Author: Pablo Gonzalez

A common concern of STEM instructors when trying to integrate writing into their curriculum is that this will take time from their teaching of the context. Of course, as WAC fellows we are taught to quickly dismiss this fear and tell them that the WAC way seeks to precisely avoid that, that’s what the “across the curriculum” stands for after all. I have noticed recently that fully realizing writing tasks for STEM classes has to avoid a certain number of pitfalls and would like to suggest here some recommendations that I think will help make WI courses a cohesive whole were the objectives of WAC pedagogy are truly met.

Most of us were not taught with WAC principles in mind, traditionally we only got big writing assignments in humanities classes. In my personal case I didn’t have to produce a serious piece of writing in my own field, Mathematics, until I had to write my undergrad thesis. I was however more than used to presenting all kinds of writing in history, philosophy or literature classes. I think the way we have been educated in which writing is a matter of the humanities heavily colors our perception and results in big problems when we try to implement writing curricula in STEM fields.

Recently, as I was reviewing writing assignments in a textbook for an algorithms class it dawned on me. While the book had writing prompts these were not about algorithms or discrete math, they were about the humanities surrounding  algorithms and discrete math. You don’t see what I am talking about? Writing assignments in STEM classes are often the ones where you are supposed to research about Einstein’s life and social context or about the ethical implications of the atom bomb, or about why Galileo was condemned by the Catholic Church. While the interest of scientists in the social background or ethical consequences of scientific advances is certainly commendable and something that should be encouraged, I want to argue that this practice is hurting the students’ formation in the STEM field itself, in the humanities issues surrounding the field and in their perception of what a writing assignment is and why they have difficulties with it.

The most problematic part of this practice is that the student is being asked to do something that the class is not preparing them for. This should be in my opinion always avoided, leaving the students to their own designs and so far afield can have devastating effects. Very often the student will know very little of the what they are expected to do and how to do it, this will lead them to produce subpar material which will lead to a bad grade. Even if the grade is not important in the class, the feeling of failure will leave students with an idea that they are bad are writing. This will ultimately reinforce the relationship between humanities and writing and an association in the student that they are not good at either. Other students might do well in this kind of assignment but it is very likely that this will take time from their study of the core of the subject, thus doing what instructors fear from writing assignments.

Additionally, the instructors are missing the potential that writing might have within their disciplines and foregoing teaching how to produce a piece of writing within the field. What’s the alternative? We need to think about writing assignments that are about what is being taught in class and that are contributing skills to the students that are adapted to the field. The problem is that these are usually harder to design, not necessarily because they are more complex but because we are not used to thinking about writing as a tool for some of these things. Let’s return for instance to the example of an algorithms class, here students need to learn the principles of how computers operate. Typical exercises usually have them modify some other algorithm, express something as pseudo-code (a language halfway between natural language and computer code) or take something in pseudo code and translate to a programing language. Natural language can fit right into this whole schema, explaining in plain language an algorithmic approach is an extremely valuable exercise, one some instructors probably already do. The problem here is often instructors either do not consider this approach or do not realize that this is precisely the kind of exercise that WAC needs to promote. Writing exercises do not have to be essays they can be anything that fits along with the rest of the courses work, be it mathematical proofs in a math class, summaries of a procedure on a chemistry lab, etc. Shifting away from the idea of the Humanities essay might be the first step towards finding this other kind of writing assignments that promotes understanding of course content and  asks students to do things that the course is actually preparing them for.

Hugo, my Colonial Literature of the Americas professor once introduced me to the class (I was a senior in a freshman class that I hadn’t come around to taking) as:

“This is Pablo, you will find that as a Literature student he is a great Mathematician, and I’m sure that in Mathematics they say he is a great Literature scholar”

It is indeed true that I very often have found myself at the intersection of disciplines, first as a dual Literature and Mathematics student in college (which happens to be the reason my schedule was too crammed to take Colonial literature until I was a senior and well known by the professor in question);  later as a graduate student in Linguistics with an expertise in semantics and then in computational linguistics, becoming the odd one now in the middle between the Computer Science and Linguistics departments.

Because of this confluence of disciplines, I have often been called to teach the courses that lie in the fringes, the ones the students feel they are not good at, or, to put it differently, the ones they always feel they “didn’t sign up for” when deciding a field of study. In humanities this means teaching the “math-y” subjects. Mathy in a broad sense of course, since I count my time T.A-ing for the latin and linguistics classes  as the start of this trend. In general, I count here as math-y, courses that required to learn a different formalism to the usual ones in the field, formal languages and strict formal rules, like grammar or formal logic.

If you want to find the math-y subjects in a humanities department it’s easy, just look for the ones no one wants to take, in Linguistics it’s Syntax or Semantics and nowadays Programing (often disguised under a title like Methods in Computational Linguistics as to lull the students into a sense of security). Students taking these classes get exposed to new formalisms, have to handle formulae and derivation processes, new codes that seem inaccessible and often inscrutable or arbitrary, the most common reaction to this is panic.

