Article written by Robert Young
Associate Professor of Mathematics
EFSC Palm Bay Campus

YoungBThe majority of mathematical functions in an algebraic setting may be expressed in many ways. They are primarily introduced as common functions such as linear, quadratic, exponential, logarithmic, absolute value, square root, and step functions. As the course progresses, students will study and graph higher degree polynomial functions and rational functions. The main representations of the aforementioned and others, often categorized as “the big three,” are graphical, algebraic, and numerical representations, but there are others as well (Garofalo & Trinter, 2009). The purpose of this paper is to research and discuss advantages and limitations of teaching with multiple representations using graphing technology.

MyMathLab.  Teaching traditional lecture, on-line, and hybrid courses at Eastern Florida State College for over 20 years, I’ve experienced firsthand how the infusion of technology into the classroom has had a dramatic impact on education and how courses are taught. Our mathematics department incorporates the use of MyMathLab which has brought teaching with multiple representations to the forefront at the college. The on-line software developed by Pearson Publishing provides instructors many avenues to incorporate the big three representations in a customized setting to enhance student learning and retention. This is achieved by tying in concepts from each of the graphical, algebraic, and numerical aspects to provide students a better understanding of functions and their applications. The use of such sophisticated mathematical software that involves the use of calculation, graphing, tables, geometry, and more provides easy access to multiple representations of mathematical problems (Pierce, Stacey, Wander & Ball, 2011).

A basic example of how this this could work is to have students solve the linear equation 4x + 3 = –2x –9. The student would use the algebraic approach along with numerical representations to solve the equation to get the answer of x = –2. Tying in the graphical approach by having them graph each line in slope-intercept form y = 4x + 3 and y = –2x–9 will demonstrate visually and reinforce as to why the equations are referred to as linear (sometimes I’ll write them as ‘line’ar) and supports the solution of x = –2 showing this is the point of intersection as it pertains to the x-axis. I’ve found that many students know how to solve an equation for ‘x’ yet do not fully understand how it relates graphically or in applications.

Students for the most part enjoy using MyMathLab because of its many integrated features. It has features such as help me solve this, view an example, watch a related video, try a similar example, and ask my instructor. There is also integration with graphing calculators encompassing the use of the TI-83. Studies about what students have to say about the use of multiple representations in College Algebra found that students were better at approaching problems with the use of multiple representations and felt it deepened their understanding. However, many students maintained the belief that symbolic manipulation is the mathematically correct way to solve problems while graphical and other uses of the calculator and software should only be used for checking purposes (Herman, 2007).

The National Council of Teachers of Mathematics states that “technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (NCTM, 2011, position statement). Moreover, technology can provide students with opportunities to explore different representations of mathematical ideas and support them in making connections both within the area of mathematics and other related major of studies (Blubaugh, 2009).

Much of what we teach in college mathematics is designed to support other disciplines. With technology being used more in many majors, fields, and areas of study, the conclusion to incorporate and use multiple representations as it pertains to mathematics instruction seems justified. Students in collegiate courses and other degree or program areas are expected to read and interpret tables, charts, and graphs. This process involves a considerable amount of mathematical understanding and reasoning and will go a long way to enhancing a student’s goals and help make them successful in their chosen career.