Wellelsey's Oscar Fernandez Says It’s Time to Change the Way Calculus Is Taught in U.S. Classrooms
The United States lags behind the rest of the developed world when it comes to math competency. Though there are many things that may be driving this national math crisis, Oscar Fernandez, assistant professor of mathematics, says a central but often overlooked driver is the way mathematics is taught.
In a blog post for the Huffington Post published last week, Fernandez writes that instead of teaching in the traditional method, which involves teaching theory then application (TTA), the more effective teaching method involves teaching application then theory (ATT).
“Definition, theorem, proof, example, and, then possibly, application. This order makes a lot of sense to a mathematician, that’s how we think, but it doesn’t make a lot of sense to a student, especially a student who is learning the material for the first time,” Fernandez says.
According to Fernandez, most students who take introductory calculus courses tend to be high school students, or in their first or second year of college. “They are still in a stage in their thinking about math where it’s very much driven by the questions, ‘When am I going to use this?’ and, ‘How am I going to apply this?’ They’re looking for ways to connect the knowledge to things they already know,” he says.
This, according to Fernandez, is key, because the structure of the existing teaching method clashes with this style of inquiry. “The teacher is starting from a very abstract idea, having known what the concept is and its ramifications and its importance,” he says. “Students who are interested enough in the math can hold out until you get to the applications part and see the application; that’s where the professor makes the connection.” However, instructors risk losing students who don’t immediately grasp the concepts.
Fernandez received a grant from the Academy of Inquiry Based Learning to develop a curriculum in which the approach is to put the application portion front and center. “The idea is to flip the script,” he said. “Ask questions that are interesting and generate the math along the way, versus presenting the math all at once. In the latter approach you probably lose 80 percent of the students, some have dozed off—though not at Wellesley—and, worse, others might say, ‘I didn’t get the start, I’m not smart enough, there’s a problem with me, so I will not take another math class.’ The idea that the ‘problem is with me,’ not the presentation or the teaching style, gets internalized very quickly.” Then we have this national crisis.
“ATT keeps the real-world problem the central focus,” He wrote in his recent blog post. “Taught this way, the math discussed has a natural context and now becomes relevant.”
At Wellesley, in the classroom and beyond, he employs the ATT model, using problem-based learning to expose students to problems that require both content knowledge and critical thinking skill. He and colleague Stanley Chang, Whitehead Associate Professor of Critical Thought and associate professor of mathematics, received a three-year grant from the Mathematical Association of America to establish the Wellesley Emerging Scholars Initiative. Now in its second year, the group comprises about 10 students who meet twice a week at Harambee House to work collaboratively on challenging calculus problems.
An applied mathematician by training, Fernandez says he strives to be a spokesperson for mathematics and its applications. In the blog, he writes, “Most of us actually learn math best through direct real-world connections.” He illustrates this concept in his recently published book, Everyday Calculus: Discovering the Hidden Math All Around Us (Princeton University Press, 2014), where he shows how calculus can play a role throughout your day—determining an optimal alarm clock setting, calculating how quickly your coffee will cool, interpreting business and political news, or figuring out the best detour around a traffic jam, just to get started.
Fernandez’s work is also already impacting other communities outside of Wellesley. This fall, the United Way of Franklin County, Pa., in partnership with the Franklin County Library System, donated Everyday Calculus to that county’s public libraries. The book was selected “because of the need for materials that support financial and mathematical literacy,” said United Way of Franklin County 2013 Campaign Chair, Jim Zeger.
Read An Insider's Perspective on Our National Math Crisis on the Huffington Post.