Michael He

February 22, 2022

College Math Courses Have Failed Us

I recent read an op-ed "why won't anyone teach me math?" The author Abigail makes salients points I deeply resonate with as a humanities-turned-math major. Given how rare that transition happens, I have thought about it a lot. This is a semi-compendium on the topic.

Unfortunately, it is difficult for students pursuing humanities and social science degrees to explore classes within STEM departments due to the inaccessibility of introductory courses. 

We see this happen to many students across many colleges, not only specific to the author at Princeton.

The way the course was run did not at all set up students to succeed — or even learn math. This begs the question: what interest does a department have in making it impossible to study?  

By not supporting students who are making an effort to study, it becomes both extremely difficult to learn material, and demoralizing to even try. I wanted to learn linear algebra! I had the correct prerequisite knowledge to do it. So why didn’t the math department encourage me in this pursuit? I would think that departments want students to fall in love with their subjects.

It is baffling to not only suspect but experience this yourself. Introductory courses are often so terrible, even students majoring in that discipline will feel dejected.

The most common and egregious flaw is how universities contract temporary instructors to teach the most fundamental courses. I also have serious doubt about listing calculus as the "basic" math course, more on that later. This alone produces and accentuates problems left and right. How can students have access to someone who's not even there all the time and is probably teaching at multiple colleges due to the inhumane pay temps receive?

This behavior forces a mentor-mentee dynamic into an obvious transaction: come to lecture, take notes, do assignments, take your exams, and adios! If you have questions, good luck figuring it out yourself. Maybe you can find someone to help you, but that's not our (university/department) concerns.

Remember, not every class comes with TAs and TAs are not always capable of answering your questions. After all they are students, not professionals with pedagogical knowhow. As a TA, I know precisely how much I can and cannot do for students struggling with the course material and very often things in their personal lives.  

Note that I am speaking about the general experience, not my personal anecdote. My home college's math department is among one of the best in the nation, in terms of accessibility and friendliness in my opinion.

If introductory courses are the best bets to attract students, then shouldn't each department pour their very heart and soul into making a great Subject101 course? CS005 at my college consortium has one of the best ratings online and through word of mouth, despite being the largest class by student attendance. That has invariably attracted a major proportion of future CS majors and minors. Compare that with calculus offerings in many universities, which not only demoralize and stunt intellectual interests for many students every year, but also discourage many who are capable of pursuing these challenging yet rewarding disciplines from even considering.

I can list a dozen reasons for how difficult it is to make an intro course engaging and substantial. Trust me, I really get it! That doesn't mean it's impossible and it definitely doesn't mean we shouldn't keep trying. In fact, isn't that what educators do? To consistently improve one's teaching, measured best by how well students engage with the curriculum and proceed from there? I think relentlessness is a virtue in pedagogy, but I may be too young and naive to realize the impossibility of such ideal... 

Psychology is the biggest obstacle to academic growth. Feeling demoralized is like a multiplier of 0 (or approaching 0 asymptotically). No matter how much effort you throw at it, the end result is zero or minuscule at best. 

Another issue institutions gloss over is how we measure performance. We measure athletic performance. We measure financial performance. Why can't we measure academic performance correctly? Grades and GPA are the de facto metrics, but shouldn't student engagement be more important? Yes, it is 
more abstract and difficult to measure engagement, but who says it should be easy? 

By focusing on the wrong metric (in my opinion), we design curriculum and manage department in a detractive manner. Not only do students suffer, the faculties, colleges, and society at large all suffer from a future generation not reaching their full potential and beyond due to dysfunctional education.  

The only reason I successfully completed my math major curriculum despite jumping ship super late (in my fourth semester) is because my department has set me up for success. We have TA (called mentors) programs for each class, many of them are former students of the same course. That builds a layer of empathy, which is important to the quality of TA sessions. Our culture is largely collaborative. Our professors deeply engage in teaching and are largely accessible. One professor actually active asks students about their state of being and that energy has a lasting impact on how I host study sessions.

There is also nuance in each faculty. Those who want to teach still have to abide by "self-imposed" regulations and specifics, whereas those who don't want to teach still need to teach per duty. This contributes significantly to an uneven distribution of teaching engagement and in turn learning engagement. I will stop here before writing a dissertation…

Yet as a humanities student, it feels extremely difficult to explore STEM fields. 

We are often told of engineering or STEM students exploring the humanities to their heart's content, but I feel that we rarely hear of students in the humanities being encouraged to take scientific or quantitative classes. 

