Teachers commonly use actions-on-objects (or actions with manipulatives) to help students understand mathematical concepts. This practice is based on the assumption that performing actions on external objects facilitates learning by changing or creating new internal ideas. Gestures are abstract, representational hand movements that can also help children to learn new ideas, but they differ from actions-on-objects in a key way -- they do not require learners to directly interact with the physical environment. I explore how this key difference between actions-on-objects and gestures affects learning outcomes in a particularly challenging area of elementary school mathematics, linear measurement. In Chapter 1, I find that for children with lower prior knowledge of measurement at pre-test, gesture-based instruction is largely ineffective. By contrast, actions-on-objects are effective for both higher and lower prior knowledge participants. In Chapters 2 and 3, I replicate this interaction between prior knowledge and movement type and further probe the boundaries of this effect. I end by situating the findings within the broader literature on the efficacy of gesture in instructional contexts. From a theoretical standpoint, the results suggest that the very features that make gesture so powerful and flexible in some instructional contexts (i.e. the fact that it does not necessitate physical interaction with specific objects) might make it inaccessible to some learners.