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A Twist on the Basics.

English, math and science have long been the sacred cows of academics. But there's always room for interpreting their delivery. Add some lively, hands-on lesson plans and you've got the latest in applied teaching. Try a couple of these ideas in your classroom.

Living Proofs

Start drawing angles on the blackboard and talking sine, cosine and tangent and most of your students will start drifting, guarantees John Milam, an applied math teacher at DuPont High School in Charleston, W.Va. Start scribbling long geometry proofs onto the overhead projector and you'll lose their attention for sure. Milam's solution? Take it outside.

"Say the word `trigonometry,' and students start to snooze," Milam says. "So one of my best lessons is to do like George Washington did--compute the length of a `line'--like a stream--by using geometry equations, trig functions and a compass. This way [students] learn how to apply their geometry and trigonometry lessons to real problems and also learn how surveyors mapped out distances back in George Washington's day."

Applied Math 1 and 2, staples at DuPont for 10 years, have drawn high marks from students and area employers who applaud the real-world aspects of the classes. The school, which will merge with another high school in the spring, plans to offer more applied classes in geometry, chemistry and other subjects.

"Many students can't learn from just sitting at their desks and watching a teacher explain math problems and techniques on the board," Milam says. "They need to see it being used and solve real problems with it--not just on paper. Then they're able to apply their math skills to future jobs. Students seem to retain more math skills from their applied classes than regular ones."

Applied math teaching methodology, which uses real-world settings and hands-on activities to teach basic arithmetic, algebra, geometry, trigonometry, probability, statistics, estimation and problem solving, is gaining popularity in schools nationwide, according to a new study on mathematics instruction from the National Center for Education Statistics. More than half of all math classes in the United States have used some applied math techniques in the last decade, the study reports.

Though traditional teaching is deeply entrenched in most schools, applied methods are creeping into daily instruction, says Michael Jameson, associate director of the National Coalition of Mathematics Instructors and a former math teacher. "The curriculum itself is evolving too," he says. "Whereas before applied math lessons focused more on entertaining, hands-on activities, which still is an important way of engaging students, more teachers are now preparing lessons to teach math with a job-related focus."

Math all around

In Applied Math 1, Milam focuses on problem solving, estimation, measurement, geometry, data handling, simple statistics, algebra and trigonometry--combining lectures with weekly field trips (on-and off-campus) and hands-on activities. For example, one lesson takes students to the school's track where they learn to compute speed by running and timing themselves on distances they've measured.

Applied Math 2 builds on the skills learned in its prerequisite by progressing to work-related scenarios. Milam revisits the lesson at the track by taking students to the West Virginia Water Plant, where his students use math formulas to compute water pressure, volume, speed and distance traveled between two disclosed points.

At Central High School in western Montana, applied math courses have an agricultural and, more specifically, a cattle-ranching emphasis. "Most of our students have a family background in these two areas, so they learn math best when they see it used in a relevant setting," says applied math teacher Julie Nelson. For example, her students learn probability and statistics by charting the cows' birthing patterns and predicting the number and characteristics of future herds.

Nelson's students learn geometric principles of area and volume by calculating seed amounts for different sizes of crop fields. "Math lessons are everywhere. You don't have to purely rely on textbooks and paper homework to teach the skills," Nelson says. "I find my students learning better and retaining more when we apply geometry, trigonometry, statistics, problem solving and other math subjects to relevant, hands-on situations."

Teaching differentials

Using applied teaching methods becomes a greater challenge, however, when it comes to more complicated math principles, Jameson says. "Developing applied math curricula for complex theories and principles is not easy. How can you teach something like differential equations--a basic calculus postulate--in a work-related, applied situation? Sometimes you can't."

Researchers at the Center for Occupational Research and Development (CORD) in Waco, Texas, a nonprofit organization known for its applied learning research, say applied methods aren't for all math subjects. Subjects that incorporate tangible functions like measuring, estimation and calculations adapt best to an applied curriculum. "I have to stop the outdoor activities when I teach algebra," says Milam, who gets his textbooks and curricula from CORD. "Some math subjects still work better in the traditional manner, but that may change in the future as well."

The Westmoreland County (Pa.) Career Prep Consortium has developed one of the first comprehensive, competency-based curriculum guides for advanced mathematical applications, offering units in:

* trigonometric concepts that use surveying techniques;

* statistical applications in a work-based setting;

* applied calculus taught through lab activities; and

* robotics theories that incorporate spatial visualization, geometric functions and algebraic equations.

Nelson recently received a Westmoreland guide and says she's eager to implement it next school year. "It's such a new thing. I need to study it over the summer and see if I can adapt it into relevant lessons for my students. I may partner with our calculus teacher to create crossover lessons between my applied math classes and her classes."

Jameson says taking applied mathematics to a higher level will require years of research, particularly at the advanced math levels. "Applied math has two benefits," he says. "Students learn how to use math in real-world problem solving and [they're] able to use their math skills in future employment. If complex mathematical concepts also are incorporated into these benefits, then math education may really begin to change."


The Center for Applied Academics in Vancouver, British Columbia, has developed an extensive series of applied math lessons as part of a Ministry of Education initiative. Exercises like the following two relate math principles to occupation-specific situations. For information on these and other lessons, visit CFAA at


Putting out a blaze requires a firefighter to predict the speed, angle, area and distance of a fire. The firefighter also must determine the right nozzle and pump. These calculations and decisions depend on pressure, friction, volume and speed. Use probability and statistics skills and the right mathematical formulas to properly douse the flames.

Building Contractor

You're bidding to build a new playground for an elementary school. How much area will the equipment you want to include safely occupy? How much sand or other playground filler will you need and how much will it cost? Will you need to erect certain structures to support the playground equipment? Use geometry and trigonometry formulas to create a proposal for the best playground at the lowest price.

Contact Milam at (304) 348-1978. For more information on CORD curricula, see "Applied Learning Resources" on page 28, or visit For more information on Westmoreland's applied math guides, visit appmath.htm.
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Author:Husain, Dilshad D.
Date:Feb 1, 1999
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