Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for…

Mathematical paradoxes often produce awe and wonder in the mathematics classroom. In this classroom episode, I share a paradoxical task, based on Simpson's Paradox, and its power as an intervention for a child diagnosed with ADHD. The Paradox leveraged his strengths to help him build understandings in proportional reasoning.

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students'…