Calculators: From Four-Function to Graphed Function

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For decades, one question has prevailed among math teachers and researchers: Do calculators help or hinder the teaching of mathematics? In a technology research brief, the National Council for Teachers of Mathematics (NCTM) synthesizes four decades of research regarding this question. Their conclusion? Almost unanimously, research, for decades, has shown that the use of calculators in math classrooms raises student achievement. Because of the overwhelming evidence that calculators improve student achievement, the question we should be asking is how teachers can make calculator use in the classroom more effective.

An important element required for the effective use of calculators in the classroom is connecting calculator usage with mathematical reasoning. Calculators should be more than a four-function task servant. Instead, teachers can use guided lessons in order to step students through mathematical processes, employing tools such as graphing capabilities to illustrate concepts.

For example, a graphing calculator such as the TI-84 Plus can be used to illustrate the effects of manipulating constants of an equation in slope intercept form. A teacher might have a student graph the following three equations:

  • Y=2x
  • Y=5x
  • Y= (1/4)x

Using a graphing calculator, a student can visualize how changing the coefficients of x affect the slope (steepness) of a line. As an extension, a teacher might prompt students to graph equations with negative coefficients (negative slope). Similarly, students can see how adding/subtracting constants at the end of the equation affects the y-intercept. Allowing students to individually investigate slope and y-intercept enables them to personalize the teaching and discover the math principle themselves.

This activity is similar to other methods that can be used to incorporate calculators effectively in the classroom. In calculus, graphing calculators can be used to show the relationship between a function and its derivative. In order to connect this to relational understanding of this concept, a teacher could first teach how to take the derivative, explaining that the derivative is a “slope-generating function” which gives the instantaneous rate of change for any given value of x. Then, a graphing calculator can be used to graph a function and its derivative, as shown below.

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The situations described above exemplify effective use of calculators in math classrooms. As NCTM has showed us, calculators do enhance student achievement. But the new question remains: How will you commit to making calculators effective in your classroom?

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