Math and Statistics Packages Solve a Range of Problems
When British mathematician Charles Babbage outlined the concept of the modern computer in 1833, it comprised a steam–;driven machine the size of a locomotive that could perform numerical calculations. Over a century later, a group of American engineers built the first large–;scale automatic calculator, known as Mark I. Today, of course, computers serve many other purposes. But now, more than ever, researchers rely on their computer to solve complex computations and analyze large masses of numerical data. In addition, math instructors at all grade levels have acquired software to help teach arithmetic, geometry, algebra, calculus, statistics and more. And, unlike a few years ago, educators today can use Macintosh and IBM–;compatible machines to run math programs with capabilities once reserved for mainframes and workstations. This article surveys some of the myriad math and statistics packages that suit education, from early learning titles to symbolic math programs with sophisticated programming languages. While limited space restricts the amount of detail provided for each product, this survey offers a glimpse of the many possibilities open to math teachers, researchers and students. "Real World" Math for K–;8 This first section examines math instruction packages for elementary and middle school students. Even younger kids can begin develo¼ng math skills with a PC, though. Edmark's award–;winning Millie's Math House introduces children ages 2 to 5 to numbers, shapes, sizes, patterns and problem–;solving. All directions and feedback are graphical or spoken. Other pre–;school programs focus on specific math concepts, such as EA*Kids' Sesame Street: Numbers. ActionMATH from Jostens Learning consists of nine CD–;ROMs intended for group instruction of K–;3 math content; each level contains five theme–;based units rich with full–;motion video and animations. For grades K–;6, Davidson & Associates' Math Blaster: In Search of Spot and Nordic Software's Turbo Math Facts test addition, subtraction, multiplication and division. A recent trend in math software is an emphasis on "real–;world" problems. Many companies also boast that their products meet curriculum and evaluation standards developed by the National Council of Teachers of Mathematics (NCTM). Plus, numerous packages are now available on CD–;ROM media, which enables them to incorporate more video, graphics and sound. For example, EduQuest's Math and More 3 for third graders poses open–;ended problems with multiple solutions and strategies. Another disc, Sanctuary Woods' Adventures in Flight helps kids ages 7 to 11 with operations, measurement, geometry and graphing; it correlates to popular textbook series from publisher Addison–;Wesley. More Than Just Software Elementary math programs often also feature extensive supplemental materials for the classroom, including teacher's guides and printable worksheets. Record kee¼ng systems and online help allow the software to be used as stand–;alone units for several weeks or even months. Brøderbund's new Tabletop Jr. for grades K–;6 includes dozens of "challenge cards," which invite students to work with partners in fun–;filled math activities. EduStar Mathematics, meanwhile, offers help in the form of hints, formulas, a glossary and a step–;by–;step tutorial. Finally, Autoskill's Mathe–;matics Program tracks individual students' training and testing histories and displays them in tables and graphs. Currently, only a handful of companies publish math–;centered videodiscs. Two notable titles are Videodiscovery's Math Sleuths, a collection of 10 problem–;solving e¼sodes for middle schools, and Optical Data Corp.'s Windows on Math. The latter helps primary–;level students "see" the meaning of abstract math concepts; T.H.E. Journal readers should inquire about a free 30–;day preview. Middle school teachers can assess students' math skills with D.C. Heath & Co.'s PACKETS, which contains activities and reading exercises developed by the Educational Testing Service (ETS). For High School and Beyond The aforementioned programs are valuable tools for K–;8 math instruction. Other packages are specially designed to teach high–;school level math or to perform advanced computations required in college or beyond. Two titles for Windows come bundled with printed materials: Schaum's Interactive Outline Series from MathSoft and John Wiley & Sons' CD Calculus. Students preparing for exams in algebra or geometry will benefit from MathMedia Educational Software's line of tutorial products for the Macintosh. And those who wish to import typeset–;quality equations into word processing or desktop publishing documents should consider Design Science's MathType. Other packages, such as Future Graph's f(g) Scholar, combine math functions with a spreadsheet and graphing utilities. When it's time for testing, teachers may load any one of ips Publishing's Exam in a Can titles to create and print tests in algebra, calculus, geometry and more. College students and instructors alike often need symbolic math packages, which can perform algebraic transformations on equations