7. Advancing STEM Education Through TEMP: Geometric Probabilities

In the preceding chapters, the computational experiment approach was used to explore different models studied at the secondary level under the assumption that these models depend on one or more parameters. In the case of algebraic/trigonometric equations it was shown that depending on the value of parameter (or parameters), different types of solutions may realize. As an algebraic/trigonometric equation with a parameter may be considered as a mathematical model the behavior of which depends on the parameter, one can assume that not only the parameter varies but, in addition, its variation may depend on random factors. Therefore, one can talk about the likelihood of the event that a solution of a certain type realizes. A geometrization of problem solving in the context of equations with parameters made possible by graphing software tools leads to the construction of regions in the space of parameters the dimension of which depends on the number of parameters involved. When parameters are chosen at random, one can interpret the corresponding likelihood by measuring regions from where parameters responsible for a certain type of solution are selected.