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Why does my math class have so few girls?

in Caps Not Crosby/Columns/Opinions by

Why does my math class have so few girls? Why did the engineering department here have only one female professor last year? These are the types of questions many girls in S.T.E.M. at Swat tend to ask ourselves. Issues of underrepresentation of women in S.T.E.M. fields don’t start at Swat. By the time students arrive here, they have already been influenced by these disciplines’ implicit and explicit biases. It is the presence of such biases, most of which begin to heighten during middle and high school, that is constantly deterring women from pursuing computational fields, and it is imperative that institutions begin to tackle these biases head on.

In high schools across the United States, boys are dominating the higher-level classes in fields of math and applied mathematics.  Approximately 2.1 million girls and only 1.75 million boys took A.P. exams in varying subjects in 2013; however, in A.P. exams in fields of math and applied mathematics, boys outnumbered girls by strikingly large margins. Despite the fact that girls take a significantly greater percentage of all A.P. exams, boys still take more exams in all S.T.E.M.-related fields. The fact that more boys are taking these exams indicates that boys outnumber girls by a large margin in A.P. classes — high school classes usually at the highest level in any given subject — concerning S.T.E.M.-related fields.

Taking these A.P. classes in a subject will naturally increase the likelihood that a student will major in that subject in college. While some math majors at Swat do start in Math 15, it is far easier to complete the major if they come in with A.P. credit, and a student will naturally gravitate towards subjects in which they feel they possess more confidence and ability.

One of the main reasons many of the speakers cited that is keeping women out of the profession are the implicit biases — negative mental attitudes towards a group that people hold at an unconscious level.  Teachers perpetuate these biases unconsciously while teaching, and they will often go unnoticed by all until they are brought to attention. A student’s subconscious will pick up things that they do not actually know they are internalizing.  

With both information and experience in mind, I have compiled a list of suggestions for improving the ways in which institutions treat women. All schools and universities should ensure that they have 50 percent female teachers in mathematics and fields such as physics and economics which require the application of mathematics. All standardized testing involving mathematics and fields of applied mathematics must not permit test-takers to bubble in their gender until after they have already taken the test.

All students should be told two statements at the beginning of their middle school careers. The first is that brains are as malleable as plastic, and anyone has the ability to learn anything regardless of their race, class, or gender. The second is that gender plays no role in the ability for a child to learn any subject, and that the stereotypes surrounding the idea that boys are naturally better at math are 100 percent false.  

For every famous male mathematician a teacher mentions in class, teachers must also mention a female mathematician. I have heard my math teachers for years go on and on about men such as Euler, Pythagoras, and Taylor.  I have never been in a math class where the teacher mentioned the name of a famous female mathematician. Though the discoveries of the men listed above may be more relevant to the lesson than the discoveries of Hypata or Maryam Mirzakhani — the first woman to win the Fields Medal — only mentioning male names sends the message to the subconscious of females that women are lacking something instrumental to the possession of a great mathematical mind.  Simply mentioning a brilliant female mathematician will help derail this implicit bias. Elementary, middle, and high schools should have posters up in their hallways and classrooms of brilliant women in mathematics as role models for students.

Teachers and school administrators in math and fields of applied mathematics must do the following: read literature on the implicit biases that work against girls in their fields.  They must be aware of these biases so as never to reproduce or ignite them. For example, a teacher should never make the statement, “girls think differently,” or “girls show their skills in different ways.”

A teacher or professor must never say the following statements to a girl studying math: “I do not understand why you are not getting this.” “You are not good at conceptual math.” “You just don’t have the intuition.” Math teachers must never attribute the success of one student to “natural ability” while attributing the success of another to “hard work,” as that distinction implicitly conveys a distinction between the two students even if they are performing at the same level.

Finally, I believe that it is critical for teachers and professors to emphasize that natural talent, whether or not male students have it inherently, is not necessary in order for a student to excel at mathematics.

Swat, for the most part, does a better job than my high school did at trying to defuse some of the already ingrained biases against women in S.T.E.M. fields. My Linear Algebra professor freshman year did an excellent job with this, emphasizing to the entire class from day one that just because people don’t look like you in this field doesn’t mean you shouldn’t pursue it. I am not arguing that female S.T.E.M. students need their hands held or to be told they can do it, I am simply advocating for the ability to work in a slightly less bias-ridden environment. As a Computer Science and English double major, I do not even know which field I would like to pursue after college.  I simply want the ability for girls to choose math to exist untainted by harmful societal perceptions, biases, and stereotypes.

