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August 15, 2002

Hot Numbers for Middle School Math

By Nancy Tassler and Paul Fleisher

Guiding students from percentages to probability, these full-featured digital math curricula offer alternatives to traditional textbook teaching.

From calculators to skill-building software programs, computer-based technologies have long been popular additions to the math classroom. Today, both Web- and software-based programs give students and teachers access to entire math curricula at school or at home, with the best of these now offering tutorials, quiz and computation tools, as well as opportunities for exploring math in real-world contexts.

We looked at a dozen popular math offerings and selected five of our favorite middle school titles, evaluating each by the breadth of its curriculum, ease of use, and support materials. Additionally, we considered how each optimizes interactive multimedia to illustrate challenging concepts by integrating such features as on-screen manipulatives, video, and audio.

All of the programs reviewed here can help teachers organize instruction, effectively sequence content delivery, and customize assignments, pacing, and feedback for individual students. Each offers standards-based curriculum and instruction, extension and enrichment activities, and interactive assessment features. Four of the five programs deliver comprehensive curricula that instructors can use to either supplement or replace a regular textbook. The fifth, Wildridge Software's Math & Music, departs from the traditional curriculum by offering an interdisciplinary approach to understanding the relationship between mathematics and music.

All deserve serious consideration by educators looking to enrich traditional classroom media with technology-based instruction.

BoxerMath: Secondary Math (Boxer Learning)

Detailed progress reports chart students' skills and performance on BoxerMath's interactive math problems.

BoxerMath's Secondary Math series delivers an online math curriculum for grades 6-12. We looked at Introductory Algebra, one of several courses in the series, which also includes Intermediate Algebra, Geometry, and Trigonometry. Like all the courses available in this robust series, Introductory Algebra offers interactive tutorial lessons on a range of grade-appropriate mathematics topics, tests, and exploratory cross-disciplinary activities.

Students begin by entering the Tutorial Center, where they'll find lessons accompanied by step-by-step audio instructions and interactive graphics, such as exploring integers on a scrolling number line, that help keep them on task. In Lesson 4, for example, Density with Basic Algebra, over a hundred multimedia-enhanced pages gradually walk kids through basic to advanced problems. The Gasoline Problem starts off slowly by asking students to calculate the answer to a simple question: "After putting five gallons of gas into your car, the tank was full. If the tank holds 13 gallons, how much gas was in it before the fill-up?" Using an interactive scale and a numerical translation of the word problem, kids work through a solution.

To practice skills learned in the Tutorial section, kids click on the Gymnasium, where they work out their math skills with additional randomly selected practice activities and tests generated from a database of problems, which are then automatically scored.

An added component is Newton's Workshop, where middle-schoolers explore cross-curricular math experiments and computation tools, such as dynamic number and algebra engines that let them factor polynomials and multiply linear fractions. For example, in Pythagoras and the Sounds of Fractions, students read about Pythagoras' discovery of the ratios of pitch, and then click on images of hammers and anvils to hear pitch ranges and determine the mathematical relationship between them.

Destination Math (Riverdeep Interactive)

Destination Math contains seven math courses, spanning the entire K-12 curriculum. We looked at Course IV in Basic Mathematics and pre-algebra topics in Course V you'd expect to find in the middle school math curriculum. A well-designed interface lets students access any lesson module with ease, and a math glossary and on-screen calculator are always available for help. Students can move around easily within lessons, repeat explanations, and quickly call up a navigation bar that takes them to any page or practice problem.

Destination Math features an alien named Dijit who accompanies students as they progress through animated lessons. For example, in the lesson Using Variables to Express Relationships, Dijit learns about balancing the sides of a freight ship. The program's narrator explains how the ship's weight needs to be balanced and how to determine an unknown amount when the ship is not on an even keel. There are frequent pauses in the explanation where students can interact by entering numerical answers or selecting the algebraic expression that represents the model. In each lesson, kids can either skip the practice problems that follow the lesson or click the Show Me button to watch another explanation.

Destination Math's well-developed lessons require that students pay close attention, since audio instructions are the primary mode of content delivery and there is little text to read on the screen. Unfortunately, hearing-impaired students would not be able to complete these lessons, and any student who needs to read for concept reinforcement might miss some of the content.

Interactive Mathematics (Academic Systems)

Practice problems in Interactive Mathematics offer students both audio and graphical explanations.

Interactive Mathematics is a comprehensive math curriculum offering complete courses in pre-algebra and algebra I and II that meet or exceed most state mathematics standards. The pre-algebra course, for example, includes instruction in whole numbers, fractions and ratios, geometric concepts, statistics, and linear equations. Lessons follow a traditional but consistent pattern of providing conceptual explanations, practical applications, and practice drills to reinforce learning.

