###### Mathematics

#### Math Anxiety: An Important Component of Mathematical Success

Mathematics education in Ontario is a hotly debated topic, a large emphasis lately being on whether we should focus on the newer “discovery math” (also known as “Inquiry-based learning”) or the older “learn-by-rote” approach. While both approaches have their merits and should be used in conjunction with one another, in actuality, this heated and highly-publicized debate represents a false dichotomy.^{1} In this context it should be noted that those advocating for the importance of basic math skills and fluency do not by the same token argue that there should be no focus on problem-solving and ‘discovery’, rather, they argue that a balance is needed. Another, equally important, issue in the math classroom is the role that emotional factors play in math achievement, and, in particular, the role of math anxiety.

Math anxiety refers to the feelings of fear, tension, and apprehension that many people experience when engaging with mathematics. Seen in students as young as six years of age,^{2} math anxiety is a global phenomenon and is highly prevalent. Across 65 countries and economies that participated in the 2012 Programme for International Student Assessment (PISA), on average, 33% of 15-year-old students reported feeling helpless when solving math problems.^{3} Math anxiety is problematic in the classroom not only because it causes the students discomfort ^{4} but also because math anxiety can actually cause students to perform below their actual ability on mathematical assessments.^{5} Indeed, across OECD countries, a striking 14% of the variation in math performance is explained by variation in math anxiety.^{3}

The relation between math anxiety and math achievement is complex in nature. On one hand, research suggests that math anxiety may cause students to perform worse in mathematics by co-opting important memory resources that are needed for success in mathematics ^{6} as well as by causing students to avoid math courses and math homework.^{7} On the other hand, research also indicates that poor numerical and mathematical skills may predispose one to develop math anxiety.^{8},^{9} The most likely scenario is that there is a reciprocal relation between math anxiety and math ability/achievement.^{10}

Given the complex nature of the math anxiety and math achievement relation, understanding the causes of math anxiety can be difficult. Here it is important to note that while particular pedagogical techniques (e.g., speeded math, discovery math, high demand for correctness etc.) may relate to the development and exacerbation of math anxiety, there is currently insufficient evidence to draw any strong conclusions on this. This is important to note since it has been frequently reported in newspapers (for example: Scientific American) that there is a strong association between speeded math and math anxiety. Contrary to these claims, there does not, at present exist evidence to

support this popular claim (for a recent discussion please see: Response to Scientific American article). And indeed, it has been shown that speeded practice can help 1st grade students at risk of developing mathematical difficulties to compensate for weak reasoning abilities.^{16}

A notable and troubling finding is that, in a number of situations, one person’s math anxiety can impact another persons’ math achievement and math anxiety.

For example, when teachers are high in math anxiety this can translate into their students learning less math across the school year and being more likely to endorse negative stereotypes about mathematics.^{2} This finding is especially concerning as elementary school teachers are known to have particularly high levels of math anxiety.^{11} It is also important to note that when parents who experience high math anxiety frequently help their children with their math homework, then this help can backfire, leading the child to learn less math and to become more math anxious themselves.^{12}

The good news is that researchers have made great strides in understanding both the causes of math anxiety and ways in which we can combat it in the classroom. A few straightforward and inexpensive techniques can go a long way in terms of reducing the impact of math anxiety on achievement. For example, simply asking students to write about their worries for a few minutes before they take a math test boosts performance for highly-math-anxious students.^{5} Further, teaching anxious students to think of math as a “Challenge“ that they can overcome, rather than as a “Threat“ to their ability may go a long way in helping them to succeed in mathematics.^{13} Also important is addressing the issue of teachers` math anxiety. Here, research has demonstrated that courses for teacher candidates that focus on how students learn math (rather than focusing on the math content that needs to be taught) can actually reduce the math anxiety of the teacher candidates.^{14} And, reducing teachers` math anxiety may go a long way in increasing the math content that students learn. As such, new policies should emphasize both (1) implementing techniques to reduce the math anxiety of teacher candidates, and (2) creating professional development courses for future and current teachers that focus on how to detect math anxiety in students and the strategies that can be helpful in reducing the negative impact of the anxiety on student outcomes.^{15}

Math anxiety is pervasive among students, teachers, and parents. Given the very real negative impact that it has on students’ achievement, and the availability of easy-to-implement and cost-effective evidence-based strategies to help combat the negative impacts of math anxiety, it is critical that math anxiety be central to the discussion around why our students are not excelling in math. Indeed, until we include math anxiety in this important discussion we will continue to be ignoring a large part of the equation.

