Causes and consequences of math anxiety in children

Scott Askey: Is there such a thing as a math brain? I’ve often heard that.

Daniel Ansari: That's a really good question. I think there is such a thing as a math brain, and we all have one. We all come into this world with a basic toolkit for having intuitions around quantities and numerical amounts and later on through schooling, we expand on that initial toolkit. Of course, there are differences between people just like there are differences between people in all sorts of aspects of life and learning. However, I think it's fair to say that we're all born with a basic toolkit for learning math, and that most children – given the right environment and the right conditions – are able to learn the most fundamental aspects of mathematics that will help them to be successful in their lives.

Scott Askey: In your opinion, and through your research, would you say some people are naturally better at math than others?

Daniel Ansari: I think that's a really difficult question to answer. Of course, there are individual differences, and there's so many factors that play into how good somebody is at any given thing, whether that be math, or carpentry, or any kind of sport activity that we might engage in. Often those things are a combination of biological factors and environmental factors – where we grew up, how we grew up, how our families interacted with one another, what kind of opportunities were being given to learn?

So, it's very difficult to say that there are some people who are naturally better at math. I think there are differences, but those differences between people are due to a multitude of factors that are both biological and environmental, and often the product of the interaction between our biology and the environments in which we grow up in. But I think the most important message is that there is no simple formula by which we can say, ‘this person is going to excel at math and this person isn't.’ 

We also need to remember that we all have the basic capacity to become competent in math, to feel confident about our mathematical abilities. At the upper levels of math, university mathematics, PhD-level mathematics – those mathematicians certainly have math abilities that exceed my own capacities, but again, there is no simple answer to the question of, how do you become a university level mathematician? It's unclear – there are so many different factors that are involved.

Scott Askey: As a former teacher and educator, I've been a principal at four schools, and now as a System Principal, I have heard countless times from adults, students and sometimes families say, I'm not a math person.

Daniel Ansari: I think that's something that people are very willing to say, especially in western societies.

I wouldn't even know what it means to be a math person. I guess it might mean that people don't like math. It could mean that they feel that they're not able to do the math, but from a research perspective, there's no evidence to suggest that there are some people who we could call math people and other people who we would say they're not math people. It's far too much of a simplistic division and I think sometimes it's just people's way of dealing with the negative experiences that they might have had with mathematics throughout their lives.

It might be about the math anxiety that they experienced, but I wouldn't say there is something as simple as saying, somebody is a math person and by implication therefore other people are not. We all have basic mathematical abilities, and if we're put into the right environments, given the right level of attention, and the right level of teaching, most people are capable of reaching a level of mathematical understanding and skills that will enable them to be successful in their lives.

Scott Askey: I was driving one of my children to one of their activities the other day and stopped at a friend’s house to pick up their child and the parent said, ‘so what is math anxiety anyway?’ How would you summarize that for this parent?

Daniel Ansari: I would say math anxiety is a feeling of apprehension, of dread when you're put in a situation where you have to engage in mathematical problem solving. It can also be associated by physical arousal, by increases in heartbeat. It can be measured using galvanic skin responses, so it's both a psychological and physiological reaction to having to engage in doing math.

What the research suggests is that when we experience mathematics anxiety, just like with any other anxiety, we start to engage in ruminations about that. We start to think, ‘I'm not going to be able to do that. I'm terrible at math.’ Those ruminations start to occupy our mental capacity so that we actually end up having less room to focus on the math itself.

In psychology, we call that a dual task. It's almost like we're trying to solve two things at the same time. We're trying to do the math, but we're also trying to deal with the emotions that the math has elicited within us – the physiological reaction, as well as the psychological reaction. So that's why some people think math anxiety affects your math performance. It's not necessarily that when you're math anxious, you're not good at math. It's that the anxiety takes away part of your available resources to actually be able to engage in the mathematical problem solving.

Scott Askey: In my former role as a school principal, I would see what you're just describing play out sometimes in the classroom as misbehaviour, or a student checking out, or daydreaming. My initial reaction would be, ‘get to work, open your textbook, grab that pencil.’ But hearing you describe math anxiety, I need to reflect on my past practice and even how I was taught when I was a student.

I think what you're saying is we're learning more about what it truly means to go through these emotions and how our brain reacts. 

