GED Math Instruction: Meeting the Challenge by Myrna Manly

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This article appeared in the November/December 1987 issue of GED Items (ISSN 0896-0518; Volume 4, Nos. 5&6), published by the GED Testing Service of the American Council on Education. Myrna Manly is a mathematics instruction consultant and former Math Test Editor for the Tests of General Educational Development (GED Tests).

### GED Math Instruction: Meeting the Challenge

The preliminary results of an analysis comparing the performance of GED examinees to that of high school seniors [1987]...reiterate[s] that mathematics instruction for GED candidates needs to be improved. Some suggestions for GED mathematics instruction follow.

Allow the use of calculators during instruction. This allows more class time for the study of mathematical processes, instead of the mechanics of computation. A study (Hembree & Dessart, 1986) shows that calculator use enhances the learning of problem-solving skills, the primary focus of the GED Tests. The students' paper and pencil skills also improved with calculator use, even when these skills were tested without allowing calculators. Additionally, calculator use allows the student to proceed directly into real-life problems. Motivation is thereby increased, and the anxiety associated with math computation is reduced.

Introduce variables to represent simple relationships and continue to use abstract symbols at every opportunity. A symbolic representation of arithmetic topics provides the student with needed review at the same time that it introduces algebra. This approach helps students prepare for "set-up" items on the GED Mathematics Test. These items ask for the method of solution rather than the actual answer.

Concentrate instruction on realistic problems which can be solved using ratio and proportion strategies. The majority of everyday situations that demand the use of high school mathematics (and, therefore, the majority of GED items) can be solved using rate/ratio/proportion techniques. An example of how to incorporate these suggestions into your GED curriculum follows.

Begin instruction by challenging the students to figure the cost per unit of various items in the grocery store (e.g. the cost per ounce or milliliter of juice). After dividing the total cost by the number of units in many specific examples, ask the students to generalize and symbolically represent what they did each time. This exercise introduces the use of variables. Nest expand the exercise into equations by showing how r = c/n (price per unit equals total cost divided by number of units ) is an algebraic transformation of the basic relationship, c = nr. This casual introduction to the use of variables and algebraic equations is not threatening to the student and provides the background needed to complete many of the algebra items on the test.

Give added meaning to fractions by introducing them as rates or division problems. For example, compare the value of various rates, including percents, by actually carrying out the division that they represent. Plot the results on the number line as they occur and note the similarities as well as differences in value. Use the occurrence of equal ratios to illustrate the law of proportionality.

By graphing direct proportions on a coordinate plane, an aspect of geometry can be introduced. For example, the relation between distance and time of a car traveling 55 mph is formalized by d = 55t. After 1 hour, the distance traveled is 55 miles. This point on the graph can be represented as (1, 55); after 3 hours it would be (3, 165) and so on. Plot these points, connect them, and use the resulting line to make predictions about other points in time.

Teaching that focuses on these fundamental relationships using real-life examples serves to build connections between unites in arithmetic, algebra, and geometry. This emphasis impresses the students with the relevance of their study and also helps reduce the anxiety associated with the study of algebra and geometry.