Math anxiety: overcoming a major obstacle to the improvement of student math performance. (Review of Research).

In today's high-tech, increasingly connected world, it is important that young children build confidence in their ability to do mathematics. This article reviews the literature on preventing and reducing math anxiety. The authors believe that as students become less anxious about and more confident in their abilities to do math, their performance on standardized test scores will improve and they will be better prepared for the future.

Extensive research on math anxiety has tried to determine why so many people in the United States demonstrate a fear or even antipathy toward math. Mathematics anxiety can be defined as an "irrational dread of mathematics that interferes with manipulating numbers and solving mathematical problems within a variety of everyday life and academic situations" (Buckley & Ribordy, 1982, p. 1). The National Council of Teachers of Mathematics (NCTM) (1989) recognizes math anxiety as a problem and established criteria to help assess students' mathematical dispositions. NCTM suggests that teachers assess students':

* Confidence in using math to solve problems, communicate ideas, and reason

* Flexibility in exploring mathematical ideas and trying a variety of methods when solving problems

* Willingness to persevere in mathematical tasks

* Interests, curiosity, and inventiveness in doing math

* Ability to reflect on and monitor their own thinking and performance while doing math

* Focus on value of and appreciation for math in relation to its real-life application, connections to other disciplines, existence in other cultures, use as a tool for learning, and characteristics as a language. (1989, p. 233)

Marilyn Burns (1998), a leading mathematics education expert, contends that two thirds of American adults loathe and fear mathematics. The 1989 Curriculum and Evaluation Standards for School Mathematics (aka, the Standards) published by NCTM included suggestions for improving mathematics test scores in elementary and secondary schools across the United States. The NCTM Standards were established as a broad framework to guide reform in school mathematics, not as a specific curriculum. In the NCTM's vision, mathematics teachers would encourage students, probe for ideas, and carefully judge the maturity of a student's thoughts and expressions (NCTM, 1989). By contrast, most current teaching practices in mathematics classrooms do not provide sufficient time for critical thought. In fact, the methods used in mathematics instruction itself seem to play a critical role in shaping attitudes toward math (Jackson & Leffingwell, 1999). Sarason (1993) maintains that any reform in education must first begin with teacher training. Thus, practicing mathematics teachers and preservice teachers need to be trained to implement the NCTM Standards.

The Third International Mathematics and Science Study (TIMSS) showed that the math scores of U.S. students decline as the students progress from grades 4 to 12 (Schmidt, 1998). According to Callahan, Tomlinson, Reis, and Kaplan (2000), "U.S. 12th-graders who were taking Advanced Placement calculus, when compared with all advanced mathematics students in other nations, performed only at the international average and significantly higher than students in just five other countries" (p. 787). Steen (1999) found that most U.S. students leave high school with far below even the minimum expectations for mathematical understanding and literacy. Educators, parents, and politicians are seeking solutions to this weakness in mathematics.

Causes of Math Anxiety

The causes of math anxiety vary. Negative predispositions may result if a child's parents have a negative attitude toward or limited experience with math. Lower socioeconomic status may mean that the family has not had sufficient exposure to the kind of education and experience that would more likely promote a positive feeling about math. The New York Times (Kutner, 1992) reported on a study that found that teachers and parents who were afraid of math could pass on math anxiety to the next generation by modeling their own discomfort with the subject. Teachers and the school system also may be a negative influence (Hackett, 1985). Oberlin (1982) states that the following teaching techniques could cause math anxiety: 1) assigning the same work for everyone, 2) covering the book problem by problem, 3) giving written work every day, 4) insisting that there is only one correct way to complete a problem, and 5) assigning math problems as punishment for misbehavior. Other causes may be students spending excessive amounts of time relearning what they had been previously taught, and lack of exposure to the everyday applications of the material being covered (Brush, 1981).

Crawford (1980) found that a student's lack of success with math might be caused by any one of several factors: poor instruction, insufficient number of math courses, unintelligible textbooks, or misinformation about math and about who should do well in math. Some researchers have focused on the gender issues associated with math anxiety. Reilly (1992) reports that females in the late junior high / early high school period begin to have higher levels of math anxiety than males. Bernstein (1992) indicates that at age 12, males felt slightly more math anxiety than females; however, by the age of 14, females were more anxious about math than males. Tobias (1993) believes that these differences between males and females in terms of math anxiety cannot be attributed to differences in innate ability. Crawford (1980) also found that many people believe that they are not mathematically inclined, that men are better than women at math, or that poor memories or learning disabilities are to blame for their problems with math.

