At a recent mathematics conference, Embry-Riddle Aeronautical University faculty member Matthew Brenneman presented a method of teaching statistics, his specialty. His method, however — which emphasizes the logic of the subject versus the steps students are taught to produce a certain answer — could be applied more generally to most empirical sciences.

“Many teachers have been trained to teach facts or specific concepts or certain techniques very well, but they’re not able to convey the bigger picture,” said Brenneman. “As a consequence, students don’t understand why they’re learning all these little factoids and learning objectives, or how they all fit together.”

Brenneman said his method, which is the basis of a book he wrote, titled “Intro Stats Done Right,” challenges the idea that starting with small building blocks such as definitions and facts is effective for generating a higher level of understanding.

“My work challenges that notion for teaching the empirical sciences,” he said.

His method, which he calls “QED” (Question, Explain, Do), focuses on the rational development of the logic underlying a subject. The principles of his framework proceed in order from the question, “Why are we doing this?” to the explanation of, “How does this work?” Then, the “do” part of the process involves learning the tools of statistics, such as notation, symbols, interpretations and software commands to apply the logic of statistics to real-world data.

Matthew Brenneman headshot.
Matthew Brenneman’s method is called “QED” (Question, Explain, Do), and it focuses on the rational development of logic underlying a subject. (Photo: Matthew Brenneman)

Dr. Hong Liu, a professor of Mathematics who has developed strategies to enhance problem-solving skills and STEM education, gave the following testimonial about Brenneman’s book:

“Outstanding textbook,” he said. “It reads like a story. I highly recommend it and will probably use parts of it in my data science class.”

Liu said he appreciates that Brenneman’s method motivates students “to actively seek their own answers and find their own methods to solve problems, instead of passively listening to the teacher tell them what to do and how to do it.”

“All knowledge is valuable, but it’s not all equally valuable,” said Liu. “Transferable knowledge is much more valuable than what students can find from Google or ChatGPT.”

Brenneman was a researcher earlier in his career and found that many students, even at the graduate level, did not have a firm grasp on basic statistics. As an instructor, he found teaching statistics difficult, so he began focusing on what helped him understand as a student. Soon, he realized that he wanted to go beyond superficial instruction of the “steps” of statistical problem-solving to focus, instead, on core principles, which brought him to QED.

“With this framework, I feel my students get the gist of how statistics works much better and much more easily than with the conventional style of teaching,” Brenneman said.

Dr. Jayathi Raghavan, chair of the Department of Mathematics, said she thought Brenneman’s method would be especially effective in a business statistics class, where students are interested in the application of statistics in their discipline, and that it could be useful in other subjects, as well.

“In general, the QED approach is good to motivate the students to learn,” said Raghavan. “Students are much more eager to learn when they understand the reason for what they are doing, and it will help them retain what they learn much longer.”