Teaching a subject that produces this kind of reaction is a mixed experience, on the one side, the frustration of your students can easily transfer to you, they will constantly say that they are no good for this, they will see their efforts as fruitless and because of this stop trying, they will often not mind having bad grades and even having to re-take the class.  More than once have I heard: “I failed Syntax but most people fail it once right?” or “All I care is to get a passing grade and forget semantics, after all it is not my area.” When you see your students stop caring about actually learning your subject it is easy to stop caring about actually teaching it.

On the other hand, this unpopularity makes it all the more rewarding when students finally “get it”, not only in the accomplishment you feel but in the accomplishment you see them feel. These courses very often feature an “aha!” moment, when the student suddenly realizes they can wrap their head around the formalism and use it to their advantage. When students perform well in a task that they once deemed impossible their happiness is contagious too.    

There is often this idea that you somehow have to suffer through the first stages of these processes to come out the other end tempered, that the moment of enlightenment will come after enough tears have been shed (a very judaeo-christian approach if I may say so). I have even seen instructors tell their programming students that, in their first semester, programming often brought them to tears too; as if this was some sort of gauntlet that has to be overcome through tears and blood. This feeling is often reinforced by older students who have already suffered through the test. This is, in my opinion and experience, the wrong approach, the students can be eased into these formalism in ways that are more gentle and effective, it does require however a lot of patience and time but this will save effort and time in the long run. If your class is seen as a gauntlet, don’t take pride in it, work to change this perception.

  In teaching these subjects, I have come to realize that the reactions of your students must be tampered from day one, any moment spent by them brooding about their inadequateness will mean extra work later, when you have to undo that feeling of powerlessness. Empowering the students starts with understanding that they come already with their own formalisms and you can piggyback on them. The students must come to perceive that the “new formulation” is nothing but a reformulation of the old ones. They already think in ways that may be translated into this new field.

Think for instance of teaching formal logic to linguistics students, the traditional way to do this starts introducing formulae and truth tables as a new tool that must be learned by heart. However, propositional logic follows rules very similar to those of natural language, there is a syntax to be followed and you can ease the students with examples from natural language. I, for instance, always talk about the necessity for verbs in natural languages when speaking about the necessity of a relation sing in mathematical formulae, an equation is no more than a sentence and when a student understands this they relate the new formalism to existing structures thus lifting the feeling of newness and inadequacy.

This approach has, of course, to be refined for every class and even for every background or student in your class, which I realize might be a tall order and will take a lot of time, especially at the beginning of the semester. All the time spent in introducing basic notions so that they articulate with students’ previous expertise will however be rewarded eventually. Avoiding any complaining will be the first boon; in making the class feel more tailored to your student’s backgrounds you are eliminating a lot of the objections and that feeling that your class does not really belong in the field. I guarantee that this will lead your class into a more efficient learning process that will make the late semester, when the more difficult material is introduced, way more manageable.

In my teaching experience, it has become evident that most problems with formal languages originate from an incomplete understanding of the concepts that underlie them. Even engineering students will often mislabel any mathematical expression as an equation or fail to provide accurate definitions of every symbol that they use. In math-y courses for humanities this gets even worse, there is a propensity to use lax language and jump to a formal representation only as a formalism, a set of symbols that you don’t truly understand but have valiantly learn to operate on. Even students that show no difficulties on the surface are prone to this, very algorithmically minded students will often process semantic derivations or sets of equations without having an inkling of an idea about what it is that happens between line and line of formalism or how to put their final answer in words.

One of the best approaches to mend this structural problem can be (you probably guessed it) writing. Asking your students to explain how a problem gets formalized, what the result of the derivation means or what the definitions of different symbols are can be a huge help to bridge their understanding. You will never see a math or semantics paper that is just streams of equations (granted a few exceptions, but these are often the bad papers). Why then do math or semantics homework so often take this exact form? Don’t jump to the formalism and the algorithm, have the students explain what the symbols mean, ease them into being comfortable with the transitions, have them translate back and forth. In my time teaching semantics I often implemented this by doing the exercises on the board and having the students explain the reasoning. I now realize that I needed to go one step further, people hand wave when they speak and space out when others speak, low stake writing might have been the key. If the students realize that formal language is just an abbreviation of something that might as well be written in full sentences, not only will they get it, but they will also come to cherish it (after all, writing equations is so much easier than writing text).

I believe this hand in hand approach, between making formalism friendlier by taking the time to relate it to the student’s already existing frameworks and using WAC methods to cement a solid understanding of this formalism, although time consuming, proves way better at introducing “math-y stuff” to all students, but is exceptionally suited  to all the ones that would have previously declared themselves naturally incompetent for math (not to use some of the more expressive language that I have heard over the years to describe this “disability”).