ABSTRACT
If you ask most adults to describe key events in their school mathematics experiences, you are likely to hear stories about the fear of standing up in front of others while playing Around-theWorld in first grade or the tense emotions felt while taking a timed test in the third or fourth grade. If you press them further to tell you about middle school or secondary mathematics memories, they are likely to describe, in some detail, their experiences with manipulating fractions or trying to make sense of negative numbers. In many cases, people will also tell you about their algebra or geometry classes. People typically remember “algebra” as being the gatekeeper course that kept many students in their schools from moving forward to more advanced classes. They view algebra as “the study of x and y” and recall solving linear equations, factoring trinomials, and simplifying rational expressions-doing page after page of exercises and assuming that no one actually uses those skills in the real world. Similarly, they are likely to remember “geometry” as “that class where we memorized a ton of theorems and postulates and wrote two-column proofs that I never did understand.” Despite geometry involving the study of shapes, they will not recall doing anything “hands on” and, instead, only remember answering questions from a book. The release of the NCTM Standards in 2000, as well as the Common Core State Standards for Mathematics (CCSSM) in 2010, however, painted a much different picture of the study of school mathematics.