Daniel Ansari: I think sometimes if students are starting to seem distracted, it's because they're trying to deal with the anxiety and some of the mistakes that they might make during problem solving, maybe due to the fact that they're essentially trying to do two things at the same time. They're trying to control their emotions, and they're trying to solve the problems. This is why some research has shown that it's really effective for students, especially older students – high school and university students – to write about their feelings towards math before they, for example, take a test, because that can externalize those negative emotions and free up their mental resources. This is something that we in psychology call working memory, their ability to hold multiple items of information in their minds at the same time, which is very important in mathematics where you often have to hold intermediary solutions in mind while you're still solving the problem. So, freeing up that working memory by essentially displacing those negative emotions on a piece of paper has been shown to be quite effective.

There are ways of coping with math anxiety. I think generally talking about it is not just helpful for students, but could also be helpful for educators who themselves might be experiencing mathematics anxiety.

The way I like to think about math anxiety, is math anxiety doesn't just occur within the individual student. It’s part of an ecosystem. Part of that ecosystem is the family, the school, the teachers, the peers – all of these different things affect the level of math anxiety that a student might experience. 

Scott Askey: I truly believe we all have a math story and sometimes we can replay that story. It starts earlier for some folks than others. For my own situation, it was grade 11 in secondary school when it finally hit, some of those feelings of anxiety. Before that I always thought I was a quite proficient in math. 

How early on do you think math anxiety starts for an individual? 

Daniel Ansari: The answer is some research suggests that even children as young as five years of age can experience math anxiety. However, I would say that the way in which researchers currently measure math anxiety is by asking students how they feel about doing math. That becomes more difficult the younger the student is. It's very difficult for kindergarten children to reflect on their own emotions. I would say the best evidence we have is in early elementary school. 

We have very good evidence to suggest that as young as grade one or grade two students can begin to experience math anxiety and it only gets worse from that point on, because obviously the math becomes more complex, and the pressure might be greater. The influence of peers might increase as you start to perceive more differences between yourself and others in the classroom. Math anxiety, as far as we know, can begin as early as kindergarten, although the evidence there I wouldn't say is yet rock solid. I think when it comes to elementary school students, there's definitely very good evidence that elementary school students experience mathematics anxiety. 

Scott Askey: We mentioned students quite a bit already during this webinar. How does math anxiety impact other individuals who interact with students? 

Daniel Ansari: There's some really interesting research on teachers’ math anxiety. Teachers, just like anybody else in the world, can experience math anxiety. The problematic thing here is that research also shows that the math anxiety of teachers can influence the math anxiety of students. In other words, there can be sort of a transfer of math anxiety.

Research by Sian Beilock at the University of Chicago showed this in several studies now that teachers’ math anxiety at the beginning of the school year predicts students’ math anxiety as well as their math achievement at the end of the school year. Although those students weren't necessarily math anxious at the beginning of the school year, they become math anxious. Her work seemed to suggest that the teachers’ own math anxiety influences the students’ math anxiety.

In one study, they found the way that math anxiety transferred from the teacher to the student was through the student suddenly endorsing common stereotypes, such as the stereotype that boys are better at math than girls. So, it’s possible that teachers can model these stereotypes inadvertently, as well as their math anxiety, and that is a dangerous cocktail that leaves students feeling math anxious. That, in turn, can affect their math performance. 

The other individuals who can be involved in this ecosystem are parents themselves. There's work by Erin Maloney at the University of Ottawa, who showed in a study that parental math anxiety also affects students’ math anxiety. It turned out that this was particularly pronounced for highly math anxious parents who engaged in a lot of homework with their children. You and I can both picture that situation where a parent who themselves is not very confident about their mathematical abilities, then engages in homework with the child and you know this can lead to a high stress situation. To the parents who are listening in tonight – I would say be aware of your own feelings towards mathematics and how that might negatively influence the way in which you interact with your child during homework. Try to think about how you might reflect on your own emotions beforehand and try to take that into account. Otherwise, the good intention of wanting to help your child with their homework could turn into something that is actually not having the desired effects. 

Scott Askey: Yes, the struggle with homework is one of the most challenging and can be one of the most stressful things for families. We've heard that for years. So as educators, we need to be mindful of all the things the families are dealing with and need to be able to support not only our students, but families as well. 

Scott Askey: You touched on this earlier, but I'd like you to go a little deeper into if math anxiety affects math achievement and achievement overall. 

