WebMath: online math communication

[Paul Strickland]

Dear June,
   I think the TREEFROG software we are developing here may be of interest
here; you can download a free demo from

http://java.cms.livjm.ac.uk/treefrog/treewin.htm

and we are also releasing a fully functional quadratic equation tutor to
anyone who wants it,

best wishes,

Paul S.

> -----Original Message-----
> From: owner-webmath at camel.math.ca [mailto:owner-webmath at camel.math.ca]On
> Behalf Of June Lester
> Sent: 01 March 2000 01:44
> To: webmath at camel.math.ca
> Subject: WebMath: online math communication
>
>
> First of all, a thank you to all of you who replied to my "mathematical
> exposition" post a while back - lots of interesting stuff there.  I meant
> to get back to this sooner, but time is getting scarcer every day, it
> seems. For those interested, I'll append a list of the contributed URLs at
> the end of this email.
>
> What I'm trying to get a handle on is how we use the new technologies to
> present/communicate mathematics effectively.  I'm using "communication"
> here to mean "directed communication", in the sense of "I have an
> idea/concept/train of thought in my head and I want to induce the
> same or a
> reasonable facsimile of it in yours."  As opposed to a resource,
> which says
> "Here's a collection of material that you can explore to look for
> information you need or just for fun."  A print analogy would be
> a textbook
> instead of an encyclopedia.  (This is not a hard and fast distinction -
> directed communication can contain examples of resources and vice versa -
> and is not meant as a valuation of either.)  More than instances of the
> *inclusion* of technology, I'm looking for examples of good *integration*
> of the technology with what is being communicated.  The aim is to develop
> criteria for effective online mathematical exposition - maybe a sort of
> Strunk & White for mathematical hypermedia. (Is S&W known outside North
> America? - if not, it's a "how to use english to communicate effectively"
> classic, <http://www.strunkandwhite.com/>.)  We all learned in school to
> write paragraphs with topic sentences, to outline essays, etc. in order to
> communicate more effectively - what new skills and rules do we need to
> communicate mathematics with the new media?  Or are we still learning to
> spell with it?
>
> To elaborate a bit on two facets of the question:
>
> HYPERTEXT. How do we structure hypertext to communicate mathematics
> effectively?  For an expository mathematical paper in the "theorem-proof"
> style, for example, one obvious option would be to have the main sequence
> of ideas and theorem statements on the first page, with linked proofs to
> the theorems on subsidiary pages and sublinks to proofs of lemmas, etc.
> Another would be an introductory section on the main page and the
> remaining
> sections as sequential links. Is either better than the other, and why?
> Are there other ways of organizing expository mathematics hypertextually?
> Or, for more educationally-oriented material, is there something more we
> can do with hypertext beyond the "click here to step through the
> details of
> the example" model?
>
> The only analysis of how hypertext works that I've been able to
> find is the
> 1989 book "Mapping Hypertext" by Robert Horn.  Interesting book (haven't
> read it all yet), but not mathematics specific or even education specific,
> so a bit too general for what I want.  Anyone have more relevant
> references/links/resources?
>
> MULTIMEDIA AND INTERACTIVITY. What makes a mathematical animation
> or use of
> interactivity relevant and effective rather than gratuitous or
> ineffective?
> I'm looking for criteria to determine things like "how well does that
> particular animation communicate the mathematical idea it was intended to
> communicate?"  And then "how does it do that?"  Or "I can drag the points
> of that geometric figure around like so.  Does my doing so increase my
> understanding of the ideas the accompanying text is trying to communicate?

> and just how?" Or "how *should* this equation behave when I click on it to
> communicate something useful about the mathematics it represents?"  In
> other words, just how does the animation or interactivity communicate/
> illustrate/illuminate the idea, and how well does it do it?
>
> For educational mathematics, this is clearly related to instructional
> design.  Do there exist ID references/links/resources which discuss these
> issues in any sort of concrete way (i.e. in specifics vs. abstractions)?
> Or other non-ed resources?
>
>
> And since this email is already long enough, I'll stop there. :o)  Any and
> all discussion, resources, links, whatever gratefully received.
> Meanwhile,
> here's the list of links contributed to my last post on this, plus a
> favourite of my own at the end.
>
> Cut the Knot!
> <http://www.maa.org/editorial/knot/knot-index.html>
>
> Animating Web Pages with the TI-92: Gettysburg 1998
> <http://ourworld.compuserve.com/homepages/davidbowers/Getty98/main.htm>
>
> Eric Weisstein's World of Mathematics
> <http://mathworld.wolfram.com/>
>
> EULER Project Homepage
> <http://www.emis.ams.org/projects/EULER/>
>
> Exploring Emergence
> <http://el.www.media.mit.edu/groups/el/projects/emergence/>
>
> Favorite Mathematical Constants
> <http://www.mathsoft.com/asolve/constant/constant.html>
>
> Fibonacci Numbers, the Golden section and the Golden String
> <http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html>
>
> Graphics for complex analysis
> <http://www.math.psu.edu/dna/complex-j.html>
>
> M niinkuin matematiikka
> <http://www.math.hut.fi/matta/Iso_M/Kansi.htm>
>
> MAA Online - Columns
> <http://www.maa.org/news/columns.html>
>
> Math Goodies: Interactive Math Lessons With A Problem-Solving Approach!
> <http://www.mathgoodies.com/>
>
> Mathematical Atlas: A gateway to Mathematics
> <http://math-atlas.org/>
>
> Mathletics, Maths Department, Portsmouth and Brunel Universities
> <http://L62.csm.port.ac.uk/mathletics.html>
>
> MathSearch
> <http://www.maths.usyd.edu.au:8000/MathSearch.html>
>
> MathsNet
> <http://www.anglia.co.uk/education/mathsnet/>
>
> MuPAD Home Page
> <http://www.mupad.de/>
>
> New Mathwright Library
> <http://www.mathwright.com/>
>
> Oundle
> <http://www.argonet.co.uk/oundlesch/>
>
> Catalog of Isohedral Tilings by Symmetric Polygonal Tiles
> <http://forum.swarthmore.edu/dynamic/one-corona/>
>
> Virtual Reality Polyhedra
> <http://www.georgehart.com/virtual-polyhedra/vp.html>
>
> W4T at UCD
> <http://www-math.cudenver.edu/w4t/>
>
>
> My favourite: the Maths Online Gallery
> <http://www.univie.ac.at/future.media/moe/galerie.html>.
> (Take a look at the Didactical Background presented with each applet.)
>
> Cheers
>
> June
>
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