Mathematical anxiety is the fear of mathematics or “a feeling of intense frustration or helplessness about one's ability to do math.” [1].
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People's fear of math can be related to test taking and performance anxiety. Some scholars have suggested a strong relation between math anxiety and math performance.[2] Current research in math anxiety concerns working memory.[3]
Math is required at many levels of life and not just at the higher academic levels of schooling. Sewing requires measuring and estimating. Carpentry requires measuring, multiplication, estimating, and geometry. Shopping requires estimating to ensure that you can afford what you are spending and that the bill is correct. Household budgets, selecting a loan, comparing savings and investments require understanding percentages. Plumbers, electricians, and HVAC technicians need to understand volumes, capacities, and flow rates. One 1993 estimate is “that starting salaries go up $2,000 per year for every mathematics course taken after the ninth grade.”[4] Within manufacturing, the Bureau of Labor Statistics predicted a shift for 669,000 assembler, laborer, and machine setter jobs to 338,000 engineering, managerial, scientist and technician jobs between 1986 and 2000.[5]
Many high school students do not know what their college major will be in and even if they do, it will likely change as they learn the realities and the possibilities of various fields. Many fields including architecture, business and finance, economics, engineering (e.g. civil, mechanical, electrical, chemical, environmental), science (e.g. biology, chemistry, physics) and computer science require strong math capabilities learned in high school. Medicine, including veterinary, requires strong science capabilities which in turn require strong math capabilities. Tobias (pg. 21) states that in 1972 of students entering the University of California of Berkeley, 57% of males and 8% of females had taken four years of high school math. By avoiding math in high school, the women unknowingly made themselves ineligible for 10 out of 12 colleges and 22 out of 44 majors. Before they had graduated from high school, they had restricted their career options “to the ‘softer’ fields: humanities, guidance and counseling, elementary education, foreign languages, and the fine arts.”
A rating scale for mathematics anxiety was written about in 1972 by Richardson and Suinn,[6] who according to a recent experimental paper in mathematics anxiety,[7] described mathematical anxiety as, "... characterized by feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts."[8]
Related to this is gender and mathematics as younger female scholars are thought to develop anxiety towards mathematics and sciences when they become more interested in social relations in their teen years. It is thought that women experience more anxiety in mathematics as a group than men and this has also been suggested in regards computer programming. See for instance [Copper, Joel, & Weaver D, Kimberlee. Gender and Computers: "Understanding the Digital Divide"] who explore computing and gender and especially have done experiments relating gender and anxiety.[9]
In the United States, many people believe that only a few "gifted" individuals have "what it takes" to learn math, and that hard work cannot compensate for this. Studies have shown "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." [10]
Another widely-held belief that contributes to math anxiety is the idea that "math is a young man's game." At the highest levels of Research mathematics, there are still more chairmanships and named professorships held by men, and probably more papers published by men in the most prestigious journals. Women mathematicians in the United States have almost always been a minority according to Margaret Murray. 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]. [11] "Since 1980, women have earned over 17 percent of the mathematics doctorates.... [In The United States]".[12]The trends in gender are by no means clear, but perhaps parity is still a way to go. Thus parity will take more work to overcome mathematical anxiety and this is one reason for women in mathematics being role models for younger women.
Causes
Students often develop mathematical anxiety in schools, often as a result of learning from teachers who are themselves anxious about their mathematical abilities in certain areas. Typical examples of areas where mathematics teachers are often incompetent or semi-competent include fractions, (long) division, algebra, geometry "with proofs", calculus, topology. In many countries, would-be math teachers are required only to obtain passing grades of 51% in mathematics exams, so that a math student who has failed to understand 49% of the math syllabus throughout his or her education can, and often does, become a math teacher. His or her fears and lack of understanding then pass naturally to his or her students. As John Taylor Gatto [13] has demonstrated at length, modern Western schools were deliberately designed during the late 19th century to create an environment which is ideal for fostering fear and anxiety, and for preventing or delaying learning.
Math is usually taught as a right and wrong subject and getting the right answer is paramount. Unlike most subjects, there is almost always a right answer. Additionally, it is often taught as if there is a right way to solve the problem and any other approaches are wrong, even if they get the right answer. When learning, understanding the concepts should be paramount. With a right/wrong approach to teaching math, students are encouraged not to try, not to experiment, not to find algorithms that work for them, and not to take risks. “Teachers benefit children most when they encourage them to share their thinking process and justify their answers out loud or in writing as they perform math operations. … With less of an emphasis on right or wrong and more of an emphasis on process, teachers can help alleviate students' anxiety about math.” [14]
While teaching of many subjects has progressed from rote memorization to the current Constructivist approach, math is still frequently taught with a rote learning behaviorist approach. That is,
Constructivist theory says the learning and knowledge is the student’s creation, yet rote learning and a right/wrong approach to teaching math ensures that it is external to the student.