^{1} Ansari, D. (2015) No more math wars: An evidence-based, developmental perspective on math education. Education Canada, 53

^{2} Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences, 107(5), 1860-1863.

^{3} OECD: PISA 2012 Results: ready to learn: students’ engagement drive and self-beliefs (Volume III) .PISA, OECD Publishing; 2013.

^{4} Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197-205

^{5} Park, D., Ramirez, G., & Beilock, S. L. (2014). The role of expressive writing in math anxiety. Journal of Experimental Psychology: Applied, 20(2), 103.

^{6} Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of experimental psychology: General, 130(2), 224.

^{7} Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for research in mathematics education, 33-46.

^{8} Maloney, Erin A., Evan F. Risko, Daniel Ansari, and Jonathan Fugelsang. “Mathematics anxiety affects counting but not subitizing during visual enumeration.” Cognition 114, no. 2 (2010): 293-297.

^{9} Maloney, E. A., Ansari, D., & Fugelsang, J. A. (2011). The effect of mathematics anxiety on the processing of numerical magnitude. The Quarterly Journal of Experimental Psychology, 64(1), 10-16.

^{10} Carey, E., Hill, F., Devine, A., & Szücs, D. (2015). The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance. Frontiers in psychology, 6.

^{11} Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for research in mathematics education, 33-46.

^{12} Maloney, E. A., Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2015). Intergenerational effects of parents’ math anxiety on children’s math achievement and anxiety. Psychological Science, 0956797615592630.

^{13} Maloney, E. A., Sattizahn, J. R., & Beilock, S. L. (2014). Anxiety and cognition. Wiley Interdisciplinary Reviews: Cognitive Science, 5(4), 403-411.

^{14} Tooke, D. J., & Lindstrom, L. C. (1998). Effectiveness of a mathematics methods course in reducing math anxiety of preservice elementary teachers. School science and mathematics, 98(3), 136-139.

^{15} Beilock, S. L., & Maloney, E. A. (2015). Math Anxiety A Factor in Math Achievement Not to Be Ignored. Policy Insights from the Behavioral and Brain Sciences, 2(1), 4-12.

^{16}Fuchs, L.S., Geary, D.C., Compton, D. L., Fuchs, D., Schatschneider, C., Hamlett,D. L., Seethaler, P. M.,Wilson, J., Craddock,C. F., Bryant, J. D.,Luther, K. & Changas,P. Effects of First-grade Number Knowledge Tutoring with Contrasting Forms of Practice, Developmental Psychology 105 (2013): 58-77.

**Erin Maloney**

Erin Maloney is a Senior Researcher at the Higher Education Quality Council of Ontario (HEQCO). She holds a PhD in cognitive psychology from the University of Waterloo and worked for four years as a Postdoctoral Research Scholar at the University of Chicago.

Erin’s research program sits at the intersection of cognitive development and education. She explores the cognitive and social factors that influence performance in mathematics and spatial processing. In particular, she focuses on the role of numerical competency, anxiety, and stereotypes in math and spatial achievement. In addition to answering basic questions about cognition, with her research, she aims to inform educational practice and policy.

**Jonathan Fugelsang**

Jonathan Fugelsang is a Professor of Psychology at the University of Waterloo. His research spans several areas in cognitive psychology and cognitive neuroscience. Most recently, his lab has focused on understanding the interplay between intuitive and analytic processes supporting complex reasoning and decision making. These decisions may involve analogical, deductive, or numerical information. His lab has also extended their lines of inquiry to look at the role of intuitive and analytic processes in real world domains, such as creativity, moral judgments, religious beliefs, and technology use.

**Daniel Ansari **

Daniel Ansari is a Professor and Canada Research Chair in Developmental Cognitive Neuroscience in the Department of Psychology and the Brain & Mind Institute at the University of Western Ontario in London, Ontario, where he heads the Numerical Cognition Laboratory (www.numericalcognition.org). Ansari and his team explore the developmental trajectory underlying both the typical and atypical development of numerical and mathematical skills, using both behavioural and neuroimaging methods. He has a keen interest in exploring connections between cognitive psychology, neuroscience and education.