Goodwin College
Making Mathematics Visible Teachers can only teach as well as they understand the topic, particularly in mathematics where teachers can execute algorithms but often fail to explain the “key developmental understanding” (KDU). Simon defines a KDU as a perception of the underlying mathematical idea in various problem types, as opposed to execution of a rote procedure to solve a specific problem. A KDU is a powerful building block for seeing connections across mathematical topics and results from student activity and reflection which can only be achieved if teachers themselves internalize the KDU, employing consistent language and visual representation. Based on the works of Simon and Thanheiser, our study focuses on the ability of a pre-service online content course to develop the KDU of placevalue, a core element of the elementary mathematics. We used Thanheiser’s three components of place-value - units, relationships, and regrouping - to code teachers’ online podcasts for evidence of their ability to unite verbally, symbolically, and pictorially the KDU of placevalue. After specific instruction, about 25% of the teachers’ presentations demonstrated mastery of the KDU of place-value, leading to the conclusion that there is a high need in teacher education for emphasis and development of KDUs in mathematic principles. 109
K ati e Dela ney SCHOOL OF ED. Elementary Education
Dr . E llen C lay Faculty Mentor School of Education
Poster Session A