On Mathematics Anxiety
Eddie Woo answers some big questions.
It seems to be that the potential for nuance in education discourse is inversely proportional to the length of the medium. In my school role, I’ve been briefed to be aware that when being interviewed by the media, what might sound in my head like an erudite treatise on adaptive teaching might end up a statement about throwing NCCD out the window. Of course when we extrapolate this to Twitter, we end up with the Reading/Math/SEL-Wars that have now infiltrated so many domains.
So imagine my surprise at the beneficence of the world when Eddie Woo got in touch, in the most polite and generous way, to set the record straight about my tweet. Typically, some of the nuance of his responses were lost in this relatively brief SMH piece. So I spoke to Eddie with the explicit purpose of unpacking the blacks, the whites and the greys of Mathematics Anxiety (ironically capitalised).
Eddie must have had a crystal ball because he started filming his classes in 2012 for a sick student, in those carefree days before COVID-19 and Zoom. He was apparently onto something great as his lessons have had more than 150 million views. More impressively, he has entered the children’s canon by appearing on Play School.
The resulting interview went both deeper and broader than I had anticipated. I started by asking why he thinks maths anxiety is so topical.
I think ‘topical’ is the right term, but I don’t think the phenomenon is very different from ages past. One of the joys of my role is interacting with people from a whole range of age groups, and I still remember speaking to a lovely woman, who was about 80 years old. She discussed with me what might be described as classic academic anxiety within the context of Mathematics – it just didn’t have that label. So I wonder if the phenomenon is perhaps not new at all.
During the past 10 to 15 years, there has been a noticeable increase in awareness and understanding of mental health and wellbeing. That whole tide has risen, so there’s an appreciation of the fact that this classic set of symptoms, that we would normally associate with regular old anxiety, come up in the contexts of the ways people have been taught Mathematics over a really long period.
There has also been a shift in the desire for Mathematics to take more of a place in society with greater emphasis on literacy and numeracy. I remember (NSW Premier at the time) Gladys Berejiklian had very strong views on the importance and value of Mathematics in K-12, but particularly in Year 10, 11 and 12 schooling. I think this shift has played a role in getting Mathematics into the zeitgeist, as it were.
Politically, there are cycles in education discourse where we might frame schooling as essential to entry into the workforce, other periods have seen Mathematics move from compulsory to optional. Rishi Sunak was recently in the news for his plans to make Mathematics compulsory. Do you think for some students, Mathematics is bound up with other pressures in their lives?
The trends tend to see-saw back and forth – society often reacts, overreacts, and then falls off on the other side of the horse. One factor that might have played a part is the last three years of the global pandemic. For better or worse, it put Mathematics in the public eye in a very real way. Remember when the daily press conferences became routine, and we made a daily ritual of reciting numbers? We were talking about graphs on logarithmic scales that were appearing on mainstream TV and expecting that people could read and interpret what was going on. Seldom within living memory has there been such a daily assault of numbers and graphs and mathematical reality. It became very explicit and loud. The mathematics was always there, but COVID-19 really brought numeracy to the surface.
I think we can all concede that being excluded from understanding aspects of news, policy and by extension daily life would be anxiety-provoking. I asked Eddie how we can protect students against Mathematics Anxiety – the question of whether it’s a real thing comes later. We talked about the role of instruction.
Mathematics possesses the power to provide clarity and cut through ambiguity in situations where there is a definitive answer. I don’t subscribe to the idea that anything goes or the notion of two plus two equalling five, as seen in the conversation that took place in California. I haven’t drunk that Kool Aid. Mathematics teachers have so many methods at their disposal that allow for the teaching and learning of those objective ideas, algorithms and concepts and still make space for a psychologically safe environment. I think there is a misconception that you just have to tell kids when it's right or wrong, and therefore you have to be cruel and impersonal while doing it. I think that's an artificial conflation.
I'm always looking for a golden opportunity at the start of every school year. It generally happens within the first fortnight. Sometimes it happens on the first day, but every class is different. I wait for that point when I pose a question to the class and I say, ‘Okay, what do you think is the answer to this?’ A variety of hands will go up and I'll select a student at random and they will give me an incorrect answer. Now, the next 45 seconds I find to be critical in terms of the future atmosphere of this class when a student makes an error.
We want to acknowledge that error. But the bigger question is about how I can incorporate that error into the classroom discussion in a way that recognises its incorrectness, while also using it as an opportunity to delve into what is correct, why it is correct, and what specific conceptual or minor errors may have led the student to make that incorrect statement. The goal is to get to the bottom of that in a way that doesn't alienate that student and makes them feel they’re a valid contributor to the conversation. And very importantly for me as the teacher, the aim is that students will be willing to put their hand up in the full knowledge that if they’re wrong, the whole class will learn something from it.
