Children learn mathematics better when allowed to use their hands to gesture—whether gesturing spontaneously or instructed to produce specific gestures (Broaders et al., 2007; Cook & Goldin-Meadow, 2006). One proposed mechanism for why gesturing enhances learning is that it lightens cognitive load. In this dissertation, I use a measure of parasympathetic activity (respiratory sinus arrhythmia) to infer changes in cognitive load throughout the learning process. Using this unobtrusive method, I investigate differences in explicit understanding of math equivalence and implicit knowledge reflected in gesture-speech mismatches (chapter 1), differences in cognitive load during spontaneous versus instructed gesture (chapter 2), and effects of instructed gesture on learning for children with varying levels of cognitive load imposed by anxious thoughts about math (chapter 3). In my final chapter I examine parasympathetic activity while children solve problems in order to identify potential differences in cognitive processing between children who learn a mathematical concept and those whose knowledge stays the same over time (chapter 4). My most intriguing findings suggest that gesture-speech mismatch is a person-level characteristic, as opposed to a problem-level state; that gesture instruction is particularly beneficial for children with higher levels of math anxiety; and that there is a parasympathetic signature of learning that sticks and remains stable over time, compared to learning that fades.