Math--that four-letter word!Abstract
Math anxiety is extremely prevalent in the general population, but tends to have gender and age as key aspects to occurrence. A factor in this may be that many elementary teachers tend to be math phobic pho·bic
Of, relating to, arising from, or having a phobia.
One who has a phobia. . This paper looks at two returning adult college students who participated in a Math Anxiety Workshop as well as follow-up mathematics tutoring and their battles with math anxiety.
As an instructor of preservice teachers, I am always faced with instances of math anxiety in my students. I teach classes in mathematics methods of instruction to both prospective secondary and elementary teachers. Interestingly, even the students who will be secondary teachers have phobias Phobias Definition
A phobia is an intense but unrealistic fear that can interfere with the ability to socialize, work, or go about everyday life, brought on by an object, event or situation. that need to be addressed, these tending most often to be in the areas of problem solving problem solving
Process involved in finding a solution to a problem. Many animals routinely solve problems of locomotion, food finding, and shelter through trial and error. , probability, or geometry. However, it is with elementary education elementary education
or primary education
Traditionally, the first stage of formal education, beginning at age 5–7 and ending at age 11–13. majors that I run into the most severe cases of math anxiety. It seems to me, after many years of working with these students, that about two-thirds of them come in with feelings of inadequacy about their math ability, fears of having to teach math, and tendencies toward avoidance of math. My present elementary education major students have been required to pass three university math courses; one college algebra algebra, branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Algebra is a generalization of arithmetic and gains much of its power from dealing symbolically with elements and operations (such as and two focused on elementary mathematics Elementary mathematics consists of mathematics topics frequently taught at the primary and secondary school levels. The most basic are arithmetic and geometry. The next level is probability and statistics, then algebra, then (usually) trigonometry and pre-calculus. , and still have these reservations. Given the amount of information that can be found on the internet regarding math anxiety (a Google search Google is owned by Google, Inc. whose mission statement is to "organize the world's information and make it universally accessible and useful". The largest search engine on the web, Google receives several hundred million queries each day through its various services. turned up 1,510,000 listings on this topic), I know this is common across the nation.
Specifically, two recent articles in the National Council of Teachers of Mathematics' (NCTM NCTM National Council of Teachers of Mathematics
NCTM Nationally Certified Teacher of Music
NCTM North Carolina Transportation Museum
NCTM National Capital Trolley Museum
NCTM Nationally Certified in Therapeutic Massage ) journal Teaching Children Mathematics (Wolodko, Willson, and Johnson, 2003; Guillaume and Kirtman, 2005) share studies of preservice elementary teachers' backgrounds in mathematics and how to deal with negative attitudes, a further indication that this problem is wide spread. Additionally, it appears that starting in adolescence, math anxiety is far more common in females than in males (Hyde, Fennema, and Lamon, 1990). Since the vast majority of elementary teachers are female, this highlights how common math anxiety is and how easy it may be to pass on the same problems to generations of students. However, it is not just teachers who are burdened with this phobia phobia: see neurosis.
Extreme and irrational fear of a particular object, class of objects, or situation. A phobia is classified as a type of anxiety disorder (a neurosis), since anxiety is its chief symptom. . In fact many people may choose not to pursue a career as a teacher because of their fear of taking and teaching mathematics courses. Walker and Karp (2005) indicate that math phobia is so widespread in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. that it "profoundly affects the country's policies, teaching practices, and ultimately students' performance" (p.39).
Having math anxiety may not, of course, mean a person cannot understand or do certain mathematical tasks, but it can inhibit the ability to learn or successfully demonstrate that learning. While a distinction must be made between math anxiety and test anxiety, which means that students may not be able to convince others of what they know mathematically (Kazelskis, Reeves and Kirsh, 2000), the two are tightly connected. Since testing is the most common means of determining acquisition of math knowledge and skills for instructors, many students tend to exhibit test anxiety primarily in mathematics rather than in other subjects. So while a math anxiety that involves avoidance or negative self-talk may cause a test anxiety, it is also possible that a test anxiety may generate a conditioned math anxiety (Hembree, 1990). In either case, the two appear to be linked for most students with math anxiety.
