Big Ideas of Mathematics: A Construct in Need of a Teacher-, Student-, and Family-Friendly Framework

Across multiple countries the term "big ideas" of mathematics has become a construct advocated as important for teachers' mathematical knowledge. Indeed, several policy or position statement documents about math learning in the United States (U.S.) have stated that "big ideas" of math is a crucial construct for teacher knowledge. With this study we sought to determine if there was consistency about this "big idea" construct that teachers of mathematics in the U.S. are advised to know. To this end, we conducted a content analysis of resources for U.S. teachers of preschool through grade 12. We determined that few resources defined a big idea and those that did lacked agreement with each other. Although most resources delineating big ideas cited Charles (2005) as the basis of their use of the construct, our analysis of the actual big ideas in each resource revealed inconsistent implementation of Charles' theoretical perspective. Thus, to move research and practice forward by more precisely defining and prioritizing this abstract construct we (a) clarified a definition, (b) specified five criteria, and (c) constructed a scholar- and teacher-friendly framework: The Big Ideas Framework. This framework consists of three ordinal levels to distinguish and prioritize the importance of big ideas based on relative size and power: Mighty Mega Math Ideas, Power Math Ideas, and Strong Math Ideas. Moreover, the big ideas construct has focused on Mathematical Knowledge for Teaching (MKT), whereas we urge the field to shift its theoretical perspective to value the entire construct or at least the two most powerful levels of the framework as aspects of Common Content Knowledge. In other words, we urge teachers and mathematics teacher educators to foreground Mighty Mega Math Ideas and Power Math Ideas with P-12 students and families to empower those we serve. Furthermore, given the dearth of peer-reviewed research about big ideas, we encourage a new branch of scholarship to analyze the impact of the practical recommendations we offered here.