--
You received this message because you are subscribed to the Google Groups "MathFuture" group.
To post to this group, send email to mathf...@googlegroups.com.
To unsubscribe from this group, send email to mathfuture+...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/mathfuture?hl=en.
The innovative and dynamic tools like Sketchpad , Geogebra ,Graphic
Calculators and Java applets have opened a new possibility for
Mathematics teachers.The traditional method of chalk and board is
being replaced by the interactive (Smart) board.
I am interested in meeting and learning from the teachers who have
used these and other tools.
I just like the fact that your email address is:
As several others have mentioned, many of us are interested in what you
wrote in your email:
On Sat, 1 Oct 2011, SG wrote:
> The innovative and dynamic tools like Sketchpad , Geogebra ,Graphic
> Calculators and Java applets have opened a new possibility for
> Mathematics teachers.The traditional method of chalk and board is being
> replaced by the interactive (Smart) board.
There are a number of places (more than I know, I'm guessing) where those
conversations and interactions between teachers/learners/developers are
taking place. This mailing list is one such community.
Welcome.
-- David Weksler w...@pobox.com
Dear Maria,
Either would help.It will be nice to visit some classes but if not exchanging mails or Skype will also help.
Thanks
Sangeeta Gulati
I will answer somewhat autobiographically, following
Nietzsche's dictum that all good philosophy is auto-
biographical in nature (my background at Princeton
was philosophy, Rorty my thesis adviser).
After Princeton, I lived in a group home with former
college mates, most of them with their eye on the
Big Apple (Manhattan) just a quick PATH ride from
Journal Square, behind Loew's Theater.
Where we lived behind Loew's:
http://www.flickr.com/photos/17157315@N00/479676592/
PATH trains next to Loew's:
http://www.flickr.com/photos/paul_lowry/1206810477/
My eye, on the other hand, was fixated on getting
a teaching job, as my heart had set on this course
sometime in my senior year, though my advisers
thought I'd come to such a decision rather late in
the game (but I thought I was supposed to get that
deep liberal arts education without too much career
focus (the latter would be decided by destiny or the
fates I guess, plus I'd learned to expect a "checkered"
career based on future forecasting by Alvin Toffler
et al)).
To make a long story short, I landed two glorious
years as a mostly-math teacher through calculus,
one of the best jobs ever. I only made myself quit
because I'd made myself promise I wouldn't make
this my life's work. I had it in my head I was still
too young to pick a permanent career track of any
kind.
This background as a full time high school teacher
has served me well in subsequent years. I was
able to work in publishing (McGraw-Hill) and for
Saturday Academy, an elite Portland, Oregon based
nonprofit that allows professionals not in the teaching
profession (but perhaps with prior experience), to
test out pioneering ideas with willing, self selected,
highly motivated students.
This background in turn proved highly advantageous
and led to my being invited to London by the
Shuttleworth Foundation to help lay the groundwork
for curriculum development in South Africa (we had
a summit in Kensington, many officials present).
Alan Kay was there, as was Guido van Rossum
(GvR), another prodigy passionate about the future
of education. So yes, having experience as a
high school math teacher on your resume can
be a very good thing.
Now at last, to technology.
What surprised a lot of us at McGraw-Hill in the 1980s
(yes, I ended up working in Manhattan after all) was
how the scientific calculator would continue to
eclipse the computer in most K-16 math teaching
for so long. This persisted well beyond the open
source revolution, when all the necessary software
became free.
We were kind of expecting all the hype around Logo
and BASIC to revolutionize math teaching, having
imbibed the kool-aid ourselves (McGraw-Hill produced
BYTE and such avatars of the PC revolution, pre-Wired
and later techno publications). We believed our own
hype, ate our own dogfood.
Little did we imagine that Texas Instruments would
continue to dominate in North America, leaving her
children further and further behind with respect to
the computer revolution going on all around them.
They'd be too computer illiterate to prevent
Wall Street from perpetrating the dot com hoax
(along with subsequent hoaxes). Their civilization
had been destroyed -- except maybe 'Sesame Street'
had saved it? (brilliant stuff, gave birth to Youtube) --
their politicians reduced to mere puppets in the
money matrix.
So most of what I've been doing has little or no footprint
in that North American federation of states known as
"the US and Canada", though with some pockets here
and there.
I use object oriented programming to teach about "math
objects". The sense of "types" you get from strongly
typed system languages like C++ is still there in
scripting languages, and reinforces ideas of set membership
ala Dolciani. Number types are N, Z, Q, R, C, with each
a subset of the subsequent. That being said, I tend to
leave "real numbers" to the analog math teachers and
focus on IEEE defined floating point etc., extended
precision etc. Last Pi Day, we had a "compute pi to
1000 places using a Ramanujan series' competition,
which was won by a student at the University of Havana.
