Mathematically inspired space adds a third dimension to equations

If you open a classroom door to find robots lurching drunkenly around the floor, you’ve undoubtedly walked into York University’s Experimental Mathematics Space.

The space, inspired by other science labs, was conceived of by Amenda Chow, an assistant professor in the teaching stream of the Department of Mathematics & Statistics. Chow equipped the space using a grant from York University’s Academic Innovation Fund and input from her departmental colleagues. The space contains a variety of equipment that helps students visualize mathematical concepts, including programmable robots, 3D geometric shapes, water tanks and an inverted pendulum. To learn more, click here.

Students work with small robots in the Experimental Mathematics Space

“Reflecting on my teaching and also my time as a student, I wanted to create this space to increase experiential learning opportunities in math,” Chow said.

“The space allows students to construct physical experiments based on mathematical theorems and concepts that they learn during classroom lectures. It deepens their understanding of the concepts, and it has all kinds of other benefits, too.

“Students learn to use mathematical software and tools commonly used in industry that will aid in the design and collection of the results of the experiment. They practise writing scientific and technical reports, and they work in a team-oriented environment.”

This space is available to any department member who wants to illustrate mathematics concepts and equations in a more dynamic, tactile and interactive way.

Professor Jane Heffernan, a colleague of Chow’s, has used the space for her Mathematical Modelling course. Her students programmed robots to demonstrate the classic mathematical equation for a random walk (i.e. drunkard’s path): a person moving along a straight line who has an equal probability of turning either left or right. To learn more, click here.

Professor Jane Heffernan (far right) works with students in the lab space

“The random walk is related to a lot of really important mathematical outcomes such as a normal distribution, which is actually a solution of the diffusion equation,” Heffernan said.

Her mathematical biology students will also use the space’s two connected water tanks to visualize an optimal control problem in pharmacokinetics: how an equation can ensure that you keep the concentration of a medicine flowing at a certain level – relevant to an IV drip that nurses use for hospital patients.

Heffernan recalls feeling frustrated during her own university days that science students always had laboratory activities, but math students simply sat in the classroom listening to lectures. This experimental math space addresses that frustration.

“It’s nice for math students to have an activity they can participate in,” Heffernan said.

In fact, her students were enthusiastic about the experience in the reflection pieces they submitted after their visit to the Experimental Mathematics Space.

“Instead of just thinking about a concept, I can visualize it,” wrote one student. “The lab was very interesting; we got to apply our course material,” wrote another.

According to Chow, the space helps break new ground.

“In math, the courses are traditionally lecture style,” she said. “In recent times, there has been a shift in higher education for more innovative teaching. The creation of this space addresses the need for an increase in experiential learning in mathematics.

“It gives students a more dynamic and fruitful education fitting for today and the future. This space makes math more fun, especially since math is a discipline that often makes people anxious.”

Students in the mathematics teacher education program have also used the space.

“I hope it will give these future teachers creative ideas for their own classes,” Chow said.

Looking ahead, Chow wants to enhance the functionality of the space and add more mathematically inspired pieces of equipment.

“My colleagues have a number of ideas which will help make the space as diversified as possible,” she said. “If we make good choices, it is my hope this space will be used for years to come by our math students.”

By Elaine Smith, special contributing writer to Innovatus