Vertically Connecting Precalculus and Calculus with Middle School Mathematics

Abstract

Middle grades mathematics teachers have a unique role in the education of schoolchildren, helping students make the connections between the foundational concepts of elementary mathematics and the more sophisticated skills and understanding required in secondary mathematics. The University of Texas at Arlingtonhas designed and implemented two capstone mathematical content courses for the pre-service middle school teachers to establish the connections. The courses are titled Precalculus for Mid-level Mathematics Teachers and Calculus for Mid-level Mathematics Teachers. Each course is designed to meet the content, pedagogy, and instructional goals of The Mathematical Education of Teachers [2] recommendations for middle grades teachers, and the certification requirements laid out by the state of Texas. Pre-service teachers enroll in the sequence of courses after completing all other mathematics requirements for their degree, which consist of elementary statistics and college algebra, and a three course sequence for elementary and middle grades teachers focusing on, respectively, number and operation, geometry, and data and modeling. Pre-service teachers complete the precalculus and calculus sequence in the two semesters before taking their middle level state content certification exam (the Texas Examination of Educator Standards in Mathematics 4–8) and pedagogy certification exam (Pedagogy and Professional Responsibility 4–8). The two courses interweave key mathematical concepts with elements designed to aid in understanding student thinking, in particular, middle school students. The courses include collaborative activities, daily discussion and questions connecting the college level mathematics topics with school mathematics (often using excerpts from middle school mathematics curricula), reading and viewing of middle school case studies, and a final project.