New Programs Help Redefine Math & Statistics Instruction
Several studies have suggested that Americans' performance in mathematics and statistics has steadily deteriorated since the 1960s, with students today scoring significantly lower than their international counterparts on standardized exams.
A 1992 "Report Card" by the National Assessment of Educational Progress (NAEP) found that just over 60% of U.S. students in grades 4, 8 and 12 were estimated to be at or above the Basic level in mathematics. Performance varied considerably within and across participating states and territories.
Critics charge that U.S. schools rely too heavily on textbooks and routine testing practices, which fail to promote higher-order thinking skills. Many view technology as a way to remedy current inadequacies in mathematics education.
This article surveys some of the latest math and statistics software packages for educators at all grade levels. These products -- and others not mentioned here due to space constraints -- can help students actively build their understanding of the subject matter without spending hours poring over workbooks.
An Early Start
Even the youngest can start developing math skills with the help of a computer. Inspired by the true experiences of an Australian boy, Brøderbund's James Discovers Math (for ages 3-6) uses a wide selection of familiar objects to encourage problem solving, reasoning and creativity.
In Math Circus by Power Industries, students complete 12 "puzzles," such as firing Captain Blunthead into a bucket of water, thereby picking up lessons in propulsion, angles and range. Another early learning program, The Learning Co.'s Interactive Math Journey leads children ages 6-9 through 25 carefully sequenced activities with progressive levels of difficulty.
Not surprisingly, several packages employ well-known storybook or TV personalities as "hosts." Creative Wonders produces Sesame Street: Numbers, in which kids visit the homes of Elmo, Big Bird, Bert & Ernie and the Count to practice counting, set classification, and addition and subtraction.
Based on Beatrix Potter's classic tales of a century ago, Peter Rabbit's Math Garden by Mind-scape rewards learners with seeds that they can use to plant an interactive garden. All art and animation was hand-drawn and hand-painted, then scanned into the computer.
Some titles feature sports themes. Two new programs -- Sanctuary Woods' NFL Math and Nordic Software's Math Majors -- allow students to learn math while playing football and baseball games respectively. In Math Majors, for example, correct answers earn a hit and possibly a home run.
Still other programs focus on a specific math concept, such as Mindplay's Fraction-oids 3 and Sunburst's Shape Up. Meanwhile, Money Town by Davidson & Associates, makers of Math Blaster and Alge-blaster, helps one compare the values of coins and bills as well as estimate costs, part of the standards outlined by the National Council of Teachers of Mathematics (NCTM).
Supporting Collaboration
As might be expected, a majority of math software has migrated to CD-ROM, enabling the delivery of more video, graphics and sound. The multimedia edition of Millie's Math House by Edmark includes two learning modes -- Explore & Discover and Question & Answer -- for many activities.
Plus, a growing number of K-12 programs support collaboration with classmates. In Lawrence Productions' Mystery Math Island, for instance, learners work alone or in groups to search for buried treasure; high scores and progress can be saved and printed.
Two math-centered videodiscs are Videodiscovery's Math Sleuths and Optical Data Corp.'s Windows on Math. A notable videotape series is called Math Made Easy; customers who purchase a minimum of three videotapes may receive 30 minutes of free, live math tutorial assistance over the telephone.
When the time for testing arrives, teachers will appreciate ips Publishing's Exam in a Can series, which measures math performance via multiple-choice and free response questions.
Finally, a handful of publishers offer comprehensive math curricula supplemented by manipulatives, teacher guides and other resources. For grades K-3, ActionMATH from Jostens Learning provides 100 interactive lessons and over 400 activities designed to meet the needs of students with diverse learning styles.
MECC's MathKeys (K-6) fully integrates with Houghton Mifflin Mathematics; it earned an A-rating in a CUE (Computer-Using Educators) newsletter. Software and blackline masters come in both English and Spanish.
A promising newcomer to the market is Tenth Planet Explores Primary Math, based on a proven learning model called Into-Through-Beyond. Each of the three geometry units covers about six weeks' curriculum, with lists of suggested resources and home investigations to help students understand the "big idea."
Case Studies Back Claims
Numerous case studies conducted by software publishers back their claims that integrating technology into the classroom can lead to increases in mathematics proficiency.
For example, from 1992-95 one K-2 class at Edgemont Elementary in Covington, Va., improved math scores on the Iowa Test of Basic Skills (ITBS) by 40% after using IBM's Math and More 1 & 2. The courseware connects mathematical concepts to student's own interests, their neighborhoods, families, friends, foods, cultures and even animals.
