*Guest post by Sachin Kotecha, Math Sessional Instructor (sachin.kotecha@uwaterloo.ca)*

This past February, I (virtually) attended the 25th SIGMAA on RUME conference. Across three days, I attended 15 talks on mathematics education research, with a particular focus on attending talks on inclusivity in mathematics (and on assessment techniques - but that’s not the topic of this blog post!)

One talk in particular resonated with me - it connected both with my experience in my days as a math (and physics) student, and my philosophy now as a math instructor. This talk, “Well, it’s obvious”: Students’ Experiences with Mathematical Microaggressions, was based on research by Anne Cawley (Cal Poly Pomona), Ryan Gabriel F Aniceto (Cal Poly Pomona), Seth Richard T Ricarte (California State Polytechnic University), and Robin Wilson (Loyola Marymount University.)

The words ‘obvious’ and ‘trivial’ were the bane of my existence (and probably of yours too) as a student. How many different ways could the inanimate mathematics textbook or the notes on the board tell me that I was inept?! In physics classes, the in-joke was that the conclusion to most problems was that ‘the rest is just math’. I’m so allergic to the word ‘trivial’ that now, as a mathematics instructor, whenever I’m forced to use it in a mathematically proper context (ie. ‘trivial solution’ in a DEs course) I preface the use of the phrase by telling my students how much I detest the word, and how un-trivial mathematics is. I often explicitly tell my students ‘this is not obvious’ when it comes to certain steps in proofs upon first viewing.

In the talk, the researchers presented a study they had conducted with 173 undergraduate students enrolled in either Calc 1 or Abstract Algebra. As part of these courses, students would regularly submit reflection assignments. In the reflection assignment of note in the study, students were asked to read Francis Su’s 2015 article on Mathematical Microagressions, and then to describe if they had ever been made to feel like they don’t belong in mathematics. The Su article is well-worth a read - it not only identifies mathematical microagressions, but provides suggestions for replacements.

From the reflections, 70% of the students reported having experienced a mathematical microagression. The most common microagression? You guessed it: being told that something was obvious/trivial/easy. There was a good smattering of students having heard that ‘the rest is just math’ and that ‘you should have learned this before’. I also found it interesting that 10% of the student reflections pushed back on the idea of mathematically microagressions (some reasons suggested by students being that these are unintentional, or that this was just a matter of political correctness.) The data presented also indicated that females reported experiencing mathematical microagressions more than males (78% vs 64%.) Also of note: most students indicated they experienced these microagressions coming from an instructor, with the minority reporting it came from a peer interaction. The researchers have further plans to analyse the data with regards to race.

I think as instructors, we all try to be as aware as we possibly can about the way we come across in lecture - we want our students to feel like they belong. It is clear however, that the experiences many of us had as students is still prevalent amongst our own students. Certainly, part of the problem is that the longer we are in our roles, we more easily lose sight of what is actually ‘obvious’ or in particular for first-year courses, what students have actually learned before they get to us. It becomes easier for these words to slip in by accident, even more so when you look at the clock and you’re crunched for time in lecture - suddenly the remaining steps in the example become obvious, or just math! Not only that, but the knowledge base that students bring with them to our institutions evolves constantly with the secondary-level curriculum.

I certainly think there is positive work that can be done here. We can emphasize some of the replacements that Su suggests in their article when we train or on-board our future/new instructors. In peer observations and teaching circles activities we can work with our peers to look out for these slip-ups. Further, proactive conversations about what students’ knowledge base coming into our courses actually is can help us avoid the ‘you should have already learned this’ and allow us to augment our offerings to ensure students have the tools they need.

From a personal standpoint, I’d really like to implement a similar reflection activity to the study in some of the second year and second term courses I teach - I’m particularly interested in how these perceptions may be different (or similar) between our core and service students. I think that engaging in conversations with our students on this topic has potential to prove enlightening.

The question remains: how do we stamp out these experiences for our students? The answer really doesn’t seem obvious, or trivial, to me!