My research interests include the study of mathematical practices such as proof and mathematical modeling at the secondary level, classroom discourse, and teachers’ use of curriculum materials. I am particularly interested in the space where these three areas intersect.
I am currently the principal investigator on the NSF DRK-12 grant: CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice (PISC). For this project, I draw on findings and artifacts from a previous 3-year study, funded by the Knowles Science Teaching Foundation, which considered the challenges of teaching proof in geometry. For this earlier study, I collected classroom and interview data before and after facilitating professional development in the areas of proof and classroom discourse. The PISC study will document the effectiveness of an intervention developed through observations made in the previous project. The design and development research study will make use of mixed methods and lesson study.
PISC Website Link: http://sites.udel.edu/math-pisc/
Mathematical modeling holds a unique place in the Common Core State Standards as the only topic that is both a Standard for Mathematical Practice and a Conceptual Category at the high school level. Implementing mathematical modeling in school mathematics is one of the more challenging aspects of CCSSM. To support this effort, I have been working with applied mathematician John A. Pelesko to facilitate professional development and develop resources for secondary classroom teachers. You can read our blog here: http://modelwithmathematics.com/
Look for NCTM’s forthcoming Annual Perspectives in Mathematics Education volume on Mathematical Modeling which will appear in Spring, 2016.
Mathematics Discourse in Secondary Classrooms
Mathematics Discourse in Secondary Classrooms (MDISC) is a case-based professional development curriculum for secondary mathematics teachers. MDISC was developed through a collaboration of mathematics educators at Michigan State University, University of Delaware, and University of Wisconsin-Milwaukee. Because there is evidence that having students articulate their ideas, explain their reasoning, and engaging in mathematical discussions improved students’ opportunities to learn, the MDISC materials focus on mathematics discourse – ways in which communication and meaning-making occur in the classroom. Read more about MDISC here: http://www.mdisc.org/
Mathematics Discourse for Secondary Classrooms will be available through Math Solutions this summer. http://mathsolutions.com/
Teachers’ Use of Curriculum Materials
Curriculum materials provided by school districts have a primary influence how teachers organize mathematics instruction. I am interested in issues related to the following research question: How do teachers learn to use and adapt impersonal curriculum materials in ways that allow them to meet their students’ needs and address multiple standards and objectives?