The application of the van Hiele Model in the teaching of *functions and its graphics in an intermediate algebra course and its effect in learning and attitudes of students

The purpose of this research was to prove if the application of the van Hiele Model to the teaching of functions and graphics produced a higher level of understanding of the concept and determine the effect of the Model in the attitudes of the students toward Mathematics. A level 0 was designed for the function concept and teaching strategies of functions and their graphics were designed based on the five teaching phases of the van Hiele Model.;All students took a workshop in the use of the TI-83 calculator, prior to the initiation of the treatment and had the calculator always available. Students received the treatment during a 12 hour period which is the equivalent to three weeks of class. The experimental group (n=50) received the learning experience with activities aligned with the van Hiele Model. The control group (n=49) was exposed to a traditional methodology.;In the study, a quasi experimental design with two instructors was used. Each one was randomly assigned a control and an experimental group. Before commencing the treatment, students completed an instrument of attitudes toward Mathematics designed by Dr. Elena Auzmendi. To evaluate previous knowledge in Mathematics, the results of the College Board exams were used. Both evaluations were used as covariate for the analysis of covariance ANCOVA.;Upon conclusion of the treatment, both the post test of attitudes and the third exam corresponding to the topic of functions and its graphics of the class was administered again. The analyses of covariance ANCOVA and t-tests reflected no statistically significant difference (a=0.05) before beginning the treatment. The statistic analyses of the post measurements reflected statistically significant differences (a=0.05) in learning in favor of the group impacted with the van Hiele Model. However, the utilization of the model did not produce statistically significant difference on the students' attitudes toward Mathematics except on their motivation to study Mathematics. It is concluded that the utilization of the van Hiele Model helps with the learning of functions and its graphics and motivates students to study Mathematics.