A Framework for Technology-Rich Explorations - Conclusions

Antonio Quesada and Michael Todd Edwards

Through an examination of various technology-based solutions for the Two Towers Problem, we have demonstrated that the incorporation of technology blurs boundaries between various levels of mathematics instruction. Exercises originally conceived for students in advanced courses (such as calculus) may now be explored meaningfully by students in introductory settings. A spiral approach to optimization through different courses preceding calculus has the potential of improving students' understanding of modeling.

Use of dynamic geometry tools, such as CABRI Geometry II and Geometer's Sketchpad, graphing calculators, and mathematical software encourage us to re-examine the accessibility of various mathematical topics. Because technology enables students to revisit problems from different perspectives based upon the depth of their mathematical knowledge, the tools encourage students to make connections among various levels (and areas) of mathematics.