The introduction of engineering practices within the "Next Generation Science Standards" provides technology educators with opportunities to help STEM educators infuse engineering design within a core curriculum. The introduction of teaching engineering design in early elementary grades also provides opportunities to conduct research investigating how young students use engineering design as a way to solve problems. There is a need for research to assess how students experience engineering design as a pedagogical approach to learning science. This article will feature research on elementary students' cognitive strategies used during engineering-design science activities. We adopted the concurrent think-aloud (CTA) protocol analysis method to capture how students conceptualize design and enhance science learning. During the 2012-2013 school year, we video recorded 66 CTA sessions, and this study examines six of those sessions. NVivo (Version 10) was used to code each video using common cognitive strategies categorized by Halfin (1973). Research findings indicate that participants increased the amount of time spent on mathematical thinking by 34% when given a math-specific design task. Pre- and post-tests showed that participants gained significant science content knowledge. However, we also confirmed that participants struggled with applying accurate mathematical and scientific knowledge to solving the given design problem.