Teachers have the power to alleviate math anxiety.

Abstract

Many students suffer from math anxiety, but teachers can incorporate skills to alleviate it for their students. In order to alleviate math anxiety teachers first and foremost need to portray a positive, enthusiastic, helpful attitude, which communicates a love and usefulness for mathematics. Math curriculum should be designed that deepens student understanding in a practical, engaging and fun way. Pedagogy should be implemented that moves from the explain-practice-memorize strategy to strategies that stress reasoning and understanding. A classroom culture that prompts student inquisition, discovery, learning and the exploration of ideas needs to replace the structured, rigid atmosphere usually associated with math class. And finally, assessment should be conducted in a variety of ways.

Introduction

Not only do students today need math remediation at an overwhelming rate, but reports state that two thirds of American adults fear and loathe math (Burns, 1998). One reason such negative experiences are reported is math anxiety, which knows no boundaries regarding race, age or gender. Math anxiety can be perpetuated in the home, in society, and in the classroom. Because most students can name the teacher they believed caused their anxiety, the exact moment when it happened and the event that triggered the anxiety in the classroom, an examination of teacher attitudes, curriculum, pedagogy, the classroom culture, and assessment is crucial to understanding and alleviating the problem. Students at all grade levels can experience math anxiety and they attest to similar characteristics and consequences. One of the most notable consequences of math anxiety is poor math achievement and poor math grades. Part of this is because students with math anxiety attempt to cope with the debilitating effects of their anxiety by avoiding math in school. This in turn can lead to limited college majors, and ultimately career choices that are restricted mathematically and monetarily. This limited exposure to mathematics is also responsible for lower math achievement and competence (Ashcraft, 2002). The anxiety, which is not significantly related to intelligence, has been shown to inhibit student learning (Ashcraft, 2002) and to reduce working memory capacity (Ashcraft & Kirk, 2001; Beilock,& Cart, 2005; Shobe, Brewin & Carmack, 2005), which in turn has a major impact on students" serf-confidence related to mathematics.

Math anxiety is often the result of repeated negative experiences related to mathematics (Kogelman, Nigro, & Warren, 1978). It is a conditioned fear that develops into a fatalistic attitude, which becomes a self-fulfilling prophecy that reinforces one's beliefs about an inability to perform mathematically. For those who suffer from math anxiety physiological symptoms such as sweaty palms, nausea, muscle contractions, difficulty breathing, tightness in the throat and chest, headaches, heart palpitations, restless behavior, forgetfulness, and a temporary boost in one's heart rate are familiar. Teachers' attitudes, curriculum, pedagogy, the classroom culture, and assessment greatly impact students. All these areas must be considered in order to alleviate anxiety in the classroom. In a 1999 study by Jackson and Leffingwell, it was discovered that sixteen percent of the students studied were first traumatized mathematically in third or fourth grade. The difficulties in fourth grade arose from new math ideas such as fractions, timed tests, and memorization of multiplication tables and formulas. Teachers at this level were blamed for hostile behavior, making derogatory comments when children did not understand concepts, appearing angry when asked for additional help, displaying insensitive and uncaring attitudes, stereotyping females as not needing math, ridiculing girls more overtly than boys, and favoring boys in the subject. Approximately twenty-six percent of the students in the study first realized feelings of math anxiety in ninth, tenth and eleventh grade. At this level students felt their anxiety developed from aspects such as angry teacher behavior, unrealistic teacher expectations, teachers ridiculing students in front of peers, gender bias, and "drill and kill" worksheets. The last noticeable level, twenty-seven percent of the study's students, experienced math anxiety in the freshman year of college. These freshmen attributed their development of math anxiety to instructors who either could not be understood, taught too quickly, belittled students for not having sufficient background knowledge, did not make time to help students, gave poor explanations, administered assessments that did not match instruction, or exhibited gender bias.