A workshop on math anxiety
During a time I was working in student support services support services Psychology Non-health care-related ancillary services–eg, transportation, financial aid, support groups, homemaker services, respite services, and other services setting, I coordinated the math tutoring services for the college. This involved one-on-one tutoring, training of peer tutors A peer tutor is anyone who is of a similar status as the person being tutored. In an undergraduate institution this would usually be other undergraduates, as distinct from the graduate students who may be teaching the writing classes. , running final exam Noun 1. final exam - an examination administered at the end of an academic term
final examination, final
exam, examination, test - a set of questions or exercises evaluating skill or knowledge; "when the test was stolen the professor had to make a new set of review sessions, and student advising. A large number of students I worked with were adults returning to college, many of them extremely fearful of the math they would need to do after many years out of school. I decided that it might be advantageous for these students to offer a workshop on how to deal with their math anxiety. I examined several of the seminal self-help books in this area (Fear of Math: How to Get Over It and Get On with Your Life, Zaslavsky, 1994; Math Anxiety Reduction, Hackworth, 1985; Mind over Math, Kogelman and Warren, 1979; Overcoming Math Anxiety, Tobias, 1978) to design activities and discussion questions. At the first meeting eight participants, only one of which was of traditional college age, showed up. Six, all women, finished the six-week program, with two of the participants attending only the first session, and two continuing to meet with me after the workshop for advising and tutoring appointments.
We began the sessions describing that anxiety affects us in three ways: physically, cognitively (or intellectually), and affectively af·fec·tive
1. Influenced by or resulting from the emotions.
2. Concerned with or arousing feelings or emotions; emotional. (emotionally). Since the participants were fully aware that they were suffering from and with math anxiety, they had a cognitive recognition of the problem and were taking a reasoned step to address it. However, dealing with the other two aspects would be key to overcoming their fears. We generated this listing of characteristics of the three domains present during an anxiety period:
Physical symptoms: tenseness, perspiring, increased heart rate, nausea. Cognitive symptoms: negative self talk, avoidance, rationalization, "blanking out." Affective symptoms: distrust of ability, fear of looking stupid, loss of self-esteem.
The first assignment for the workshop was to write a math autobiography. Students were instructed to think over their experiences in and outside of school that may have influenced their attitudes toward math. They were asked to try to pinpoint when they might have begun to feel uncomfortable or negative about their abilities or their experiences in math. From this we were able to develop a spirited discussion about the root causes of their fears. The ones discussed appear to be commonly reported by others (Perry, 2004) and fall into the three categories of poor or insensitive teachers, breaks or gaps in learning, and attitudes of others.
When it came to teachers, the workshop participants said that many of their teachers did relatively little to explain the reasoning behind what they were learning but usually only presented processes. Most admitted what was so bothersome to them was that it appeared the other students in the class always understood what was going on. They felt they were the only ones who were struggling with the material and so did not blame the teacher for poor teaching, just for not being able to help them learn. However, there were also some horrifying stories of teachers bullying and embarrassing students when they didn't know the answer. In particular, several students recounted having to stand at the board trying to finish a computation, for which they had no clue where to begin, while the rest of the class laughed. A student mentioned she much preferred when instructors used a white board or PowerPoint so that they wouldn't need to see the blackboard (1) See Blackboard Learning System.
(2) The traditional classroom presentation board that is written on with chalk and erased with a felt pad. Although originally black, "white" boards and colored chalks are also used. .
Gaps in learning could be explained in several ways. Though several people mentioned they got lost on a particular topic or level (usually fractions, long division or algebra) and just never felt confident or competent after that, the reasons for the gap were often not the result of the student at all. In one case, a woman recounted moving and changing schools. At the new school, the class was well ahead of where she was in the old school and she never got the opportunity to "fill in the missing pieces." Similarly, a woman reported she had missed about two months of school due to a serious illness when she was in fourth grade. Though she could make up the content from the other subjects she never quite got back up to speed in math. Finally, one woman reported that her mother died when she was young and she was in math class when the principal came to her class to tell her. The negative connection was never broken for her.
Finally, the attitudes of others appeared to be influential in participants' attitudes. Several of the women reported school counselors A school counselor is a counselor and educator who works in schools, and have historically been referred to as "guidance counselors" or "educational counselors," although "Professional School Counselor" is now the preferred term. who told them it was fine to do poorly in math because women do need it as much as men. Almost all of them had mothers who said that they had done poorly in math as Mathematics courses named Math A, Maths A, and similar are found in:
Story intended to elicit a strong feeling of fear. Such tales are of ancient origin and form a substantial part of folk literature. They may feature supernatural elements such as ghosts, witches, or vampires or address more realistic psychological fears. of parents, siblings siblings npl (formal) → frères et sœurs mpl (de mêmes parents) , or teachers telling them they were stupid and that they would never be able to amount to something.
Once we examined the root causes, we analyzed the "truth" of the situations. By examining the events as "history," participants were able to intellectually see the irrationality of the fear. For another activity, we spent some time doing an exercise that required them to look at various math symbols and expressions and told to indicate their immediate response as comfortable, uncomfortable, or panic. This revealed two things to the participants. First, that they were comfortable or only mildly uncomfortable in seeing many of the symbols and only a few really bothered them. This gave them a sense that the problem wasn't nearly as overwhelming as they thought. Second, it clearly pinpointed the areas of "gaps" in knowledge. It indicated for them a place to go back to for relearning re·learn·ing
The process of regaining a skill or ability that has been partially or entirely lost.
re·learn v. . We even went through a few "math lessons" on fractions and equations and they were amazed a·maze
v. a·mazed, a·maz·ing, a·maz·es
1. To affect with great wonder; astonish. See Synonyms at surprise.
2. Obsolete To bewilder; perplex.
v.intr. at how quickly and easily they could comprehend the material. A reminder that a forty-year-old has a much better background to understand the math information than a ten-year old did, finally was clear to them.
