Geometry in the Common Core State Standards
Summary: The Common Core State Standards describe an approach to geometry that is both new and old. It is new in the sense that it bases geometric reasoning on the fundamental concept of a transformation, rather than on some version of Euclid’s axioms. It is old in the sense that these transformations are essentially just the intuitive backing behind notions such as Euclid’s principle of superposition. Thus, for example, they allow for the resurrection of that notion in defining congruence—two figures are congruent if one can be superimposed on another—while providing a rigorous foundation for that definition. Thus they allow a geometry course to bypass the long dry march through intuitively obvious statements that characterize traditional courses, while providing a stronger backbone of reasoning to more recent reform style courses. In this presentation I will describe the approach and give some examples of its affordances in curriculum.
Duration: 60 minutes
Format: Online seminar via Zoom web meeting software with questions and discussion. Detailed instructions for joining the seminar will be emailed to registered participants.
Bill McCallum, co-founder and CEO of Illustrative Mathematics, is a University Distinguished Professor Emeritus of Mathematics at the University of Arizona. He has worked both in mathematics research, in the areas of number theory and arithmetical algebraic geometry, and in mathematics education, writing textbooks and advising researchers and policy makers. He is a founding member of the Harvard Calculus Consortium and lead author of its college algebra and multivariable calculus texts. In 2009–2010 he was one of the lead writers for the Common Core State Standards in Mathematics. He holds a Ph. D. in Mathematics from Harvard University and a B.Sc. from the University of New South Wales.