Teachers who actually understand what they are teaching tend to encourage questions from the students. Those teachers who do not understand much about their subject, on the other hand, impose fear on the students to prevent them asking questions which might expose the teacher's ignorance.
It has long been well established that anyone (other than a tiny minority who have serious learning disabilities) can learn any area of mathematics, given a desire to learn, a coherent presentation of the information, and adequate practice. Nevertheless, many educational administrators continue to profess the belief that anything more complex than simple arithmetic is too difficult for most people.
In spite of the unfortunate design of the modern school system, a remarkably high percentage of schoolchildren continue to find mathematics interesting, relaxing, easy, and enjoyable.
Solutions
Studies by Herbert P. Ginsburg, Columbia University, show the influence of parents' and teachers' attitudes on "'the child's expectations in that area of learning.'... It is less the actual teaching and more the attitude and expectations of the teacher or parents that count." This is further supported by a survey of Montgomery County, Maryland students who "pointed to their parents as the primary force behind the interest in mathematics." [15].
Math Academy Online / Platonic Realms [16]contends that math has two components. The first component, commonly focused on in many schools, is to calculate the answer. This component also has two subcomponents, namely the answer and the process or method used to determine the answer. Focusing more on the process or method enables students to make mistakes, but not ‘fail at math’. The second component is to understand the mathematical concepts that underlay the problem being studied. “… and in this respect studying mathematics is much more like studying, say, music or painting than it is like studying history or biology.”
Amongst others supporting this viewpoint is the work of Dr. Eugene Geist, Associate Professor at Ohio University – Athens, Ohio and an early childhood education specialist[17]. Dr. Geist's recommendations include focusing on the concepts rather than the right answer and letting students work on their own and discuss their solutions before the answer is given. Emphasis is given that young people hate to be wrong and hate situations where they can be embarrassed by being wrong.
National Council of Teachers of Mathematics (NCTM) (1989, 1995b) suggestions for teachers seeking to prevent math anxiety include:
- Accommodating for different learning styles
- Creating a variety of testing environments
- Designing positive experiences in math classes
- Refraining from tying self-esteem to success with math
- Emphasizing that everyone makes mistakes in mathematics
- Making math relevant
- Letting students have some input into their own evaluations
- Allowing for different social approaches to learning mathematics
- Emphasizing the importance of original, quality thinking rather than rote manipulation of formulas
Math (and Statistics) Therapy is a combination of coaching and counseling, provided for adults by people with credentials in both counseling and math education. In Math Therapy the reasons for anxiety are addressed, as well as the mathematical skills which are lacking. New coping skills are introduced and practiced, so that fear, distaste or other negative emotions do not block math (or statistics) learning.
Studies have shown students learn best when they are active rather than passive learners [18].
The theory of multiple intelligences suggests that there is a need for different learning styles. Math lessons can be tailored for visual/spatial, logical/mathematics, musical, body/kinesthetic, interpersonal and intrapersonal and verbal/linguistic learning styles.
Everyone is capable of learning, but may learn best in different ways. Therefore, lessons must be presented in a variety of ways. New concepts can be taught through play acting, cooperative groups, visual aids, hands on activities or information technology. [19] To help with learning statistics, there are many applets found on the Internet that help students learn about many things from probability distributions to linear regression. These applets are commonly used in introductory statistics classes, as many students benefit from using them.
Active learners ask critical questions, such as: Why do we do it this way, and not that way? Some teachers may find these questions annoying or difficult to answer, and indeed may have been trained to respond to such questions with hostility and contempt, designed to instill fear. Better teachers respond eagerly to these questions, and use them to help the students deepen their understand by examining alternative methods so the students can choose for themselves which method they prefer.
However, there is still a large part of school math teaching which consists of memorization, repetition, and mechanically performed operations. Times tables are one example where rote learning is absolutely essential to mathematics performance. When a student fails to learn the times tables at a young age, that can result in anxiety later, when all the students' classmates can remember the tables but he or she cannot. The solution is simple: the student must take the time, several hours perhaps, to learn the times tables!
Children learn best when math is taught in a way that is relevant to their everyday lives. Children enjoy experimenting. To learn mathematics in any depth, students should be engaged in exploring, conjecturing, and thinking, as well as in rote learning of rules and procedures.[20]
   | Defence Mechanisms against Mathematics - psychoanalitic research:defence mechanisms against mathematics |
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