TECHNOLOGY INTEGRATION IN PROBLEM SOLVING
Technology should be used to “amplify the mathematics,” bring out the mathematics concepts to the forefront, using specific affordances. Specific opportunities that technology rich mathematics environments afford teachers and students are the abilities to: (a) build representational fluency by making connections among multiple representations; (b) experiment and test out conjectures which efficiently develop reasoning and proof; and (c) facilitate the communication of mathematical ideas through problem solving (Suh, 2010).
In the handshake applet below, we see how one can employ technology to enhance the understanding of the solution approaches to the handshake problem. We will now describe an applet that has been custom created that can be employed as a tool to discover the associated pattern. A technology tool is also helpful to generalize a pattern observed for larger numbers.
Let us consider seven members shaking hands with each other. The technology tool allows students to enter the number seven for the “number of people” and as they proceed to solve for the handshakes, the tool can help prompt the steps in the process. For instance, the illustration below shows that the first person has performed six handshakes (denoted by yellow bold lines), and the last one by red bold line. Note that besides a visual confirmation of the handshakes on the left, the number of handshakes is recorded as circles in the center and also as a part of the lower row in the 6 x 7 rectangle shown in the right.
As the student continues to navigate through the process, one can obtain intermediate steps like the one shown below that helps the student to make a connection between the representations and guess a growing pattern. Eventually, as the students go through the process, they would observe not only the connections but also build a representation that makes sense algebraically. The final step is shown below:
For more practice with the technology tool, the students may be encouraged to visit: http://completecenter.gmu.edu/java/handshake/index.html