More on New Math Courseware: Other titles, new companies & extra tools for math instruction
Larson's Leapfrog Math, from Meridian Creative Group, is based on the techniques and expertise of Dr. Roland E. Larson, a widely known author of math textbooks. Originally the Leapfrog series covered grades 3 through 6, but a K-2 Elementary component was added this spring.
Heavily multimedia, the interactive programs integrates skill development, real-life applications, number-sense activities, models, conceptual questions, data analysis and more. The name comes from animated characters who guide students: Lily Leapfrog motivates older students with encouraging words; Tad, a younger brother, is the helper for younger children.
In Grades 3-6 Leapfrog Math, ten (10) topics are covered in each grade and five (5) levels comprise each topic. Students explore a topic, are exposed to its skills and then put them into practice - in five levels from "rookie" up to "master." At the end, they take a Challenge Test, which expressly combines all degrees of skill in all topics, to provide an accurate assessment of students' mastery.
Older students must apply deductive & inductive reasoning in order to solve Commander Problems and Get Real scenarios. The scenarios are key - connecting concepts to real life, forcing one to apply concepts and skills, and demonstrating how math is used in everyday living.
Leapfrog Math Elementary Series (K-2) uses similar instructional techniques but presents them for a younger mind. Frog Hollow is the setting for student activities. Again each grade level has 10 topics, each of which sports 3 to 5 activities on skills or concepts. Each activity comprises 8-12 separate tasks.
Flexibility for classroom teachers was kept paramount. So the K-2 Teacher's Guide has suggestions for follow-up and alternate activities, plus lists of additional resources. Full-color storybooks and physical manipulatives are included, as are assessment checklists, plus a set of customizable letters for parents.
For the Grade 3-6 series, packages include CD-ROMs for students and a Classroom Management CD for teachers, 24 student portfolios, a Teacher's Resource Guide, a User's Guide, an Extra Practice Book, plus stickers and a poster.
Larson's Leapfrog Math can be purchased by individual grade levels for single users or a sites, or each of the two series is also offered under a site license. The CDs are Mac/Windows hybrids. This is not the only math software offered by this firm and inservice training is also available from Meridian Creative Group, Erie, PA, (800) 530-2355, www.meridiancg.com.
, long a provider of high-quality courseware, has teamed with relative newcomer Academic Systems
for Interactive Mathematics: Algebra 1 and Algebra 2
. These new products address the need for better college-prep courseware, meet state and national mathematics objectives, and aid school-to-work efforts.
Media-rich, the program organizes algebra into 17 topics, which are then broken down into lessons. Each lesson features an overview with a pre-test, explanatory sections (where main instruction occurs), applications section for student practice; exploratory sections, and, finally, evaluation sections.
Unlike other products, Interactive Mathematics: Algebra is a full algebra curriculum, complete enough to replace traditional textbooks in grades 6-12 - in magnet schools, for example, or traditional settings. It also works in conjunction with Jostens' curriculum-management software.
For Windows 95, the courseware package includes print-based Personal Academic Notebooks for students, which have homework and content reviews. The Instructor's Guide has implementation guidelines, full scope and sequence info, and summaries.
Interactive Mathematics is available in separate Algebra I and Algebra 2 levels or as a single package. Jostens is based in San Diego, Calif., (800) 521-8538, www.jlc.com
adds to their burgeoning algebra line with Astro Algebra
, a companion to their new Mighty Math Cosmic Geometry program. Mighty Math programs are for grades K-9.
Astro Algebra suits grades 7-9. Students command the spaceship Algebra Centauri and meet "math-challenged" aliens in their journey. Activities (dozens of them) utilize Virtual Manipulatives, an Edmark technology. And Grow Slides offer increasingly difficult challenges as students skills improve. All activities have both Q&A (directed) and Explore (self-directed) learning modes.
Astro Algebra is on a hybrid Mac/Windows CD and includes a Teacher's Guide with lesson plans and reproducible activity sheets - all packaged in a 3-ring binder. Contact Edmark in Redmond, Wash. at (800) 691-2985, www.edmark.com.
For a completely different tack, check out MathView Internet
, a plug-in for Waterloo Maple
's MathView. The latter is a symbolic math & graphing software program that visualizes abstract concepts with 2D and 3D color images. Indeed, MathView is the renamed and revamped Theorist product.
MathView Internet (you can download it from Waterloo, etc.) lets one not only view Web-embedded mathematics, but also retrieve fully functional MathView notebooks, the "workpages" created by teachers or students. It's just one part to their firm's Internet strategy.
Another part is CyberMath, a unique website -- that you need the MathView Internet plug-in to use. CyberMath supplies live, interactive and editable mathematics via the Web. The site's content can be searched by grade level and by various math subjects for high schoolers and up. Forums aid sharing between and among students and instructors.
