to deliver old content, but modify the content -
eg different ways to construct, say polygons, or find primes, or
whatever the nominal maths is  ...the discipline or learning a
programming language could run parallel to learning maths...but that
also requires a something of a reset in curriculum in how IT and maths
relate... which seems even more unlikely, unfortunately  ..maybe I'm
wrong  

Papert's complaint about the state of 'school maths' getting ossified in
one historical state really would require maths content to change like
this ...and the education system hasn't yet signed on to that, as far as
I can see ..computing as productive child's play for learning maths (via
say Logo - or maybe Mathematica today) isn't really in view anymore..
(this would shift the 80/20 balance - could allow say 50-50) 

Re the direct instruction vs constructivism/constructionism thing - I
think that one can teach 'directly' in a way that still respects that
students have to 'construct' their own understanding ...

Most 'direct instruction' maths lesson (indeed most maths lessons
everywhere - according to various international video studies) have
portions of direct instruction, and portions of students attempting to
work more or less independently to apply some of that to 'problems' -
which is at least some concession to the need to 'make your own
connections' even after you've been 'told' 

(there is an Australian novel 'all the green year' where the main
character praises his new teacher - 'she taught simultaneous equations
so well I felt I had discovered the art myself' - which reconciles the
two approaches ..and seems a feasible comment to me)

If maths learning is always limited to that level it no doubt risks
getting too closed and mimetic, (eg may create a culture of maths as
simply right answers to closed textbook questions) - but there is still
a little nod to constructivism in the need to attempt various problems
and work out understanding on one's own - while there is still the
bigger challenge of feeling maths as more open and productive - maybe
representing learning in another form - say writing a program to model
or explore it - is a good way to stretch beyond those limits ... 

its this I remember from my own schooling as one of the few times that
all that math learning really felt creative to me  - and why I feel we
have left something out of the mix in schools today, even though there
are countless more computers around  ... even the top end of maths
learning in school does not push much creative modelling etc in this
sense

One thing I liked about the 'drawing on the right side of the brain'
approach is that it respects the need to load up your mind with
conscious material - to wrestle with it and tackle it - and then also to
walk away and turn things over ...ie the role of 'the unconscious' in
pondering and delivering insights  and solving problems - Poincare like
- is not well respected in school

I think direct instruction needs to keep this in mind - the grappling
with difficult things and coming back to it - constructing understanding
- is partly how we learn - not just consciously reciting modelled
processes

more in the learning stew

Rob 


> -----Original Message-----
> From: iaep-bounces at lists.sugarlabs.org [mailto:iaep-
> bounces at lists.sugarlabs.org] On Behalf Of Albert Cahalan
> Sent: Wednesday, 6 May 2009 5:02 AM
> To: kathy at kathyandcalvin.com; iaep
> Subject: Re: [IAEP] educational brew
> 
> Kathy Pusztavari writes:
> 
> > "You could set up '4th grade math for Massachusetts' as a list of
> > things to master. It's quite similar to setting up a Makefile
> > with a target that exists purely to have a list of prerequisites."
> >
> > Albert - that is exactly what I was referring to.  A set of
curriculum
> > to get you started but a good teacher could then go in and adapt the
> > files or make file for their standards (or find a local nerd to
help).
> > I referred to Turtle Typing.  Being a linux numbskull, I
accidentally
> > ran the MAKEFILE and found out that it seeds your lessons.
Honestly,
> > I had heard of MAKEFILE but I didn't know what it did.
> 
> Sorry about that. The explanation wasn't any good for non-programmers.
> I suppose I can try to explain "make". Here you go:
> 
> Suppose you had a file, commonly called "Makefile", containing this:
> 
> ###########################
> 
> 4th-grade-math: 4th-grade-fractions long-division
> 
> long-division: simple-division big-multiplication
>         teach long-division.lesson
>         teach long-division-extra-work.lesson
>         teach long-division-extra-work-2.lesson
> 
> simple-division: simple-multiplication
>         teach simple-division.lesson
> 
> 4th-grade-fractions: simplify-fractions measure-fractions
> 
> measure-fractions: ruler
>         teach measure-fractions.lesson
>         teach measure-fractions-extra-work.lesson
> 
> ruler:
>         teach ruler.lesson
> 
> simplify-fractions: lcd gcd simple-division what-fraction-is
>         teach simplify-fractions.lession
> 
> [ ... lots of stuff missing ... ]
> 
> count-to-3:
>         teach count-to-3.lesson
> 
> ###########################
> 
> Each item on the left, before a colon, is something you could create.
> (in this case, you're creating an education) Each item to the right,
> after a colon, is a prerequisite for the item to its left. The
indented
> lines are commands that are needed to create things.
> 
> To learn 4th-grade-math, you don't actually need to create anything.
> You just need to satisfy the prerequisites. So if we ask the "make"
> program to create 4th-grade-math, it adds 4th-grade-fractions and
> long-division to the list of things you want to learn and starts in
> on them. Once those prerequisites are done, 4th-grade-math is done.
> 
> The long-division knowledge also has prerequisites, simple-division
> and big-multiplication. Prerequisites must be done prior to starting
> a lesson, so we add those to the list of things to learn and keep
> going. Unlike 4th-grade-math, long-division has lessons to teach.
> We have to come back to those after the prerequisites are satisfied.
> 
> 4th-grade-fractions is more like 4th-grade-math. It doesn't have a
> lesson by itself; it is just a list of other things to learn.
> 
> Eventually you get to a starting point with no prerequisites. That is
> count-to-3 in my example. There may be more than one starting point,
> in which case they may be done in any order. Reasonable starting
points
> always have lessons. Those are taught, completing the starting points.
> This satisfies prerequisites for other things, which thus become
> available as starting points. Ultimately 4th-grade-math becomes a
> starting point, which is trivial because it has no lessons. Since that
> was the original request, you're done.
> 
> If we were actually going to run that file using "make", we'd need a
> command called "teach". Maybe the "teach" command sends a text message
> to a human teacher, or maybe it runs a Sugar activity. The "teach"
> command just needs to ensure that the material is taught.
> 
> There are plenty of details that keep this from working exactly as
> written. Students may forget things. I used spaces instead of tabs
> to indent the lines. I left out a big chunk. I hope this cleared up
> what I meant though.
> 
> That "MAKEFILE" you mention might not be a real Makefile. It might
> be a script that runs the "make" command with a particular Makefile
> specified.
> _______________________________________________
> IAEP -- It's An Education Project (not a laptop project!)
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