Focus On Active Learning Improves Drop Rate for Calculus Classes

By ALLY FRIEDMAN

A shift from rote memorization to active learning is producing measurable, positive results for students taking Calculus I.

The Fall 2019 drop/add rate fell from UCF’s historical 54% to 18-22% across all calculus courses after Professor Eduardo Teixeira, Ph.D., deployed a technique called meaningful learning theory.  The statistical majority grade also rose to an A.

Teixeira points to the course improvements as proof students are looking for more meaningful interactions with math courses.

“Math is not the art of computing things, but rather solving problems through logical reasoning,” he said. “The debate is settled. Active learning strategies are much more effective than traditional learning.”

Traditional learning teaches through memorization; homework tests ability to recall, not application. This technique results in low knowledge retention and a prevailing attitude that the class is just a hurdle on the path toward a degree, according to Teixeira. He and others believe that such a cursory experience is why students under appreciate math.

To challenge this traditional method, Teixeira and colleagues drew from the respective concepts of educational psychologists David Ausubel’s meaningful learning theory and Benjamin Bloom’s taxonomy.

Meaningful learning theory emphasizes the combination of familiar information with new information. Teixeira applies this theory in his lectures by assigning adaptive homework assignments before the lecture to give students a sense of familiarity on a subject before going into depth, thereby using it as a part of the learning process. Bloom’s taxonomy is a tiered categorization of thinking skills, ranging from lower-order to higher-order thinking. The bottom three levels of the tier compromise the facets of lower-ordered thinking: remembering, understanding, and application. The top three higher-ordered thinking skills are evaluation, analyzation and creation. By encouraging students to think with higher-ordered thinking skills, knowledge becomes more meaningful and increases the retention of information. Students must make the effort to think before making computations, rather than attempt to perform such computations with little understanding of their real purpose.

Teixeira also argues that the physiological concept of neuroplasticity plays a viable role in higher-ordered thinking. Neuroplasticity, or the ability of the brain to change its synapses and neural connections over time, is best achieved through struggle while learning new information, explained Teixeira.

He posits that engaging in higher-ordered thinking allows new knowledge to become more meaningful and more easily retained, in addition to the creation of new synapses via neuroplasticity. One of the greatest benefits of encouraging higher-ordered thinking, Teixeira continues, is that these new skills transcend beyond the scope of calculus courses.

“To be creative, think outside the box, and work collaboratively to solve a complex problem — these are necessary skills for students entering the job market,” he said. “And we have now designed calculus with that format.”

This is not Teixeira’s first experience improving mathematics education. In 2017, he was awarded the prestigious Ramanujan prize for his work forming and directing a major research group in nonlinear partial differential equations in his home country of Brazil. Continued collaboration with his colleagues to enhance other mathematics courses, including in the graduate program, is his next goal.