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Topic: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Replies: 19   Last Post: Oct 4, 2013 9:29 PM

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kirby urner

Posts: 1,723
Registered: 11/29/05
Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Posted: Sep 26, 2013 2:04 PM
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Every time Benezet comes up, or Davydov, I think
we should also mention Caleb Gattegno, founder
of the equivalent of the NCTM in the UK, and an
exponent of using Cuisenaire Rods to teach the
four operations in algebraic expressions, including
fractional notation.

His reliance on color coding was extreme and
would put color-blind students at a disadvantage.
Studies were done, videos made, and to this day
his memes propagate and re-inspire, much as
Benezet's do -- but lets be clear they're not
advocating the same thing.

[ I think Benezet's + Haim's solution would be a
fun experiment: no math up to 6th grade and
then no math higher than 6th grade level i.e.
get all the arithmetic you need in one year and
you're off the hook -- opt in if you want more
but it's your choice, not Nanny State's. ]

I like how they do it in PER (physics education
research) a little better: they give a pre-test and
a post-test, with the experimental and conventional
programs in between, both designed to impart X
(e.g. Newtonian mechanics say). Who scores
higher after six months or a year or even just
a week of learning regimen Y?

Six year longitudinal studies are great, but those
who don't believe in your approach will always
explain away the data.

In Benezet's case, we say "they learned at home"
-- a hole they can't plug. Significance drains away.
So was it worth six years to (a) preach to the choir
and (b) recruit zero defectors from the opposition?

A better approach is to have experiments that
are easier to implement (six days vs. six years).
Give me six weeks with 8th graders to both teach
basic Python and apply that to rational numbers
and operations with rational numbers (Q), versus
another teacher with six weeks and only scientific
calculators for technology. Give a pre and post
assessment tests.

In my class, we "construct" (note "constructionism"
-- a spin-off of "constructivism") a rational number
as a Python type:

class Q:
* initialize / reduce to lowest terms
* add
* multiply
* add inverse (subtract)
* multiply by inverse (divide)
* return reciprocal
* return negative
* exponentiate

Each of the above starred items corresponds
to a Q class method, with "reduce to lowest
terms" relying on Euclid's Method which must
be clearly explained, preferably by means of
cartoons involving architecture / construction
(bricklayers need lengths to come out even
i.e. with no remainder). [math-teach 1]

We're clearly setting up for abstract algebra
latter because even when the type changes
from Q (rational number) to P (permutation)
we'll still have:

class P:
* initialize
* multiply
* multiply by inverse (divide)
* return multiplicative inverse
* exponentiate

A permutation would be like a bijective function
of A to itself, where A is the set of alphanumeric
characters, or just the 26 English lowercase if
applicable / relevant to our students' other work.
A Python dictionary serves beautifully to hold
the permutation data while the surrounding type
apparatus allows them to be multiplied and
inverted.[recap on edu-sig 2]

We may also look at class M, M for Modulo.
These would be integers that do everything
modulo N.[3]

After Python, we probably transition them to
Mathematica and reinforce a lot of the same
concepts using more traditional notation and
piling on the nuances. In 10th grade we do
a lot more with spatial geometry with calculus
as neither the apex nor principal be-all-end-all
goal of a strong STEM education at this level.
Analog math is still important, but not the only
kid on the block. You still should know it, its
notation. Get to it through Big-O notation when
expression algorithms' powers.[Knuth 4]

When you get to the college level, that's when
to decide how much more calculus to take on.
If you're going into a discrete math or statistical
subject, or one that needs trig, you may go with
a different sequence than the physics major
does (to the extent we still call them "physics
majors" in this future). In high school, we have
a stronger STEM footprint than ever, but not so
weighted towards calculus. Those that do
calculus are probably also using Mathematica.[5]

Some of our students dive into web development
right out of high school and enjoy the rest of
their educations as paid professional development
time. They might take more economics and get
more math through that window (except in this
future we've replaced "economics" with "general
systems theory" which is more robust and
and pays more attention to the biosphere aka
"motherboard Earth"). Use of simulations is key
(ala SimCity / SimEarth), as well as programming
simulations. Cellular automata were a core
topic in high school, making use of those new
programming skills. The PSU Systems Science
degree program is pioneering this curriculum
today, with schools like LEP allowing students
to access college content from within a high
school matrix.

Regarding Benezet, I think there's an argument
for not starting on Python until 6th grade. They
need some typing skills first, which most get from
communicating on the Internet (with keyboards
at home, not just thumbs on a smartphone). They
will learn with more mental drills and abacus before
that, with such New Math topics as union and
intersection but previewing SQL.

Instead of dreary hands-on work with databases
(dreary because typing is still a chore), they'll
watch exciting documentaries in which real people
both do and explain their jobs.

School is really a time to day-dream about the
personality you'll be in your next adult incarnation
(even if you're already an adult).

