In our modern society, the use of technology is prolific, and the classroom is no exception. For many years, teachers have utilized various conveyance technologies (i.e. PowerPoint, document cameras, interactive boards) in order to present lessons and instructive materials. Less common, however is the use of a variety of mathematical action technologies, and even rarer still, the effective use of such technologies.
As defined in the text Focus in High School Mathematics, mathematical action technologies include those which can complete mathematical tasks by responding to user input. Examples include calculators, computer simulations, and dynamic geometry environments. While it is evident that technology such as the calculator has become common place in math classrooms, other math technology is used more rarely.
The authors of Focus in High School Mathematics highlight the importance of making math technology more than a task servant. That is, math technology should be more than a means by which to mindlessly crunch numbers or compute answers. Instead, these technologies should promote problem solving and strategy development, illustrate connections among concepts, and allow for reflection on the reasonableness of answers. Most importantly, math technologies should ensure mathematical fidelity (staying true to accurate math theorems and procedures) in addition to cognitive fidelity (alignment of student perception with mathematical meaning).
GeoGebra is an example of a dynamic geometry environment, allowing for the creation and manipulation of geometric figures (see previous post). GeoGebra exemplifies a meaningful math action technology because its interactive interface enables students to explore the world of geometry. A specific example is using GeoGebra to illustrate the relationship among various quadrilaterals. A teacher might have his or her students use GeoGebra to construct the following quadrilaterals: square, rectangle, and parallelogram. After ensuring the mathematical fidelity of their shapes (i.e. after the drag test a square remains a square), students can manipulate their shapes in order to uncover which shapes will form the others. This would allow a student to see the following relationship:
Alternatively, Geometer’s Sketchpad is a licensed dynamic geometry environment whose conceptual layout is similar to that of GeoGebra (learn more about Geometer’s Sketchpad here). However, using Geometer’s Sketchpad is less intuitive than using GeoGebra, and functionality is more limited. A careful prescription of steps would be necessary for students to efficiently use Geometer’s Sketchpad, yet providing such steps denies students critical thinking opportunities in their attempt create legitimate geometric structures. For this reason, Geometer’s Sketchpad is a less effective math action technology than GeoGebra.
A third math action technology is the TI-Nspire CAS app. While this app includes a dynamic geometry environment with functionality similar to that found in GeoGebra, the app also encompasses a calculator, graphing tools, spreadsheets, and statistical analysis. Overall, this app is easy to use once you have gone through a built-in, self-guided tutorial. Specifically, the graphing capabilities of this app make it an effective math action technology. With only a few keystrokes, a student can graph the sine and cosine functions, then he or she can manipulate the functions to graphically see how the graph of cosine can be changed to get sine.
We have highlighted a small sample of the huge variety of math action technologies available for classroom use. Investigate to find the right one for your classroom!