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# Visualizing Mathematical Ideas With Technologies (page 2)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

### Visualizing Formulas With Graphing Calculators (by Fran Arbaugh)

The National Council of Teachers of Mathematics (NCTM) recommends that mathematics instruction at all grades enable students to create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena (NCTM, 2000, p. 360). Handheld graphing calculators (such as those made by Casio, Hewlett-Packard, and Texas Instruments) are portable tools that students can use in the classroom or at home to support their mathematical sense making.

Students often have difficulty distinguishing important features of functional relationships. For instance, to build understanding of linear relationships, students can use different representations, generated by the graphing calculator, to make connections between what is happening contextually, numerically, graphically, and symbolically for a particular mathematical relationship.

Students using a graphing calculator can easily move between the symbolic, graphical, and numeric representations of the two functions. They can trace along both functions to find (x, y) values graphically. They can then compare those values to the (x, y) pairs in the table. Students can find x and y intercepts on the graph and table and discuss how to manipulate the symbolic representation to find the same information.

Research indicates that the use of graphing calculators has a positive influence on students’ understanding of mathematics (Ruthven, 1990). In addition, Dunham and Dick (1994) report that students who use graphing calculators are more flexible problem solvers, are more persistent when faced with a new problem situation, and are highly engaged in the act of problem solving. As more and more mathematics textbooks incorporate the use of a graphing calculator in learning and teaching high school mathematics, more research needs to be conducted on the impact of this technology on student understanding.