"Career orientation" should not just be left to once-
a-year assemblies with booths in the gym. You
need those serious documentaries right during
school hours, when you're on the meter, earning
credits (exchangeable for real goods those credits
though not "same as cash" given how their not
easily transferrable).


Kirby

Notes:

[1]

If you have this hole in your own knowledge, consider yourself shot through
the head by your own alma mater and seek medical / remedial attention
immediately. Not knowing Euclid's Algorithm means you should think twice
about voting or registering an opinion on any matter. Don't get up in the
morning. Get out your smartphone and learn it instead.

That's what the Math Wars are all about. Those without any knowledge of
Euclid's Method by the end of high school are the losers, and that goes for
any professors in the same boat. Lets help these poor vanquished back on
their feet again shall we? I urge empathy towards the world's least
privileged. Lets start a new charity if need be.

http://mathforum.org/kb/message.jspa?messageID=9138447

[2] Permutations:

https://mail.python.org/pipermail/edu-sig/2013-July/010862.html
https://mail.python.org/pipermail/edu-sig/2011-March/010219.html

[3]

https://mail.python.org/pipermail/edu-sig/2009-January/009039.html
http://worldgame.blogspot.com/2009/01/modulo-numbers.html

[4]

http://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/

[5]

http://worldgame.blogspot.com/2013/09/a-crossroads.html
(recent pilgrimage to Champaign-Urbana)





On Wed, Sep 25, 2013 at 6:57 PM, GS Chandy <gs_chandy@yahoo.com> wrote:

> Jonathan Crabtree posted Sep 25, 2013 8:06 AM (
> http://mathforum.org/kb/message.jspa?messageID=9282611):

> >
> > a) They are lazy.
> > b) It's their job to teach existing courses, not
> > experiment with new courses.
> > C) They don't know about Benezet
> > d) They don't care about Benezet.
> > e) No retraining has been mandated.
> > f) Parents would complain if their child was not
> > taught math at the same age they were.
> > g) Parents would arrange tuition and undermine the
> > principles of Benezet.
> > h) The Russian (Davydov) method is better.
> >
> > Repeat question with Davydov instead of Benezet.
> >
> > Repeat responses a) to g).
> >
> > Strike out a) as teachers are usually overworked and
> > underpaid.
> >

> I don't know enough about either Benezet's work or Davydov's to comment
> about their breakthroughs. In India, reason 'a' is not on - as you've
> noted, teachers are usually overworked and underpaid.
>
> However, the 'general culture' IS in fact to be intellectually lazy (AND
> to punish intellectual 'exploraton').
>
> Witness for instance (as instances of intellectual laziness):
>
> - -- i) Professor Wayne Bishop's panacea to the ills of the educational
> system ("BLOW UP THE SCHOOLS OF EDUCATION!"); or
>
> - -- ii) Haim's ("PUT THE EDUCATION MAFIA IN JAIL!") or
>
> - -- iii) Robert Hansen's ("Children must be PUSHED to learn math!").
>
> On the other hand, I suspect that this intellectual laziness IS in fact
> pretty widespread. As Mr Crabtree has indicated, at his reason 'b':
>
> - -- "b) It's their (teacher's) job to teach existing courses, not
> experiment with new courses."
>
> - -- "C) They don't know about Benezet".
>
> Many individual teachers do indeed try to think beyond this business of
> "teaching existing courses" and do try (and sometimes succeed) to make
> their teaching interesting to students and useful, they do their own
> research and find out about say, Benezet, Davydof (and, of course,
> Montessori to begin with). But none of that can compensate for 'system
> inadequacies' [which enable the sloganeering noted at i), ii, and iii)to
> prosper].
>
> The 'system itself' of course does not effectively allow for 'retraining'
> as Crabtree has observed at:
>
> - -- "e) No retraining has been mandated."
>
> Often the system would actually punish teachers who try to go beyond the
> 'permitted' means and methods.
>
> Of course, all of the above are various aspects of serious 'system issues'.
>
> By and large, the teachers often do not themselves have a 'culture of
> learning'. Observe various other valid reasons listed by Crabtree:
>
> - -- "f) Parents would complain if their child was not taught math at the
> same age they were."
>
> - -- "g) Parents would arrange tuition and undermine the principles of
> Benezet"
>
> - -- "h) The Russian (Davydov) method is better".
>
> All of the above indicate the need for widespread 'system' reform.
>
> GSC
>
>



Date Subject Author
9/24/13
Read Why Have K-12 Educators Ignored Benezet's Breakthrough?
Richard Hake
9/25/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Wayne Bishop
9/25/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Jonathan Crabtree
9/25/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Louis Talman
9/26/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
Wayne Bishop
9/25/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
9/26/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
9/27/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
9/27/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
9/29/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
9/29/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
9/30/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
9/30/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
9/30/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
10/1/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
10/1/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
10/1/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
10/2/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy
10/3/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
kirby urner
10/4/13
Read Re: Why Have K-12 Educators Ignored Benezet's Breakthrough?
GS Chandy

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