Teacher Attitudes

Teacher attitudes greatly influence math anxiety (Harper & Daane, 1998; Ruffell, Mason, & Allen, 1998). Ruffel, et al. (1998), stated that the most dominant factor in molding student attitudes is teacher attitudes. Good (1979) stated that teachers impact student achievement more than either curriculum or teaching methods. Teachers need to model a positive math attitude. This is specifically noted in The Professional Standards for Teaching Mathematics (1991). Standard six (p. 104), states first that the teacher should promote a positive disposition by communicating a love for mathematics and a spirit that illustrates that math is a great invention of the human mind. Second, it states that the teacher should demonstrate the value of math as a way of thinking and illustrate its application in other disciplines as well as in society. Finally, teachers need to promote student confidence, perseverance, curiosity, and inventiveness by assigning appropriate, engaging tasks. Additionally, they should encourage independence and logical thinking, and they should focus on why algorithms work, instead of on memorization. Teachers need to give interactive feedback, maintain high expectations, and locus on learning goals instead of searching for one right answer. According to Sowder & Schappelle (2002), they also need to build in a 70% success rate in order to obtain continued student engagement with work that is considered to be challenging enough to warrant effort and easy enough to expect success.

Teachers especially need to be aware of stereotypes related to mathematics. Very often, teachers contribute to the attitude that math is a male domain by expecting more mathematically from their male students. This is evident in asking higher-order questions of boys and encouraging males to discover alternate solutions (Tobias, 1993). Some teachers have been socialized to believe that boys have the innate ability to perform mathematically and that girls have to put forth more effort than boys to succeed. Teachers also unknowingly make comments about children's abilities that directly affect the way children perceive success and failure. In a study cited in Garber and Seligman (1980), they noted that teachers attributed boys' failure to a lack of motivation eight times more often than they did that of the girls'. Thus when a boy fails, he does not view failure as a reflection of his work, but as a reflection of the teacher's attitude, which is unrelated to his behavior. Even if he does view the failure as a reflection of his work, he can attribute it to a lack of motivation--a nonintellectual quality. The view of his intellectual adequacy is not altered.

Conversely, feedback that was given to girls was work-related criticism 88.2% of the time (Garber and Seligman, 1980). Girls could not attribute their failure to conduct or to nonintellectual aspects as the boys did because the feedback they received was directly aimed at intellectual abilities. Because the girls received praise more often than boys on a regular basis, they could not attribute the criticism to teacher bias as the boys did. Since teachers view females as more highly motivated toward school in general, it is implausible to attribute failure to lack of motivation. Therefore, girls are led to conclude that the negative feedback is a direct reflection of their competence. The result is that girls internalize the negative feedback as indicative of their self-worth and they will be less likely to persist at future tasks. Teachers who are math anxious themselves, or not confident with the subject or pedagogy, often transmit a math fear to their students. It has been shown that elementary teachers who suffer from math anxiety do not exhibit behaviors characteristic of effective math teachers (Tishler, 1980). Tishler noted that math anxious teachers tend to teach more skills than concepts and use less problem solving strategies, games, small group activities and individualized instruction. They are also more likely to spend less time on math in the classroom (Trice & Ogden, 1987).

Curriculum

Another issue that teachers need to consider is curriculum. Between the grades of two and eight, most of the math curriculum is repetitive, with the exception of third grade. The other grades contain mostly repetitive information. An analysis of the TIMSS (1999) video study revealed that math problems presented in American classrooms were considered review problems 53% of the time whereas the Japanese classrooms (the highest scoring country in 1995 and the second highest in 1999) used review problems only 24% of the time. Instead 60% of the problems in the Japanese classroom involved new content whereas the American classrooms consisted of new problems only 23% of the time. More time can be given to new material, discovery and application if repetition is limited. For most students in the primary grades, math is normally one of the most liked subjects. At this level, students believe that they are competent and that hard work will bring success. Then something happens about the time the child enters fourth grade. Math anxiety often surfaces at this grade because a shift is made in the curriculum from using manipulatives and concrete mathematical experiences to more abstract thinking.

By the time students reach middle school, they believe that success is due to innate ability, that effort rarely results in success, and that only the fast succeed. After middle school, the mathematics curriculum becomes more abstract. Memorization and knowledge of past strategies isn't enough to get by any more. Students need to be constantly trained to apply their knowledge to new ideas and to use math as a discovery tool. The curriculum needs to deepen understanding of topics and enhance skills. Repeating the same things year after year disadvantages students in learning, applying, and discovering new mathematics opportunities.