I mostly use Python though I've done some publishing
around J, with help from Kenneth Iverson himself. Inside
my little subculture, I'm a known quantity vectoring to
Vilnius and Gothenberg or most recently to the
downtown Hilton (Djangocon US).
Having a room more like a theater with students able to
take the helm, good bandwidth, these are important.
Everyone has laptops pretty much.
I use VPython a lot (Visual Python) when we get to vector
operations, rotation matrices. The custom geometry is
quite friendly to Euclideans even though it's more digital
than analog. 'Heuristics for Teachers' on WikiEducator
gives more of the flavor (not a textbook). There's also
a current thread on Math Forum with more reading.
Both links below.
http://wikieducator.org/Digital_Math
http://mathforum.org/kb/thread.jspa?threadID=2299146&tstart=0
Kirby Urner
Oregon Curriculum Network
Hawthorne District, Portland, Oregon
________________________________
--
Do you have a brand of Tablet PC that you recommend?
Regards,
_______________________________
Deborah D. Boatwright, M.Ed.
District Technology Integrator
T. 603-292-7979 EXT.0
F. 603-659-4716
boatw...@newmarket.k12.nh.us
>>> "Feldon, Fred" <ffe...@coastline.edu> 10/03/11 5:04 PM >>>
I edited a market report on educational software in 1981 in which I
pointed out that computers could not revolutionize education until every
child had a computer running the same software, so that it could be
integrated into the curriculum, and that that software could not be canned
lessons, usable with only one set of textbooks. Children need
general-purpose tools covering a wide range of math, science, art, music,
literature, multimedia, and so on. We are coming to that point today with
Sugar software, but it was not possible when children had access to only
commercial software in computer labs, only once or twice a week.
One of the great advantages of calculators in this context is that they
all calculated the basic five functions the same way, differing only in
numbers of digits shown, keyboard layouts, and other points irrelevant to
basic classroom use. (Although TI succeeding in dumbing down the subject
significantly, cutting out the use of HP RPN calculators.) Even the use of
graphic calculators for algebra and calculus was not impeded by the use of
different brands and models, since graphs of functions differed mainly in
resolution and in rendering of decorations (axes, labels, and so on).
The other great advantage of calculators was of course price, which meant
that many students could buy their own calculators for use at home as well
as at school.
Computers are of course much more powerful than calculators. But computers
run all kinds of different software. Even implementations of nominally the
same programming language may not be compatible when applied to math
topics. Certainly commercial and Free Software are likely to have
incompatibilities. Mathematica and Maxima, for example, in symbolic math.
> Little did we imagine that Texas Instruments would
> continue to dominate in North America, leaving her
> children further and further behind with respect to
> the computer revolution going on all around them.
> They'd be too computer illiterate to prevent
> Wall Street from perpetrating the dot com hoax
> (along with subsequent hoaxes).
Ah, well, that took a lot of other work from a lot of other opponents of
an informed electorate making sure that economics, statistics, and civics
don't get taught in our public schools, because they won't be on the tests
that determine funding.
> Their civilization
> had been destroyed -- except maybe 'Sesame Street'
> had saved it? (brilliant stuff, gave birth to Youtube) --
> their politicians reduced to mere puppets in the
> money matrix.
I was at an Occupy Wall Street type protest in Indianapolis on Saturday,
and will be at another in Bloomington, IN soon where education will be a
major focus. (Bloomington is the home of Indiana University.) We need to
raise this issue throughout the movement.
> So most of what I've been doing has little or no footprint
> in that North American federation of states known as
> "the US and Canada", though with some pockets here
> and there.
>
> I use object oriented programming to teach about "math
> objects". The sense of "types" you get from strongly
> typed system languages like C++
"I invented the term Object-Oriented Programming, and C++ is not what I
had in mind."--Smalltalk pioneer Alan Kay.
> is still there in
> scripting languages, and reinforces ideas of set membership
> ala Dolciani. Number types are N, Z, Q, R, C, with each
> a subset of the subsequent.
And others: Finite rings and fields, subfields of the algebraic numbers
(such as the Euclidean numbers generated by the rationals plus square
root), vector spaces, non-standard numbers of many kinds, Conway numbers
and games, and more, not just in a single hierarchy.
