Monday, March 03, 2008

Innovative Math Mashups for Education, Commerce, and Social Networking

Integrated math-based mashups and web applications can bring together demographic information and other kinds of data sets in useful, engaging, and productive ways. Any database can be used, and sources of information could range from census bureau data, GIS repositories, satellite information, to online shopping inventories (amazon.com), restaurant reviews, iTunes, video-rating social networks, and more. All involve math, and all engage learners and users in real-life information, which make the instructional activities more relevant. The applications are also interdisciplinary, which allows learners to explore real-life uses for new approaches with Web 2.0.

Podcast / downloadable audio:
http://www.beyondutopia.net/podcasts/math-mashups.mp3

In addition, learners and users can think of other integrated, interdisciplinary math-focused applications, which could include community planning, urban renewal, traffic management, retirement planning, and even vacation planning.

Further, integrating the information from demographic databases with social networking (MySpace, Facebook, LinkedIn), can help pinpoint individuals who may share interests, purchase patterns, or areas of expertise. (link to social networking software)

The purpose of this blog post is to provide links to repositories of information, useful Web 2.0 applications that may help young math learners, and to posit ways to combine applications.

You may wish to employ cluster analysis, artificial neural networks, or other approaches to the data. For algorithm development, Wolfram's Mathematica 6 is highly recommended.

The key is dynamic interactivity. Here is what Wolfram Labs states:

Mathematica 6 brings a revolution in the concept of interactive computing—for the first time allowing dynamic interfaces to be created instantly as a routine part of everyday work. Based on a series of inventions at Wolfram Research, Mathematica 6 builds on Mathematica's powerful core symbolic architecture to allow sophisticated interactive interfaces to be created from single lines of input—as easily as getting answers to simple calculations. (Wolfram on dynamic interactivity).

If you last worked with SPSS in a college statistics course, you might be surprised at their array of browser-based data collection and display products, as well as the data mining, text mining, and analytical programs. SPSS focuses on predictive analytics in what they refer to as the predictive enterprise.

Basically, this blog looks at fairly simple approaches to using math-based web applications. The goal is to think about integration:

1. Foundations: Learning the basics of math by finding helpful information on the web.

2. Data: Finding sources of useful information, and learning how / where to put the information to good use.

3. Combining information: Meta-tags, tags used in folksonomies, isbns, upcs, zip codes, altitude, latitude and longitude, are some of the gatherable data that can be brought together. They can yield interesting new looks at the world around us.

4. Tools: There are numerous websites that discuss how to use igoogle and myyahoo as a foundation for combining Flickr, Picasa, and amazon information. It might be more interesting to move forward a bit and use powerful analytic tools provided by Wolfram and SPSS.

Demographic Information: Practical Math Applications, Interdisciplinary Approaches

World Facts:
CIA World FactBook Country Listings:
https://www.cia.gov/library/publications/the-world-factbook/countrylisting.html

U.S. Census Information:
http://www.census.gov

Free Demographics:
http://belay.extendthereach.com/api/

graphic from http://belay.extendthereach.com/api/

State Demographics:
http://www.cross-culture.org/regions/mapdoc.htm

MelissaData: Free Lookups
http://www.melissadata.com/lookups/

State Demographics:
Texas:
http://encyclopedia.thefreedictionary.com/Texas

Community Tapestry
(from ESRI's website): Identify the top three neighborhood lifestyles to better serve your customers. ESRI's Community Tapestry segmentation system classifies each U.S. ZIP Code based on socioeconomic and demographic characteristics to create 65 distinct market segments. Author note: The information is very intriguing. http://www.esri.com/data/community_data/community-tapestry/index.html


(graphic from ESRI's ArcGIS software information page)

ESRI: Best Data for the Best Business Decisions
http://www.esri.com/data/community_data/traffic/index.html

Math Applications and Math Tools: Perfect for Developing Instructional Activities


Wolfram Mathematica 6: Users and uses
Examples include
Diagnostics for eye cancer prevention.
Geo-positioning for targeting accuracy (defense application).
Designing children's playground equipment. (combining multiple values)
Predicting likely degradation rates of biofuels.

SPSS: SPSS has a full array of analytic tools and programs that far exceed the limited SPSS package one uses in one's college statistics courses. SPSS's new embeddable building blocks create flexibility. It is not clear whether or not the blocks can be used in web applications, but one could, of course, use the obtained from web applications.

OEM embeddable components
SPSS 16.0
Text-Mining with Clementine (R)
Surveys and Data Collecting (web-deployed) with Dimensions
Browser-based Reporting Platform (Showcase)

Squidoo.com -- check out the various lenses
http://www.squidoo.com

Kids Online Resources -- think of how to combine with Flickr, Google Maps, or other mashup-able databases

Fractions:
http://www.kidsolr.com/math/fractions.html

Famous Curves:
http://www.geocities.com/famouscurves/

Number Skills:
http://www.woodlands-junior.kent.sch.uk/maths/index.html

Geometry, Fractions, Algebra:
http://math.rice.edu/%7Elanius/Lessons/

In Spanish!
http://math.rice.edu/~lanius/fractions/spindex.html

Practical Money Skills for Life:
http://www.practicalmoneyskills.com/english/index.php

Individual Retirement Accounts:
http://www.learnerinstitute.org

Differential Equation Java Generators:
http://www.sci.wsu.edu/idea/JCGTemplates

Here are some text-based lessons that encourage individuals to bring in widgets, and mine different databases:

Teachers.net - Lesson Bank // Math: http://www.teachers.net/cgi-bin/lessons/sort.cgi?searchterm=Mathematics

Now for something completely different

Road Sign Math
http://www.roadsignmath.com/
This is a rather bizarre concept that is not really a mashup, but something more akin to gematria. The goal is to find mathematical relationships within the numbers found in road signs. It's an interesting puzzle -- almost like a living brain-teaser. It's an amazingly clever idea. The site has to be visited to really appreciate the depth of the cleverness. Hashing out the algorithsm and teasing out the mathematical relationships should not be done while driving. (!) Record the signs with your camera phone or digital camera.

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