With the changes proposed above, girls will not have to walk into a math class and feel inhibited by their gender, and I believe that every student deserves to walk into a math class without feeling like they are at a disadvantage before they even begin to solve problems.  Removing implicit biases, stereotype threat, and media influences that keep girls out of mathematics will result in more girls in the higher level math classes in high schools, and subsequently, more girls with the ability to realize their potential in mathematics.

When constantly bombarded with the ubiquitous and pernicious images conveying a lack of intelligence surrounding their gender, young girls are socialized to believe that they are inferior intellectually, and thus incapable of tackling the hard problems.  We are severely limiting ourselves and our society based on perceptions created by the media and stereotypes perpetrated implicitly by teachers and institutions.

When mathematical reasoning gets murky

in Op-Eds/Opinions by

In a recent piece for the Phoenix, “Why Mathematical Reasoning Should Be a Part of Civic Education,” Zhicheng Fan advocates expanded mathematical education as an antidote to the post-factual political climate into which the U.S. has unfortunately ventured.  The argument, in essence, rests on two assertions: (1) mathematics reinforces the notion of universal truths, leaving “alternative facts” deservedly exposed as the sham that they are, and (2) the precision and logical rigor incumbent on a mathematician trains one to think and act more rationally.  Thus, it appears that by encouraging a broader spectrum of society to study mathematics, we would expect to see a cultural shift toward a greater adherence to logic, truth, and attention to detail.

I absolutely agree that mathematical education should be embraced and enlarged. I particularly support Fan’s suggestions of bringing proofs, both the banal and the beautiful, into the curriculum at an earlier stage and incorporating more math history to contextualize and humanize the material and inspire students. However, I wish to add an additional layer of consideration.  I believe that transferring mathematical reasoning to the “real world” is not so simple as Fan’s quixotic zeal suggests. While the qualities Fan ascribes to mathematical reasoning are indeed staples of the discipline, there is yet another that I have found to be essential though often overlooked: using intuition to guide exploration.  I draw the same conclusion as Fan, that math education should be broadened, and in the same ways he suggests.  However, my premise is a slight variant: I claim that mathematics not only teaches us to write clearly, accurately, and honestly, but also to think creatively, metaphorically, and imprecisely—but in a productive way!

Allow me first to clarify some points for context: (1) Fan invited me to write this response piece, and my goal in doing so is to encourage a continued civil, fruitful discussion where we build on each other’s ideas; (2) Fan is currently my student in Modern Algebra, but I have already learned as much from him, both in that class and in this editorial discussion, as he perhaps has from me as his professor; (3) the other course I am currently teaching is Introduction to Mathematical Thinking, the class Fan recommends toward the end of his article, and I wholeheartedly reaffirm Fan’s suggestion to take it—particularly those of you who might have had a scarring mathematical experience in the past.

Let me begin with the challenges of applying mathematical reasoning to non-mathematical situations.  An example from Fan’s article conveniently illustrates the point.  The mathematical existence of the Weierstrass Function, a graph fluctuating in such an inconceivably dramatic manner that it is impossible to draw, is said to demonstrate that it is “conceptually possible for a car to move without speed at any moment.”  I highly doubt such an occurrence is possible, or that it even makes sense.  Thus, the confidence established by mathematical certainty leads one precipitously off a cliff of plausibility when adapted to a physical setting.  In other words, transferring mathematical fact to the real world leads to what Fan refers to as a “conceptual possibility,” which arguably is none other than our foe, the “alternative fact.”  If such a simple case as interpreting the derivative of a function as the speed of a car is problematic, imagine applying mathematical reasoning and certainty more broadly to the world of beguiling complexity and nuance in which we live. Some believe the 2008 financial crisis was exacerbated by false-confidence resulting from this discrepancy between the precision of mathematical models and the chaotic uncertainty of the real world.  For a fascinating discussion of the over-zealous reliance on mathematical models that our society has in recent years been consumed by, see the recent book “Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy” by Cathy O’Neil.

