{"id":731,"date":"2004-03-01T01:11:00","date_gmt":"2004-03-01T01:11:00","guid":{"rendered":"http:\/\/localhost:8888\/cite\/2016\/02\/09\/the-graphing-calculator-as-an-aid-to-teaching-algebra\/"},"modified":"2016-06-01T20:11:38","modified_gmt":"2016-06-01T20:11:38","slug":"the-graphing-calculator-as-an-aid-to-teaching-algebra","status":"publish","type":"post","link":"https:\/\/citejournal.org\/volume-4\/issue-2-04\/mathematics\/the-graphing-calculator-as-an-aid-to-teaching-algebra","title":{"rendered":"The Graphing Calculator as an Aid to Teaching Algebra"},"content":{"rendered":"
Graphing calculator technology is recommended by national standards in mathematics (National Council of Teachers of Mathematics, 2000). Even more significantly, research has shown that such technology has a positive effect on student performance (Ruthven, 1990; Smith & Shotsberger, 1997; Tolias, 1993). Reasons teachers employ the technology, however, are varied. Many teachers may not have analyzed why they use graphing calculators or how calculators can help students learn. In NCTM\u2019s Technology Standard (NCTM, 2000), several purposes for graphing calculators and other technology are discussed, including the following:<\/p>\n
Over the years, graphing calculators have become more sophisticated. One relatively recent development is the inclusion of a tutorial on the calculator to help develop skills. The Casio FX2.0 series of graphing calculators features a student tutorial for four different types of algebraic problems: linear equations, linear inequalities, simultaneous equations, and quadratic equations. This tutorial can also be installed on the FX1.0 series. Consequently, a fifth purpose for graphing calculators, facilitating the development of important skills, becomes possible. For this study, we sought to determine if the tutorial helps students learn to solve linear equations.<\/p>\n
The linear equation tutorial on the Casio FX2.0 leads students step-by-step through symbolic reasoning to solve a linear algebraic equation. In this study, students used the tutorial to help them solve linear equations during a 3-week unit in a college algebra class. The hypothesis was that this tutorial would increase confidence in doing algebra and enable better understanding of by-hand symbolic manipulation.<\/p>\n
Although the degree to which students should be required to master the skills of symbolic manipulation is often a topic of debate among educators, we were convinced both by the literature (e.g., Nathan & Kroedinger, 2000a, 2000b; NCTM, 1989, 1991, 2000; Usiskin, 1995; Waits & Demana, 1992) and the researchers\u2019 experiences that solving linear equations by hand is essential for success in algebra, provides stimuli for higher order mathematics, and helps students understand fundamental algebraic principles that serve as prerequisite skills and concepts for future courses.<\/p>\n
Previous Research<\/p>\n
Palmiter (1991) studied the use of Computer Algebra Systems (CAS) in a calculus class. Both the experimental and control groups used the same text. However, the experimental group, which used a CAS system, covered the material in 5 weeks; in contrast, the control group took 10 weeks to cover the same material. Furthermore, the experimental group significantly outscored the control group on both computational and conceptual exams; however, despite efforts to ensure the same teaching style, the difference in conceptual scores could be explained by teacher variation. Palmiter also claimed that the experimental group \u201cfaired as well\u201d as the traditional group in future classes. Further, the CAS group overall had slightly more confidence in their success in future mathematics courses, and a larger percentage of students in the experimental group indicated that they had learned more in this class than in any other mathematics class. Ninety-five percent of the experimental group claimed they would sign up for another class using a CAS system.<\/p>\n
O\u2019Callaghan (1998) studied the effects of a computer intensive algebra (CIA) system on university students in a college algebra course. CIA focused more on concepts, employing symbolic manipulators to perform most of the skills. Three of four hypotheses for greater conceptual understanding were supported, with significant gains found in the ability to model functions, interpret functions, and translate functions. No difference was found in manipulative procedures. Hembree and Dessart (1986) found that, when calculators are integrated with regular instruction, students at all achievement levels show an improved attitude toward mathematics, improved test scores in basic operations, and improved scores in problem solving.<\/p>\n
These findings address Bartow\u2019s (1983) fear that students would depend too heavily on the calculator and that their individual skills would \u201catrophy.\u201d Instead, the use of CAS allows students to generate symbolic, graphical, and numerical representations, to reason with these representations, and to improve students\u2019 work with symbols (Heid, 1997; Heid & Edwards, 2001). These results certainly support the use of technology in the classroom. However, no data have been found regarding a tutorial such as that featured in the Casio FX2.0.<\/p>\n
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The Tutorial<\/p>\n