When the University announced earlier this year that preceptors would be subject to more stringent English proficiency standards, many undergraduates reflexively pointed to math as the department that is most often plagued by language barriers between students and instructors.
But some believe that problems associated with math education at Princeton are about a different kind of barrier. When students do not understand their instructors, they say, it is because they don't understand the international language of math.
Lack of preparation
Jeremy Wall '02, an electrical engineer who has taken MAT 104, 201 and 202, said he was not well prepared for college-level math. "But my high school was really a special case," he said, noting that he thought his instruction in high school was especially poor. Wall's school in Vermont had very low Advanced Placement test scores, and though he was at the top of his class, he did not feel well prepared for his first math class in college.
Instructors agreed with Wall's assessment that a lack of preparation in high school math can be a problem in Princeton's introductory courses.
Math graduate student Andrew Booker, who taught MAT 103 last fall, said, "Many students are not prepared for what we expect of them."
Yuri Tschinkel, a visiting professor who is originally from Germany and taught MAT 104 in the fall, took a stronger stance. He said the language barrier is not the problem when students have trouble in introductory math courses. "I don't think English is an issue at all," he said. "It might be sort of an excuse by the students."
Most students with problems have basic misunderstandings about math, Tschinkel said. "The difficulties I've seen in my class are on the very basic level — middle school or high school mathematics," he said. He also noted that students in his native Germany receive a stronger math education in high school. "Certainly students in Germany, freshmen in Germany, are better prepared," he said.
Tschinkel places much of the blame on students' preparation for college-level math. "Many students come unprepared and are shocked to discover that they are not as strong as they thought," he said.
Yi-Jen Lee, an instructor who is teaching MAT 104, agreed that language did not seem to be a problem for math students. "Most of my students don't have a problem with my English, I don't think," she said. "There are a lot of foreign teachers in the math department. Most of the native English-speaking teachers have the same problems with their students as the foreign teachers."
Math department chair Charles Fefferman took a more balanced view of the issue. "Students come to Princeton with a wide variety of math backgrounds, ranging from math anxiety to very high levels," he said in an e-mail yesterday.
Math instructor Wladimir Pribitkin agreed with Fefferman that communication was important but that preparation was also a factor. "I think [the language barrier] is a problem and obviously it's not ideal if it's difficult to understand the professor, but I honestly don't know if it's a legitimate excuse," he said.
"In general, my students are well prepared," Pribitkin added. "When a student flunks or does poorly in a math course, a lot of it stems from not being sufficiently prepared in high school."
Pribitkin said MAT 104, which he is teaching, moves faster than high school math classes and is more difficult. He said he thinks many students just need time to adjust.
Eduardo Duenez, a math graduate student who taught MAT 203, emphasized the role of early, more basic math education — as opposed to high school math preparation — in determining students' later success in more advanced math.
"Whether a person likes mathematics or not is something that is determined by early mathematic education, in elementary school or junior high," he said. "By the time [students] get to college, even if they have a sufficient background, they have a bit of an attitude problem."
The right level?
Not only the math department is involved when it comes to students' math proficiency. Economics professor Elizabeth Bogan — who often observes students' basic math skills in teaching ECO 101 and 102 — said she finds that most undergraduates are well prepared in math. "I feel when students fail their first math class at Princeton, it's because they are not placed at the right level," she said, echoing the views of some students.
Mike Cohen '02, an electrical engineer who has taken several math courses, said there is a wide gap between students who feel comfortable with math and those who do not. "In general, it seems that most math majors seem to believe that there's no problem," he said.
Wall said he believes quality of preparation in math is more varied than in other subjects. Cohen agreed and said that the quality of instruction at Princeton varies immensely too, regardless of the English skills of the teacher. "I've had some good math teachers, but there are some real losers floating around there. But some of them are fantastic," he said. Cohen also noted that the nature of advanced math makes it difficult for instructors to relate to their students' concerns. "Some of these people in math are on such a higher level than the students," he said. "To them, it's second nature."
But Fefferman said that regardless of students' preparation or instructors' English, most students perform well. "Our math students learn successfully, but it can be a struggle," he said, noting that very few students fail 100-level math. "Most students at all levels and at all schools find that math takes a lot of work."
Tschinkel agreed that most students ultimately succeed. "Students who are unprepared can catch up," he said. Most of the kinks, Tschinkel said, are worked out after the midterm. "After six weeks, after the midterm, most of them get in the habit of studying systematically," he said, explaining that students become accustomed to the demands of college courses.
Non-majors
There are explanations for students' trouble in math other than the language barrier or the quality of their high school preparation.
From Bogan's position outside the department, she sees a problem with how math instruction is designed at Princeton.
Bogan, who was originally a math major in college, said she thinks the math department is not accommodating non-majors who need to take math classes.
"I view a lot of college-level math as what used to be called service courses," she said, explaining that the math classes that are appropriate for engineers and math majors are not always appropriate for economics students or humanities majors.
"Our students come here and the vast majority are very good at math. That's how they got in, and they can do plenty of math, but not at a major level. Very few of our students want to be math majors," she said, but noted that many students need some math instruction for their own concentration. "A lot of disciplines become more quantitative," she added, "but they don't need MAT 203 or 204."
Language barriers
All of which is not to say that an instructor's level of English proficiency does not play a role in the quality of math classes at Princeton — only that there might be other factors at work as well.
Indeed, though Wall attributed some of his problems in math at Princeton to his poor preparation, he also had difficulty understanding one of his preceptors.
While most of his math instructors spoke English well, one of them was very difficult to understand.
"I either put all my attention into figuring out what she was saying, or into taking notes," he explained. "You needed to pay complete attention to what she was saying, and by the time you figured it out, you were behind."
Booker, who is a native English speaker, said his students have told him that they were relieved to find he spoke clearly. "I've been told that they're really happy that I speak English," he said.
Fefferman also acknowledged the importance of instructors' English language skills. "I think it's important for out teachers to communicate effectively in English, but I don't think we should try to hire fewer foreigners," he noted.
For her part, Bogan theorized that good communication was especially important in introductory-level classes. "In elementary courses, the ability of the instructor to speak English is very important," she said.
Cohen also explained that regardless of students' abilities, they seem to seek out math instructors who speak good English.
Even math instructors, like Booker, agree that students prefer and often choose instructors who speak English well.
But Duenez, who is not a native English speaker, said of instructors' English proficiency, "I think it has less weight than other factors."
"I think if you don't have a favorable attitude toward math, if you are predisposed against it, it's likely that small factors can provide a certain excuse to justify dislike for the subject," he said.
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