Pedagogy

The pedagogy used to teach math can cause math anxiety more than the subject matter itself (Greenwood, 1984). Herbert and Fumer (1997) wrote that ineffective teaching techniques are often the source of anxiety. Greenwood discovered that the main cause of math anxiety was teaching methodologies that were used to teach basic math skills. He states that the "explain-practice-memorize" strategy is the main source of math anxiety because memorization is stressed instead of the understanding of concepts and reasoning. Students often view mathematics instruction as disjointed, repetitive and tedious with no apparent relevance to students' personal lives. When students taught this strategy begin to encounter material that goes beyond memorization, they do not have the reasoning skills to perform more difficult tasks.

The key to improving student learning lies in the quality of classroom teaching (TIMSS Video Mathematics Research Group, 2003). The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) made it clear that math instruction needs to change to meet the demands of our growing information society. Teachers need a math skill level that goes beyond a basic understanding. Teachers need to be able to constantly solve problems in the classroom. They need to be aware of and understand student confusion and frustration. They need to exude confidence that shows they can work through problems with persistence to create new insights, and they need to notice new patterns and be able to reason why they make sense. They also need to be able to pose questions in an effort to continuously learn. At all levels the frequency of rote practice, memorization, the search for one right answer, calculations that can be performed by calculators and computers, and the teacher as the disseminator of information needs to be decreased. These instructional techniques need to be replaced with strategies that develop meaning such as practical application problems that are related to the students' lives. Projects that call for students to explore solutions individually and in groups need to be incorporated. Activities that lead students in investigating and formulating questions should be added and students should be encouraged to verbally, numerically, graphically, and symbolically represent everyday situations. Teachers need to provide numerous and varied experiences that teach children an appreciation for the role of mathematics in our society.

Classroom Culture

The classroom culture is another source of trauma for many students. Math anxiety often stems from structured, rigid classroom practices (Harper & Daane, 1998). Students complain that there is little opportunity for debate or discussion. They do not like the fact that the focus of math class often tends to be a search for "one right answer." They desire recognition and rewards for the cognitive process involved in solving the problem. They do not like the fact that much of the math work depends on answering quickly and that tests are often timed. Promoting speed in problem solving does not encourage students to think about their processes or analyze results. Teachers need to provide classrooms that encourage students to ask questions, discover learning, and explore ideas. They need to provide an atmosphere where students are secure in taking risks and not embarrassed for wrong answers. Teachers need to acknowledge students' thinking processes and not just right answers. Finally, teachers need to discourage speed in answering and encourage students to take time for reflection.

Assessment

Tests are often the primary source for students' anxiety. Part of the reason for this is that students are increasingly being pressured to perform on high-stakes tests. Tests often demote student confidence. Students have no flexibility in the testing process and they often cannot persevere in a testing situation. The tasks being analyzed often do not pique curiosity or inventiveness. Tests, although at times necessary, should be limited and not timed. Unfortunately, tests are often used as a filter into upper level mathematics courses and ultimately as a filter into the advanced realms of society. Poor assessment practices should not be allowed to deny students the opportunity to advance mathematically or socioeconomically. It is suggested that decreased attention be given to testing for the sole purpose of assigning grades, ranking students, or measuring isolated skills. Instead, students should be assessed on how they think about mathematics. Assessment should be broad and represent a holistic view of mathematics that requires application of a number of mathematical ideas. Assessment should consist of multiple methods, including written, oral and demonstrative formats and it should not exclude the use of calculators and computers. When feedback regarding the assessments is given, it should be focused on a lack of effort instead of ability (Altermatt & Kim, 2004) so that students will remain confident in their efforts to improve.

Teachers can alleviate testing injustices as well as the aspect of math anxiety caused by test taking by applying the NCTM assessment standards as noted in Assessment Standards for School Mathematics (1995). The standards emphasize fostering growth toward highly set expectations and measuring that in a variety of ways. The NCTM (1995, p. 11-21) outlines six assessment standards that should guide assessment practices. These are:

1. Assessment should reflect the mathematics that all students need to know and be able to do. Assessment should include real-life activities that provide student opportunities to formulate problems, reason mathematically, make connections, and communicate mathematically.

