### About Professor Beckmann

Sybilla Beckmann is a professor of mathematics at the University of Georgia who combines her background in higher mathematics with a desire to improve the teaching and learning of school mathematics. Her current research interests include mathematical cognition and the mathematical education of teachers.

Professor Beckmann was a member of the writing team of NCTM’s Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, and a member of Committee on Early Childhood Mathematics of the National Research Council. She has worked on the development of several state mathematics standards and was a member of the mathematics writing team for the Common Core State Standards for Mathematics.

She has won several awards for contributions to education, including the Josiah Meigs Distinguished Teaching Professorship, which is the highest teaching honour awarded by the University of Georgia, along with others that can be seen on her webpage.

Jointly with colleague Andrew Izsák, Beckmann is currently studying future teachers’ cognition around interrelated multiplicative topics that include division, fractions, proportional relationships, and linear functions.

### Abstract

Approaches to reasoning about quantities that vary together in a proportional relationship have often taken a "multiple-batches" perspective. In this presentation, I will discuss an additional way to approach proportional relationships, a "variable-parts" perspective. I will argue that the variable-parts perspective may be an important foundation for topics involving geometric similarity, such as slope and trigonometric relationships, as well as for other topics such as the derivative and probability. I will also present empirical results from a study of future middle grades and secondary teachers, which indicate that the variable-parts perspective is accessible and useful for generating and explaining equations for proportional relationships.

Reasoning about proportional relationships from a variable-parts perspective from MND, Stockholms universitet on Vimeo.