> That being said, I tend to
> leave "real numbers" to the analog math teachers and
> focus on IEEE defined floating point etc., extended
> precision etc. Last Pi Day, we had a "compute pi to
> 1000 places using a Ramanujan series' competition,
> which was won by a student at the University of Havana.
>
> I mostly use Python though I've done some publishing
> around J, with help from Kenneth Iverson himself.
I am putting Iverson's math textbooks online in J translations, now that
they are under Creative Commons licenses, and J is under GPL3.
http://booki.treehouse.su/algebra-an-algorithmic-treatment/edit/
> Inside
> my little subculture, I'm a known quantity vectoring to
> Vilnius and Gothenberg or most recently to the
> downtown Hilton (Djangocon US).
>
> Having a room more like a theater with students able to
> take the helm, good bandwidth, these are important.
> Everyone has laptops pretty much.
>
> I use VPython a lot (Visual Python) when we get to vector
> operations, rotation matrices. The custom geometry is
> quite friendly to Euclideans even though it's more digital
> than analog. 'Heuristics for Teachers' on WikiEducator
> gives more of the flavor (not a textbook). There's also
> a current thread on Math Forum with more reading.
> Both links below.
>
> http://wikieducator.org/Digital_Math
>
> http://mathforum.org/kb/thread.jspa?threadID=2299146&tstart=0
>
> Kirby Urner
> Oregon Curriculum Network
> Hawthorne District, Portland, Oregon
--
Edward Mokurai
(默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر
ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://wiki.sugarlabs.org/go/Replacing_Textbooks
Yes. I started working at McGraw-Hill right after Reagan got
elected to a 2nd term (versus Mondale).
Part of my job was to review educational computer games
coming in from all over, sometimes already commercial
products but seeking greater distribution.
I remember a cool one about AIDS, where you played on
the side of the immune system, learned about T-cells.
This book publisher wasn't really cut out for this game,
but editors were learning a lot just surveying the field.
One of the best submissions I recall was from a guy who
was pioneering place based education in the sense that
his curriculum materials would fill with the names and
histories of his own students and town, in a way that might
work elsewhere.
What a cool thing -- but the antithesis of publishing the
same thing for every zip code, with a focus on California
and Texas (how the game was really played back then).
This was 1984 and pre Free/OS, pre "dot com" or any of
that.
BASIC and Logo were all the rage.
We had PCs. The Mac was only just coming out.
Hewlett Packard was still big in the calculator market.
The studies I was reading were ranking educational software
on a spectrum, from "electronic page turners" and multiple
choice quizzers, to open-ended, explorable, yet structured
environments.
Squeak, not yet available, would be a good example of the
latter.
Computer games in general got higher marks than these
glorified textbooks with gazillions of facts they'd try
to help you memorize.
On the other hand, a large educational publishing company
has lots of access to recyclable facts, and precious few
programmers... so those products we actually did have
were maybe not among the most stellar.
But then McGraw-Hill had staked its reputation in other
arenas.
I was in some obscure office on the 28th floor, a contributing
editor.
I recall learning Childrens Television Workshop was casting
about for a new math show and sent them a write-up for
The Videogrammatron. It was to be a growing database
of short clips, organized around key concepts (just like
Sesame Street, but into more advanced topics, like
complex numbers).
Years later, we had Youtube (but still not with many
curricula wrapping those clips, weaving them into coherent
shows (Viiv at Intel sort of died on the vine)).
> One of the great advantages of calculators in this context is that they
> all calculated the basic five functions the same way, differing only in
> numbers of digits shown, keyboard layouts, and other points irrelevant to
> basic classroom use. (Although TI succeeding in dumbing down the subject
> significantly, cutting out the use of HP RPN calculators.) Even the use of
> graphic calculators for algebra and calculus was not impeded by the use of
> different brands and models, since graphs of functions differed mainly in
> resolution and in rendering of decorations (axes, labels, and so on).
>
True. It's somewhat unfair (to calculators) to compare them
with computers at all. They're designed for working with
numbers, whereas so much about computers has to do
with text, pictures, audio, video, saving / retrieving / editing
files. When you teach about functions on a computer,
you can have a domain and range of character strings,
talk about palindromes. You can model objects with their
attributes (properties) and methods (behaviors). The math
takes on a whole different flavor.
What ended up happening later is that some schools went
towards a network model, with a shared classroom server
or even whole school servers. The TuxLabs an another
example. We had LTSP for K12.
http://en.wikipedia.org/wiki/Linux_Terminal_Server_Project
I taught in various computer lab settings through the 1990s
using either these "dumb terminals" or networked
standalones (most recently at a local college, though
with teenaged students -- Martian Math). I did this through
a school for self selected middle and high school aged
students willing to work extra-curricularly for no credit,
a privileged minority to say the least.