We were then able to concentrate on the ways we sabotage sabotage [Fr., sabot=wooden shoe; hence, to work clumsily], form of direct action by workers against employers through obstruction of work and/or lowering of plant efficiency. Methods range from peaceful slowing of production to destruction of property. ourselves in our learning. The class was able to discuss elements for improving study habits like setting short-term goals, rewarding themselves for accomplishments, being more assertive as·ser·tive
Inclined to bold or confident assertion; aggressively self-assured.
as·sertive·ly adv. in seeking out help, and generating more positive talk. In role-playing a tutoring session, participants were encouraged to say aloud everything they were thinking as they worked. Most often they were thinking things like, "I'll never get this" or "This is so stupid" or even "I'm so stupid!" We worked on changing that talk to "What am I sure I know about this problem?" and "What do I do first?" Once the talking was focused on the topic rather than on the feelings, participants were much better able to concentrate on the task.
Though dealing with the emotional aspect of the fear is certainly the hardest thing to overcome, building a cognitive awareness and minimizing the physical symptoms is necessary reduce the feelings of inadequacy. To deal with the physical aspects, we practiced common therapeutic techniques of breathing exercises, imaging, and desensitization desensitization
Treatment to eliminate allergic reactions (see allergy) by injecting increasing strengths of purified extracts of the substance that causes the reaction. . Using relaxation messages to reduce tenseness and slow the heart rate, one is less likely to be overcome by the anxiety. The imaging we did helped them develop a routine to control breathing and other physical responses and we were gradually able to spend more time during the imaging in the "math place." However, acknowledging that students were currently in classes and under time constraints In law, time constraints are placed on certain actions and filings in the interest of speedy justice, and additionally to prevent the evasion of the ends of justice by waiting until a matter is moot. , we identified things we could do to help in the process. Participants were encouraged to discuss the issue of their math anxiety with their math instructors, and I sometimes advocated on their part. They found that often their instructors were willing to help in several ways such as letting them take tests in the instructor's office or in the tutoring lab, extend the time limit for the test, meet with the instructor in his/her office to get questions answered instead of in front of the whole class, and bring tape recorders tape recorder, device for recording information on strips of plastic tape (usually polyester) that are coated with fine particles of a magnetic substance, usually an oxide of iron, cobalt, or chromium. The coating is normally held on the tape with a special binder. into class so they could double check their notes.
A closer look at two students
As mentioned previously, of the six participants, only two kept close contact with me after the workshop. These two had the most dramatic stories and had reached the highest level of anxiety. They also had much in common. Both were in their late 30s, studying for business degrees, had extremely negative educational backgrounds, had significant people in their life telling them they wouldn't be able to finish, had jobs that were integral to the financial welfare of their families, and reported similar anxiety reactions to math and tests. Most importantly Adv. 1. most importantly - above and beyond all other consideration; "above all, you must be independent"
above all, most especially , both were enrolled in calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. the following semester se·mes·ter
One of two divisions of 15 to 18 weeks each of an academic year.
[German, from Latin (cursus) s . They had been routinely using the tutoring facilities at the college, which had been instrumental in their successful completion of math classes to that point.
When "Emily" and "Rose" started their calculus class, both continued to come to the tutoring lab for help. After taking her first test, Emily came into my office in tears. She had done horribly, she "blanked out" on many of the answers, and she was sure she had failed. We discussed whether she was able to do some breathing and relaxation techniques Relaxation technique
A technique used to relieve stress. Exercise, biofeedback, hypnosis, and meditation are all effective relaxation tools. Relaxation techniques are used in cognitive-behavioral therapy to teach patients new ways of coping with stressful during the test and she said she did, but then she worried she would run out of time, so didn't continue (Emily did not have a math instructor who was willing to make any adaptations for her anxiety). I said we would go over the test when she got it back. Rose was not as upset as Emily about her test, but did admit that she also struggled with "blanking out" during the test.
