WebWatch- Innumeracy

CLICKING ON THE WEB... Innumeracy and K-12 curriculum standards dominate current thinking about math. Technological advances and math curriculum revisions challenge students to learn in new ways-homework now requires more conceptual reasoning than rote computation. The misuse of statistics and mass media miscalculations further complicate math literacy.

On the web, parents can find entertaining ways to help their children review fundamental math skills. Adults and high school students can access calculators and math tools; manipulatable 3-D illustrations and interactive forms allow multidimensional learning. The three main sites address curricular standards, practical skills, and math literacy. Alternate sites cover skills review, math history, and advanced topics.

Standards for teaching mathematics in K-12 have changed substantially and with some controversy. Many parents question the reliance on calculators and software, pointing to the seeming decline in basic computational skills. Nevertheless, schools have revised their curricula, and this site-sponsored by the world's largest math education association-explains those changes.

In the upper right corner of the page are links to sections for teachers, families, researchers, and education leaders. Click on Family Corner for information about the NCTM Standards and links to resources. Web Sites lists 13 annotated web site links to directories and activities to help children learn math.

At left on the Family Corner page, Quick Links includes Illuminations, which offers exploratory interactive math problems based on real-life situations, like calculating the elimination of medicine from the body, aimed at K-12 levels. The Selected Web Resources list is substantial and easy to browse. Some 500 recommended and annotated links are built into an interactive table.

Click on NCTM Standards on the left margin for the Electronic Edition, also called E-Standards, full text in HTML. E-Standards is searchable. Five to six Electronic Examples (interactive applets) for each of four levels (grades PreK-2, 3-5, 6-8, and 9-12) illustrate the concepts and principles.

The Bottom Line: NCTM sponsors a well-organized and media-rich set of web sites for learning new-standards math. Creative sections like Illuminations and the comprehensive web directory make this is an essential source.

MATH IN DAILY LIFE
www.learner.org/exhibits/dailymath
Date Visited: 2/4/02
Developer/Provider: Annenburg Foundation/Corporation for Public Broadcasting

This site focuses on practical math skills for adults. After a brief introduction, each of the six sections contains a concise, informative essay with a selective list of relevant links. Users can learn how to calculate square footage of materials needed for home decorating or to manage money better by understanding compound interest in credit card debt. Hands-on activities are available in the Savings and Credit and Population Growth sections.

Click on Related Resources for a selective list of web sites; each of the 31 well-annotated sites is activities-based, ranging in theme from general interest mathematical skills to specialized calculators and tools. The bibliography of 17 recommended books would help with collection development.

Navigation is generally quite easy, but be warned that the Home button at the top of the page leads to the Annenburg/CPB Learner.org host site.

The Bottom Line: Salient examples used by adults in everyday life teach users fundamental, prealgebra principles. The site is concise and cleanly designed.

JOHN ALLEN PAULOS AND THE SPORADIC EXPONENT
www.math.temple.edu/~paulos
Date Visited: 2/4/02
Developer/Provider: John Allen Paulos

Paulos popularized the concept of innumeracy in books like Innumeracy: Mathematical Illiteracy and Its Consequences (1988). He maintains an irrepressible love of mathematical truths, viewing current issues through a rational, mathematical lens and breaking down issues into understandable parts.

Click on the in-text link Current or Archived to jump to his 'Who's Counting' monthly columns. In insightful, sometimes sarcastic essays, Paulos debunks the current fervor over shark attacks and the superstitious hysteria of numerology and terrorist attacks on the World Trade Center. He assumes a fair level of math familiarity, though he does explain critical concepts.

The opening page is packed with the text of one long paragraph. With few pages, the site serves mostly as a directory to Paulos's writings and lists his professional affiliations, interests, and accomplishments. Miscellaneous Writings links to several older essays and reviews. Other Stuff has a few more outside links but needs updating; several links were dead. Paulos's sense of humor can be distracting.

The Bottom Line: Though John Allen Paulos's site is self-promoting, his columns are required reading for those concerned about math literacy.

Alternate Sites

Math Forum
mathforum.org
At this megasite (hosted by Drexel University), click on the footer link Math Library for a searchable directory of hundreds of annotated sites. This is far more comprehensive than the Selected Web Resources at NCTM, indexing college- and research-level sites as well as those for K-12. At Forum Features click on Ask Dr. Math to find text answers to all kinds of problems, elementary through college. If the answer is not in the Archives, you can submit a problem via e-mail. The Dr. Math FAQ features classic problems and formulas. This site also supports discussion among researchers, teachers, and students.

