Title: Fostering the development of abstract concepts in complex domains

Abstract: How do learners learn and develop abstract knowledge in complex domains? In this talk, I will present three completed studies and some current on-going work in which I: 1) leverage insights from various theories in psychology and cognitive science to develop empirical learning interventions to help students learn abstract concepts; 2) Employ various methodologies and integrate cutting-edge learning technologies to conduct experiments in authentic student learning environments; and 3) apply research insights to the design, test, and validation of classroom curricula and teachers’ professional development programs.

Title: Understanding learners’ challenges with fraction reasoning

Abstract: Which is bigger, 1/3 or 1/4? 11/7 or 4/3? Reasoning about the magnitudes of fractions is notoriously difficult for both children and adults. In this talk I will present findings from two studies that utilize different methodologies to explore what makes fractions so challenging. Results from these studies indicate that difficulties have many sources. Some difficulties stem from features of the fractions, such as their symbolic format and their need for units coordination. Other difficulties stem from features of the learners, such as strategy knowledge and attitudes towards mathematics. Finally, time pressure also affects learners’ performance. These factors come together to make fractions challenging for learners.