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Mathematics Anxiety
Written by:
Alex M. Moore, M.A., Ph.D. Candidate and Mark H. Ashcraft, Ph.D., Department of Psychology, University of Nevada, Las Vegas
Published online:
2012-04-05 21:32:36
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The topic of mathematics anxiety is receiving increasing attention within the psychological literature due to its persistent and often detrimental influence on educational achievement. Briefly, mathematics anxiety is a negative affective or emotional reaction to numbers, math, and mathematics calculations (Ashcraft & Moore, 2009).  Richardson and Suinn (1972) originally defined math anxiety as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (p. 551).  These situations may include, but are not limited to, calculating the tip on a restaurant bill or taking a consequential math examination (e.g., college entrance). Although some reactions to math may be mild and perhaps insignificant (McLeod, 1994), others are more pronounced or even severe.  As an example, we had a college adult burst into tears because of the anxiety experienced while completing simple subtraction problems (Ashcraft, 2002).
Historically, research in math anxiety has focused on its relationships to similar affective states, such as test or generalized anxiety, and how these factors relate to educational outcomes.  More recently, research has focused on how math anxiety alters ongoing cognitive performance.  The evidence shows that math anxiety disrupts cognitive processing at many levels, and can be a significant impediment to math achievement.
Key Research Questions
1) What is math anxiety related to and what are its consequences?
2) How are mathematics anxiety and math performance related?
3) What are the risk factors of math anxiety and who is susceptible?
Recent Research Results
What is math anxiety related to and what are its consequences?
We characterize math anxiety in our research by appealing to the construct of “avoidance.”  By this, we mean that the presence of math anxiety in the individual is strongly associated with a host of negative beliefs and attitudes towards math, such that the individual attempts to distance him or herself from situations that involve mathematics (Ashcraft, Krause, & Hopko, 2007; Ashcraft & Moore, 2009). Examples of this include speeding through unavoidable tasks in order to finish quickly, regardless of errors, or avoiding elective coursework, and even career paths, involving math.  Such behaviors allow the individual to minimize or avoid experiencing math anxiety, although with unfortunate consequences on math achievement.
Summaries about the relationships between math anxiety and other personal and educational factors come from two meta-analyses on the topic, one by Hembree (1990) and one exclusively on students under the age of 18 by Ma (1999).  An important point to make explicit is that math anxiety is not a strong correlate of intelligence. Correlational data do indicate a weak relationship with overall IQ, but if only verbal intelligence scores are considered, the relationship between math anxiety and IQ disappears altogether (see Hembree, 1990, and Ma, 1999, for all statistical values). Math anxiety does correlate with other anxiety measures, however.  The strongest relationship is with test anxiety, and somewhat weaker relationships exist with general, trait, and state anxiety.  Thus, although there is some overlap, math anxiety is considered to be a separate form of anxiety from other, more familiar forms of anxiety.
Importantly, math anxiety is inversely related to desirable attitudes towards mathematics.  These relationships suggest that math anxiety belongs to a group of “avoidance” affective states (Ashcraft & Moore, 2009; Moore, Rudig, & Ashcraft, submitted). The relationships among avoidance and desirable attitudes towards mathematics are quite strong.  Higher math anxiety is associated with lower enjoyment and lower self-confidence in math tasks among students under the age of 18, and also with overall lower math motivation.
The most alarming relationships, though, are the inverse relationships between mathematics anxiety and educational outcomes.  In high school samples, math anxiety correlates negatively with math achievement scores and high school math grades.  Similar negative relationships are found in college samples.  Thus, it is clear why math anxiety is important to understand; high school and college students need to excel in standardized examinations (e.g., mandated proficiency tests) to continue in their education, and yet students with higher math anxiety tend to have lower math achievement and lower grades. 
How are mathematics anxiety and math performance related?
In addition to the distressing relationships between math anxiety and math achievement, further evidence demonstrates that math anxiety is strongly associated with difficulties in online math performance. This has been observed in relatively challenging math calculations in arithmetic (Ashcraft & Faust, 1994; Ashcraft & Kirk, 2001; Faust, Ashcraft & Fleck, 1996), as well as some basic math skills such as counting (Maloney, Risko, Ansari, & Fugelsang, 2010b) and number comparison (deciding which of two single-digit numbers is larger or smaller; Maloney, Ansari, & Fugelsang, 2010a).  Thus, this impediment related to math performance and math anxiety seems to be present at any level of computational difficulty.
To explain these deficiencies in performance, a large body of research indicates that the specific mental mechanism affected by math anxiety is working memory (see http://literacyencyclopedia.ca/index.php?fa=section.show§ionId=239 for a full review).  Briefly, working memory commonly refers to a limited capacity mechanism employed to integrate, compute, and manipulate information at the forefront of an individual’s attention (Baddeley & Logie, 1999; Engle, 2002; Miyake & Shah, 1999).  This mechanism has been long known to be integral for a wide range of cognitive domains, such as language, memory, and overall intelligence. More recently, working memory has been shown to play a vital role in mathematics performance (e.g., De Rammelaere, Stuyven, & Vandierendonck, 1999; DeStefano & LeFevre, 2004; Imbo & LeFevre, 2010; Imbo & Vandierendonck, 2007, 2008; Raghubar, Barnes, & Hecht, 2010; Seyler, Kirk, & Ashcraft, 2003).      
For example, Ashcraft and Kirk (2001) tested high and low math anxious participants in a two-column addition task (e.g., 25+13).  The experiment required participants to complete these additions while simultaneously holding either two or six random letters in memory for later recall, thus consuming important working memory resources needed for efficient addition.
The results from this “dual task” experiment showed that addition placed a heavy load on working memory, especially when carrying from the one’s to the ten’s column was required (e.g., 28+15 where adding 8 + 5 yields a carry to the ten’s column, that is regrouping 13 into 3 ones and 1 ten).  This was shown through an increase in errors on letter recall. Relevant to the math anxiety debate was the finding that high math anxious participants showed an especially pronounced increase in errors compared to the low anxious participants.