> The other great advantage of calculators was of course price, which meant
> that many students could buy their own calculators for use at home as well
> as at school.
>
> Computers are of course much more powerful than calculators. But computers
> run all kinds of different software. Even implementations of nominally the
> same programming language may not be compatible when applied to math
> topics. Certainly commercial and Free Software are likely to have
> incompatibilities. Mathematica and Maxima, for example, in symbolic math.
>
Yes true. For me, the school itself is what I consider
the primary radius for a curriculum. Import whatever goodies,
but then customize and value add. Go with "place based"
specialcase features. Focus on the real environment
actually at hand.
I like the trend towards open source curricula / textbooks /
media for just this reason: you can alter them at will to reflect
local needs and requirements. That goes with the territory
if you're a teacher. Sourcing original curriculum is every
school's responsibility (then save it to servers -- accumulate
wealth).
>> Little did we imagine that Texas Instruments would
>> continue to dominate in North America, leaving her
>> children further and further behind with respect to
>> the computer revolution going on all around them.
>> They'd be too computer illiterate to prevent
>> Wall Street from perpetrating the dot com hoax
>> (along with subsequent hoaxes).
>
> Ah, well, that took a lot of other work from a lot of other opponents of
> an informed electorate making sure that economics, statistics, and civics
> don't get taught in our public schools, because they won't be on the tests
> that determine funding.
>
Yeah, so much vital info just never trickles in. One
of the high schools I visited recently was running this
poster campaign teaching kids to distrust what was
called the "free Web" with the message that any useful
information was obviously worth paying for. I don't
know who was behind this campaign, but I consider
it insidious (these posters were in the *library* for
crying out loud). Kids are in a terrible thralldom, very
Dickensian in a lot of ways. They have consumer
power, but like you say, but don't learn much civics
and don't get to vote.
[ I've written a lot about how every high school should
have in-house voting machines (open source) so
that students may run and understand their own
elections, and apply this knowledge realistically
to the larger society. ]
>> Their civilization
>> had been destroyed -- except maybe 'Sesame Street'
>> had saved it? (brilliant stuff, gave birth to Youtube) --
>> their politicians reduced to mere puppets in the
>> money matrix.
>
> I was at an Occupy Wall Street type protest in Indianapolis on Saturday,
> and will be at another in Bloomington, IN soon where education will be a
> major focus. (Bloomington is the home of Indiana University.) We need to
> raise this issue throughout the movement.
>
Good for you. Lets keep that thread alive as well.
>> So most of what I've been doing has little or no footprint
>> in that North American federation of states known as
>> "the US and Canada", though with some pockets here
>> and there.
>>
>> I use object oriented programming to teach about "math
>> objects". The sense of "types" you get from strongly
>> typed system languages like C++
>
> "I invented the term Object-Oriented Programming, and C++ is not what I
> had in mind."--Smalltalk pioneer Alan Kay.
>
He likes Python though.
>> is still there in
>> scripting languages, and reinforces ideas of set membership
>> ala Dolciani. Number types are N, Z, Q, R, C, with each
>> a subset of the subsequent.
>
> And others: Finite rings and fields, subfields of the algebraic numbers
> (such as the Euclidean numbers generated by the rationals plus square
> root), vector spaces, non-standard numbers of many kinds, Conway numbers
> and games, and more, not just in a single hierarchy.
>
Yes. All these, or a lot of them, can be taught with
various types of "math object". You learn how to
code them in order to learn what makes them tick.
A Polyhedron is a "math object" made of other
objects, such as vectors (from the origin) and
line segments (each defined by two vector tips).
>> That being said, I tend to
>> leave "real numbers" to the analog math teachers and
>> focus on IEEE defined floating point etc., extended
>> precision etc. Last Pi Day, we had a "compute pi to
>> 1000 places using a Ramanujan series' competition,
>> which was won by a student at the University of Havana.
>>
>> I mostly use Python though I've done some publishing
>> around J, with help from Kenneth Iverson himself.
>
> I am putting Iverson's math textbooks online in J translations, now that
> they are under Creative Commons licenses, and J is under GPL3.
>
> http://booki.treehouse.su/algebra-an-algorithmic-treatment/edit/
Way cool. J is such an interesting language.
Kirby
> I've written a lot about how every high school should
> have in-house voting machines (open source) so
> that students may run and understand their own
> elections, and apply this knowledge realistically
> to the larger society.
Can you provide any of those writings? I could make good use of them.
