Hand-Held Graphing Technology in the Developmental Algebra Curriculum

Graphing Calculator vs. the Scientific Calculator Many argue that every piece of technology used to teach mathematics takes away from teaching time. But learning to properly utilize the graphing calculator in the context of teaching an algebraic topic can be a teaching enhancement, not something that detracts from teaching mathematics. This article will provide two simple examples (using a functional approach) that demonstrate why the graphing calculator is the appropriate teaching/learning tool of choice for the developmental algebra curriculum. It has been my experience that graphing technology provides exciting ways of presenting most topics taught in the beginning and intermediate algebra curricula, yet the majority of developmental mathematics educators are not using hand-held graphing technology in the mathematics classroom as confirmed by a 1998 national survey (Laughbaum, 1998) since only 26% of the developmental faculty reporting were using graphing calculators (also see Lutzer, 2002). The graphing calculator is not only a teaching tool in the classroom in the hands of the teacher, it is also a teaching tool in the hands of students when they are given investigations, concept development and guided discovery exercises, open-ended homework exercises, and summative modeling projects. In addition to these teaching tools, the introduction of calculator applications has opened the door for many new kinds of activities. Two Examples of Uses for the Graphing Calculator For these two examples to be fully effective, a function approach should be used. Typical content is restructured by beginning with an expanded introduction to function concepts. This includes the study of functions as real-world data relationships in numeric, graphic, and then symbolic forms. This is followed by the analysis of geometric behaviors of functions and the study of the parameter-behavior connection. Students are then ready to use the concepts of function to help them understand other traditional algebra topics like definitions, laws and properties, operations with polynomials and other expressions, factoring, solving equations and inequalities, etc. In addition to using the concepts of function to teach algebraic ideas with understanding, function also gives students another method for doing algebra through the use of hand-held graphing technology. The following examples illustrate appropriate uses of the graphing calculator for developmental students learning algebra from a function approach. The examples are student activities that require, or are enhanced by, graphing technology. Teacher notes are provided. Example 1: Solving Equations Solving equations is a topic that has been radically changed by the use of a graphing calculator and the use of a function-based curriculum. Students can now solve most kinds of equations with varying degrees of complexity using the zeros, intersection, tabular (numeric), or trace methods. Students usually prefer the zeros method because it relates well to the parent of the - the function, and they have already found zeros of functions in the introduction section. The Numeric Method for Solving Equations A 12,000 square foot lawn is being mowed at a rate of 300 square feet per minute. When will the job be finished - except for the last 500 square feet? No matter what method the developmental algebra student selects, the mathematical model of the situation must be created by the student in symbolic form. In this case, it is A (Area) remaining to be mowed = 12000-300t, where t is time in minutes. If the student selects the numerical method, it goes something like this: After symbolic form is entered in the Y= editor, the student argues that there is no need to start checking at time = 0 since common sense says it will take awhile. So in table setup, the student starts checking the area remaining at 20 minutes and decides to check every 1-minute as shown in Figure 1. …