MAA Online: The Mathematical Association of America
www.maa.org

Mathematically Correct
mathematicallycorrect.com

The Mathematical Association of America site opens with a straightforward design of simple text links and a table of site categories. Click on Columns for accessible (high school to undergrad) topics from writers like Keith Devlin ('The Math Guy' on NPR's Weekend Edition). Click on Teaching and Learning for the link to 'The MAA and the New NCTM Standards'-a report that critically assesses those standards. The more activist Mathematically Correct documents the development of grass-roots resistance to the NCTM Standards and so-called 'fuzzy math.' From the Site Index-near the bottom of the long homepage-click on True Standards That Parents Can Use to find the oppositional Standards from Kindergarten Through Pre-Algebra. The homepage is one long scroll.

Curious and Useful Math
personal.cfw.com/~clayford

Discovery School's Webmath
school.discovery.com/homeworkhelp/webmath

Math.com: The World of Math Online
www.math.com/students/calculators/calculators.html

Curious and Useful Math includes an eclectic range of tricks and rules for solving problems like determining ages and calendar dates. Garish colors give Discovery School's Webmath kid appeal, yet the calculators available at the Real World Problems link are practical for everyone, showing how to figure a tip or gauge wind chill. Click on any of the categories in the topic index for a Problem Solver form. Topics range from elementary- to high school-level math. Several additional types of online calculators-from basic to high school integral and vector-are offered in the Student section of Math.com. College-level converters, interactive forms for equations, and plot-graph tools are also available. This site has numerous ads and pop-up windows.

Probability/Statistics Objects Library
www.math.uah.edu/psol

Spreadsheet Page
j-walk.com/ss

Statistics Every Writer Should Know
nilesonline.com/stats

The Probability/Statistics Objects Library is a directory of open-source applets and components for college-level probability and statistics, sponsored by the University of Alabama, Huntsville, Mathematics department. In contrast, Statistics Every Writer Should Know is entirely introductory. Journalist Robert Niles shares ten text-based lessons on basic concepts such as mean/ median and standard deviation. Another practical site is the Spreadsheet Page by John Walkenbach, a consultant and writer. He focuses on tips for using Excel, as well as offering advice to users and spreadsheet designers.

Glossary of Mathematical Mistakes
www.mathmistakes.com

Innumeracy.com
www.innumeracy.com

Glossary of Mathematical Mistakes, created by former high school teacher Paul Cox, criticizes the media's misuse of math. The In the News section abstracts and critiques occasional news items in which math concepts are misconstrued. The Mistake of the Month takes on A Beautiful Mind. At Innumeracy.com (which has no association with John Allen Paulos), Steve Head also collects links to articles and web pages related to the use (or misuse) of math and logic. Each month he focuses on one topic area: in January, he offered links for descriptive statistics and data analysis. Despite its title, this site also emphasizes philosophy and critical thinking skills.

MacTutor History of Mathematics
www-groups.dcs.st-and.ac.uk/~history/index.html

Women Mathematicians
www.agnesscott.edu/lriddle/women/women.htm

Look to the MacTutor History of Mathematics for 1300 authoritative biographies. Each also links to biographies of mathematicians from the same country. Additionally, the editors provide 30 articles in their History Topic Index. Search by keyword, or browse alphabetical or chronological indexes. Additional sources include a glossary and an index of 42 female mathematicians. Women Mathematicians currently offers over 130 biographies from the fifth century BCE through the 1960s, indexed alphabetically and chronologically.

MathWorld
mathworld.wolfram.com

Advanced math comes alive at MathWorld, created by Eric Weisstein and hosted by the publishers of Mathematica software. Click on the Animations tab for GIF movies and applets (Java required). The Recreational Mathematics section has more than 150 examples. A hierarchical index makes it easy to drill down through the subject headings.

Fantastic Fractals Online
www.techlar.com/fractals

Official String Theory Web Site
superstringtheory.com

These two sites deal with advanced topics. Find tutorials on the properties and creation of fractals at Fantastic Fractals Online. Click Explore on the navigation bar for dozens of briefly annotated links. The Official String Theory Web Site explains the key concepts needed to understand string theory and black holes.