Mathematical anxiety

Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p. 1).[1] The academic study of math anxiety originates as early as the 1950s, where Mary Fides Gough introduced the term mathemaphobia to describe the phobia-like feelings of many towards mathematics.[2] The first math anxiety measurement scale was developed by Richardson and Suinn in 1972. Since this development, several researchers have examined math anxiety in empirical studies.[1] Hembree[3] (1990) conducted a meta-analysis of 151 studies concerning math anxiety. It determined that math anxiety is related to poor math performance on math achievement tests and that math anxiety is related to negative attitudes concerning math. Hembree also suggests that math anxiety is directly connected with math avoidance.

Ashcraft[1] (2002) suggests that highly anxious math students will avoid situations in which they have to perform mathematical calculations. Unfortunately, math avoidance results in less competency, exposure and math practice, leaving students more anxious and mathematically unprepared to achieve. In college and university, anxious math students take fewer math courses and tend to feel negative towards math. In fact, Ashcraft found that the correlation between math anxiety and variables such as confidence and motivation are strongly negative.

According to Schar,[4] because math anxiety can cause math avoidance, an empirical dilemma arises. For instance, when a highly math-anxious student performs disappointingly on a math question, it could be due to math anxiety, or the lack of competency in math because of math avoidance. Ashcraft determined that by administering a test that becomes increasingly more mathematically challenging, he noticed that even highly math-anxious individuals do well on the first portion of the test measuring performance. However, on the latter and more difficult portion of the test, there was a stronger negative relationship between accuracy and math anxiety.

According to the research found at the University of Chicago by Sian Beilock and her group, math anxiety is not simply about being bad at math. After using brain scans, scholars confirmed that the anticipation or the thought of solving math actually causes math anxiety. The brain scans showed that the area of the brain that is triggered when someone has math anxiety overlaps the same area of the brain where bodily harm is registered.[5] And Trezise and Reeve[6][7] show that students' math anxiety can fluctuate throughout the duration of a math class.

The impact of mathematics anxiety on mathematics performance has been studied in much recent literature. An individual with math anxiety does not necessarily lack ability in mathematics, rather, they cannot perform to their full potential due to the interfering symptoms of their anxiety.[8] Math anxiety manifests itself in a variety of ways, including physical, psychological, and behavioral symptoms, that can all disrupt a student's mathematical performance.[9] The strong negative correlation between high math anxiety and low achievement is often thought to be due to the impact of math anxiety on working memory. Working memory has a limited capacity, and when solving mathematical problems, a large portion of this capacity is dedicated to problem solving. However, in individuals with math anxiety, much of this space is taken up by anxious thoughts, thus compromising the individual's ability to perform.[10] In addition, a frequent reliance in schools on high-stakes and timed testing, where students tend to feel the most anxiety, can lead to lower achievement for math anxious individuals.[11] Programme for International Student Assessment (PISA) results demonstrate that students experiencing high math anxiety demonstrate mathematics scores that are 34 points lower than students who do not have math anxiety, equivalent to one full year of school.[12] These findings demonstrate the clear link between math anxiety and reduced levels of achievement, suggesting that alleviating math anxiety may lead to a marked improvement in student achievement.

A rating scale for mathematics anxiety was written about in 1972 by Richardson and Suinn.[13] Richardson and Suinn defined mathematical anxiety as "feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts".[14] Richardson and Suinn introduced the MARS (Mathematics Anxiety Rating Scale) in 1972. Elevated scores on the MARS test translate to high math anxiety. The authors presented the normative data, including a mean score of 215.38 with a standard deviation of 65.29, collected from 397 students that replied to an advertisement for behavior therapy treatment for math anxiety.[15] For test-retest reliability, the Pearson product-moment coefficient was used and a score of 0.85 was calculated, which was favorable and comparable to scores found on other anxiety tests. Richardson and Suinn validated the construct of this test by sharing previous results from three other studies that were very similar to the results achieved in this study. They also administered the Differential Aptitude Test, a 10-minute math test including simple to complex problems.

Calculation of the Pearson product-moment correlation coefficient between the MARS test and Differential Aptitude Test scores was −0.64 (p < .01), indicating that higher MARS scores relate to lower math test scores and "since high anxiety interferes with performance, and poor performance produces anxiety, this result provides evidence that the MARS does measure mathematics anxiety".[16] This test was intended for use in diagnosing math anxiety, testing efficacy of different math anxiety treatment approaches and possibly designing an anxiety hierarchy to be used in desensitization treatments.[15] The MARS test is of interest to those in counseling psychology[17] and the test is used profusely in math anxiety research. It is available in several versions of varying length[18] and is considered psychometrically sound.[19] Other tests are often given to measure different dimensionalities of math anxiety, such as Elizabeth Fennema and Julia Sherman's Fennema-Sherman Mathematics Attitudes Scales (FSMAS). The FSMAS evaluates nine specific domains using Likert-type scales: attitude toward success, mathematics as a male domain, mother's attitude, father's attitude, teacher's attitude, confidence in learning mathematics, mathematics anxiety, affectance motivation and mathematics usefulness.[20] Despite the introduction of newer instrumentation, the use of the MARS test appears to be the educational standard for measuring math anxiety due to its specificity and prolific use.[21]

