The New Calculus
It is well understood that today’s university students learn in vastly different ways than their predecessors of even 20 years ago. And yet one could argue that little has changed over the last century in the way we teach Calculus. At Stevens, we believe that more effective learning of Calculus and integration of this learning with engineering science, leads directly to significant improvement in early-years retention and ultimately in better understanding of engineering principles.
We have seen the immediate benefits of this new approach. Due in large part to a revolutionary new method of teaching calculus, the Schaefer School of Engineering and Science experienced a remarkable 96% retention rate among its first year students during the 2012-2013 academic year.
Introductory calculus courses now consist of diversified modules that include live and video lectures, team workshops, and the use of clickers, which provide students with a feedback mechanism. Students access the course online, using an intelligent and adaptive interface to diagnose and respond to concepts they don’t understand, thus identifying where they need to improve.
“We’ve made problem solving interactive,” says Alexei Miasnikov, Distinguished Professor and Department Director, Mathematical Sciences. “We don’t want them just to do exercises,” he says. “They have to think—we help teach students through a natural process.”
“There have been adaptive mathematics learning systems, but this is different, says Keith Sheppard, Professor and Associate Dean of Engineering and Science. The algorithm is very accurate.”
With this new approach to calculus instruction, the passing rate has already dramatically risen to 97%; students also retain a deeper understanding of mathematical principles, which they carry over and translate into advanced coursework.
“Top-notch professors are integral to this new approach,” says Michael Bruno, Feiler Chair Professor and Dean, School of Engineering and Science. “They have everything to do with our student success rates.”
The Calculus 1 and 2 course sequence includes a variety of components such as online exercises, online gateway assessments, written assignments, participation in weekly workshops; self-study projects, exams, and the use of clickers in response to in-class lectures, which indicate their understanding of essential concepts in real time.
A primary advantage of this modular approach is that the students who fail a module will be able to retake it immediately and resume learning with the rest of the class by catching up via inter-session modules. Grading is dynamic; students don’t have to wait until the end of the term to remedy areas of weakness. Likewise, in the early stages of the course, students are able to more precisely identify problems with understanding the course material, because each module is dedicated to a specific aspect of calculus and is graded independently from other parts.
“The material is more difficult now than it was when more students were failing,” says Dean Bruno. “We made the course more challenging, interesting, and relevant to why they’re here—to study engineering and science,” he says.
The unique teaching system improves the learning experience and helps students acquire a deeper understanding of mathematics, achieve mastery of the most essential calculus skills, and acquire experience in the application of calculus techniques to problems in science and engineering.
“Calculus shouldn’t be an academic obstacle,” says Miasnikov. “Our goal for the first semester is that all students will get through the course feeling proud of their achievement.”