Double-Number Lines, Area Models, and 15 Years of the Common Core Standards for School Mathematics

• In Event: Mathematics Teaching: A Focus on Pedagogical and Content Knowledge

Abstract

In this paper, we examine changes in teachers’ understandings of double number lines, possibly because of the Common Core. We revisit a paper we published in 2012 focused on teachers’ understanding of the double-number line representation. Then, we compare that paper to our experiences in Summer 2024 in which teachers had no discernable issues with double-number lines. We ground our work in knowledge in pieces as well as a definition for mathematical understanding grounded in representations. We present our findings about current teachers’ understanding of double-number lines and area models for reasoning about fractions and proportions, then conclude with discussion of the implications of our noticing for teacher preparation and teacher professional learning.

Authors

• Chandra H. Orrill, Rethink Learning Labs

• Kun Wang, Rethink Learning Labs

• Rachael Eriksen Brown, Pennsylvania State University - Abington