Tobias (1987) attempted to dispel two myths about mathematics: that higher level math is too difficult for otherwise intelligent students to master, and that without mathematics you can live a productive intellectual and professional life. Students must overcome any fears of mathematics and be challenged to take higher level math courses; otherwise, their career choices may be affected.

A number of researchers (e.g., Anton & Klisch, 1995; Hendel & Davis, 1978) have found distinct connections between math anxiety and test anxiety. Sarason (1987) contends that math anxiety, like test anxiety, may be driven by cognitive concerns about performance and emotional reactions to stress. Arem (1993) believes that poor test preparation and test-taking strategies, psychological pressures, and poor health habits may lead to test anxiety. Test anxiety can become caught in a vicious cycle. Superintendents may place pressure on principals, who then may place pressure on teachers to have their students perform well on standardized tests. In response, teachers spend large amounts of time having their students take pretests in preparation for the standardized test. Day in and day out, teachers send messages to students stressing the importance of doing well on the test. This leads to a great deal of pressure for students.

Educators' Responses

According to Zemelman et al. (1998), the role of the principal is extremely important in helping to implement best practices for teaching mathematics. They suggest that principals can do the following in order to help students overcome math anxiety:

* Educate staff about the NCTM Standards, as well as any other pertinent local, state, or regional standards

* Hold Family Math Nights to educate parents

* Maintain funds for professional development

* Encourage the use of math manipulatives and supplies

* Encourage teachers to use a variety of assessment methods

* Encourage teachers to share and network with each other regarding ideas that work for them, and provide inservice workshops for colleagues. (p. 151)

Education leaders must help teachers to work more effectively when teaching mathematics, and they must bring faculty members up-to-date on best practices in mathematics instruction. Teachers need to know about the NCTM Standards and current research in mathematics education. One principal the authors spoke with stated,

My job as a principal is to see that every child gets the best education possible. I feel it is safe to say that reading and mathematics achievement are two of the primary academic concerns a principal has. It is ... important that teachers and parents [be] equipped with the tools for successful performance of their students. One issue that impedes success in mathematics is the level of students' math anxiety. If teachers can help to reduce and prevent math anxiety, then students will more likely find more success and develop more confidence in their ability to do math. (personal communication, February 1998)

It is important that teachers recognize the distinction between preventing math anxiety and reducing math anxiety. If possible, teachers should try to prevent students' math anxiety from ever happening. It is important for teachers to get a feel for their students' dispositions toward mathematics. The teacher can help students overcome math anxiety by incorporating writing into the math curriculum, encouraging students to think critically, utilizing alternative forms of assessment, and being willing to work with other math teachers in the elementary and middle school programs in articulating the curriculum.

Marzano's Dimensions of Learning Model (1992) is based on the premise that students must have good attitudes and perceptions toward learning before real learning can occur. If students have good attitudes about learning math, they will be more likely to truly understand the concepts and develop confidence in their ability to perform mathematical operations.

Best Practices for Mathematics Instruction

Math instruction should focus more on process and problem solving than on computation and using only one method to solve a problem. Teachers need to emphasize more communication in the classroom through discussion, problem solving, discourse, and writing. 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. More and more of the standardized tests are geared toward this type of response (through long- and short-response questions). With less of an emphasis on right or wrong and more of an emphasis on process, teachers can help alleviate students' anxiety about math.

Saxe (1991) and Scribner (1984) support the idea that an individual's mathematics ability is significantly influenced by his or her participation in everyday applications, such as going grocery shopping or counting change. Making such connections may help students realize that math is an important tool.

The NCTM Standards (1989, 2000) call for: 1) teaching how to think for oneself, 2) working in groups at all levels of math, 3) efficiently using technology, 4) teaching estimation, 5) including more statistics and probability in the early grades, 6) incorporating fewer computational drills and practices, 7) using manipulatives, and 8) focusing on more realistic problem-solving exercises. Zemelman et al. (1998) found that the use of the following methods constituted best practices for teaching mathematics: 1) manipulatives (to make learning math concrete); 2) cooperative group work; 3) discussion; 4) emphasizing the importance of questioning and making conjectures; 5) justifying one's thinking; 6) writing as a way to explore mathematical thoughts and problem-solving methods; 7) the problem-solving approach to instruction; 8) and calculators, computers, and other technology.

