Exploring the Use of STEM-Related Hands-On Instructional Activities to Support Students' Understanding of Algebra and Geometry

Through a series of three manuscripts, this dissertation explores how STEM-related hands-on instructional activities can be use to support students’ understanding of algebra and geometry. For the first manuscript, fifth-grade students participated in a digital-fabrication augmented surface area unit in which they fabricated their own rectangular prisms using computer-aided design software. Digital fabrication provided students with the opportunity to develop a conceptual understanding of surface area, as well as two problem solving strategies (Keeping Track and Seeing What’s Not Visible). For the second and third manuscripts, students experimentally derived Ampere’s Law, which relates three independent variables (number of wraps of wire, length, and electric current) to a single dependent variable (magnetic field strength generated by a solenoid). Rising eighth-grade students participated in a four-part version of the Deriving Ampere’s Law activity in which they developed intermediate models analyzing each independent variable separately before developing the final model. Pre-service mathematics teachers and pre-service science teachers participated in a holistic version of the Deriving Ampere’s Law activity in which they were asked to only derive the final model. Both the rising eighth-grade students and the pre-service teachers were able to successfully derive Ampere’s Law and their participation in the activity revealed different modeling strategies and applications of prior knowledge.