A number of first-year or introductory-level classes, including Math 51, Chem 31A, Econ 1A and CS 106A, with 600 students enrolled this quarter, have seen increased enrollment over the past few years, while various departments have employed a variety of tactics to keep students engaged.

Math 51 is one of the most commonly taken introductory courses, with 300 students enrolled this fall. Besides being a prerequisite for many classes, mathematics professor Rafe Mazzeo believes that the class is popular because it is crafted specifically for students who have completed the AP test in calculus.

“Unlike [students at] a lot of other colleges, people at Stanford come in with AP credit in calculus,” Mazzeo said. “However, few people have taken linear algebra. So it’s a class that puts everyone on the same playing field and evens out the disparities.”

However, instead of teaching one big lecture, the department decided to split Math 51 into seven different lectures taught by four professors. Each professor has two teaching assistants assigned to teach sections.

“We decided to keep lectures to 50 students and sections to 25,” Mazzeo said. “Students have responded really well, and speaking as a teacher, it’s more fun and more engaging to teach a class of that size.”

Mazzeo and his colleagues also meet regularly to make sure that they are on the same page in terms of teaching pace and homework.

“We coordinate because students shop around at the start of the year,” he said. “We try to have things as uniform as possible so students can switch [between lecture classes] if they need to.”

Kenji Kozai, a Math 51 TA and fourth-year graduate student in mathematics, believes that having multiple sections with different TAs is better for the students.

“Different students learn better from different teaching styles,” he said. “Having a variety of TAs to choose from makes it more likely they can find something suitable to their own learning style.”

In the Chemistry Department, enrollment in the introductory-level Chem 31A has also increased over the years, rising sharply from 192 students in 2004 to 462 this year. The class is split into two groups: morning and afternoon lectures.

“Besides lectures, we have weekly lab and discussion sections with small groups of students, outreach sections twice a week, nearly daily office hours by instructors or teaching assistants and an online question-and-answer system,” said chemistry professor Hongjie Dai. “Students are taught in these different settings to make sure that they grasp the important chemistry concepts and have mechanisms in place to give students personal attention and help when needed.”

While Math 51 and Chem 31A have chosen to subdivide the class into lecture sections, other introductory courses have chosen to teach all students together. Some of these classes, like Econ 1A and CS 106A, are popular in part because of their lecturers — both economics professor John Taylor Ph.D. ‘73 (Econ 1A) and computer science professor Mehran Sahami ’92 M.S. ’93 Ph.D. ’99 (CS 106A) have achieved “celebrity” status on campus.

Both Taylor and Sahami aim to keep class entertaining so that they can engage with all the students.

“In the lecture, we encourage questions and comments from students, now providing microphones so everyone can participate,” Taylor said. “To liven things up, we do various other things. I invite my family to join me on the stage to illustrate economic concepts and use YouTube videos to give examples of current events.”

Sahami is known for pelting his class with candy in return for questions and for using a light saber as a pointer. He draws on anecdotes and funny analogies — most recently, an extended analogy involving the Mona Lisa and a chainsaw — to demonstrate concepts in programming.

Students seem satisfied with the various accommodations the departments have chosen to take.

“I think Stanford does a pretty good job with large classes,” said Kuno Choi ’14, who is taking Math 51 and Econ 1A. “The lecture-section-homework triangle covers the material well enough.”

Ultimately, the success of these large-sized introductory classes is not so much in what tactic the professors choose to employ so much as their commitment to meeting their students’ needs. Mazzeo summed up these professors’ attitudes toward finding the best way to teach.

“You have to be continually vigilant,” he said.