But hope is not lost. Mathematics is not a useless Platonic realm confined to our imaginations, nor simply a progenitor of pernicious mathematical models.  Mathematics provides the backbone for a great deal of science and technology and has had a tremendous, very real, and often extremely positive impact felt across the planet.  Of course, this includes a positive impact in the classroom as well.

Classroom mathematics can be deceptive. The clean, accurate, polished form with which mathematical facts, or theorems, are presented in textbooks belies their oftentimes controversial histories and messy prior incarnations.  Mathematics continually develops itself by envisioning greater levels of generality and more rigorous foundations and then summoning past knowledge, placing it within modern language and perspective.  In doing so, mathematics acts as a self-cleaning oven, deftly erasing its history of missteps and vagaries while offering a feeling of timelessness and universality.  When the name of a 17th century prodigy comes up in class, for instance, we seldom describe the theorem the way it was stated and viewed at the time of its publication. Instead, with statements that have evolved over centuries, we see only the most recent incarnation.  Thus mathematical ideas percolate through continual modernization, even if the words themselves grow stale.

The mathematical world seamlessly blends irrefutable reality with resplendent fantasy.  When I think about math, I think in terms of metaphor and cartoon simplifications of complex notions.  Details, logic, and precision only enter the thought process at a later stage at which I am ready to probe further the depths of a mathematical thought or to communicate it to others.  Thus, while I agree that math helps train the brain in rigor and truthful properties, what strikes me most about my years of doing mathematics is somewhat the opposite. Rather, math has trained me to embrace the uncertain, to heedlessly leap into vast hinterlands of vague thought while grasping for familiarity, to recognize that creativity arises from uncertainty, and to become cognizant of the difference between an idea and a written or spoken manifestation of it.

Since Fan ended his article with a beautiful theorem demonstrating the enduring elegance of mathematical truths, allow me to end mine with an equally accessible example of a conjecture. That is, a simple statement whose rigorous verification continues to defy the entire mathematical community.

The Collatz Conjecture: Given any positive integer n, divide by two if it is even or multiply by three and add one of it is odd; repeat this procedure and you will eventually end up with the number one.

Try it!  Here is an example for n = 10:

10 —> 5 —> 16 —> 8 —> 4 —> 2 —> 1

Computers have checked unimaginably many values of n yet no general pattern has emerged allowing us to firmly establish this result for the infinitude of possible values.  Mathematics is as much about the unknown as it is about the known, and that’s why I love it.

Why Mathematical Reasoning Should Be a Part of Civic Education

in Op-Eds/Opinions by

We now live in a world where reason and truth are under siege on a daily basis. The Economist declares that we have entered an era of “post-truth politics.” Falsehoods are called “alternative facts.” Science is subject to ideological manipulation. On both sides of the aisle, moral relativism and partisan politics have largely replaced commitment to constitutional principles and our inalienable rights. For many conservatives, religious freedom is important only if the religion is Christianity. For many liberals, the core liberal tenet of free speech is now somehow contingent on the identity of the speaker. While people everywhere used to struggle for our indivisible and inalienable human rights, we now like to manipulate these principles to fit our own narratives. I think part of the problem is lack of appreciation; learning about history or politics in oppressive regimes can help. The other part of the problem is inability or unwillingness to reason on both sides. Mathematical reasoning, I argue, provides an antidote to this culture of relative truth.

First, some clarifications on terminology. By relativism, I mean the belief that moral truths are relative to individual perspective, and that universal moral truths do not exist. By mathematical reasoning, I mean the ability to use proofs and rigorous arguments to generate indisputable mathematical knowledge. Mathematical reasoning is different from numeracy in that the latter denotes only the ability to work with numbers and calculate them.

The culture of truth and certainty that is generated by the method of proof in the mathematical world is sorely needed in the political and social sphere. In mathematics, once someone has proven that there are infinitely many prime numbers, no distortion or reframing or political maneuver or “alternative facts” can change that. This does not mean that skepticism has no place in mathematics, or, as political scientist Andrew Hacker apparently believes, that mathematics thrives under oppressive regimes. Basic assumptions in mathematics are often revised in light of evidence that shows a system can generate paradoxical results. For example, our intuitive understanding of sets as collections of objects was discarded after the discovery of the famous Russell’s paradox: the set of all sets that are not members of themselves can neither contain nor not contain itself. All mathematics asks is this: believe what you have a strong argument for, unless reason shows otherwise, in which case you must not believe.

