TECHNOLOGY INTEGRATION IN PROBLEM SOLVING
One of the essential understandings of the problem involved graphing the situation that was modeled via tabular approach or repeated subtraction method. For those students that are visual learners, a graphical approach is often a great way to engage in a conceptual understanding. The following tool provides an opportunity for students to discover and learn about a variety of important concepts such as slope and y-intercept (see Figures 6.7 and 6.8).
The technology allows the students to enhance their learning by manipulating the slope (m) and the y-intercept (b) to see when two lines intersect when there is a unique solution and when they are parallel (and not intersect) when there is no solution as illustrated below.
Figure 6.7 Learning by manipulating the slope (m) and the y-intercept (b) to see when two lines intersect with unique solution.
Figure 6.8 Learning by manipulating the slope (m) and the y-intercept (b) to see when two lines are parallel with no solution.
Such technology-enhanced learning helps students to connect to the mathematics in the problem. For example, the problem illustrated in the graphs shown may be thought of as a scenario where two people start with different amounts $10 and $6 as shown. Both lose a constant amount each day. In the first illustration, we assumed this constant amount was different, and hence, we noticed that the lines intersected and the second illustration; the amounts deducted are the same and therefore leading to the same slope for the two lines. Such important connections between algebraic reasoning in the problem make the mathematics more meaningful. Giving the flexibility to the students to manipulate the toolbar to play with values of “m” and “b” helps them to reinforce this discovery learning through technology.