Choosing Math as Your Major?
The Unseen Side of Mathematics
—By Xu Jiang
As the fall semester comes to an end, many sophomore students are going to face one of the most important challenges in their life: declaring a major. Although it is common for many students to switch majors, it costs more money and time in school. Therefore, a thorough consideration for the major is necessary for every student at the crossroads of academic life. At the University of Michigan, math is a popular subject that each year attracts approximately 750 students declaring it as their major. However, according to the report from the U.S. Department of Education, there are almost 52% of students who initially major in math end up pursuing other degrees in the US. This figure raises several concerns in math education: Why do so many students give up math and what should educators do to keep their students?
Reasons for giving up math
There are three main reasons students leave math. First, there are many misconceptions regarding the study of mathematics. Nir Gadish, a math professor at U of M, remarks, “Many students give up math because they don’t really know what math is teaching. Before they went to college, they only learned the algebraic part of math. However, as they go deeper, they will realize algebra is only a small part of math.” It is a common phenomenon that people consider math merely as a study of calculation and function graphing, since math education before college focuses on these topics. YiXuan He, a current undergraduate math major at U-M, said “Before studying Math 217, I thought I was good at math, since I did well in calculation and solving integrals. But Math 217 told me I was not good at math. Math is about writing proofs and dealing with conceptual theorems.”
In fact, pure math is mainly composed of five big topics at the college level: algebra, geometry, topology, real analysis, and probability theory. Each of the topics goes beyond the level of simple calculation or operation of mathematical formulas. It requires the ability to understand the conceptual theorem and formulate one’s own statement or claim in rigorous mathematical language. As said by professor Nir, “Math is a means of logical expression.” Therefore, many people mistakenly think they love math because they have some misconceptions about it. They are only interested in the computational part, but they ignore the existence of the theoretical part which is even more essential to the study of math.
Another second reason that many students drop out of math is that they hold the belief that “I am not a math person.” In the article “ The Myth of “I am Bad at Math,” authors Miles Kimballs, Noah Smith, and Quartz introduce a prevalent perception among students that the ability in math is primarily determined by genetic factors rather than hard work. I asked a relevant question to Yixuan in our interview: which one is more important in studying math? Genes or hard work? She answered without hesitation: “genes.” This popular perception that math ability is genetic has a great impact on each student who is struggling in math. Some students may consider the frustration as a chance to improve, while more students will simply be stuck in the myth that “I am not a math person” and give up math study.
The third reason is that many students believe that math cannot help them get a job. Hongfan Zhou, an economics student at U of M, comments, “I prefer computer science and finance to math. Math is too general and theoretical for me. I don’t think it would be helpful for me to get a job.” He is not alone to have this kind of belief. Many people want to study a subject that can be applied to a practical field and solve real world problems. However, as they learn deeper in math, they will find out that complex analysis or topology seems to only deal with those abstract concepts and logical proof with little practical use. As a result, many students would switch to a major that is seemingly more “practical” or “useful” to them.
Reasons for not giving up math
While the above reasons make some sense, they are not always the case. The first misconception I would clarify is that math ability is genetic. Let me emphasize that math ability is by no means genetic. The effort a person puts in generally plays a more important role in succeeding this subject. Purdue University psychologist Patricia Linehan conducted a study comparing two groups of students: students with an incremental orientation and students with an entity orientation.Students with incremental orientation believe that intelligence would increase with effort, while students with an entity orientation believe that intelligence is non-malleable. The result of this research shows that the incremental orientation generally leads to a good outcome but the entity orientation leads to a bad outcome. Mathematical thinking is not an innate ability. It can be developed and improved through active brain training. Therefore, a person with the incremental orientation will generally spend more time training their brain and developing better math ability. The result implies that every ability, including math ability, is not fixed by the permutations of DNA. To be more precise, even though DNA has a great influence on your math ability, a positive attitude and hard work can still make a big difference.
The second misconception needed to be eliminated is that math is useless in solving real world problems. In fact, math is one of the best tools in solving real world problems. Many areas of study are strongly related to math, such as computer science, physics, engineering, finance, and chemistry. Professor Kim Dongham, who is teaching financial math at U-M, remarked, “Math can lead to breakthrough discoveries in the finance area. It’s the stochastic differential equation that helps Donsker develop his model to predict the stock price. Without the knowledge of math, he can never find out the rules in the stock market.”
Although many theoretical topics in math cannot be directly applied to practical fields, a thorough comprehension of these topics can still help a student build strong skills in logic and equip him/her with excellent analytical skills, which are useful in almost every field of study, helping a person to qualify for a job like a business analyst, computer programmer, and even a philosopher. In our interview, Yixuan said, “Math helps me improve in various aspects. For example, math proof writing teaches me how to write a coherent and logical paper.” Drawing parallel to paper writing, mathematical proof goes through a similar process: come up with a claim or argument, use logic and evidence to prove the argument, and finally draw a conclusion. As a result, mathematical thinking can be helpful for students to formulate a coherent argument and write a logical justification.