While there are overarching similarities concerning the acquisition of math skills, researchers have shown that children's mathematical abilities differ across countries. In Canada, students score substantially lower in math problem-solving and operations than students in Korea, India and Singapore. Researchers have conducted thorough comparisons between countries, and have determined that in countries such as Taiwan and Japan, parents place more emphasis on effort rather than one's innate intellectual ability in school success. By parents placing a higher emphasis on effort rather than one's innate intellectual ability they are helping their child develop a growth mindset.[22] People who develop a growth mindset believe that everyone has the ability to grow their intellectual ability, learn from their mistakes and become more resilient learners. Moreover, parents in these countries tend to set higher expectations and standards for their children. In turn, students spend more time on homework and value homework more than American children.[23]

Another difference in mathematic abilities often explored in research concerns gender disparities. There has been research examining gender difference in performance on standardized tests across various countries. Beller and Gafni's have shown that children at approximately nine years of age do not show consistent gender difference in relation to math skills. However, in 17 out of the 20 countries examined in this study, 13-year-old boys tended to score higher than girls. Moreover, mathematics is often labeled as a masculine ability; as a result, girls often have low confidence in their math capabilities.[24] These gender stereotypes can reinforce low confidence in girls and can cause math anxiety as research has shown that performance on standardized math tests is affected by one's confidence.[25] As a result, educators have been trying to abolish this stereotype by fostering confidence in math in all students in order to avoid math anxiety.[26]

The principles of mathematics are generally understood at an early age; preschoolers can comprehend the majority of principles underlying counting. By kindergarten, it is common for children to use counting in a more sophisticated manner by adding and subtracting numbers. While kindergarteners tend to use their fingers to count, this habit is soon abandoned and replaced with a more refined and efficient strategy; children begin to perform addition and subtraction mentally at approximately six years of age. When children reach approximately eight years of age, they can retrieve answers to mathematical equations from memory. With proper instruction, normally functioning children acquire these basic mathematical skills and are able to solve more complex mathematical problems with more sophisticated training.[26] (Kail & Zolner, 2005).

High risk teaching styles are often explored to gain a better understanding of math anxiety. Goulding, Rowland, and Barber[27] (2002) suggest that there are linkages between a teacher's lack of subject knowledge and ability to plan teaching material effectively. These findings suggest that teachers that do not have a sufficient background in mathematics may struggle with the development of comprehensive lesson plans for their students. Similarly, Laturner's research[28] (2002) shows that teachers with certification in math are more likely to be passionate and committed about teaching math than those without certification. However, those without certification vary in their commitment to the profession depending on coursework preparation.

Moreover, a study conducted by Kawakami, Steele, Cifa, Phills, and Dovidio[29] (2008) examined attitudes towards math and behavior during math examinations. The study examined the effect of extensive training in teaching women to approach math. The results showed that women who were trained to approach rather than avoid math showed a positive implicit attitude towards math. These findings were only consistent with women low in initial identification with math. This study was replicated with women who were either encouraged to approach math or who received neutral training. Results were consistent and demonstrated that women taught to approach math had an implicit positive attitude and completed more math problems than women taught to approach math in a neutral manner.

Johns, Schmader, and Martens[30] (2005) conducted a study in which they examined the effect of teaching stereotype threat as a means of improving women's math performance. The researchers concluded that women tended to perform worse than men when problems were described as math equations. However, women did not differ from men when the test sequence was described as problem solving or in a condition in which they learned about stereotype threats. This research has practical implications. The results suggested that teaching students about stereotype threat could offer a practical means of reducing its detrimental effects and lead to an improvement in a girl's performance and mathematical ability. Concluding that educating female teachers about stereotype threat can reduce its negative effects in the classroom.

A view associated with Francis Galton author of Hereditary Genius (1869)[31] suggests that "when asked to explain why some children do better in math than others, Asian children, their teachers, and their parents point to hard work, their American counterparts to ability."[32]

According to Margaret Murray, female mathematicians in the United States have almost always been a minority. Although the exact difference fluctuates with the times, as she has explored in her book Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America, "Since 1980, women have earned over 17 percent of the mathematics doctorates.... [In The United States]".[33] The trends in gender are by no means clear, but perhaps parity is still a way to go. Since 1995, studies have shown that the gender gap favored males in most mathematical standardized testing as boys outperformed girls in 15 out of 28 countries. However, as of 2015 the gender gap has almost been reversed, showing an increase in female presence. This is being caused by women's steadily increasing their performance on math and science testing and enrollment, but also from males' losing ground at the same time. This role reversal can largely be associated with the gender normative stereotypes that are found in the Science, technology, engineering, and mathematics (STEM) field, deeming "who math is for" and "who STEM careers are for". These stereotypes can fuel mathematical anxiety that is already present among young female populations.[34] Thus parity will take more work to overcome mathematical anxiety and this is one reason why women in mathematics are role models for younger women.

• Online information about and demonstration of a short mathematics anxiety test
• Defence Mechanisms against Mathematics