Each of the 22 logically sequenced lessons in the pre-algebra program comes with plenty of examples and practice problems, which are explained both graphically and with clear audio narration. Students begin lessons with an evaluative pre-test, and then follow instruction with practice problems that ask them to apply core concepts to real-world models. In the unit on fractions, for example, students apply their knowledge by calculating in fractions the time they spend on various activities. In another section on signed numbers, students gather and then chart Web-researched data about temperature changes in a city of their choice. Each lesson also includes homework problems selected to meet individual students' needs and a post-test to evaluate their progress. Students receive immediate feedback as they proceed through the lesson; online explanations are available when they need help.

The Web-based version of Interactive Mathematics lets teachers design their own courses by selecting from the lessons they think are most appropriate for the students they teach. Additional customization features include options for posting lesson plans for students, adding notes-including extra questions or assignments-to any instructional screen, or creating links to Web resources. However, educators cannot add to or modify pre-populated problems.

Math & Music (Wildridge Software, Inc.)

From using the abacus to calculating the physics of sound, Math & Music gives everyday calculations a context.

Math and Music combines math instruction with lessons on the science of sound and the history of music, creating an innovative cross-disciplinary approach to mathematics.

Using the abacus, calculating ratios and areas, and performing trigonometric functions are among the simple to sophisticated math drills students perform as they learn about the numeration systems of ancient Egypt, Babylon, and Rome. The program also presents lessons on the physics of sound and the anatomy of hearing, harmonics, scales, intervals, chords, and other essential musical concepts. For example, since the days of Pythagoras, scholars have known that the frequency of a vibrating string is directly proportional to its pitch and that musical harmonies are based on the ratios between different frequencies. To illustrate this lesson, students read and respond to questions about simple ratios of frequencies. They then apply their understanding of different ratios as they produce familiar harmonies, such as how the ratio of 1:2 produces an octave, how 2:3 produces a fifth, or how 4:5 results in a major third.

Text and audio narration deliver well-scripted lessons, but given most students' familiarity with music videos, they may find the program's simple visuals and didactic style a bit dry and humorless. Music samples, from Gregorian chant to modern rock, come in brief snippets, and some pieces, such as rock music samples, are synthesized rather than original versions. Math & Music also bypasses American jazz and African-American musicians in its outline of music history. Despite these weaknesses, however, Math and Music is a conceptually exciting, cross-disciplinary approach to teaching math and its contextual applications.

Math Expeditions (PLATO Learning)

Kids experiment with Math Expeditions' on-screen manipulatives to solve project-based math problems.

Math Expeditions is a project-based online math curriculum for kids in grades K-8. We looked at Levels G, H, and I, the most appropriate sections for middle school students. An impressive number of activities in numeration populate the menu for these levels, including topics ranging from fractions, decimals, ratios, and proportion, to geometry, graphs, probability, and statistics.

The theme of the expedition establishes a context for each level. In Level G, for example, students use mosquito populations in the Everglades to practice adding mixed numbers; in Level H an Arkansas Wildlife Refuge; and in Level I, kids head to Philadelphia to unearth buried historical information.

All activities and lessons for Level G take place within the context of the Everglades, where students are given a problem to solve using grade-appropriate mathematical functions. In this case, it's controlling the growth of the invasive malelueca tree. To do so, kids have to calculate the area and square mileage of sections of overgrowth, and then use algebraic equations to simplify their calculations as tasks grow increasingly more complex. Students first practice their algebra skills by filling in the numbers for the formula and can access the on-screen calculator or query the math glossary to determine the answers to more difficult problems. After working through this process, they complete a series of ten practice problems, with feedback, and then take the online quiz for that level.

Each expedition includes fascinating facts about the mission locale and gives a real-world feeling to the use of math. A Macromedia Shockwave file loads each activity, which consists of a tutorial, practice, and quiz. Student progress within lessons and test scores are saved by the management system. However, tutorial pages are linear and text-heavy, and kids can't skip problems or move easily around lessons.

While Math Expeditions' context-based approach to instruction is a refreshing departure from the traditional textbook format, we hope future versions of the program will optimize Web-based interactivity and more robust multimedia for interactive page design.

Nancy Tassler is a technology specialist at Daniel Wright Junior High in Lincolnshire, Ill. Paul Fleisher teaches gifted middle-schoolers in Richmond, Va. His most recent book is Ice Cream Treats: The Inside Scoop.

Editor's note: T&L's staff and editors evaluate only those products we can endorse for educational use. Web site reviews are based on content and tools that are available and accurate at the date of publication. We'd like to thank Apple Computer and Gateway for loaning us the equipment to perform in-house evaluations.

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