Mathematics also teaches important skills that are transferable to political and social debates. First, mathematics teaches attention to detail. For example, try solving for x: ax = b. If your answer is x = b/a, then you miss the case in which a = b = 0 (which would mean x can be anything), or the case in which a = 0 but b is not 0 (which would mean there is no value x can be for the equation to hold.) Getting into the habit of considering all the “borderline cases” and scenarios can be useful in discussions about technical issues, such as affirmative action or voter ID law. Second, mathematics teaches basic strategies of argumentation. For example, in calculus, to show the claim that continuous functions must be differentiable somewhere is false, mathematicians created a counterexample called the “Weierstrass function.” In essence, it means that it is conceptually possible for a car to move without speed at any moment. One can also use “proof by counterexample” to show that freedom of speech is not absolute. For example, one cannot falsely shout fire in a movie theater. Third, mathematics teaches how to identify assumptions and gaps in arguments. One famous example in mathematics was the proof of Fermat’s Last Theorem: for any integer n greater than 2, there are no three positive integers x, y, and z such that xn + yn = zn. It took mathematicians 358 years to prove this result, but the first version of the proof contained a fatal error that was discovered during peer review. Eventually, the mathematician Andrew Wiles fixed his proof after a year of hard work, just before he was about to give up. The obsession with the rigor of argumentation in mathematics trains students of mathematics to develop a critical eye for arguments in general, as I have personally experienced. Fourth, mathematics teaches problem solving skills that can be particularly useful in policy-making and nonprofit work. The best proofs in mathematics are those that can be written in relatively few lines but are hard to discover. The best policy ideas are usually the same: easy to state, but hard to come by. Finally, mathematics teaches how to write well. Mathematical arguments are often more technical than arguments in other disciplines. Clarity of writing, therefore, becomes key in the discipline. Évariste Galois, one of the most important mathematicians in the 20th century, developed group theory in a paper that was considered “incomprehensible” by some mathematicians. It was only after he rewrote his mathematical manuscripts and published them the day before he died in a duel that his mathematical contributions became well-known.

Learning mathematical reasoning need not be difficult or stressful. Mathematical proofs should not be included in standardized tests such as SAT. Rather, exposure to mathematical reasoning can take the form of exposition and exploration. Teachers can show the most beautiful and famous proofs in different areas of mathematics, and guide students through each step of the proofs. Teachers can also present students with propositions that they can either prove or disprove. Finally, teachers can include tales from history of mathematics to illustrate how mathematical results can have profound philosophical implications. My favorite example is how Kurt Gödel’s and Alan Turing’s results in mathematical logic have shed light on the nature of human mind. Since this article is partly my opinion on educational reform and partly an advertisement for mathematics, I include here one of my favorite proofs in mathematics. If you like this argument or this way of thinking, you should definitely consider taking one of the mathematics classes offered at Swarthmore, such as Introduction to Mathematical Thinking.

Prove that there are infinitely many prime numbers.

Proof: Assume there are only finitely many prime numbers. Let p1, p2, p3, … , pn be all the prime numbers, arranged from the smallest to the largest. Let p = p1×p2×p3×…×pn + 1 (take the product of all the prime numbers and add 1).  Then p is larger than any of the prime numbers, since it is at least larger than or equal to p1 + 1, p2 + 1, … , pn + 1. Therefore, p is not one of the prime numbers, since our list contains all of them. p is thus a composite number, and it must be divisible by one of the prime numbers. However, the remainder of p divided by any of the prime numbers is 1, meaning that p is not divisible by any of the prime numbers. We have a contradiction. The only possibility, then, is that our assumption at the beginning was wrong. Therefore, there are infinitely many prime numbers. Q.E.D.


Diversity Continues to Elude Science Departments

in Around Campus/News by

It is no secret that some racial and ethnic minorities are underrepresented in the math, engineering, and the sciences. According to data from the most recent census, 31 percent of the American population is either black, Latino, or Native American. But only 17.8 percent of bachelor’s degrees and 6.9 percent of doctoral degrees awarded in the sciences went to those groups, and those minorities held only 5.9 percent of full-time professorships.

Swarthmore is no exception. According to faculty, the school is lacking when it comes to diversity in science departments. “I do not think the natural science and engineering departments, in general, have diverse students or faculty,” said Lynne Molter, chair of the engineering department.

