Technology and Mathematics

Incorporating technology into the classroom, especially the mathematics classroom, can be a difficult task. Many technologies that are available tend to be much too expensive to warrant their use. The SmartBoard, for example, is far too limited in its capabilities to produce relevant in-class activities to merit its purchase. Therefore, in considering technologies relevant to the mathematics classroom, the key appears to be looking for what’s inexpensive and readily available.
The unit that we’ll be exploring as we attempt to incorporate technology will revolve around the use of a basic linear equation of the form y = mx+b. The goal in using technology with this topic will revolve around manipulating equation data to demonstrate for students in real-time how changing different variables of the basic equation translates into changes of the graphical representation of the equation. This will primarily be done using both a projector, access to the internet, and a web manipulative program. Web manipulatives are available through the internet and can commonly be found through shareware. A simplistic program will suffice for manipulation of variables and demonstrating in real-time what different variable changes will look like. For instance, if we were to manipulate the “b” variable in our equation and made it larger, we could demonstrate for our students how the line shifts vertically along the y-axis of our graph. Likewise, if we make the “m” variable in our equation negative, students will be able to see that the graphic representation of the line is reflected across the y-axis. Once students have been allowed to watch these real-time changes of variables, then we can switch our focus to a traditional whiteboard for the duration of the lesson. In my mind, this is where a SmartBoard could come into play, if one was available. However, since I cannot truly justify the cost of a SmartBoard when a traditional whiteboard will suffice, there is simply no utility in purchasing one. Students can demonstrate their knowledge of variable manipulation on a whiteboard, which will sufficiently wrap up the use of technology for this particular topic.
It should be noted that the use of a web manipulative may not be flawless in its design. Relying on technology at any point can cause major slowdowns during class lectures due to technology failures that can occur. For instance, it is entirely possible, (and maybe even probable,) that a shareware program would not work as well as one might hope. It will be important to test all programs before using them in the classroom. In addition, it is important to make sure that the sources from which shareware is downloaded are reliable. It would not be beneficial to the classroom if the shareware program being used contained a virus that damaged the classroom computer. It is also possible that the projector may fail, in which case, the entire planning and preparation revolving around the proposed demonstration was for naught. After all, how helpful is a visual demonstration without the visual. Because technology failures can, (and in so many case are likely,) to happen, it is important to plan for such failures by preparing for the worst. If a projector did happen to fail, or a program did not run as planned, the teacher would more than likely need to resort to the use of a traditional whiteboard to demonstrate how manipulating different variables would look graphically.
In the end, technology is a double-edged sword. Relying on its use is an excellent way to save time. Demonstrating numerous different ways that a line can be affected by changes in variables would be a much slower process using a whiteboard. By using web manipulators and a projector, a teacher could demonstrate all the major graphical changes of a linear equation in only a fraction of the time. However, the danger that technology may not work will always loom. But when you consider that using a whiteboard takes the same amount of time whether or not technology is used, it does not make sense to avoid its use. If it works, great; you have just saved precious class time. If it doesn’t work, class time is not truly lost; it is just converted to a slower activity.