Academic journal article Journal of Developmental Education

Ideas in Practice: Graphing Calculators in Beginning Algebra

Academic journal article Journal of Developmental Education

Ideas in Practice: Graphing Calculators in Beginning Algebra

Article excerpt

Close to 50% of students entering community colleges need developmental education (Foshay & Ferez, 2000); mathematics can be particularly challenging, both to institutions and students. According to Hall and Ponton (2005), mathematics is the subject having the strongest tie to student success in degree attainment. Affective factors, such as negative attitudes and low motivation regarding mathematics, further inhibit student success (Ferren & McCafferty, 1992). Therefore, improving student attitudes regarding mathematics is an issue of major importance in increasing pass rates in any developmental mathematics class (Miller, 2000).

The American Mathematical Association of Two-Year Colleges (AMATYC) has proposed a series of sweeping reforms intended to update both the content and pedagogy of all college mathematics courses before calculus in Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus (1995) and Beyond Crossroads: Implementing Mathematics Standards in the First Two Years of College (2006). Based on a thorough examination of the pre-i995 research on the teaching and learning of mathematics, Crossroads made compelling arguments for several changes in the teaching of collegiate mathematics, one of which proposed increasing the intelligent use of technology, including graphing calculators, to improve student comprehension and problem-solving abilities in all developmental and early transfer-level mathematics courses.

Research on the use of graphing calculators in mathematics classes is mixed: Many articles give wonderful advice on how to use the graphing calculator to teach a specific concept, but significantly fewer articles report studies which compare the success rates of the traditional approach to teaching algebra versus the graphingcalculator-based approach to teaching algebra.

Articles by authors such as Darken (1995) and Akst (1995) reveal that leading figures in mathematics education have enthusiastically embraced the teaching of all levels of mathematics by using the graphing calculator. In fact, Bert Waits goes so far as to assert, "to deny college students at any level the power of computer-generated numerical and graphical visualization today is academic misconduct" (Akst, 1995, p. 19). Moreover, "several recent research reports addressing this issue of the relationship between graphics calculator use by secondary or early college students and their understanding of functions...are nearly unanimous in their claim that benefits can be derived from appropriate graphics calculator use" (Wilson & Krapfl, 1994, p. 256). The authors went on to cite several studies supporting the use of graphing calculators to improve students' confidence and overall attitudes regarding mathematics. Unavailable at that time, however, was the observation from Goos, Galbraith, Renshaw, and Geiger (2000) that the active inquiry, calculator-based classroom must be implemented with great care.

Placing graphics calculators in the hands of students gives them the power and freedom to explore mathematical territory that may be unfamiliar to the teacher; and for many teachers, this challenge to their mathematical expertise and authority is something to be avoided rather than embraced. (p. 318)

AMATYC's 1995 Crossroads publication set forth three sets of curriculum and pedagogy standards for the teaching of introductory college-level mathematics: (a) Standards for Intellectual Development, (b) Standards for Content, and (c) Standards for Pedagogy. The Standards for Intellectual Development and the Standards for Pedagogy both advocate the use of technology, as well as the use of modeling and multiple approaches, in working with mathematics.

Graphing calculators provide a means of concrete imagery that gives the student new control over her learning environment and over the pace of that learning process. It relieves the need to emphasize symbolic manipulation and computational skills and supports an active exploration process of learning and understanding the concepts behind the mathematics. …

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