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 scores merged with the lesson plans, which helped me search for patterns among the different lessons. Additionally, I wrote narratives of each teacher’s experiences with BBM, which became a rich source of information. Results show that BBM lessons increased higher-order thinking across all three teachers when compared with their “typical” baseline lesson. The cognitive rigor of the mathematical tasks showed especially strong growth. Additionally, students were highly engaged and active in mathematical discourse. Those BBM lessons determined to be “exemplary,” based on their extremely high PAQT scores, had several important design features in common, including strong integration between the work of art and the mathematics content, the use of Visual Thinking Strategy questions, and a cycle of problem solving. Inquiry-based pedagogical practices and the culture and climate of the classroom and school were found to be additional keys to the success of BBM lessons. Products from this study include: a set of instructions that will allow other teachers to create BBM lessons; a BBM workshop that I facilitated at the local art museum for math and art teachers from around our county; a collection of twelve BBM lessons for the museum’s library and website; and collaboration between one of the teachers and myself to design a workshop for a fall NCTM conference