Maths AnxietyUntil I began taking a keen interest in educational research, I must confess that I did not quite realise just how significant a problem maths anxiety is. Ashcraft defines maths anxiety as a feeling of tension, apprehension, or fear that interferes with maths performance. And that is one of the really sad things about maths anxiety - it stops students reaching their potential. In this section I will discuss a number of papers that have had a profound effect on me, and look at their practical implications for the classroom and beyond.
Research Paper Title: Math
Anxiety: Personal, Educational, and Cognitive Consequences
Author(s): Mark H. Ashcraft
This article is a summary of Ashcraft's 30 years of work into the study of maths anxiety. There are a number of key points raised in the paper, but here are a selection that caught my eye:
1) Highly maths-anxious individuals avoid maths. They take fewer elective maths courses, both in high school and in college, than people with low maths anxiety. And when they take maths, they receive lower grades. Highly math-anxious people also espouse negative attitudes toward maths, and hold negative self-perceptions about their math abilities. The correlations between math anxiety and variables such as motivation and self-confidence in math are strongly negative. Now, of course our secondary school students cannot formally opt-out of studding maths until A Level, but they can informally do so. They can study less at home, take part less in class, and talk themselves out of even so much as attempting a problem. And with practice in maths being so vital to success, we end up in a vicious cycle with avoidance leading to poorer performance, which inevitably adds to the existing anxiety.
2) Maths anxiety is only weakly related to overall intelligence. Moreover, the small correlation of 0.17 between maths anxiety and intelligence is probably inflated because IQ tests include quantitative items, on which individuals with maths anxiety perform more poorly than those without maths anxiety. This was a surprise to me. I had assumed a strong relationship between intelligence and maths anxiety. But when I think about it, I can recall many students I have taught over the years who were highly able mathematically, and yet had (what seemed to that stupid, uninformed me) an irrational fear of the subject. The next paper addresses this crucial point further.
3) Timed tests seem to cause anxiety. The researchers found no anxiety effects on whole-number arithmetic problems when participants were tested using a pencil and- paper format. But when participants were tested on-line (i.e., when they were timed as they solved the problems mentally under time pressure in the lab), there were substantial anxiety effects on the same problems. This may seem obvious,. but it in fact poses us with two major problems. Firstly, every major exam that students encounter has a timed element to it. Secondly, as we will see in the Fluency section, without the time pressure students are unlikely to develop the kind of automatic knowledge of key number facts that they need to free up capacity in working memory to solve more complex problems. Perhaps the key is to introduce the timed element slowly and carefully, in a supportive atmosphere, together with a policy of never collecting in or announcing students' scores.
4) Maths anxiety lowers performance because it takes up vital space in working memory. Anxious individuals devote attention to their intrusive thoughts and worries, rather than the task at hand. In the case of maths anxiety, such thoughts probably involve preoccupation with one’s dislike or fear of math, one’s low self-confidence, and the like. Maths anxiety lowers math performance because paying attention to these intrusive thoughts acts like a secondary task, distracting attention from the math task. It follows that cognitive performance is disrupted to the degree that the maths task depends on working memory.
5) Related to this is the finding that maths anxiety to does lower performance in all areas of maths - just the more cognitively demanding ones. Routine arithmetic processes like retrieval of simple facts require little in the way of working memory processing, and therefore show only minimal effects of math anxiety. But problems involving carrying, borrowing, and keeping track in a sequence of operations (e.g., long division) do rely on working memory, and so should show considerable maths anxiety effects. Higher-level math (e.g., algebra) probably relies even more heavily on working memory, so may show a far greater impact of math anxiety. There are two things we can do to help students with this. The first is to try to reduce maths anxiety, and the final paper in this section looks at strategies for this. The second is to ensure students have the relevant knowledge and procedures stored in long-term memory to free up capacity in their working memories. This, of course, is easier said than done, going back to Point 3).
6) Finally, the authors make what I feel is a key point: note how difficult it will be, when investigating high-level math topics, to distinguish clearly between the effects of high math anxiety and low math competence.
My favourite quote:
Math anxiety is a bona fide anxiety reaction, a phobia, with both immediate cognitive and long-term educational implications.