2. Assessment should enhance mathematics learning. The primary goal of assessment should be to advance students learning and inform teachers in making instructional decisions.

3. Assessment should promote equity. Equitable practices assess high standards set for all that honor students' unique qualities and experiences.

4. Assessment should be an open process. Assessment should not be used to surprise or trick the students. Teachers should always make students aware of assessment procedures and expectations for performance.

5. Assessment should promote valid inferences about mathematics learning. Conclusions about a student's cognitive process that cannot be assessed directly can be assessed through various methods, including observations, interviews, open-ended tasks, extended problem situations, and portfolios.

6. Assessment should be a coherent process. The assessment process should be in harmony from the design stage to the reporting stage to the application of results.

Conclusion

Research indicates that mathematic performance improves when anxiety is alleviated (Ashcraft, 2002) and when anxiety is not an issue, students will not seek to avoid the subject. In order to mathematically encourage students to pursue math courses and math-related careers, teachers need to exude confidence and excitement for the subject. They also need to portray positive attitudes, design effective math curricula, implement effective pedagogy, create classrooms focused on inquiry and discovery, and assess fairly. Teachers who can do this have the power to alleviate math anxiety in the classroom.

References

Altermatt, E. R., & Kim, M, E. (2004). Can anxiety explain sex differences in college entrance exam scores?. Journal of College Admission, 183, 6-11.

Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185.

Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224-237.

Beilock, S. L, & Carr, T. H. (2005). When high-powered people fail: Working memory and "choking under pressure" in math. Psychological Science, 16(2), 101-105.

Burns, M. (1998). Math: Facing an American phobia. Sausalito, CA: Math Solutions Publications.

Garber, J., & Seligman, M. E. (1980). Human helplessness: Theory and applications. New York: Academc Press, Inc., 197-221.

Good, T. L. (1979). Teacher effectiveness in the elementary school. Journal of Teacher Education, 30, 52-63.

Greenwood, J. (1984). Soundoff: My anxieties about math anxiety. Mathematics Teacher, 77, 662-663.

Harper, N. W, & Daane, C. J. (1998). Causes and reduction of math anxiety in preservice elementary teachers. Action in Teacher Education, 19(4), 29-38.

Herbert, T. P., & Furner, J. M. (1997). Helping high ability students overcome math anxiety through bibliotherapy. Journal of Secondary Gifted Education, 8(4), 164-178.

Jackson, C. D., & Leffingwell, R. J. (1999). The role of instruction in creating math anxiety in students from kindergarten through college. The Mathematics Teacher, 92(7), 583-586.

Kogelman, S., Nigro, E., & Warren, J. (1978). Mind over math: Overcoming math anxiety at the Dalton School. Independent School, 44-46.

National Council of Teachers of Mathematics (1995). Assessment standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35(1), 1-18.

Shobe, A, Brewin, A, & Carmack, S. (2005). A simple visualization exercise for reducing test anxiety and improving performance on difficult math tests. Journal of Worry and Affective Experience, 1(1), 34-52.

Sowder, J. & Schappelle, B. (Eds.). (2002). Research related to teaching: Introduction. Lessons Learned from Research (pp. 5-7). Reston, VA: NCTM.

Tishler, A. (1980). A study of attitude-treatment interaction in mathematics with preservice elementary school teachers. Paper presented at the Annual Meeting of the Mid-South Educational Research Association, New Orleans, LA (ERIC Document Reproduction Service No. ED 195 400).

Tobias, S. (1993). Overcoming math anxiety. New York: W. W. Norton & Company.

Trice, A. D., & Ogden, E. D. (1987). Correlates of mathematics anxiety in first-year elementary school teachers. Educational Research Quarterly, 11(3), 2-4.

TIMSS Video Mathematics Research Group. (2003). Understanding and improving mathematics teaching: Highlights from the TIMSS 1999 video study. Phi Delta Kappan, 84(10), 768-779.

Darla J. Shields, Slippery Rock University, PA

Darla Shields is an Assistant Professor and teaches math.