Examining Graphing Calculator Affordances in Learning Pre-Calculus among Undergraduate Students

Examining Graphing Calculator Affordances in Learning Pre-Calculus among Undergraduate Students

Francis Nzuki (Stockton University, Galloway, NJ, USA)
DOI: 10.4018/IJICTE.2016040104
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Abstract

This study examines graphing calculator affordances in learning mathematics among college precalculus students. The study draws from the Cognitive Load Theory (CLT) and the “Intelligent Technology” theoretical framework proposed by Salomon, Perkins, and Globerson (1991). From these perspectives the effects “with” the graphing calculator technology include the potential for this technology to offload students' extraneous cognitive load (e.g., the presence of unwieldy numbers), and in turn optimize their germane cognitive load (e.g., freeing students to focus on the key mathematical ideas). To examine students' perceptions on the adoption of the graphing calculator instructional approach a questionnaire was administered towards the end of the semester. The findings showed that the graphing calculator afforded students' learning in a variety of ways. Also considered is the challenge for educators to develop strategies that encourage appropriate use of graphing calculators in mathematics classroom in order to ensure that their integration is effective in instruction.
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Statement Of Problem

Mathematics is viewed by many students as one of the most challenging subjects and one which they would not undertake if they had an option. From my experience, a lot of students come into the math classroom prejudiced that math is a hard and boring subject and that they do not need it for anything in the real world. To counter these preconceived notions and to develop students’ interest and motivation in learning mathematics, scholars have come up with various innovative techniques that teachers can adopt in their mathematics classrooms. One such technique is the incorporation of technological tools (The National Council of Teachers of Mathematics (NCTM), 2000). The ability to produce visual images of mathematical ideas, the power to organize and analyze data, and the power to compute quickly and accurately are all characteristics of electronic technologies that augment student learning. Of the potentially available technologies in the classroom, the graphing calculator is more accessible to students because of price, portability and ease of use (Dick, 1996; Waits & Demana, 2000).

Research has shown that the use of graphing calculators facilitates students’ understanding of functions and graphing concepts. For example, Schwarz and Hershkowitz (1999) found that the treatment group who used the graphing calculator were better at selecting appropriate dimensions for the axes when graphing functions, preferred graphical representations of functions for problem solving, exhibited a dynamic notion of function, and were better able to develop representations of whole graphs of functions from partial graphs. Results from several studies also indicate that graphing calculators provide an opportunity of a multiple representation approach of mathematical concepts by promoting a multiplicity of linked approaches (numeric, algebraic, graphical) to the same problem (e.g., Graham & Thomas, 2000; Hollar & Norwood, 1999).

Moreover, graphing calculators have been found to be useful in helping students acquire mathematical modeling skills. For example, Drijvers and Doorman (1996) found that students gained a significantly better understanding of the concept of modeling real-world problems when compared to those who lacked access to this technology. Graphing calculators were also found to facilitate the development of spatial visualization skills (Ruthven, 1990) and to encourage students to explore mathematics ideas and use flexible solution procedures (Doerr & Zangor, 2000). In addition, Farrel (1996) found that students using graphing calculators had greater perseverance and focus in trying to understand the problem conceptually rather than simply focusing on the computation. In sum, the consensus of research reviews is that the use of graphing calculators has the potential to increase students’ achievement, understanding of function and graph concepts, problem solving strategies as well as their conceptual understanding of mathematical concepts. More importantly graphing calculators enhance students’ ability to handle complex mathematical problems and concepts.

This study was conducted in a precalculus class of which the author was the instructor. As mentioned earlier, graphing calculators have the potential to influence students’ understanding of the concept of function, which is the central focus of precalculus. The aim of the study was to examine students’ perceptions towards the adoption of the graphing calculator instructional approach in learning precalculus. The focus of the study, thus, was in exploring the students’ opinions of the ways in which the integration of the technology in the course afforded their learning. More specifically, this study addresses the following research question:

  • What are undergraduate students’ perceptions of the affordances of the graphing calculator in learning precalculus?

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