Daniel Ansari: One of the things that's clear from a lot of studies from around the world is there’s an association between math anxiety and math achievement. Students who have higher math anxiety typically have lower math achievement, but this association is very small. It's not a very strong association, and I think that's a very important thing to note. 

There is a consistent relationship between math anxiety and math achievement, but we don't know what the direction is. We don't know whether math achievement leads to math anxiety or math anxiety leads to math achievement, or if they are fluidly interacting, which I think is quite likely. The important thing here is that anybody who experiences math anxiety, we shouldn't assume that they are not capable of learning mathematics, or that they aren’t good at mathematics.

There's now work coming out showing that students who have math anxiety approached the whole task of engaging in mathematical problem solving very differently. They're very quick to look for shortcuts. They don't focus on challenging problems. It's not just in the ability, but it's also in the approach to mathematics that math anxiety expresses itself.  

I think it's really important to note that math anxiety is not the same thing as having, for example, a weakness in math or a developmental dyscalculia or math learning difficulties. Math anxiety and dyscalculia (math learning difficulties) are two very different things. Students with math anxiety, on average have poorer math achievement, but that association is very small, and we don't know the direction of it. I think that gives us some level of hope that when students are experiencing math anxiety, we shouldn't assume that they are not capable of doing the math. There's something emotional in their way. We can work towards alleviating this by having conversations about it, by thinking about strategies to alleviate it. I think that's a hopeful message, at least for me as a researcher, because it suggests that these things are very different and that the emotional and the cognitive side of doing math are different things, although they interact. 

Scott Askey: There's just so much information out there and it's such a complex issue, but isn't some level of anxiety healthy? Is a certain level of stress good for performance? 

Daniel Ansari: There's certainly a function whereby a certain level of arousal is positively related to all sorts of learning outcomes. If it exceeds a certain threshold, it starts being negative. The question is, where's that threshold for an individual? 

There is some work suggesting that a certain level of math anxiety may actually be productive in certain situations. It's when it becomes something that is essentially arresting the individual and they're not able to cope with the situation that requires them to engage in problem solving or recall facts – it is in those situations that I think it’s particularly debilitating. 

We also have to remember that in this context you cannot say somebody has math anxiety or somebody doesn't. It's on a spectrum; it's on a scale. You can have some students that are very highly math anxious and some that are sort of middle to low math anxious, so it's not categorical in that way. It's more of a continuous scale on which we rate students’ math anxiety. It's the ones at the higher end that we should be particularly worried about.  

Scott Askey: I like how you phrased that, because sometimes I find we're all or nothing. Then the student believes they’re not good at math. So, you're saying certain level of anxiety is okay, we just need to know our children or students to know what that critical threshold is. 

Scott Askey: Let’s get to some strategies. If we, in our classrooms see students with a high level of anxiety, or maybe it's with homework at home, what are some things that we can do?  

Daniel Ansari: I think the first thing is to have a conversation about those emotions to try to acknowledge them. Try to make the student feel as though their reactions towards math are not something that is unusual or an indication of a problem. Then start to suggest solutions: taking more time on a particular task. Having a conversation with the parents when possible to make them aware that this is a situation and that there are also things in the home that can be done to lessen that anxiety. Not exerting a lot of pressure on the student to put them in situations where the math anxiety may be exacerbated. I think those are some strategies that one could develop. 

There's this expressive writing idea where you write about your feelings; write about your anxiety. You might be able to do that through drawing as well with younger children. I think it's that openness, and I think that educators and parents need to be part of that and acknowledge their own math anxiety, if it does exist, and how that might play into the student’s math anxiety. 

Interestingly, we've also in a recent paper found that when we think about math anxiety, it's not just that the individual student has math anxiety that affects their math performance. We found in a study of almost a million students taking data from international comparison studies, that there's also an effect of math anxiety at the classroom level. In other words, in classrooms where there are more students with high math anxiety, there's also on average lower math achievement. We call that a contextual effect. For example, there is Johnny, who has math anxiety, and that math anxiety affects his math performance, but then if Johnny is put into a classroom with lots of other high math anxious individuals, that problem actually gets exacerbated. But if Johnny is in a classroom with students who on average have low math anxiety, that might mitigate his individual high level of math anxiety.

Going back to your question, what can we do? I think there's also something around the classroom atmosphere and how certain students are grouped together and which students are working together collaboratively on math problem solving. It’s probably best not to group all the highly math anxious students together because of that contextual effect. 

