Rebecca Borowski

Number lines have become ubiquitous in elementary classrooms. The phrase “number line” appears in the Common Core State Standards for Mathematics 34 times and appears in the standards for every grade from second through high school; it appears in seven different strands and has its own glossary entry. Yet what, exactly, is a number line? This representation can be used in many different ways, and the assumptions underlying its use are rarely made explicit. In this presentation, I will address how three big ideas ways students learn to count and conceptualize of discrete quantities, how they learn to measure, and how they construct notions of continuous quantity are intertwined in understanding students conceptions of this representation. I will share data from a study which employed teaching experiment methodology to analyze four fifth-grade students’ conceptions of number lines over the course of 12 40-minute teaching episodes and will share initial findings
which indicate students’ understanding of this representation is complex, multi-faceted, and worthy of continued study.