and math expressions. One of the best–;known symbolic math programs is Wolfram Research's Mathematica; it ships in versions for over 15 platforms, including Windows, DOS, Mac, OS/2 and Sun. Most versions support MathLink, which exchanges information between Mathematica and other applications. A quarterly journal is devoted to the use of Mathematica in education, from economics to medicine. Plus, the MathSource handbook, accessible online, contains supplemental programs and research papers. Like Mathematica, Maple V from Waterloo Maple Software performs thousands of different symbolic and numeric calculations quickly and accurately; it too runs on a wide range of platforms. With the firm's Theorist, one can explore math numerically and graphically using click–;and–;drag commands. The Brooks/Cole Publishing Co. offers a student edition of Maple V and other college–;level math software. Version 3 of Soft Warehouse's DERIVE, a Mathematical Assistant boasts enhanced plotting and programming functions. The software fits on a single diskette, and memory requirements are low. Some highlights of another symbolic math package, Macsyma, are its speed and formatting flexibility as well as its graphics animations; versions are available for DOS and most workstations. Finally, for engineering, the MathWorks' MatLab offers fast matrix operations and broad object–;control systems. Besides price, among the variables with these programs are their degree of programmability and quantity of support literature. Of course, not everyone will require a high–;end math package, which usually calls for a larger investment in both hardware and time. Evolution of Statistics As with the other branches of mathematics, there is a long history of employing computers for statistical analysis. Herman Hollerith patented a machine that helped sort statistical information for the 1890 U.S. census; in 1896 he founded a company to manufacture similar machines, which later merged and became the International Business Machines Corp., now known simply as IBM. Statistics packages have also migrated from the mainframe to the PC. Today's menu–;driven packages often have built–;in data editors that suit a wide range of applications. Though more specialized products exist, this article focuses on general–;purpose statistics packages for data analysis and visualization. But the following programs are far from limited. In fact, many of them are sold as base systems with optional modules for more detailed procedures. From Sunburst Communications comes a statistics program for grades 9 to 12: Statistics Workshop offers histograms, bar charts, scatterplots and more. Similarly, Course Technology's MYSTAT for Windows is an introduction to the world of statistics; it includes a textbook, software and data sets. A leading statistics package for higher education is MINITAB, which runs on over 35 platforms. Release 10 for Windows performs basic, advanced and quality–;control statistics, including confidence intervals, ANOVA regression and Pareto diagrams. New tools and menus make operations hassle–;free. Two other Windows packages, SPSS and BMDP's New System take advantage of that platform's user–;friendly interface and context–;sensitive help. StatPac Gold IV focuses on survey and marketing research; its merge command facilitates work with multiple sets of data. Resampling Stats, meanwhile, is the outgrowth of a new "computer–;intensive" approach to statistics. The firm says a majority of college students report that resampling is "less frightening" than conventional methods. Several Macintosh statistics packages now run native in PowerPC mode for the new Power Macs. Data Description's Data Desk provides a variety of statistical plots and procedures for exploratory data analysis. A non–;transferable license edition is designed for full–;time college students. Also for the Power Mac are SAS Institute's JMP and Abacus Concepts' StatView. The latter integrates spreadsheet, graphing and drawing capabilities for creating dynamic reports. Needless to say, not all statistics packages are built alike. Novices will not need the same software as advanced statisticians. Some users will benefit from a cross–;platform product, which can import and export data in almost any file format. Graphing quality and data management tools are just two other considerations when it comes time to select a statistics package. A Final Word Many more math and statistics packages are available in addition to those described here. And several new titles come out each month. Educators usually can't go wrong by selecting a product that has earned a favorable reputation over the years. Yet recently released programs also provide innovative solutions for teaching or research. Those with complex or changing needs may want to spend some extra money now to ensure that they won't outgrow their software in the future. Most of the products mentioned offer numerous academic pricing options, including site licenses and lab packs. Thus, early visionaries such as Babbage can rest assured that computers will continue to play a central role in math and statistics for many years to come.