I know that the new math curriculum also includes socio-emotional learning, so it seems that these less cognitive and more emotional issues are being taken more seriously these days in school systems around the globe. I think that's a positive sign for helping those students who have math anxiety who are otherwise perfectly capable of doing the math. Hopefully they’ll eventually discover the beauty of math and a fascination with math. 

Scott Askey: Individuals are complex. Our lives are complex. We don't come into a situation without any previous lived experiences, biases, or beliefs. I think we, as parents, families, and educators, need to be aware of all that our children and students are bringing with them to our classrooms, to our dinner tables to do homework. None of these factors act in isolation. 

Many educators across the Thames Valley District School Board and I'm sure other districts across Ontario are really trying to focus on connecting with families and really understanding our students in a deep way. Math is so much more than just correct and incorrect answers.  I think sometimes in our culture in our western society that's often lost, and we need to know what our students are dealing with, and have them go through a number of experiences so they can see all the opportunities that math can afford them. 

Daniel Ansari: You know, context is everything when it comes to any aspect of child development. This is also really important because sometimes we try to find something to blame. And unfortunately, human beings are much more complicated than that. We don't have some single cause that makes us experience math anxiety. It's a multitude of causes. I think that's really important that we try not to adopt the lens whereby we try to find this single factor that we could turn this dial and then everything will be okay. We have to look at it more holistically and the overall context is critically important.

We can document the contextual effect that we found whereby the average level of math anxiety in the classroom over and above the individual’s math anxiety in that classroom affects math performance. We also found that this varies a lot between different countries. Again, pointing to that role of the context – that things play out differently in different contexts, so these things need to be taken from that contextual lens. It's great to hear that schools and school boards are thinking along those lines, because I think that's one sure recipe for ensuring great engagement and success in the long run. 

Scott Askey: I know our educators are really focused on understanding our students’ lived experiences, cultures, and everything that the student brings with them to the classroom. I really enjoyed listening to you speak about how our brains react when we're in various situations. As an educator, the science of how our brain operates might not be my first go-to in the classroom or as a principal visiting classrooms during math class. But it's certainly important for us to be aware as educators about what's happening physiologically to our bodies and then what we can do in the classroom to help alleviate some of that stress and anxiety for our students. 

You've mentioned writing, possibly drawing, talking it out, and doing some rehearsals before a test. Some other strategies that I know our educators are working on are mindfulness activities, breathing to disconnect from that stressful situation, so then you're more available and open for that test or that learning situation. Anything else come to mind off the top of your head? 

Daniel Ansari: Maybe one that people should be a bit careful about doing is immediately running to tutors. 

One of the things we found in this large international study – this is work by my postdoc, Nathan Lau. What Nathan found was that there was a negative association between tutoring and math anxiety. So, on average, those students who have more extracurricular tutoring, experienced higher math anxiety. The same was true for homework. Of course, we can't say that's causal, but I think sometimes as a parent you worry and then you think, maybe I should enroll my child into tutoring. In certain situations that may be advantageous, but just be aware that there is also research literature on the effects of tutoring. Maybe you are a very keen parent. You really want to help your child learn math and you buy all sorts of books and go to the library and then you say, ‘let's sit down for one hour every night and do math.’ As a parent, it of course comes from a very good place. You think this is going to really help your child get more confident at math, but it may also produce the opposite. Sometimes the things that we think will be the fixes or will be the kinds of things that will help our children excel, could also invariably turn out not to be that and could turn out to be the reverse. 

Scott Askey: Does math anxiety mean maybe more math would be better? 

Daniel Ansari: I would certainly say not in situations where the child is resisting because that is then going to exacerbate the anxiety and potentially harm the mathematical relationship between the parent and the child. Maybe that’s something to treasure that you have – you can talk about math and have challenging math questions. For example, in the car as you ride to hockey practice. It doesn't need to be a sit down for one hour and you must complete this worksheet. I think those things could backfire for a student who's already feeling overwhelmed by their math anxiety. I would also say, especially for the parents out there, trust your schools and the teachers within those schools to know your child and to alert you when there is something going arise. There are systems in place that allow for that, and I think that there are ways in which red flags will be communicated. 

Scott Askey: We know not everything can be fun, but we definitely want to change the narrative of maybe what some of us experienced as adults in math classrooms. When you were talking about worksheets, that's what many adults remember from their schooling as children and I just want to reassure the families, parents and caregivers that are listening that we do so much more in our classrooms than just paper, pencil worksheets. Learning math can mean so much more than just regurgitating basic facts. Math can be really deep, higher-level thinking, problem solving, discussing mathematics, collaborating, working together. It can involve games. 