The explanation for these results was that those with high levels of math anxiety had already used a large portion of their working memory resources by having to cope with anxious thoughts brought on by the anxiety, thus leaving fewer resources with which to work on the addition problems.  When confronted with an especially taxing addition problem involving the carrying operation, the high math anxious participants had fewer working memory resources available for completion of the task, which became even more problematic because of the simultaneous letter memorization.  In later work, we proposed that this three-way competition for working memory resources led to an “affective drop” in performance, a noticeable drop in performance associated with this emotional reaction to mathematical information (Ashcraft & Moore, 2009).
What are the risk factors of mathematics anxiety, and who is susceptible to develop it?
We know that females from Grade 6 through college tend to report somewhat higher levels of math anxiety than males.  Also, math anxiety peaks around the ninth and tenth grades, after which it levels off into adulthood (Hembree, 1990).
Because little research exists concerning very young children, we recently proposed a model concerning risk factors, susceptibility, and developmental onset, in order to spark research on this topic (Ashcraft, Krause, & Hopko, 2007). Essentially, the model proposes that those children who have adequate levels of math skill, motivation, and working memory will advance adequately throughout mathematics curricula.  However, a child of low ability, motivation, or working memory could be susceptible to developing math anxiety, as would a child vulnerable to social- or performance-based anxiety.  These risk factors could contribute to the child’s struggles with even basic level math concepts.  This failure to develop math proficiency, then, could lead a child to fall behind in mathematics compared to their peers, and influence the progression of later deficiencies in mathematics (De Smedt, Verschaffel, & Ghesquière, 2009; Dehaene, 1997; Geary, 2011; Jordan, Kaplan, Olah, & Locuniak, 2006; Siegler & Booth, 2004). The logic follows, then, that inadequate proficiency in math, and inadequate progress in comparison to peer performance would prompt negative feedback from parents and teachers, which could then influence the child to develop negative attitudes and low motivation towards mathematics.  Children with lower working memory could also share this trajectory of development, as the literature indicates the importance of working memory in math calculation, especially as the math problems become more complex (Engle, 2002; LeFevre, DeStefano, Coleman & Shanahan, 2005; Raghubar et al., 2010).
These factors could then lead to the avoidance characteristics of math anxiety, resulting in the individual avoiding higher-level math courses, or performing poorly if enrolled.  This will then leave them underprepared for math testing situations, causing the affective drop in performance discussed earlier (Ashcraft & Moore, 2009).  This cycle of math failure, even in young children, could result in the pairing of math situations with high degrees of anxiety, leading the individual to dread situations involving mathematics.
Future Directions
Notably absent in the math anxiety literature is a thorough assessment of math anxiety in young children, and evidence on how math anxiety develops in childhood.  As mentioned, however, research has begun to examine these issues.
Although at first glance seemingly unrelated to the development of math anxiety, Maloney and colleagues have begun exploring the extent to which math anxiety and basic numerical abilities are related in adults.  These studies have shown that fundamental skills like counting (Maloney et al., 2010b) and number comparison (Maloney et al., 2010a) are correlated with math anxiety.  It stands to reason that if adults show these base level process deficiencies, there may be exaggerated effects in children, given the early age at which these processes appear.  Maloney suggests the possibility that deficiencies in such basic math abilities could be one precursor for the development of math anxiety (see also Rubinsten & Tannock, 2010, for a similar argument). 
Another promising line of research would explore societal roles in the development of math anxiety.  Hembree (1990) reported that college students preparing to be elementary school teachers actually have the highest prevalence of math anxiety, compared to other majors.  A distinct possibility, therefore, is that math anxious teachers might convey this anxiety to their students, and negatively influence their students’ performance.  To explore this, Beilock, Gunderson, Ramirez, and Levine (2010) measured the math anxiety of first and second grade teachers, and tracked the math performance of their students, at the beginning and end of the school year.  Because children at this age are susceptible to same-gender stereotypes, they predicted that female students especially would be affected by (female) teachers’ math anxiety. As a consequence of internalizing these attitudes, students’ math performance would suffer at the end of the school year.  This is exactly what they found.  Although there were no gender differences in performance at the beginning of the year, they found that the higher the teachers’ math anxiety, the worse the female students’ performance was at the end of the year.  The males’ performance was not altered.  Because elementary school teachers are almost exclusively female (at least in North America) and elementary school teachers are the group with the highest prevalence of math anxiety, it seems that the female students were probably learning the apprehension conveyed by their teachers in the classroom during math instruction.  In support of this, Gunderson, Ramirez, Levine, and Beilock (2012) showed that both teachers and parents hold strong gender-related math attitudes and stereotypes, with negative stereotypes for females, and that they convey these stereotypes to children.
This review highlights the importance of understanding the onset, development, and mechanism of mathematics anxiety.  We feel that this endeavor is a necessary one, especially with the increasing reliance on standardized math testing for entrance and exit exams in education, and the need for mathematical literacy (“numeracy”) in today’s society. Despite our current knowledge about mathematics anxiety, many gaps are present in the literature.  Most importantly, little research has been conducted to understand how this affective condition develops.  As an area of study, however, research on mathematics anxiety is advancing rapidly, and we expect to see many of these important questions addressed in the near future.
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Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 8, 97-125.

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Moore, A. M., Rudig, N. O., & Ashcraft, M. H. (submitted). Affect, motivation, working memory, and mathematics. To appear in R. Cohen & A. Dowker (Eds.), The Oxford handbook of numerical cognition.

Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20, 110-122.

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