Waterloo Maple (Waterloo, ON, Canada) is the maker of Maple V and licenses its math technology to other firms such as MathSoft, the MathWorks and TCI. (800) 267-6583, www.maplesoft.com
For grades 5-8 is An Odyssey of Discovery: Fractions
from Pierian Spring Software
(Portland, OR). As a supplement to other math instruction, it's very narrow focus helps both teachers and students with a difficult skillset to teach and to learn.
Fractions are presented in a 3D, real-world environment in this program. Covered are not just number activities, but also conversions to decimals and words. Full class, small groups and individual use is all facilitated by the software's design. It's on a Mac/Windows hybrid CD-ROM.
Also check out The Fractionator -- a Java applet that is a very cool tool -- from Pierian. (800) 472-8578, www.pierian.com
A new series -- Math At Work
-- seeks to answer that ubiquitous question from students: "Why do I have to learn this?" From CORD Communications
, each program uses a real-world setting and problems in which to teach skills.
For example, Cyber-Snacks, which covers pre-algebra content, has students run a vending cart at an outdoor concert. They have to use "market research and analysis" to maximize their profits while adhering to a budget.
Gearing Up moves students into more complex algebra as they determine a bicycle race course, the gears to put on their bikes, and where to use which gears.
Pooling Around turns students into swimming pool contractors. First they must schedule their sub-contractors in the right order and for the right time. Then they employ geometry skills to supply sub-contractors with the correct measurements. All must be achieved within a certain time and budget.
User's Guides accompany each title, and where appropriate, even provide the answers to problems. It's the process that is key in this series of courseware.
Math At Work may look like games, but they're really frameworks. They transport a student to a believable environment in which to solve problems - which are meaningful enough to engage a youth's interest. CORD, (800) 231-3015.
Another new title for early learners is Sunbuddy Math Playhouse
, from Sunburst Communications
(Pleasantville, NY). In this interdisciplinary program, a theatre stage is the main setting. The Sunbuddy characters will be familiar to many kids, however.
Students watch a 12-act musical play and read the dialogue along with character Hopkins. They can "play along" by activating "clickables" in each scene, which introduce kids to simple math concepts like counting by 5s.
The Sunbuddy musical production offers up ten (10) original songs, which can also be accessed from a jukebox, located backstage. Four (4) math games are also entered into from the backstage area. One introduces the very young to mapping concepts, for instance.
Sunbuddy Math Playhouse comes on a Mac/Windows hybrid CD-ROM, with a comprehensive Teacher's Guide, packaged in a 3-ring binder. Single user, five packs and other site-license options are offered. A free 30-day preview can be requested from Sunburst at (800) 321-7511, www.nysunburst.com.
is a collection of puzzle-like math-oriented activities for K-8 all set under the big top. From Power Industries, Inc.
, (Wellsley Hills, MA), this newest version of Math Circus suits grades K-8.
At first blush, this appears to be a program for young kids, but don't let the circus themes fool you. These actually serve as clever hooks for problems. In the Trapeze activity, for instance, students learn about pendulums. And Captain Blunthead teaches about propulsion, angles and more in a Cannon Shoot activity. There are a dozen activity themes, some with multiple tasks.
A special School Edition lets teachers adjust skill levels of puzzles and keeps a record of students' problem solving. Teachers also receive a special manual, blackline masters. complementary products and free support by telephone or e-mail.
Math Circus, revised in early 97, is now offered in a Windows 3.1/95 version. Sound has been added to Mac & Windows versions so that students can play be themselves. Sound/music effects can also be disabled. Plus adaptive switches and other devices for physically challenged students are now supported.
Developed by Greygum Software of Australia, Math Circus is available in Mac, Windows and DOS formats, plus School and Home editions from Power Industries, (800) 395-5009.
's very popular TouchDown Math
series will debut new multimedia versions sometime in October 97, the firm noted at June's NECC meeting. Each of the five (5) titles in the series will boast enhanced graphics and audio elements. Also improved are the tutorial assistance components.
GAMCO is part of the Siboney Learning Group, formed by parent company, Siboney Corp., to manage its educational software interests, of which GAMCO has been a part for 36 years. GAMCO's facility in Big Spring, Texas, will continue to process, ship and support its titles. GAMCO, (888) 726-8100.
, from MathSoft, Inc.
, is not just a mere upgrade; it's a whole new generation. According to an interview with the firm, both power and flexibility were added. It also runs on Windows 95/NT.
Some new features are tailored for multi-platform usage; others give a nod to the Web's soaring star. Combined, the move is towards "paperless teaching methods," where instruction is delivered over intranets or the Web. Thus one can "publish" live math on the Web for collaborations and more, for example.
