A Mind for the Abstract
Bernadette Tutinas does the math
Bernadette Tutinas has a mind for the abstract. It’s one thing the professor wishes people realized about math after high school—you get to forget what you know and imagine what could be possible. Like with linear algebra, one of her favorite classes to teach.
“It’s totally different from calculus,” she said. “You have to start thinking about things you can’t see. You can’t draw them, you can’t visualize them, you’re working in your head, and it’s a milestone for students.”
Another example is non-Euclidean geometry (which, basically, means geometry that doesn’t exist on a flat plane). “We throw away all of the geometry from high school, and say, OK, that’s just a theory. There are other possibilities for describing the physical world; you can’t imagine them because your mind is set in the Euclidean world you think you live in,” she said. “We would throw away all the presumptions and rebuild possibilities for geometry. It’s so hard and so challenging because you are trying to think of things that are in conflict with what you think you see, and that, of course, is always tons of fun to teach.”
Tutinas, who retired as a mathematics professor after 37 years at Goucher, also had tangible methods in the classroom. In some courses, she said, “we literally played. We used blocks, toothpicks, and gummy candies to build things, and dominoes, cords, and ribbons, all to make an idea more concrete. Those were really the favorite courses for a lot of students, and I loved teaching them.”
While the math major in its current form will no longer be offered to new students at the college, Tutinas points out the mathematics program at Goucher has always evolved and embraced the future.
“The mathematics major went through many changes during my years at Goucher, but one thing that was constant was the ability of the department to adapt its curriculum to the needs of the student body,” she said.
In the early days of her career, the technology consisted of chalk and a blackboard. Very quickly, the program began to use computers in mathematics instruction, starting with exploratory computer labs for calculus in the 1990s and continuing to real-world data analytics projects in calculus and other courses now. In fact, “data analytics” is now an area all students are required to achieve proficiency in, through a two-course sequence that includes an elective or exploration course.
With time, almost every mathematics course incorporated software for computation and visualization, as well as different ways of learning. “The variety of pedagogical techniques utilized by Goucher mathematicians is staggering, including every type of active learning, flipped classroom, inquiry-based learning, capstone-research experiences for all majors, and more,” Tutinas said. “We did not hesitate to discard components that seemed dated and to add ones that were more modern.”
She added, “I don’t think we realized how brave and versatile we were in revising our curriculum until we compared it to other colleges. In fact, I remember someone from another college commenting, ‘Does your department let you try such ideas?’ and responding, ‘Our department expects us to try such ideas.’”
Tutinas is, of course, sad about the discontinuation of the mathematics major, especially when considering all the students who have gone on to satisfying careers both in and out of the field. She knows, however, how hardy her fellow professors are. “Though nothing will replace the pure joy of doing mathematics,” she said, “my former colleagues’ initiative to introduce a data science major is another example of the resilience of mathematicians. For this, I salute them.”