Touchy Pinchy Integers (TPI) is a touchscreen-based learning system that uses embodied interaction to teach integers. It connects mathematical operations with intuitive touch-based gestures, and integrates two pedagogical models: walking on the number line and neutralization. Pilot studies showed that TPI improves students’ understanding of integers, by combining formal mathematics elements with interactive gestures and relatable language. In this paper, we investigate how TPI improves the understanding of integers. To examine this question, we did a qualitative study of TPI use by four students, analyzing in detail their engagement and learning outcomes. The data collected included pre and post-tests, and videos of interviews. Based on an interpretation of the data using the conceptual blending theoretical framework from cognitive science, we argue that actions based on TPI allows students to blend different mathematical and pedagogical elements. This blending process leads to a clearer understanding of integers and their operations, compared to text-based learning of rules. Our analysis demonstrates the use of conceptual blending as a framework for designing and analyzing embodied (and possibly other) learning technologies, particularly for learning complex concepts, which require students to integrate multiple cognitive and conceptual elements.