Emily returned with her test, on which she received a D, again in tears. We spent quite a while as I focused her attention on each item and went over what she had done correctly and how far she had gotten on each item, and that she had attempted each item in spite of her fear of not finishing in time. Rose would not show me her test, just said she didn't do well and we focused on the new work. This was pretty much the pattern established for the rest of the semester, with Emily bringing in her tests and going over them with me. I would point out each improved grade and how much more she accomplished each time. She became less upset and more analytical the about process each time, knowing this is what we would do. Rose continued to come to the tutoring center for help with homework, but did not share any information about her grades. Although Emily ended up in the hospital at one point towards the end of the semester, and missed a test, she was able to complete the final and earn a B in the class. Rose did not finish the semester.
What appears to be key here that differentiates the two women's experiences is Emily's ability to deal with the cognitive aspect of her anxiety. Ho et al (2000) point out that there are two different dimensions to test anxiety, affective affective /af·fec·tive/ (ah-fek´tiv) pertaining to affect.
1. Concerned with or arousing feelings or emotions; emotional.
2. and cognitive, similar to those domains mentioned previously in relation to math anxiety. According to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. Ho et al, "the test anxiety measures may have tapped more into cognitive anxiety, which is related to interference of task completion" (p. 375). In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently , Emily was better able to control the problems she was having both in learning math and in test-taking, by not only attending to the physical and emotional aspects, but by learning to focus her thinking. Rose, getting the same emotional support and continued reminders for handling her stress, never cognitively addressed her progress by identifying her successes and well as her errors.
My experiences with the Math Anxiety Workshop and individual students appear to be consistent with the literature on math and test anxiety identified in this paper. However, both experience and research highlight the cognitive nature of the phobia that must be as carefully and consistently attended to as the physical and emotional domains. So in summary, and in addition to making efforts not to create the anxiety, instructors should:
1. Acknowledge that math anxiety is real, is pervasive, and is debilitating de·bil·i·tat·ing
Causing a loss of strength or energy.
Weakening, or reducing the strength of.
Mentioned in: Stress Reduction .
2. Provide accommodations, especially for test taking, to help alleviate the conditions that aggravate the anxiety.
3. Clearly identify connections and distinctions among topics, concepts, and skills.
4. Reduce the number of formulas or items that must be memorized for a test, as that information is the first to experience interference from anxiety.
5. Provide evidence of where errors are made so students can distinguish their errors from what was done correctly.
Similarly, students who are experiencing math anxiety should:
1) Give voice to their anxiety and find a supportive person or group to listen and give feedback. It is important that this support is not simply one that hears complaints or gives instructions.
2) Consciously work on changing negative self-talk to content focused talk.
3) Be assertive in working with instructors to get needed information and accommodations, as well as getting questions answered.
4) Practice relaxation and breathing techniques in less stressful times to get efficient in their use.
5) Go back to the math where the gaps exist, relearn Verb 1. relearn - learn something again, as after having forgotten or neglected it; "After the accident, he could not walk for months and had to relearn how to walk down stairs" those concepts and skills before trying to move forward.
6) Get specialized counseling if necessary.
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Hyde, J.S., Fennema, E., and Lamon, S.J. Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin 107, 139-155, 1990.
Ho, H.Z.; Senturk, D, Lam, A,G., Zimmer, J.M., Hong, S, Okamoto, Y, Chiu, S.Y., Nakazawa, Y, and Wang, C.P. The affective and cognitive dimensions Cognitive dimensions are design principles for notations & programming language design, described by researcher Thomas R.G. Green. The dimensions can be used to evaluate the usability of an existing interface, or as heuristics to guide the design of a new one. of math anxiety; a cross-national study. Journal for Research in MathematicsEducation, 31, 362-379, 2000.
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Kogelman, S. and Warren, J. Mind over math. New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of , McGraw-Hill Publishing, 1979.
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Tobias, S. Overcoming math anxiety. New York. W.W. Norton & Company, 1978.
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Wolodko, B.L., Willson, K.J., and Johnson, R.E. Metaphors as a vehicle for exploring preservice teachers' perceptions of mathematics. Teaching Children Mathematics 10, 224-229, 2003.
Zaslavsky, C. Fear of math: How to get over it and get on with your life. New Brunswick, New Jersey This article is about the city in New Jersey. For the Canadian province, see New Brunswick.
New Brunswick, also known as "the Healthcare City" or "Hub City", is a city and the county seat of the County of Middlesex, New Jersey, USA. , Rutgers University Press Rutgers University Press is a nonprofit academic publishing house, operating in Piscataway, New Jersey under the auspices of Rutgers University. The press was founded in 1936, and since that time has grown in size and in the scope of its publishing program. , 1994.
Melissa Freiberg, University of Wisconsin-Whitewater The University of Wisconsin–Whitewater (also known as UW-Whitewater) is part of the University of Wisconsin System, located in Whitewater, Wisconsin. It became Wisconsin's second public college on April 21, 1868 when it opened its doors to 39 students taught by nine
Melissa Freiberg, Ph.D. is an Associate Professor of Curriculum and Instruction specializing in mathematics education.