Suggestion for students who are considering majoring in math
Be Confident and Keep Going: Math at college level is by no means easy, especially the math education in U-M. Even if you are one of the most intelligent students in math, it’s still inevitable that you will come across a tricky topic that makes you feel tortured. Therefore, when feeling frustrated, you should not make a quick judgment that you are not a math person. It’s a natural thing to get frustrated in math. Instead of giving up, you could work harder and give yourself more chances to discover your potential in math. Besides, if you need further assistance, you should remember that there are many tutoring opportunities provided by the Math Learning Center at UMich. One of the advantages is that you can have a one-on-one tutoring session for free. Without extra burden on your budget, you can receive a one-on-one tutor, which is customized to your personal demands. These opportunities will definitely help you improve in math.
Switch Concentrations First: In the process of learning math, you may finally find out that math is not the suitable path for you. My friend Jonathan Niu is an example. After studying two years of pure math, he finally switched his major to computer science. He said, “I hate topology and abstract algebra. They ruin my whole life.” When he started his academic path in computer science, he obtained confidence and happiness. Therefore, if you feel math is destructive in your life, it’s a wise choice to switch majors, but this choice comes with a price. Jonathan spent three more semesters to get his bachelor degree, and he had to take a set of completely different courses in the school. The extra tuition he had to pay also put more burden on his life.
As a consequence, before switching majors, you should know that you can keep your major but switch concentrations. Each concentration shares similar courses and topics with others, so you don’t need to take a completely different set of courses. Under the math department of UMich, there are five concentrations in math, including pure math, data science, financial math, actuarial math, and honor math. If you are tired of studying pure math but interested in calculation, financial math and actuarial math are possible options for you. Similarly, if you want to have more background in computer science or statistics, data science will meet your demands. Hence, to save time and money, you could consider whether one of these concentrations works for you.
Join the Math Club: If you are determined to major in math, you could attend weekly events held by the math club. Math is not all about exams and homework. Sometimes, you can simply solve a math problem for fun. Every week, the math club will introduce you to an interesting math topic, including the application of probability in gambling and using linear algebra to study quantum physics. There is also afternoon tea for you to enjoy. Solving these problems may not directly contribute to your grade, but it can definitely foster your interest and strengthen your mathematical thinking, which will benefit your whole life.
The prospect of math education
Now, we go back to the initial discussion: a great proportion of math students end up pursuing other degrees in the U.S. From a student’s viewpoint, changing majors is a natural and common thing, but from the educator’s perspective, how to keep students staying in the math area is an important issue. Professor Kim Donghan remarks, “Mathematics is a difficult subject for most students, so many students often feel frustrated by complex math concepts and find math not a subject that interests them. In Western countries, education emphasizes individual interest and inquiry-based learning methods, but in Eastern countries, like Korea or China, hard work is a top priority in education. As far as I know, when facing difficulties, students in Eastern countries tend to think that they are not hard-working rather than not smart enough. It is impossible to say which is the best, but the United States can emphasize more on how endurance is an important quality for students.”
To foster student’s resilience, a study conducted by John Griffith Moala and Roberta Hunter brings us many useful points. The most important one is to figure out the extent to which students are resilient and what’s the real cause of not being resilient. In fact, a student’s development of resilience in math is subject to various factors, including the type of teaching used, the nature of math itself, and the persuasive belief that mathematical learning ability is genetically fixed.
For different causes, the educator needs to implement different strategies. For example, a student may dislike math simply because of the teaching style of the teacher. In this case, the educator may want to substitute the traditional lecture with discussion, which gives students more space to collaborate with classmates and prove the theorem by themselves instead of directly accepting the knowledge from the teacher. For students who are not confident enough in this subject, a teacher can emphasize the fact that math ability is not genetically fixed. Instead, hard work plays a more important role in math learning. In addition, the study shows that a collaborative environment is likely to boost student’s confidence. A teacher can promote collaboration over competition in his/her class.
Yixuan also provides a valuable comment from the student’s perspective. “I like math, but I don’t like the exam part. Solving math problems is an interesting thing, but when it comes to exams, everything has changed.” As a math student, I have a great empathy with Yixuan. In U-M, almost eighty percent of math courses have at least three exams each semester. Many courses even have weekly quizzes and online tests. A number of students with passion for math will be discouraged by the pressure ensued with the exam and quizzes. Pressure sometimes will kill the interest. Maybe, to keep more students staying in the math area, one option is to reallocate the proportion of homework and exams by increasing the amount of homework and slightly reducing the frequency of exams.
Conclusion
Given the data provided by the U.S Department of Education, students who start out studying math are likely to change majors. This situation is partially due to the fact that learning math is stressful and there are many misconceptions about math, but most students drop out of math because they don’t believe that math is useful enough to bring them a job. However, as said by the renowned mathematician Issac Barrow, “Mathematics, the unshaken foundation of science, and the plentiful fountain of advantage to human affairs.” Math plays an indispensable role in the world, and it penetrates in every area, such as technology, economy, biology, and military. We should never overlook the power of math, and the current educators could also refine the education system to emphasize both enthusiasm and endurance in studying to keep more students interested in math and encourage them to create more and more magical formulas to bring breakthroughs for various areas.
Photo Credit: Photo by Annie Spratt on Unsplash