The UTeach teacher preparation program for students majoring in science, mathematics, and computer science has been replicated at more than 40 universities around the country. The National Academies report, Rising Above the Gathering Storm, identified UTeach as an “innovative program with the potential to significantly address science, technology, engineering, and mathematics (STEM) teacher shortages” (The UTeach Institute, 2015b, Replicating UTeach, para. 3). For all mathematics-intended UTeach majors, a content course taken within the first two years of study, usually called Functions and Modeling or Functions in Mathematics, is a required course that typically follows a second-semester calculus course. The intent of the course is to deepen preservice secondary mathematics teachers’ experiences with the mathematics that they will teach, immerse them in an inquiry-based learning environment, and develop a profound understanding of important concepts for secondary school mathematics. UTeach Arlington is one of the most successful UTeach replication sites in its cohort (The UTeach Institute, 2015a).
The UTeach curriculum materials include the course manuscript, Functions in Mathematics (Armendariz & Daniels, 2011), which is disseminated by the UTeach Institute. The materials, used by thousands of preservice secondary mathematics teachers nationwide, contain 23 lessons, each consisting of several explorations that are meant to be implemented using an inquiry-based approach. The explorations involve prospective secondary mathematics teachers in tasks that delve into topics related to functions, rates, and patterns from a viewpoint not typically encountered in other college-level mathematics courses.
After several iterations of offering the course at UT-Arlington, we began this project to enhance available materials and create new explorations for use in the course which focus specficially on further developing preservice secondary teachers’ understanding of functions versus equations, covariation, graphical connections to function patterns, and other important function concepts. The resulting 11-lesson unit, Explorations on Functions and Equations, is a collection of 13 explorations which include 38 new tasks and 55 supplemental questions added to existing explorations. Also, the project created instructor notes to the lessons in the new unit to assist mathematicians and other instructors not familiar with inquiry-based learning, active learning strategies, and questioning strategies that promote mathematical discourse.