Research Paper Title: Math
Anxiety, Working Memory, and Math Achievement in Early
Author(s): Gerardo Ramirez, Elizabeth A. Gunderson, Susan C. Levine, and Sian L. Beilock
The key finding from this paper is both fascinating and worrying: Students with the highest level of working memory capacity show the most pronounced negative relation between maths anxiety and math achievement. How can this be? We have seen that maths anxiety depresses maths performance because it eats up working memory space. So, wouldn't these students have spare working memory capacity, so anxiety would have less of an impact? The authors explain that there is no definite explanation for this, but that one possibility is that students with the most working memory (WM) capacity tend to rely on more advanced problem-solving strategies. High-WM children, for example, are more likely to use direct retrieval as opposed to finger counting when solving math problems, and retrieval efficiency is particularly disrupted by interference. In contrast, low-WM children’s maths achievement may remain relatively unaffected by maths anxiety precisely because they use less sophisticated (and less WM-demanding) problem-solving strategies. Hence, the association between math anxiety and math achievement may be present among high-WM (but not low-WM) children because math anxiety disrupts the resources that high-WM children rely on to retrieve basic facts from long-term memory and to inhibit competing answers. Even more concerning is the suggestion that maths anxiety-induced disruption of WM leads high-WM children to switch to less successful problem-solving strategies as a means of circumventing the burden of maths anxiety on WM. Ironically, something that usually helps students in maths — large working memory capacity— becomes vulnerable to disruption when they are anxious.
My favourite quote:
In conclusion, our results highlight the potential of math anxiety to negatively impact children’s math achievement as early as first and second grade. The finding that children who are higher in WM may be most susceptible to the deleterious effects of math anxiety is particularly worrisome because these students arguably have the greatest potential for high achievement in math. Investigating the development of math anxiety from the earliest grades will not only increase our understanding of the relation between math anxiety and math performance across the school years but is also a critical first step in developing interventions designed to ameliorate these anxieties and increase math achievement.
Research Paper Title: Math
Anxiety: can teachers help students reduce it?
Author(s): Sian L. Beilock and Daniel T. Willingham
This is a wonderful overview of the research into maths anxiety, including some shocking statistics as to how widespread it is (see quote below). What I found most useful was the authors offering up four practical strategies teachers can employ to help reduce maths anxiety in their students:
1) Ensure fundamental skills. Once again we see the importance of knowledge, not just for thinking but for reducing anxiety. The authors state that enhancing both numerical and spatial processing may help guard against the development of maths anxiety in younger students.
2) Focus on teacher training. The is based on the finding that a teacher's anxiety about maths can be transferred to their students. Ensuring teachers are confident both in their knowledge of the subject and effective ways to communicate content may help with this. I would argue that well-planned lessons following a model of explicit instruction, with worked examples and structured purposeful practice, are easier to deliver and "control" than more inquiry based lessons.
3) Change the assessment. We have seen the maths anxiety is more strongly linked to poor performance when students take a timed test due to the burden it places on working memory. So removing the time element is likely to be beneficial by reducing worries and giving students time and space to consider their answers
4) Use a writing exercises. I must admit,l I had not considered this one. Giving students around 10 minutes to write freely about their emotions concerning an upcoming event (such as an exam) can alleviate the burden negative emotions place on working memory and hence boost test performance.
5) Think carefully what to say when students struggle. Often consolation in the form of "it's okay, not everyone can be good at these kind of problems", validates students' view that they are not good at maths. Better to focus on how you are convinced that hard work will help them get better, crucially following this up with concrete, effective study strategies like those outlined in the Revision section.
My favourite quote:
Math anxiety is not limited to a minority of individuals nor to one country. International comparisons of high school students show that some students in every country are anxious about math. It is perhaps unsurprising that there is an inverse relationship between anxiety and efficacy: countries where kids are less proficient in math (as measured by the Program for International Student Assessment, or PISA) tend to have higher levels of math anxiety. In the United States, an estimated 25 percent of four-year college students and up to 80 percent of community college students suffer from a moderate to high degree of math anxiety. Most students report having at least one negative experience with math at some point during their schooling.