Please take a look at Open Voting Consortium (openvoting.org), which
offers voting software in Python under GPL for anybody to download and try
out. I would like to get it packaged for Fedora, Debian, and Ubuntu, and
put into Sugar for millions of schoolchildren to try out. In addition to
the Free Software aspect, we provide a number of technical advantages for
security and believability, starting with printing paper ballots that can
be read and counted by either machines, for speed, or humans, for
verification, with checksums for preventing addition or removal of
ballots, and other shenanigans.
>> I was at an Occupy Wall Street type protest in Indianapolis on Saturday,
>> and will be at another in Bloomington, IN soon where education will be a
>> major focus. (Bloomington is the home of Indiana University.) We need to
>> raise this issue throughout the movement.
>
> Good for you. Lets keep that thread alive as well.
I am creating a shared Education Working Group, along with others in the
movement. See
http://educationwg.wordpress.com
for thoughts on what is needed plus links to resources that we are creating.
>>> I mostly use Python though I've done some publishing
>>> around J, with help from Kenneth Iverson himself.
>>
>> I am putting Iverson's math textbooks online in J translations, now that
>> they are under Creative Commons licenses, and J is under GPL3.
>>
>> http://booki.treehouse.su/algebra-an-algorithmic-treatment/edit/
>
> Way cool. J is such an interesting language.
Have you taken a look? I haven't gotten this far yet in the book, but
(-b) +,- (%:(*:b)-4*a*c)%2*a
returns both roots of a quadratic. It is a direct translation of the usual
quadratic formula.
Or, once you understand how that works, you can use the root-finding
primitive:
p._1 0 1
┌─┬────┐
│1│1 _1│
└─┴────┘
(Looks best in a monospace font)
Multiplier and roots of x�-1, from which the original polynomial can be
constructed in the form
m(x-r1)(x-r2)
> Kirby
This search pulls up quite a bit, a lot of it by me. I'll check a few
for relevance:
Hey, this looks like a great intro:
http://mathforum.org/kb/message.jspa?messageID=7112862&tstart=0
> Please take a look at Open Voting Consortium (openvoting.org), which
> offers voting software in Python under GPL for anybody to download and try
> out. I would like to get it packaged for Fedora, Debian, and Ubuntu, and
> put into Sugar for millions of schoolchildren to try out. In addition to
> the Free Software aspect, we provide a number of technical advantages for
> security and believability, starting with printing paper ballots that can
> be read and counted by either machines, for speed, or humans, for
> verification, with checksums for preventing addition or removal of
> ballots, and other shenanigans.
>
We also have DemocracyLab.org around Portland, which has had a booth
at OSCONs the past few years.
Some of my blog posts also link Open Source Convention (OSCON) to
voting / polling technology.
Basically, it's a geek responsibility to provide safe and secure
infrastructure, not a politicians' responsibility.
Kirby
An excellent initiative, but it addresses a quite different issue, that of
helping voters choose when there are large numbers of parties. Kirby and I
have been talking about supporting the mechanics of voting and vote
counting, and of educating children in the issues that surround them.
The subject is riddled with paranoia, propaganda, and fantasy. I have just
had a conversation with someone who hates voting machines so much that she
is adamant about supporting only paper ballots, manually filled out and
manually counted. As though "Landslide" Lyndon Johnson and other ballot
box stuffers, and the rest of the ganefs never existed. Magical, wishful,
cargo cult thinking. If only our ballots are sincere enough, the Great
Pumpkin will rise up out of our polling places on election day and put
everything right.
"For any given problem, there is a solution that is simple, obvious, and
wrong."--H. L. Mencken
I'm more like: talk talk talk, if Americans cared about democracy
they'd already have open source voting machines in their high schools,
but they don't, for no good reason, except here's living proof they
don't really care about democracy. Many more hypocrisies they get
away with, on an everyday basis. Sick of it.
However, when it comes to small villages, you can just get consensus
on the ground rules, e.g. voting "machines" (electronic, programmed)
are OK or not OK? Decide that as a ground rule and then role the tape
forward. People who are adamant that only paper balloting is OK
should pick a different village, and guess what: thousands upon
thousand upon thousands to choose from.
Consequence: this science fiction we all need to agree and sign some
paper in some big momentous room somewhere ("world peace") is just
devastatingly idiotic. Either / or thinking (I'm right or you are) has
close to devastated human language (at least English is damaged,
perhaps well beyond repair).
Anyway, I wander, my usual polemics. Ho hum. Just saying: deadlines
have passed and I don't think the USA has any claim whatsoever on
being a democracy anymore. Nostalgia trippers, give it up.
Kirby