University rethinks calculus instruction
October 7, 2015Tweet
When it comes to teaching calculus, Binghamton University could have been compared to most other campuses around the country – until now, that is. Recent changes to the way the campus prepares students in the challenging subject could soon be a model for others to follow.
The biggest issue observed by both calculus instructors and those who teach courses where calculus is a required skill is this: students often arrive on campus without the pre-calculus skills required to succeed.
“Some students need more background and to fill holes in their background,” said William Kazmierczak, hired as director of calculus in 2014. “It’s not the calculus they necessarily have trouble with, but rather the pre-calculus and the pre-calculs skills needed to solve calculus problems. They’re missing steps from pre-calc to calc and that gets huge later on when they don’t have that foundation.”
Since Kazmierczak came on board, a pilot program has been expanded so that all beginning calculus classes are now flipped, using technology to push introductory material to students, freeing their class time for coached, group sessions and active learning. Improvement in student learning was seen, but that was just the beginning.
“We had already made significant progress with the calculus pathway,” said Donald Loewen, vice provost for undergraduate education and enrollment. “But we wanted to think about how to segment classes a bit more to allow students to catch up if they get behind – to give them a softer landing you might say.”
The softer landing comes with an easier entry. “What we’ve done is taken Calc 1 and stretched it out over a semester and a half instead of a semester,” said Kazmierczak. “We’ve created a two-credit course that students who need it can take their first seven weeks, called Introduction to Calculus (223).
Overall, Calc 1 and Calc 2 have been segmented into five modules, with an additional two credits to what had formerly been two 4-credit classes. In the fall and the spring, calculus has been broken into two 2-credit modules. Once the pattern is established, it becomes a continuous cycle.
“One advantage,” said Loewen, “is that it resolves the dilemma of having to choose between putting students into a four-credit pre-calc class that might be more than they need, or a Calc 1 course that they might not be ready for. Either option could threaten their academic success. Engineering students in particular could get behind schedule.”
The result is better initial placement. “We’re placing students at the level that’s appropriate for them, not directly into the deep end when they are not prepared,” Loewen said. “Previously, a student might have struggled for the entire semester with poor grades – or withdrawn – and wasted four credits in their schedule, putting them further behind.”
The new path is to help students who aren’t fully prepared to get up to speed with two credits in Introduction to Calc, then shift in the second half of the semester to differential calculus (224), which used to be the first half of Calc 1. In this scenario, students who fall behind and withdraw are only withdrawing from two credits and we’re staffing the same course a few weeks later. There are lots more opportunities to get back on track after falling behind, Kazmierczak said.
“Students will be two credits behind for the spring semester, but they have options,” Loewen said. “They can take two credits in the Winter Session (225) and be back on track for 226 and 227 (Calc 2) in the spring.”
“But students don’t have to take the Winter Session course to stay caught up,” Kazmierczak added. “They can catch up in the fall the next year if they want, since we’ve coordinated with departments across the University to make sure that they’ll know enough calculus to succeed in their other courses, whether it’s engineering, physics, chemistry or economics.”
“The real credit here is to Bill and to the Math Department for their willingness to work with departments across campus,” Loewen said. “This new path provides students what they need to be successful at any particular point in their semester by aligning the calculus modules for smooth forward progress or a chance to catch up if needed.”
“We didn’t really have to ‘sell’ this model to colleagues on campus when explaining the concept,” Loewen said. “Everyone realized it made sense and said, ‘How can we make this happen because the benefit to the students is so obvious. The sell was not particularly difficult, but the execution was complicated.”
Scheduling of the new modules has been a massive undertaking, requiring a dedicated block of rooms, additional instructors and intricate logistics. Amber Stallman, associate director for student records; Michelle Ponczek, director of Course Building and Academic Space Management; Kathy Brunt, Harpur assistant dean for academic affairs; and Anton Schick and the Math Department have all worked to make this model work, Loewen said.
In addition to creating a different calculus path for students, the placement exam given during Orientation was used a bit differently for placement by Kazmierczak. “We’ve kept it consistent with the data from prior exams, but I keep track of how the students do after they take the placement exam and use that to help us get the fewest students doing poorly or withdrawing,” he said.
“We’ve had people come in and meet with the Math Department and say this is pretty innovative – a broad new initiative where we have enhanced the instructor training model and given them a chance to be part of a very different approach. We hope that will be huge opportunities for the grad students doing this. Plus we’re using the flipped model.
“Down the road, we have the potential to be ‘the place that teaches calculus well,’” Loewen said.