His research involves the study of how post-secondary students of mathematics and professional mathematicians learn and do mathematics. More specifically, he works in the area of the teaching, learning, and doing of mathematical proof and argumentation. He will primarily research the teaching (pedagogical strategies, curriculum development, and TA training) and learning of proof (the process of proving, student comprehension of various proof strategies such as mathematical induction) within the context of MTH 299, the introduction to proof course. Also, Shiv and his collaborators are currently working on developing and validating measures of neuro-cognitive load experienced as individuals prove mathematical statements.