Mathcad 7- - now supporting OLE 2.0 with automation, HTML browsing & more -- works seamlessly with any other application, and vice versa. You can also cut/paste or drag/drop into, and out of, other applications.
LiveMath is their patented user interface and it's extremely easy to use. One just writes on the screen in "plain math" and the software converts it into equations and more.
More power is illustrated by a 60% improvement matrix manipulation speed. There's also a fully functional language integrated in the product, as well as programmable live symbolics and string functions.
Two editions of Mathcad 7 serve different needs, but at excellent prices for both. The Professional Edition for technical staff & corporate project teams retails for $129. The Student Edition of Mathcad 7 (no, it's not "crippleware") is just $69.
A separate and brand new tool is MathConnex -- a visual programming tool for integrating data and application components from Mathcad and/or other programs. Not merely for math, this tool suits science, engineering and other technical environments.
Ideal for "demonstrating the behavior of a system," one uses MathConnex to build a flowchart of a system by dragging and dropping components onto a "whiteboard." Components can be a Mathcad routine, a 3D plot, an equation, etc. or elements from other programs like Excel, MATLAB or any other OLE-compliant application. This approach affords a very quick path to solutions, yet facilitates work by teams and re-usable components. MathSoft, Inc., (800) 628-4223, www.mathsoft.com
A new company, Mathpert (short for MathXpert) also believes in step-by-step instruction. They call their approach an "expert system that mimics" the way people learn and think.
No replacement for textbooks, instead their "Assistant" series is like having a math teacher instantly available -- any time -- to show you how a problem works.
San Jose State University math professor Dr. Michael Beeson, took seven years to develop and test the products. Algebra Assistant is $95; Pre-Calculus Assistant is $145 (or a $60 upgrade). Calculus Assistant, which includes the previous two as well, is $195.
Students can input any math problem and the program will visually demonstrate its solution, step by step. Lists of equations from several textbooks -- over 25,000 typical problem sets -- are also integrated.
Mathpert titles also have graphing engines; and feature Hint, ShowStep, AutoStep and AutoFinish buttons. Students control how much, or little, the program will do automatically. Based on their mastery, they are guided to additional resources by topic.
The Assistant series is for Windows 3.1 or later systems from Mathpert, (800) 361-1001, www.mathpert.com.
Another helper for calculus students is by Cogito. Part of a very broad line is their An Electronic Companion to Calculus, "a multimedia course review," as they phrase it. Again, the emphasis is on process, not answers.
This interactive CD-ROM serves as both interactive workbook and supplemental data sets to a traditional calculus textbook. Dr. Keith Devlin, author of 16 math books, is the expert educator behind this CD.
The Companion titles (each about $30) cover key concepts. There are reviews, narrated animations, movies and interactive art to help students better understand. Then they can test themselves. Multiple-choice, true/false, fill-in and drag/drop are all included in the question formats.
All answers - both right and wrong - receive feedback from the software. The intention is to keep students on track, so that they know why their answers were right or wrong. All questions also have hints.
Another Companion title is offered for Statistics, and there are some for science topics too. All are Mac/Windows CDs. Cogito Learning Media, Inc., is based in New York, NY, (212) 361-6330, www.cogitomedia.com.
Finally, lots of students just cannot do paper-and-pencil math - some because they are physically or developmentally challenged. For special needs students, MathPad
may be of help.
From IntelliTools, Inc. (Novato, CA), this package comprises software (a math processor) plus keyboard and other input-device overlays for math functions. In usage, students solve the problem but the software handles the navigation and data-input tasks.
The MathPad software works with the IntelliKeys keyboard, a generic keyboard, a mouse or a switch. It'll move automatically between input devices so that different students using different devices can still work at the same program. The program can also alter font sizes, background colors and speech options to accommodate all types of special needs.
Teachers may use the 300 sample problems included, enter their own problems directly; or import lists made with a word processor. MathPad sets up problems using the correct vertical format.
MathPad, a Macintosh-only product, was developed by grants from the National Institute on Child Health and Human Development and the National Science Foundation. It's backed by a 60-day, money-back, no-questions-asked guarantee. Multi-user pricing in addition to single user and five packs is offered by IntelliTools (800) 899-6687, www.intellitools.com.
In related news, an even newer NumberMaze Challenge (from Great Wave Software) that runs some 65% faster -- will be available in September or early October. It features additional customization options such as turning off animated characters' speeches or The Maze game if strict reinforced learning is the goal. Registered users can upgrade and receive the new CD for $10 shipping and handling.
Also from Great Wave is KidsMath, another award-winning package. Designed for grades Pre-K to 3, the program includes eight (8) entertaining activities to teach and reinforce basic math concepts, while introducing 18 different skills. Great Wave is in Scotts Valley, CA, www.greatwave.com.
This article originally appeared in the 08/01/1997 issue of THE Journal.