Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that promote a conceptually indexed, broad-based foundation of mathematics knowledge for teaching which encompasses the establishment and strengthening of mathematical connections. The purpose of this concurrent exploratory mixed methods study was to examine prospective middle grades teachers' mathematics knowledge for teaching geometry and the connections made while completing open and closed card sort tasks meant to probe mathematical connections. Although prospective middle grades teachers' mathematics knowledge for teaching geometry was below average, they were able to make over 280 mathematical connections during the card sort tasks. Curricular connections made had a statistically significant positive impact on mathematics knowledge for teaching geometry.