“Intentional” is how Mathematics Instructor Anthony Bosman sums up his teaching style. Bosman, a graduate student in Mathematics, teaches Single Variable Calculus I and II (Math 101 and 102) and Multivariable Calculus (Math 212), by thoughtfully preparing materials that will connect the students to the subject matter and its applications in every day life. He realizes many of his students take the course only to complete a major requirement. So for some it is their last math class at Rice–even more motivation to make each lecture engaging and expose them to the practical uses of math.
As Bosman explains in his teaching blog, “Students become invested when they see how the material they’re studying will connect with the lived experiences of those in their immediate community. Real data examples help to make this connection. Even if not fully flushed out, they indicate that the things we’re learning have a purpose. They let students know that calculus can fight crime. It’s one thing to tell students that the gradient of a function lies perpendicular to its level sets. It’s quite another to show that a crime-fighting hero can calculate the gradient of a crime density function to find the hottest crime spots. That’s right, real heroes use vector calculus.”
Bosman aspires to reignite the sense of curiosity and wonder that abounds everywhere for young children but is often missing from classrooms labeled as formal places for learning. A slight change in topic can make a big difference in interest. In his Math101 class last summer, many of the students were athletes. In his lecture on why you might use the shell method for calculating the volume of an object rather than the disk method, Bosman selected a football as the object of study. Once the disk method proved inadequate to calculate the volume of the football, Bosman transitioned to the shell method and the class was able to verify the answer on the Internet.
Student engagement: holding a class outside on a perfect spring day, sample page of "notes with holes," and using everyday objects like soda cans as case studies.
To keep students actively engaged, Bosman literally gets them out of their seats. He conducts lectures outside on beautiful days or has team problem-solving competitions in the classroom with students working at the blackboards with their teammates behind them offering assistance. Bosman conducts his classes with a conversational tone so students feel like they are co-discovering new materials. All questions are celebrated by Bosman. “Instructors crave for students to ask questions–even the ‘bad’ ones–because they reveal what aspects of the lecture the students are understanding and what ideas haven’t been communicated effectively yet.” He hands out “notes with holes” at the start of each class that have some key topics listed with plenty of space for students to add their own notes. Often his assignments give students plenty of flexibility to find a subject they are interested it in so it overlaps with their life. One challenge was to graph something cool: responses included the Rice owl mascot and a student’s favorite football team’s logo.
Homework is not over once the student turns it in; it is returned so the student has the chance to make corrections and continue learning. After midterms, Bosman requires students to have a one-on-one meeting with him, which strategically increases their comfort level for future office visits. In these sessions, he encourages students to examine the areas of an exam that challenged them so they can focus on these areas for improvement. He discusses Stanford psychologist Carol Dweck’s theories on fixed and growth mind-sets to help them recognize that if they develop a growth mind-set they can develop their intelligence and learn from adversity. One of his students, who struggled early in the class, embraced this method and was one of the few with a perfect score on the final.
His students take the standard end-of-term questionnaire, but he explains, “by then, it’s too late to make changes.” So Bosman continually seeks feedback from his students in discussions, and brief surveys (some anonymous) throughout the semester, He prefers checking in on a regular basis to make sure he is in tune with this class. “If students were expected to understand everything the first time they saw it, we could simply record a lecture once and show it to all future generations of students. But this isn’t how learning works. Every classroom has a unique set of students that needs to have the content of a lecture uniquely tailored to them. It is the interplay of students asking questions and professors formulating responses that accomplishes this.”
Bosman credits Principles of Effective College Teaching as a valuable resource offered by Rice’s Center for Teaching Excellence. In addition to reviewing the literature on teaching and learning, the class challenged him to consider professors who modeled engaging teaching, such as Oliver Knill, his Harvard multivariable calculus summer course professor who started each one of his classes with a demonstration in order to form a connection between students and math.
For a class session on Halloween day, students determined the surface area of a pumpkin carved with the necessary formula. Bosman provided frosted doughnuts for calculating the surface area of the frosting–with the sweet treat as the reward for the correct answer. Bosman’s intention is to bring math alive by showing how it fits into daily life, “On the last day of class, I ask the students to reflect on what they would take with them from the course. One responded, ‘I’ll never eat a doughnut again without thinking of double integrals.’ Mission accomplished.”
Halloween Class Fun: Calculating the surface area of a pumpkin and of a doughnut to find out how much frosting there is on it.