Dr. Kristy vanMarle studies the mathematical abilities of infants and toddlers, seeking new insights into how the human brain develops, formats, and represents concepts of quantity. Basic cognitive quantifying abilities progress into ideas of number, time, and space, and are crucial to the everyday tasks that our adult brains perform. “Babies,” Dr. vanMarle tells SyndicateMizzou, “give you a window into what kind of initial, foundational core [mathematical] capacities are there, how they get elaborated, and what kinds of experiences are necessary for different capacities to come online.”
Black holes loom large in the public imagination. Mathematical physicist Adam Helfer offers a definition: “Roughly speaking, a black hole is a region from which nothing can ever escape.” In other words, in its most simple definition (one uncomplicated, for the moment, by the nuances of scientific inquiry), it is the Alcatraz of the cosmos.
During our recent visit, Dr. Helfer, Professor of Mathematics and Adjunct Professor of Physics & Astronomy, cautions that black holes are only a portion of what he studies, but in general, he enjoys working on problems with real-world applications. Regardless of his topic, Dr. Helfer is a prime example of a scholar whose interests lie at the intersection of different fields—in this case, mathematics and physics.
Craig Kluever’s dream was born as he found himself awestruck in front of a grainy black-and-white television screen watching Apollo 11 land on the moon. He was in kindergarten. As he puts it, “that just made a big impact on me. Of course, the first thing I wanted to be was an astronaut.” Those early dreams of becoming an astronaut turned instead into a pursuit of the science behind the rockets. Today, the MU Professor of Mechanical and Aerospace Engineering works behind the scenes to solve the kind of problems involved in designing space travel—such as how to take off, how to reach a target, and, more importantly, how to return safely to Earth.
Ian Aberbach confesses that he thought about pursuing English as a major in college, but found the problems in a modern algebra class so engaging that he was drawn inescapably to mathematics instead. Taking that fork in the road has led Aberbach to a career in commutative algebra. During our interview, the math professor patiently allowed me to test the claim that “no question is a stupid question.” When asked to explain his research to the general public, Aberbach admitted that he wasn’t sure whether that was possible, referring to the highly specialized language, concepts, and theory in which his work is situated—concepts that are crucial for algebraists, but challenging for those outside of that subfield to wrap their minds around. In spite of the highly technical language, Aberbach does his best to explain his research in layperson’s terms.
Dr. vanMarle discusses the origins of our quantifying abilities with regard to our evolutionary history, and the connection between our own abilities and those of other species. The implication is that these abilities stem from a time millions of years ago when humans and other animals shared an ancestor.
The results of Dr. vanMarle and her team’s research give us new insight into how we learn math. These insights have important implications for how we teach math in the classroom, and Dr vanMarle is optimistic about the future of her research and improvements in future math education.
Dr. Kristy vanMarle tells Syndicate Mizzou about her entrance into developmental cognition, and her early experience in lab research with infants.
Dr. vanMarle explains some of the philosophical questions related to studying math abilities in babies. She also describes the connection between her work and the field of cognitive science, and the implications of our new understandings.
Dr. vanMarle’s work in the Developmental Cognition lab uses a technique of measuring babies’ “looking time” in order to gauge their visual attention. Researchers then examine changes in visual attention over multiple trials in order to analyze babies’ ability to discriminate between stimuli. Analyzing the data gathered from this process is the key to the lab’s insights into developmental cognition and beyond.
One of Dr. Helfer’s more recent projects, working on theories of gravitational waves, involves the application of his geometry background to problems of energy.
Dr. Helfer’s goal is to pursue solutions to problems that have real world applications.
One of the courses Dr. Helfer particularly enjoys teaching is the History of Mathematics. According to the MU course description, this “includes topics in the history of mathematics from early civilizations onwards”, and the subject is explored “as an abstract discipline and as a subject which interacts with others and with practical concerns.”
In this segment, faculty members talk about how their research and creative activity contribute to better teaching, as well as the relationship between these two aspects of their work. Frequently, the two endeavors intersect, profitting both. Carmen Chicone remarks, “If you are actively involved in your subject, you’re bound to be a much better teacher.”
When asked about why they were drawn to this area of research or creative activity, MU faculty provide interesting and compelling responses. In some cases, they continued in school because the drive to learn new things was so great, because family provided a sense of identity and career direction, or because of initial interest in a related field. In other cases, they stumbled upon the field quite by accident. Regardless of the reason, the passion they hold for their work is obvious.
In the most basic definition of his field, Kluever explains that engineers apply math and science knowledge to real problems, taking existing knowledge from mathematics and the physical sciences to construct some real device or to make some system better. “What do engineers do at work?” he laughs irreverently, “they go to a lot of meetings, they work on projects, and they try to stay on budget!”
Being a mathematician in an engineering department.