One of the number one pieces of guidance I like to relay to all families is when you're working with your child at home, make it fun. Math is everywhere. Math is in your kitchen. Math is in creating a budget. Math is when you're getting gas at the gas station, calculating how many litres, and estimating. I think sometimes that's often forgotten. We get caught up in what we remember learning used to look like 40+ years ago. Our school board and our math department are really focused on learning math for real purposes and for everyday life reasons. We see that reflected in the new Ontario curriculum for grades one to nine with financial literacy, with coding, developing a budget, sales tax, etc. So make it fun. Rest assured our educators are doing their best too. 

Daniel Ansari: One thing you mentioned that really resonated with me is this idea of discussing math, of working on a single problem and exploring it. There was a study some years ago now called the TIMSS Video Study. It produced two great books: one called The Learning Gap and the other called The Teaching Gap. It was about international comparisons. What they were able to show was through filming math classrooms – these were grade 8 math classrooms –they were able to show that in the United States, which never does particularly well in international comparisons of math education, teachers will present a lot of problems in any given class unit. While teachers in Japan will sometimes only present two problems but discuss them in great depth and discuss multiple solutions. They let students generate solutions but don't immediately correct them. They don't immediately say this is wrong. They try to get the opinion of somebody else. I think that really illustrates that when you're doing math at home, sometimes less is more. Really talk about a problem and think with your child about multiple strategies that you could use to approach that problem. 

The other thing is using visualizations can be so powerful – number lines or other ways of visualizing math. Spatial ability, spatial cognition, and mathematical cognition are so intertwined in the brain that I think using some kind of external reference – if you've got a blackboard where you normally put your shopping list, or you do it on a computer screen – can be really important as you discuss mathematics with your children. Since they are doing it in class, they can sometimes show you strategies as well!

Scott Askey: I have so many classrooms in mind where I know our educators are focused on letting students explore the mathematics with an end goal. Knowing those students learning needs; trying to meet students exactly where they are; personalizing the instruction to bring them along at the right pace, so the challenge is just right; and, using different strategies, different representations, or even tactile-like concrete tools.  

I find sometimes we are too quick as adults to take on an abstract concept and try to have students learn it in an adult way, or in a way that we remember we learned it. But we need to break down those concepts. Our educators are really finding the use of different concrete tools – whether that's counters or different models like linear models or bar models – are quite helpful.

Scott Askey: What I've gathered more than anything is how complex this issue is. You’ve provided some great strategies that we can go forward with in our classrooms and in our own households too.  

Daniel Ansari: We shouldn't adopt a simplistic view of math anxiety. Remember that if you experience math anxiety, that doesn't mean math is cut off for you. It might be quite the opposite. It might be an opportunity to think about how you might enjoy math differently. 

The other thing is it's really important to remember that math is so many different things, which is why I like the fact that in the UK, you call it maths to pluralize it, because it really is that. In this way, it's different from learning to read. There are so many different aspects of math so if you weren't particularly good at calculation, it doesn't mean that you're not going to be very good at geometry or statistics or some other aspects of mathematics or coding or financial literacy. There are many entry points to mathematics as well, and I think it's important to remember that if you're anxious about one thing, that may not mean that you wouldn't enjoy and not be held back by anxiety when it comes to other aspects of math.  

Scott Askey: I love how you said entry points, because that's how our educators are approaching mathematics in the classroom on a daily basis. Trying to find that right entry point on any given day for any given student so they can be successful. Too often in the back of our mind we’re very product focused, task-oriented in our culture. We don't want to lose sight of just getting the job done. We need to break things down to make it really accessible for all students and then gradually work to the more complex without jumping too quickly to that abstract. 

What role do you think that rote learning procedures and memorization plays in math anxiety? 

Daniel Ansari: That we don't know yet. I think if it's done right, it shouldn't play a role. It could play a role if it's done under great pressure situations. I know of people who are investigating this very question. I think this would be a broader conversation, but if we think about procedural versus conceptual, these are always interacting with one another. If one does procedural right, it can be incredibly fun for students, but if it's attached with pressure and high stakes, that could potentially also result in math anxiety. But that link is not yet clear from the research literature.