Little is known about the variety of ways students conceptualize matrix multiplication, yet this is a fundamental part of most introductory linear algebra courses. My dissertation follows a three-paper format, with the three papers exploring conceptualizations of matrix multiplication from a variety of viewpoints. In these papers, I explore (1)…

The fields of pattern recognition and machine learning are on a fundamental quest to design systems that can learn the way humans do. One important aspect of human intelligence that has so far not been given sufficient attention is the capability of humans to express when they are certain about a decision, or when they are not. Machine learning…