The drastic increase in the use of technology in our everyday lives over the past decade has altered our habits and interactions significantly. As with many changes throughout history, our adaptation in the math classroom seems to be lagging behind the rest of society. We continue to limit the impact of technology on student learning by continually treating the classroom as a secure testing site! The potential of graphing calculators to enhance and extend students’ conceptual understanding is seldom realized if they are not used appropriately. Standard for Mathematical Practice 5 implores us to consider all available tools.
Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
Using a graphing calculator for mere computation and generating an occasional graph to be copied onto a student paper does not provide any insight into the underlying mathematics of a classroom task! So what are appropriate uses of graphing calculator technology? Among other reasons, graphing calculator technology should be used to
- extend beyond what could be done without technology,
- make connections among concepts as well as to real world phenomena,
- and incorporate multiple representations.
Why do we buy tools? Besides Father’s Day gifts, we get a tool when we need to perform a task that could not be accomplished without it. A graphing calculator allows us to dynamically repeat a process multiple times within a short period in order to look for patterns or repeated reasoning. Here is one such example.
Determine the effect on the graph of f(x) by replacing it with g(x)=f(x+c).
The calculator allows students to explore what happens by changing the value of c, as well as confirm their conjecture by testing it with different functions f. This process would take an impractical amount of time if students had to graph each individual case separately. Even more powerful, using a dynamic calculator such as Desmos, allows students to visualize these changes live. (Click each image for samples.)
Capitalizing on Media
Our access to digital media continues to increase daily. From photographs to videos to live streams, students’ ability to not only access media, but create it as well, has added new ways of engaging students in their own learning. In its simplest form, students can explore the key features of a function, by trying to generate a graph that matches a structure in a photograph. In minutes, a student can import a picture from their phone or the web into a graphing utility to determine the effects of changing the coefficients of the equation.
Understanding the connection between verbal, numerical, algebraic, and graphical representations of a concept will enhance student’s understanding and their willingness to tackle novel problems. Looking at different forms of a quadratic function, for instance, gives meaning to the structure of each representation.
In what ways do you encourage students to make decisions about the tools they use, an more importantly, when it is appropriate to use those tools?