Kyeong-Hah Roh

My research examines how undergraduate students understand advanced mathematical concepts, definitions, propositions, and proofs. My work began with students' conceptions of calculus, and gradually expanded as questions arising from one study led to the next. Research on sequence convergence led me to examine rigorous definitions, quantification, and dependence and independence among quantified variables; these questions led to studies of multiply quantified and conditional propositions; and this work, in turn, led to an investigation of how students interpret logical relationships and read and evaluate mathematical arguments and (dis)proofs. 

Major strands of this research program include:

• Students' images of the limit concept and their interpretations of rigorous definitions
• Quantification and dependence/independence among variables in mathematical definitions and propositions
• Coordinating mathematical registers: The VALLS framework
• Comprehension and evaluation of mathematical arguments and proofs
• Logical consistency and proof competency

This research program is grounded in the view that intuitive, visual, and formal thinking are different but complementary ways of engaging with advanced mathematics. I do not view intuitive or informal thinking as an early stage that should eventually be replaced by formal reasoning. Intuition remains important even in sophisticated mathematical activity, while formal reasoning is essential when mathematical situations and purposes call for it. From this perspective, my research investigates how students develop these different ways of thinking and learn to draw on them appropriately as they conceptualize mathematical ideas, interpret definitions and propositions, and engage with mathematical arguments and proofs.