Graphing Calculators Aren't Just for High School Students.

ing the learning and teaching of mathematics. Students can view and manipulate graphs of functions in a matter of seconds. Such features as "plot," "graph," "trace," and "zoom" offer opportunities for users to develop an understanding of the terms variable and function. According to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), these concepts are vital aspects of the middle school curriculum. According to the standards document, "[A]n ideal 5-8 mathematics curriculum would expand students' knowledge of numbers, . . . patterns and functions, and the fundamental concepts of algebra" (pp. 65-66). In addition, "[Technology, including calculators, computers, and videos, should be used when appropriate" (p. 67). It stands to reason that tools to aid in understanding such concepts as variable and function, specifically graphing calculators, should not be reserved for high school juniors and seniors. This article discusses the use of graphing calculators by students of middle school age in an enrichment program for academically able, but ecoIAIa AhcAItlufl nomically disadvantaged, students. wit? UMdCI "vil jhe exercises described helped stuCOIif idfiflCG dents develop an understanding . about variable and function. Stu?rOW III OUT dents were actively engaged in ciurlante problem solving that involved SlUUeillS hands-on, real-life activities. In this program, students worked with scientific calculators to aid in constructing tables representing relationships before they were introduced to the graphing calculator. Table-building activities were developed in a problem-solving situation in which the students investigated relationships that evolved from specific problems. After building tables, students approached the same or similar problems from a graphical point of view by hand plotting the pairs of numbers found in the table. According to Leitzel and Osborne (1985), this hand-plotting activity reinforces the concept of a graph's being a collection of points generated by the function. Table building naturally led to the concept of variable and was used as a device to create an algebraic expression that enabled the student to extend the table. Experiences using a computer spreadsheet in more extensive table building added to these students' concept and intuition of number sense. By the time the TI-81 graphing calculator was introduced, the students were proficient at building tables. The Curriculum and Evaluation Standards (NCTM 1989) advocates "[b]ecoming confident in one's own ability" (p. 6). We observed this confidence in our students as they made some decisions about the mathematics they were doing. For example, students were given the task of setting the parameters of the graph. When asked, they gave reasonable suggestions for the scaling of the axes. At times it was necessary to extend the #-axis to view the | function for larger values of x. With the graphing calculas tor, changes could be made without losing data or te| diously redrawing the axes. The students seemed to be5 come more assertive in their engagement with | mathematics, and they eagerly offered suggestions and | explanations for the changes. g