"Learning to Make Mathematical Connections"
Assistant Professor Lindsey Richland has received a 5-year NSF CAREER Grant: "Learning to Make Mathematical Connections." Dr. Richland investigates cognitive development, memory and reasoning, technology, and classroom discourse.
Project Summary
This project uses a novel approach to optimizing classroom opportunities for drawing connections during problem solving by bridging cognitive science models of comparative reasoning.
A series of experiments will test six ecologically valid, practice relevant teaching strategies for supporting students' learning to draw connections from instructional comparisons. The tested strategies emerge from an integration of coding typical classroom practices of comparison internationally and cognitive scientific theory regarding what kinds of supports could facilitate students' connected thinking by reducing processing demands and drawing attention to key relationships. Upper elementary students will individually interact with videotaped classroom instruction to test the efficacy of each strategy, and a last set of studies will examine the impact of training teachers to use the most effective strategies. The instruction will focus on fraction or ratio concepts. The six tested strategies are:
- using at least one well-known representation
- making representations visible
- making compared representations visible simultaneously
- visually organizing the representations to highlight key connections
- using gestures between connected representations
- using visual imagery
Research findings will be integrated into classes taught to pre-service teacher credential students (100+ per year), and small-scale evaluations will be conducted to determine optimal strategies for disseminating to new practitioners. Many of the credential candidates become teachers in schools with high proportions of English Language Learners and underrepresented students, meaning that the research could have systemic educational implications for all of these students.
The project has the potential for broad impact on mathematics teaching in the United States. Importantly, the work does not aim to dramatically reform teaching practices, but rather to provide strategies for optimizing teachers' existing practices. International studies suggest that U.S. teachers often create high quality learning opportunities for students to draw comparisons, but the instruction of these opportunities reduces the complexity and depth of students' learning. Major changes in teaching are difficult to sustain due to the cultural nature of instructional routines. Thus, easily implementable strategies for improving student learning are more likely to have broad impact.
