Beautiful, beautiful math: using objects of art as catalysts for higher-order thinking in mathematics lessons

Thesis (Ed. D.)--University of Rochester. Margaret Warner Graduate School of Education and Human Development, 2016.
Students in the United States have historically struggled with mathematics, especially with problems that require higher-order thinking. Even struggling students, however, often show considerable interest in the arts. Unfortunately, the literature sheds almost no light on how the arts might be useful in helping students become proficient in rigorous mathematics. I created Beautiful, Beautiful Math (BBM), to both intrigue students and require them to use higher-order thinking. In BBM lessons, students interact with an object of art in order to learn mathematics. My overarching research question was: “How can objects of art be used as effective catalysts for higher-order thinking in mathematics lessons?” In this study, “higher-order mathematical thinking” was operationally defined as having students actively engaged, working and talking together, on math tasks that require high levels of Webb’s Depth of Knowledge. Three research sub-questions informed this study: 1. What do exemplary Beautiful, Beautiful Math (BBM) lessons look like? 2. To what extent do BBM lessons result in students’ higher-order thinking in mathematics? 3. What are key design features and other implementation factors that need to be in place for BBM lessons to have the desired outcomes? A constructivist learning philosophy coupled with recent cognitive psychology research informed my study. Using an action research methodology, three teachers participated in two cycles of creating BBM lessons. I collected eight sources of data: The Performance Assessment for Quality Teaching (PAQT) scores for each lesson, including a baseline lessons and two BBM lessons for each participant; video recordings of the BBM lesson implementations; lesson plans; audio recordings of planning sessions; audio recordings of post-lesson debriefs; audio recordings of my post-study interviews with the participants; student survey responses; and my researcher’s journal. I then created tables of the PAQT s