TITLE: The Mathematical Inquiry Project: Key Conceptual Themes in Entry-Level Math Courses

AUTHORS: Allison Dorko, Michael Tallman, John Paul Cook, Josiah Ireland, Michael Oehrtman, Bus Jaco

ABSTRACT: The Mathematical Inquiry Project (MIP) is a long-term collaboration of mathematics faculty across the 27 institutions of higher education in Oklahoma. To date, faculty have participated in four week-long workshops focused on identifying key conceptual themes in the following courses: quantitative reasoning, college algebra, precalculus, and calculus. A fifth workshop focused on academic success skills. All the workshops centered on connecting the conceptual themes to the MIP’s three pillars of inquiry: academic success skills, meaningful applications, and active learning. In this talk, we will report on the conceptual themes the Oklahoma faculty collectively identified and some of the mathematical tasks faculty members have developed that help students develop those conceptual ideas via the pillars of inquiry.

TITLE: Helping Entry-Level Math Students Understand Concavity

AUTHORS: Allison Dorko, John Paul Cook

ABSTRACT: Students often understand concavity in terms of "concave up like a cup, concave down like a frown." This can be helpful, but we would also like our entry-level students to understand concavity in terms of rates of change. In this talk, we will describe how we teach concavity in Math 1483 (Mathematical Functions and their Uses). We will share tasks that help students develop quantitative and covariational meanings for concavity. This talk is intended to be useful for instructors of entry-level math and calculus.