There is a huge inequality between how STEM students and humanities students can approach one another’s disciplines. To be fair, there is inherent inequality. STEM students can still read and write essays to participate in most humanities courses. On the other hand, Humanities students often do not have all the pre-requisite coursework to venture beyond introductory offerings. If all they can get are subpar intro courses, then no wonder they will feel dejected and say "I'm never learning more than calculus."

This leads to both obvious and non-obvious consequences. Humanities students will take less STEM courses, which lead them to miss out on potentially useful knowledge and skills. More importantly, STEM departments have inadvertently turned away many students who are more than qualified to study STEM and force them to stay in humanities. That is a net loss for everyone. Imagine someone with a serious anthropological background at a tech company. That may lead to some serious difference between product design and business ethos. And I’m definitely not pointing fingers at any big tech company…

We shouldn't let this initial difference snowball into something demoralizing in the first place. I have observed most STEM intro courses for "non-majors" at my college. They are deficient in one form or another, though some professors are keenly aware of the challenges and are actively improving course quality. I give most professors a benefit of the doubt, but I won’t cut slack for those who don’t acknowledge this systematic issue (especially department heads and college administrators). 

Education is a field of multi-order effects. We have surfaced some serious flaws and their implications, but our larger commentary has just begun. 

A much darker trend is the systematic divide between (and within) disciplines, which has now transgressed from the research portion of academia into instruction. It's rare to have college courses that intensely rehash arithmetic (and teaching some students for the first time) citing the same reasons - it's basic, everyone knows it, students are not here to learn basic operations, etc. Even though arithmetic is undeniably the most important aspect of math for most people in their daily life! I know calculus well, but I have never actively done calculus in my head out of necessity. I do multiplication and division every hour. It pains me to see students who cannot do addition and subtraction in their head, because I know we are all capable of that. 

We haven't really figured out how to make STEM truly accessible to people who may not major in engineering or physics. The issue is we are not even trying. There is no ongoing dialogue and most dialogues are non-inclusive (of students). There is definitely not enough experimentation with the format and curriculum. We don't even have any generally accepted AND true principles that can guide us to make this a reality. It's literally a blob of mess right now. 

The conclusion is inherent. We have failed as educators in making math (and STEM in general) accessible to students. And that raises the real question: which masters are we (educators) serving? What do institutions value?

Princeton promises students a “liberal arts education,” and defines that as an education offering “expansive intellectual grounding in all kinds of humanistic inquiry.” 

In a way, this critique paints a jarring but accurate picture on the downfall of the liberal arts ideal. Liberal arts is now a catch-all phrase that has all these wonderful connotations and implications and romantic contexts. But we haven't consistently delivered that, not at liberal arts colleges nor at elite institutions that pride their traditions on this model. Just look at the fastest growing departments at every college that self-proclaims to be following a liberal arts model. Computer science, economics, engineering, medicine, and law related departments are growing the fastest, receiving the most funding, meanwhile they are imposing an increasingly difficult curriculum to prevent (intentionally or unintentionally) students from venturing outside their majors. The exact opposite of liberal arts is happening to liberal arts. It’s a dangerous hypocrisy whose existence public does not even know. 

If we can't deliver, then let's not shamelessly market liberal arts education in college brochures and cook up all this wonderful imagery for students to only trash their dreams down the line, often fueled with student debt on par with mortgage down payments.

And personally, I find this trend in math education (in college and beyond) incredibly alarming. Math is the foundation to science and also understanding the world in a quantitative manner (which a;sp improves our qualitative understanding). Failing to let students master math and statistics is one of the guaranteed ways to destroy progress that could have happened. Read The Three Body Trilogy and you see how not advancing scientific knowledge among the general public has hastened the destruction of Earth by aliens. That's not fear-mongering as much as a warning for our current trajectory. Imagine all the good things that can happen in a society of numeracy. Is that much harder to achieve than sending people to Mars? 

It’s also interesting how there is almost always a disconnect between the math you learn in school and the math you use in life. We should be very upfront and thoughtful about our purpose as to not waste anyone’s time. If I were to teach any college intro level math course, it would be focused on cultivating numeracy, not any specific knowledge in a specific field. You should walk out of your final exam confident in arithmetics, algebra (to solve any real-life world problems), geometry (mostly shapes, volumes, and triangles), statistics (to understand how right and wrong news articles are), probability (basic calculation of expected value), and most importantly, the confidence that you can learn any of this math, so long as you push forward steadily and give it time and patience. 

That is what education should be, no?

Thanks to my beloved friend Charlotte Nim for writing encouraging messages.