Similarly, according to Principal Verdi Avila of the CIS 82 Intermediate School in Bronx, N.Y., 100% of the students who spent ten or more hours using the Autoskill Math Program in 1994-95 raised their scores on standardized tests, and over one-third of them advanced by one or more quartile.
Although the preponderance of math programs target grades K-8, more titles have emerged for middle and high schools in recent years. Chris Randles, vice president of marketing for MathSoft, says teenagers, many of whom have computers at home, are especially comfortable using math software.
Reflecting the trend in other subject areas, Randles predicts that the Internet will play a larger role in math education. His firm's Mathcad 6.0 Student Edition allows users to enter formulas and equations, create live graphs and animations and share information via e-mail and the World Wide Web.
Among the highlights of Math Trek 10, 11, 12 by the NECTAR Foundation are randomly generated tests and examples, interactive tutorials and a management system. The courseware covers algebra, geometry, statistics, probability and relations.
Finally, MathMedia offers a six-part series spanning an entire year of high school geometry. It comprises introductions, examples, flashcards, questions with step-by-step solutions, and a 30-question test at the end of each module.
Advanced Computations
Several packages support more advanced computations or explain complex topics commonly found in upper-level high school and college courses.
John Wiley & Sons' Calculus Connections presents real-life applications of calculus concepts -- a plane taking off, a bridge collapsing, a skydiver jumping. With HighText's CrashCourse in Calculus, students proceed through the material at their own pace, repeating portions of the course as often as necessary.
Expressly designed for scientific math, CHEMiCALC by Chemical Concepts helps one with balancing equations, unit conversions, calculation of formula weights, empirical formula determinations, etc. And Soft Warehouse's DERIVE has been fine-tuned to perform algebraic operations with no round-off error.
More packages include built-in utilities for producing presentations or reports. Future Graph's f(g) Scholar 2.0, for instance, lets students create lab reports that combine calculations, graphs, pictures, tables, equations and even animations.
The two leading symbolic math programs now go so far as to deliver full word processing functionality. Dubbed the "Power Edition," Maple V Release 4 from Waterloo Maple adds more ways to input text, a multiple document interface, inter-process communications (OLE 2.0 and AppleEvents) and more typeset-quality math. Hyperlinks in Maple V offer single-click connection to an unlimited number of worksheets that execute live. A full-text search engine is also integrated into help.
Wolfram Research introduces Mathematica Link for Microsoft Word, which allows one to combine text, live calculations and graphics using custom dialog boxes, toolbars and onscreen forms. Simply enter calculations in a Word document, then the Mathematica engine invisibly evaluates them and results appear in the same document.
Many high-end products have narrowly focused add-ons. MATLAB, from The MathWorks, for instance, has a variety of "toolboxes" that extend its functionality; their most recent one is the Partial Differential Equation (PDE) Toolbox.
User-Friendly Statistics
Like the aforementioned mathematics products, the new generation of statistics software has gone a long way toward achieving true "user-friendliness." Students no longer need a Ph.D. to work with confidence intervals, ANOVA regression and Pareto diagrams.
Abacus Concepts' StatView 4.5 for the Macintosh thoroughly implements Apple Guides, System 7.5's context-sensitive help system. A new 134-page reference manual describes in detail each function, including syntax rules and examples.
Several programs have been upgraded to take advantage of the Windows 95 operating system or Power Macintosh. SPSS 7.0 for Windows 95 lets users reorganize and view results from different angles simply by dragging an icon.
MINITAB for the Power Mac Release 10 Xtra also promises high-resolution graphics. Data can be imported from Excel, dBase/FoxPro, Lotus and text files, whether fields are separated by spaces, commas, tabs or even an arbitrary character.
In a novel approach adopted by Resampling Stats, clear-cut simulations replace formulas. According to the firm, those taught by computer-intensive resampling methods are more likely to remember and use statistics several years later.
For More Information
With so many options, selecting a math or statistics package requires some homework. Educators can obtain volumes of information for many products by calling a toll-free number or logging onto publishers' Web sites.
Two recommended starting points with links to other math-related Web sites are the Eisenhower National Clearinghouse (www.enc.org:80), devoted to K-12 instruction, and Mathematics Archives (archives.math.utk.edu), for colleges and universities.