Conclusion

All too often, students' first approach to mathematical objects is via an abstract representation such as a formula or an equation. In the case of parabolas, students often have to deal with their analytic definitions before they develop familiarity with many examples and develop an intuitive grasp about them. Using interactive string designs, students can build on previous or simultaneous experiences with string designs and develop familiarity with parabolas through a kinesthetic experience. At the same time, students can experiment and enjoy the inherent beauty of the designs.

Somervell, an early 20th century proponent of young children's use of string designs, emphasized the dynamic aspect of doing the designs to generate curves. She stated that certain perceptions could provide a kinesthetic, rhythmic approach to mathematics. According to her, children can get acquainted and develop pleasurable associations with these curves, so that later the mathematical treatment is seen by them as "orderly explanation of experiences long familiar" (Somervell, 1975, p. 17). With dynamical geometry programs students can now can make the string designs interactive.

Other curves can also be obtained from straight lines, such as pursuit curves, spirals, the cardioid, the nephroid, and epicycloids with three and four cusps (Somervell 1975; Millington 1996). For interactive figures of these curves see Flores (2002). In the same way that students can learn and connect many mathematical ideas when looking at string parabolas, there is a wealth of mathematical ideas they can learn with other string designs.