Assessment methods are also critical. Reys, Suydam, Lindquist, and Smith (1998) and NCTM (1989, 1995a) suggest that teachers align assessment with the curriculum's goals, math content, instructional approaches, and activities, including the use of calculators and manipulatives. Reys et al. (1998) and NCTM (1989, 1995a) believe that assessment should allow for multiple sources of information, with tasks that present the same math concept or procedure in different contexts and formats. Also, appropriate assessment methods and uses need to be taken into consideration based on the type of information sought, how the information will be used, and the developmental level and maturity of each student. Alternative forms of math assessment include: observations, questioning, interviews, performance tasks, student self-assessments, work samples, portfolios, writing samples, paper-and-pencil tests, and standardized tests (Reys et al., 1998). Schools need to give students multiple opportunities to demonstrate their full mathematical understanding, align assessment with curriculum and instruction, and regard assessment as continual and recursive (NCTM, 1995a).

Preventing or Reducing Math Anxiety

Teachers and parents can play a critical role in helping children to develop positive attitudes toward math. NCTM's (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

* Characterizing math as a human endeavor.

The approach for reducing math anxiety is different from that which is suggested for preventing math anxiety. Teachers almost have to take on the role of a counselor to help lower or overcome students' anxiety toward math. Treatments effective in alleviating math anxiety include systematic desensitization and relaxation (Hembree, 1990; Schneider & Nevid, 1993; Trent, 1985). Davidson and Levitov (1993) advocate the use of relaxation in conjunction with repeated positive messages and visualizations.

How else can math anxiety be reduced? Teachers must help students understand how their math anxiety was created. According to Hackworth (1992), the following activities will assist in reducing math anxiety: 1) discussing and writing about math feelings; 2) becoming acquainted with good math instruction as well as study techniques; 3) learning study methods that enable students to recognize different types of information learning; 4) being an active learner and creating problem-solving techniques; 5) evaluating one's own learning; 6) developing calming, positive ways to deal with fear of math (e.g., visualization, positive messages, relaxation techniques, and "frustration breaks"); and 7) building confidence in math through gradual, repeated success. Tobias (1987) suggests that students can learn to recognize their feelings of panic, and be able to move past them in order to work on the problem.

Journal writing, by allowing students to express their understanding of and feelings about mathematical concepts, may be one way to reduce math anxiety. Using children's literature also can be helpful as students relate to characters who share their anxiety about math. Math Curse, by Scieszka and Smith (1995), is an excellent book to use as a prompt for student discussions about their own feelings concerning math.

Teachers' Own Anxiety

Teachers' own math anxiety can interfere with students' learning and often create math anxiety for their students. W. V. Williams (1988), in a paraphrase of a Chinese proverb, said:

Tell me mathematics, and I will forget; show me mathematics and I may remember; involve me ... and I will understand mathematics. If I understand mathematics, I will be less likely to have math anxiety. And if I become a teacher of mathematics, I can thus begin a cycle that will produce less math-anxious students for generations to come. (p. 101)

It is important that all teachers have a strong knowledge base for teaching mathematics. Teachers not only need to come to terms with their own math anxiety, but also need to be familiar with best practices for teaching mathematics and to incorporate national and state standards into their instruction. Taking refresher courses/ workshops on new research-based best practices for teaching mathematics is critical in a world where technology is quickly changing what and how math is taught. It is also important that students receive consistent instruction in mathematics as they move from one teacher to the next.

Family Math

Parental involvement can change children's attitudes toward math. Family math nights (Stenmark, Thompson, Cossey, & Hill, 1986) are a popular means of involving families by bringing them to school, where they participate in math activities together. Family math nights can help parents learn about the content that students are learning in mathematics, as well as how teachers are teaching this subject. Parents can learn about the new math standards, math manipulatives, and problem solving and active approaches to learning math.

It is important that parents work closely with their children's teachers by asking their child's math teacher for a schedule of math topics to be taught. Parents should try to follow their children's progress by examining their math books, tests, and homework. It is also important for parents to encourage their children to concentrate and have a positive attitude, especially if a child is insecure about his or her math abilities.

Summary

Educators may need to take a more proactive role in encouraging students to become excited about math and see themselves as successful, confident, mathematical problem solvers. If we, as educators, can do something about helping our students develop their confidence and ability to do math, we will benefit their lives forever. Our students' careers, and many decisions in their lives, could be significantly influenced by how we decide to teach math. Educators can play an instrumental role in fostering an environment that focuses on numeracy, and help reduce students' feelings of inadequacy and lack of confidence when working with mathematical ideas. By utilizing "best practices" in mathematics instruction, educators can reduce or even prevent math anxiety and thereby begin to see greater gains in math achievement among their students.

References

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Joseph M. Furner is Associate Professor, Mathematics Education, Florida Atlantic University, Jupiter, and Barbara T. Berman is Manager, Human Resources Department, Contra Costa County Office of Education, Pleasant Hill, California.