When Gateways Become Tunnels

Learning Threshold Concepts

Think back to before you learned algebra. Back then, only numbers were numbers, and life seemed pretty simple. You could add, subtract, multiply, and divide just about anything. Sure, it could be hard, but it could be done. Order of operations gave you some standardized rules to follow, like a grammar of numbers, and your brain hurt for a bit once you were introduced to fractions. But still, they were numbers, and things were pretty sane.

Then somebody came up with this idea that the letter X could be a number. And you never knew what that number was. Suddenly, math was a great big game of cat-and-mouse wherein you were always trying to figure out the ever-changing identity of this elusive and mysterious X.

At first, the idea that a letter could be a number was tantamount to blasphemy. But once you learned to work with the concept of variables, you understood how algebra worked. Variables are a threshold concept in mathematics. You cannot go back to thinking of numbers only as numbers again. By thinking in terms of variables, you’ve passed through a gateway into new mathematical thinking.

Writing classes at most schools—secondary or collegiate—don’t often teach threshold concepts like the variables of algebra, but that’s a topic for another blog post.

Threshold Concepts in FYC

At my institution, our FYC curriculum serves as an introduction to composition studies and, much like algebra serves as an introduction to algebraic thinking, our writing courses strive to indoctrinate students into thinking like a compositionist. We work with students to change their view of the writing process from a predictable, step-by-step flowchart into a messy, recursive scenario that is flexible and unpredictable. We help students identify groups of people that are held together by the things that they write, and then to identify the characteristics of those writings. We show students that knowledge is not simply handed from one person to another but instead is constructed by individuals, especially when reading others’ texts. And finally, we introduce the idea of rhetorical situations in which all writing takes place, suggesting that recurring rhetorical situations become genres.

That’s a lot for a student to digest in a single semester. Many of those concepts change the way our students are you writing, even though they have been writing in school for years. Some of the ideas are familiar to students, and we are simply giving a name to an instinctive habit. For instance, students already know that they write one way in a text message and another way in an academic essay. But to call those “rhetorical situations” gives a degree of discipline-sanctioned legitimacy that a basic awareness does not receive. In our FYC classes, teachers were all semester to help students build legitimacy in composition, thereby being more prepared for the variety of writing situations in which they will find themselves later in school … or in life.

A few problems creep up when teaching so many threshold concepts in rapid succession. Think about how I may have felt when you first learned that the letter X could represent an unknown number. That thought is rather unsettling at first, causing a student to rethink the concept of numbers (or even math). Imagine being unsettled by one topic, growing to be comfortable by it, then being unsettled by another, and repeating that cycle for sixteen weeks. The sense of confidence students have built during their thirteen years of primary and secondary education become a little shaky after we make so many repeated adjustments.

Transitions in Practice

When students come into my FYC course during their first semester as college students, many of them are experts at the five-paragraph essay form that they were taught in high school and that allowed them to successfully pass all their state-mandated and advanced-placement exams. The first major paper I asked my students to write emulates a traditional research report in journals, including Introduction, Methods, Results, and Discussion sections (the IMRD format). While it is a new structure for my students, they understand the idea of using predefined sections of an essay to determine what they write; their uncertainty in the face of a new format is mitigated by the familiarity of writing an essay in a predictable, predetermined pattern.

However, the IMRD format does not apply to any other papers written throughout the semester. This means that, in addition to the threshold concepts mentioned above, my students are simultaneously struggling with for an assay formats. This struggle is a problem because my students need to apply their brain power to the content of their essays, but the format only adds to the challenge of each assignment. Anastasia Efklides refers to this trouble as the combination of intrinsic cognitive load (what the students are supposed to be struggling with) and extraneous cognitive load (the other things, such as essay format, that they struggle with at the same time).

In other words, we want our students to learn these threshold concepts, but they are distracted by learning other things that seem important to them but that really have little significance. My instinct, as one who has exclusively taught freshman for a dozen years, is to simplify the important concepts and make them easier to digest. However, researchers have found that a simplified interpretation of a threshold concept leads students to naïvely accept the simplified version “as a proxy for the fuller, more sophisticated understanding which it was intended to lead on to” (Land, et al., 203). It appears that students have to work with challenging concepts in order to best understand those challenging concepts; simplifications do not assist … they limit.

Facing the Challenge

In FYC courses, we want our students to understand and adopt several threshold concepts in the field of composition research. If we simplify the concepts, we risk teaching our students information that is less useful and does not hold true to what the students should learn. If we change too much of our students’ assumptions, we risk overwhelming their brains by distracting them with extraneous cognitive load. If we do not push the point and emphasize the newness and strangeness of the knowledge, we risk having our students revert to the habits they brought with them into the class–the very habits we wish to change. How can a full-semester course, loaded with threshold concepts, possibly hope to succeed? What is the trick to ensure our students gain the exposure and experience necessary to adopt the new ways of thinking we present?

I’m afraid I don’t have a simple answer to this question. Indeed, Meyer, Land, Cousin, and Davies (established researchers in the field of threshold concepts) made several suggestions in the conclusion they wrote to text titled Overcoming Barriers to Student Understanding. One of those suggestions was that teachers must pay careful attention to the sequence of the content taught in their courses. Content sequence clearly matters when certain concepts in the curriculum give students the ability to view a particular field through a discipline-specific lens. Until the threshold concept is understood, students have little chance of understanding the nature of the field they’re studying.

But what of courses such as mine, where the majority of the content of the curriculum is made up of threshold concepts? How do you decide where to start and how to proceed? Through conversations with other instructors as we train, adopt, and adapt our course content, we found that different instructors feel most comfortable approaching the content from different starting points. It would seem that even the instructors who are experienced with material (in other words, “expert”) have a specific path into the mate
rial that make sense for them and makes them comfortable presenting the challenging concepts. We each have our convictions, and our department allows us the flexibility of choosing our own sequence for our content.

While this flexibility might be beneficial for teachers, so that they can present material in an arrangement that works best with their understanding and ability to instruct, it also emphasizes the variety of learning methods and patterns involved in difficult concepts. If a student would make sense of the material best if presented in A-B-C order, what happens when a student is in the classroom of a teacher who makes the most sense of the material by presenting it in C-B-A order? How significant is the difference in student learning, and is there a way to determine what order would work best for each student before the student enrolls in the course?

These questions involve far too many variables and dive into relatively unexplored territory. It is unlikely that definitive answers, much less enrollment practices, can be determined quickly. However, the uncertainty behind those questions weighs on me as I create my course syllabus to try and teach the threshold concepts of FYC one more time. I can only hope that the course sequence I have chosen works not only for me but also for my students. I hope that I can take the sequence of gateways that each threshold concept represents and create from a cohesive and well-structured tunnel through which my students will emerge with a better understanding of the world of composition.