Tom Stephenson, the college provost and a chemistry professor, agreed. According to Stephenson, the school could do a better job of recruiting minority faculty. “I think Swarthmore’s not doing nearly well enough,” he said. “I think we could be more deliberate about how we recruit faculty.”

Twenty percent of Swarthmore’s current tenure-track faculty identify as members of racial and ethnic minority groups. While there is no recent data that gives a breakdown of minority students and faculty by department, past studies have showed disparities. Stephenson, for example, said a prior report indicated that the attrition rate in the sciences was higher among groups that are historically underrepresented.

For many students of color, this makes studying in science, technology, engineering and mathematics (STEM) fields more complicated. “There can be some difficulties just because you feel like they’re not a lot of students of color,” said Alana Burns ’13, a biology major who identifies as black. “It’s a little hard because you feel like you’re the only one.”

Charles Armstrong ’13, who graduated early with a minor in biology and also identifies as black, goes further, arguing that the lack of racial diversity in the sciences leads not just to a sense of isolation, but also to unfair treatment. “There’s this kind of social divide. If you feel like you can’t culturally relate to different students, you might not want to have them work with you in the lab,” he said.

This can create difficulties. “In the group study sessions, I’ve felt especially excluded and watched other students feel excluded,” he said. As a result, his study groups are usually quite small and consist of him and other racial minorities. The small size, he says, leads to less assistance. “We’re kind of triaged at the bottom in getting the proctors’ help for problems.”

Chanelle Simmons ’14, a chemistry major, expressed similar sentiments, saying she has to assert herself more than white students. “They are very scrutinizing towards me,” Simmons, who identifies as black, said. “You always have to prove something to them.”

“I can’t make a statement and say, ‘Oh, we’re not being treated equally,’ because I don’t have concrete evidence,” Simmons continued. “But I definitely perceive a difference.”

Armstrong agreed. “I think that with any type of school or institution where you get minority students of a certain kind, there is this underlying assumption that they come from a different background,” he said.

This misconception is not, he says, the whole problem. Indeed, he feels that students of color often do have different backgrounds. “Minorities aren’t always equally prepared as their counterparts,” he said.

But he argues that the prognosis can keep students further behind. “Even if that assumption pans out, I don’t think the solution is remedial chemistry.”

Being a minority, according to Burns, also leads to pressures and judgments from other students. “I was talking to one of my friends, and I was worried about what I need to be doing to prepare for medical school,” she said said. “And she was like, ‘Oh, you’re a black woman, there aren’t a lot of black women doctors out there. It should be easy for you.’”

Not everyone, however, feels minorities face unequal treatment. “In my experience, I haven’t really seen that,” said Akida Lebby ’16, a prospective neuroscience major who identifies as black. “I haven’t really experienced any type of discrimination towards me.”

While Lebby has noticed that professors treat students differently, he does not attribute that to racial prejudice. “Some professors will cater towards one group a little bit more because people are different and people have their own biases,” he said.

PJ Trainor ’16, a prospective math major and computer science minor with Latino heritage, agreed. “I don’t see anything that would be unfair,” he said, adding that from what he has seen, at least in the math department, the school seemed to be accommodating of everyone. “Everyone has a lot of opportunities to work with other people,” he said.

While Burns said she has not had any incidents of being treated unfairly, she sees why some students feel that way. “It’s just difficult when you feel like you’re the only person there,” she said. “Any time something happens, it can make you feel like it’s because of race.”

According to Stephenson, this itself is a problem. “It almost doesn’t matter if it’s true or not,” he said. “If [students] walk away from an interaction with a faculty member and think that, in some ways, impression becomes reality. If that’s a widespread impression, then that’s an issue we need to work on.”

Michael Brown, the chair of the physics and astronomy department, had similar opinions. “We have to be more open and more supportive, particularly of first-generation students,” he said.

Burns thought that further diversifying the science department faculty could, at least partially, solve problems of perception and fairness. “I feel like if they had some more diversity, it would definitely help,” she said, adding that having minority professors can give students of color more role models. “It sort of helps to see that someone else has made it and maybe you can too.”

She also believes that creating networks of support for students of color could be helpful. “It’d be good if there was a student group of minorities in the sciences so you can get together and say, ‘Oh, there’s other people doing this.’”