Another way to create safety is to generate questions with enough substance that it takes two or three people to work together. This way, the solution requires a plenary discussion, or there might be a gallery walk where there’s group ownership (and therefore safety) in sharing those ideas. If something is incorrect, then the whole group can stand beside one another and explain why. It removes the personal anxiety about being wrong. Little moves and strategies like this bring the anxiety temperature down.
I love that Dylan William quote where he says, mistakes are a sign that the work you're doing is hard enough to help you learn. I think it's an important idea to embrace. It says to the student who is struggling and repeatedly getting things wrong, there's hope here. This counteracts the idea that a student is just bad at the subject. And it also says something to that high potential or gifted student who is just sailing through and is very comfortable, that perhaps this is a place for them to push – that they’re not in their zone of proximal development anymore.
Eddie and I spoke about the anxiety that can be caused when poor readers are expected to read aloud in English. We tend to ask interpretive questions and often (but not always) require subjective verbal responses. We can create a safe space in this area, but when it comes to reading aloud in front of peers, and without time or coaching for fluency, students can be highly anxious. But Eddie pointed out that Mathematics has a unique problem with the very structure of the subject. He said,
Mathematics in a school context is relentlessly hierarchical, and that causes issues just like language learning. Without the ability to form that strong foundation, you're effectively prevented from progressing. Those issues start early on and may not be an accident. Don’t get me wrong – we rely on our great out-of-subject teachers. But by the end of year ten, around 87% of students had an untrained teacher for at least a six-month period.
Do you think it's a coincidence that the proportion of students who are taking Advanced or Extension subjects in years 11 and 12 is about the complement of 87%? It's about 13%. Now, the reason why that's important is because students without mathematical fluency have no entryway into the ideas being discussed and the skills being developed in lessons, because they’re potentially missing three years of content. Now, as you said, reading is very similar to that, but not all of English is reading. If a student doesn’t understand how enjambment works in a poem, they can still appreciate poetry, even write poetry. English is more cumulative.
In Mathematics, that essential knowledge starts all the way back in Stage Two with developing multiplication facts. If students don't develop that, the train moves on without them. And by the time they arrive in Stage Four, they're developing multiplicative thinking, which is the foundation for fractions, decimals and percentages. Students are up the creek without a paddle without this understanding.
Most of school Mathematics in New South Wales is headed towards calculus, which is underpinned by a basic idea called the derivative, which is a very fancy, specialised fraction. That's all it is. Yet students will often perform all the algorithms and the processes and determine correct answers to questions without ever developing that underlying concept because they missed it six years earlier. This is problematic because it is the development of that deeper understanding which is actually the point. That relentless hierarchy of learning in the school context has wide ranging implications.
The next question I asked Eddie was the most contentious and the trickiest. Essentially, I wanted to know if Mathematics Anxiety deserved its own DSM-5 entry. Students experience many forms of academic anxiety, but only Mathematics has its own brand.
That’s a great question that gets to the nub of the issue. The answer comes in two parts. Do I think it deserves its own categorical classification as separate from all the other varieties of academic anxiety? I think that's a mistake. Do I still think of it as a useful construct, especially when I'm speaking with students and their parents? Could the term help them to understand what they’re experiencing? Could the term help me to help them? I do think the term can be helpful.
I use the term as a sort of compromise because my priority is to communicate as efficiently as I can. People identify in this way, and then that becomes a gateway to unpacking their experiences in more detail. We can talk about other ways to think about Mathematics, and the way that it's taught can free students from those feelings. After that, we can talk about the fact that this kind of anxiety is one breed among many. We’ve talked about reading aloud in English as similar. Let’s acknowledge that it’s real but without treating it as something that’s categorically different to other anxieties.
The prevalence of anxiety does say something about the way Mathematics is being taught. It’s not a given that students will develop mathematical fluency early and therefore have feelings of competence and confidence. Similarly, it’s not a given that they will develop Mathematics anxiety, but give them time in the right environment and you can guarantee that they will.
Why is that? It’s certainly an issue and we as Mathematics teachers need to own it and admit that we’re clearly doing something systematically wrong here. Other subjects don’t have this problem in the endemic way that we do. Let's call that Mathematics Anxiety and recognise there's a problem that we as Mathematics educators need to tackle.