Technology has transformed the mathematics curriculum. Instructional techniques are constantly evolving because of efforts to maximize the benefits of technology. To continue this process of enhancing the mathematics curriculum, this thesis will examine the following questions. What concepts, that are foundational to calculus, can be taught, with the assistance of the graphing calculator, at a level before calculus? How well do current precalculus textbooks incorporate these concepts? Finally, how well do practicing secondary mathematics teachers understand these concepts?
To answer the first question, several concepts foundational to calculus were identified. Next, we examined how accessible these concepts were to secondary students. Finally, the concept list was narrowed to those that have been rarely emphasized in the secondary curriculum. This paper will address seven of these concepts. The goal of identifying these concepts is to promote the integration of them before calculus to enable students to make connections between pre-calculus (any course before calculus) and calculus.
To answer the second question, twelve precalculus textbooks were examined to see how well they integrated these concepts. To accomplish this, a grading rubric was created to evaluate the textbooks. Then each textbook was reviewed and scored based on the rubric.
To answer the third question, an assessment was given to a group of forty-one secondary mathematics teachers taking part in a continuing education workshop. The assessment was given at the beginning and at the end of the workshop. This was done for two reasons. The initial assessment was given to provide general information regarding how well teachers understood the topics that we propose are foundational to calculus. The post test was administered to determine the effectiveness of the workshop.