According to faculty, concerns about diversity are issues that the school is working on. “We’re trying to work on making faculty aware of unintended actions,” said Stephenson, adding that the school has hosted workshops about issues of race and diversity.

Indeed, the college has received grants to try and diversify the composition of students in the sciences. Last year, the college received a four-year grant for $1 million from the Howard Hughes Medical Institute, in part to help increase diversity among students who study science.

Molter emphasized steps that engineering was taking. “I can only speak for our department, but we advertise [for positions] through … the National Society for Black Engineers and the Society of Women Engineers, in addition to the sub-disciplinary publications within Engineering,” she said.

But according to Armstrong, this is a problem that minorities will need to address themselves. “We can demand an external solution, but I think it’s hubris to expect one,” he said. Minorities who are interested in the sciences, he said, need to take on the challenge themselves. “I think the solution has to come from within.”

Students Struggle With Math Placement Exams

in Around Campus/News by

Olivia Edwards ’14 knew she wanted to major in biology when she came to college. In order to do that, Edwards needs to take some math. “It’s required for my major,” she said.

So, as an incoming student, Edwards took the math placement test. And while she does not remember exactly how well she did, she knows the end result. “When I actually attempted to take a class, they told me I needed to be remediated.”

Based on her score, Swarthmore prohibited Edwards from taking a math course that allows for further work in the department or is required by other majors. She is not the only student who has had difficulty with the math placement process. “I could not take any math classes here,” said Michael Wheeler ’16, who also failed to score high enough on his placement test to take Math 15, Elementary Single-Variable Calculus.

Phillip Everson, the math professor in charge of placement, says the department is aware that this happens. “If they don’t do well enough on the readiness test, then we require them to do something first,” he said.

Kaitlyn Litwinetz, the academic support coordinator for the math department, agreed, saying the department, in general, is strict about not allowing students they consider unqualified to take calculus. “In the last couple years, the professors have really cracked down on not letting students into Math 15 who aren’t prepared to take it,” she said.

For some students, like Edwards, the lack of a precalculus course has made life more difficult. “It kind of sucked,” said Edwards, who was told she needed to do review work over the summer and then re-take the exam to enroll in Math 15. But that summer, she was occupied by an internship. Hence, Edwards felt she did not have the time to adequately prepare.  “I had to move around my whole schedule because of not taking it,” she said.

But Everson feels the process is fair and accommodating. “If they aren’t happy with it, they come and talk to us,” he said. He pointed out that the department offers review materials, and in 2008, hired Litwinetz to help people in exactly that situation.

“I reach out to students,” said Litwinetz. “People that don’t really place into Math 15 could come talk to me,” she said. Litwinetz said she distributes review material to students who need assistance in preparing for math.

Litwinetz, like Everson, argued the department was accommodating, and that in spite of strict standards of admittance to Math 15, professors were willing to accept students who truly needed to take the course. “I think the professors would kind of work with them and let them take it,” she said.

Indeed, even some students barred from taking math are not too disappointed. “I did not plan on taking any math classes here,” said Wheeler, who added he felt the problem was not widespread. “I have a feeling that the number of people for which this is actually a reality for it is incredibly low,” he said.

Edwards agreed. “I knew I was going to be a bio major when I came to this school, so it was not enough to dissuade me,” she said.

Still, students felt the system could use improvement. “It’s a little bit of a hit to the self esteem,” said Lauren Mirzakhali ’15, who, like Wheeler and Edwards, was ineligible for Math 15.

Wheeler felt that the system was not as flexible as Everson made it out to be. “It was very dismissive,” said Wheeler. “It was very much like, ‘Figure this out on your own, or it’s a no.’”

Some students said they thought the school should have a precalculus course they could do during the semester instead of as summer work. Even Litwinetz felt it might not be a bad idea. “I do think there are some students who would benefit from it,” she said, adding that she thought it might be good for the school to offer a summertime, “no credit,” course.

However, Everson said that there was only so much the department could do with its resources. For example, he said that while the math department would like to offer a precalculus course, it did not have the means. “We just don’t have the possibility of offering a preparatory course for Math 15. We don’t have the staffing,” he said.

But students seem to understand those issues and the lack of need. “It just seems a little counterproductive to start something that you’d already be behind in,” said Mirzakhali.

Wheeler agreed. “I can only imagine there are a handful of people here who are as bad at math as I am.”

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