Published on

18-Mar-2017View

212Download

0

Transcript

Action in Teacher Education Winter 1998, Vol. XIX, No. 4. pp. 29-38

Causes and Reduction of Math Anxiety in Preservice Elementary Teachers

Norma Wynn Harper Judson College

CJ. Daane University of Alabama

Abstract

This study analyzed the math anxiety levels of 53 elementary preservice teachers before and after a mathematics methods course. Additional information was gathered about factors that played a part in creating their math anxiety. Interviews were conducted with those showing the greatest math anxiety differences between pretest and posttest scores. The study showed that there was a signi$cant reduction in the level of math anxiety at the end of the methods course. Factors causing the original anxiety centered amundan emphasis on right answers, word problems, fear of making mistakes, timed tests, and confidence levels. Math anxiety levels were discussed with the preservice teachers at the end of the study. It is recommended that preservice teachers be made aware of their individual levels of math anxiety and learn ways of preventing their own negative dispositions toward mathematics from being transmitted to their future elementary students.

Many elementary teachers begin their collegiate studies with apprehension of and anxiety toward mathematics. They are not confident in their ability to use mathematics and consequently hold attitudes and beliefs about mathematics and mathematics learning and teaching that are contrary to the NCTM Standards. They tend to view mathematics as rule- bound procedures and an arbitrary collection of facts (Ball, 1990). If reform in mathematics teaching and learning is to occur as outlined in the NCTh4 Standards (NCTM, 1989, 1991, 1995), future teachers must bring dispositions to the classroom that are in keeping with the Standards. If this does not happen, future elementary teachers will be barriers to, instead of catalysts of, change. As early as 195 1, research relating elementary preservice teachers negative attitudes toward mathematics was published. Dutton (1 95 1) found that elementary methods students reported a lack of understanding of mathematics, a lack of interest in mathematics, a fear of making mistakes, and feelings of insecurity and inferiority. Later studies showed that many preservice elementary teachers had a weak understanding of mathematics which was compounded by negative attitudes and anxiety toward mathematics (Lester, 1984).

Hadfield and Lillibridge (1 991) reported that elementary school mathematics experiences, in many cases, have led to mathematics anxiety. These experiences have tended to lower confidence in ones mathematical ability which has led to mathematics avoidance by the time the student was in secondary school. Thus, the elementary mathematics classroom might be considered as a beginning point for creating mathematics anxiety in many students.

29

Hilton (1980) also considered the elementary mathematics classroom as a cause of math anxiety among some students. He associated teachers lack of mastery of mathematics and their authoritarian teaching style with causing mathematics anxiety. He also included the prevalence of rote calculations, the dependence on memorization, and unrealistic applications or problems as other causes.

Reyes (1984) indicated that there were several variables which were typically cited by preservice teachers as increasing their math anxiety. She divided these variables into two categories: previous mathematical experiences and beliefs about mathematics and oneself. In the previous mathematical experiences of mathematics anxious persons, teachers played a key role. Subjects repeatedly related negative experiences with past mathematics teachers (Frank, 1990; Tobias & Weissbrod, 1980; Widmer & Chavez, 1982). The instructional practices of teachers appear to have influenced mathematics anxiety. Common practices leading to increased anxiety were emphasis on drill and practice, getting the right answer and using the right method, taking timed tests, memorizing formulas, and applying rules. There was little use of group work, concrete materials, and applications to the real world (Kelly & Tomhave, 1985; Stodolsky, 1985; Tobias, 1978).

In the category concerning beliefs about mathematics, mathematics anxious persons tended to feel helpless, fearful, insecure, inferior, and not confident about their mathematics ability (Dodd, 1992; Tobias, 1988). These feeling coincided with beliefs about themselves, for example, they were just not good at mathematics and they could never work hard enough to do mathematics well. Many believed they lacked an understanding of mathematics and that mathematics was not useful. In addition, word problems were difficult.

There have been numerous ways suggested for mathematics teachers to decrease their students mathematics anxiety. Creating a supportive environment has been advocated as being of prime importance ( Morris, 1981). Dodd (1992) suggested a process-oriented approach with games and activities, while other researchers saw positive benefits from the use of concrete materials (Frank, 1990; Morris, 1981). Group work was proposed by Buerk (1985). Larson (1983) advocated that instructors demonstrate the usefulness of mathematics in relation to other subjects, use diverse ways to solve problems, and use different instructional strategies.

Unfortunately, the instructional strategies currently used by many teachers are not necessarily those advocated by the Standards. Bush (1989) found that there was a slight tendency for math anxious teachers to be more traditional in their teaching. Their students have been assigned more seatwork and have spent less time playing games, problem solving, and doing small-group activities. More skills and fewer concepts have been taught by these teachers.

The NCTM Standards (NCTM, 1989, 1991, 1995) created a vision of what mathematics should and could be. It should help produce confident and capable problem solvers with teachers being the key to the realization of this vision. Merseth (1993) stated that teachers attitudes and beliefs can greatly influence their

30

pedagogical practices in teaching mathematics. According to the Professional Standards (NCTM, 1995), instructors of preservice mathematics teachers should model the instructional practices and positive dispositions eventually needed by preservice teachers if reform is to occur. This includes engaging students in appropriate mathematical tasks to foster problem solving and mathematical discourse, using group work, and demonstrating beliefs and attitudes about learners and mathematics consistent with the Standards. Since the mathematics methods course is probably the last opportunity to influence preservice teachers attitudes toward mathematics, it must be designed to build confidence, help alleviate math anxiety, and promote effective teaching and learning as outlined in the Standards.

The purpose of the study was twofold: (a) to determine what factors originally contributed to the math anxiety of elementary preservice teachers, and (b) to examine the effects of a mathematics methods course on the math anxiety of preservice teachers. The findings were used to: (a) enable future teachers to see what caused their own math anxiety in order to extrapolate how to lessen the math anxiety of their own students and (b) help refine the math methods course by determining what factors of the course were the most favorable to help overcome some of the math anxiety exhibited by preservice teachers.

Method Program Description

There were 53 preservice elementary teachers enrolled in three sections of an undergraduate elementary mathematics methods course at a mid-sized Southeastern university. The methods course consisted of 10 three-hour class sessions with 28 full days of fieldwork experience during the 15-week semester. A typical class session consisted of (a) a discussion of previously assigned readings, (b) whole group work centered on the topic for the day (such as geometry), (c) small group work with manipulatives, focusing on problem solving situations, (d) discussion of and involvement in games and activities for reinforcement, and (e) whole group discussion of assessment/evaluation measures. During the 28 days of the field experience, the students were assigned to one supervising teacher. They helped the teacher with mathematics instruction on a daily basis and were required to teach at least a week of math lessons on their own.

Data Collection Information was collected in four ways. Three instruments were administered

to all students while semistructured interviews were conducted with 11 students.

Mathematics Anxiety Rating Scale (MARS). To determine pretest and posttest levels of math anxiety, the 98-item MARS was

administered. Richardson and Suinn (1972) constructed the MARS to measure the anxiety associated specifically with mathematics. The instrument was given the first and last weeks of the semester to determine if there was a significant difference in the students level of math anxiety prior to and after completing the math methods course.

31

Factors Influencing Mathematics Anxiety (FIMA). To determine which factors had the greatest influence on the students math

anxiety prior to the math methods course, a 26-item checklist, the FIMA, was developed by the authors of the research. The items on the checklist (see Appendix A) were based on the literature pertaining to math anxiety. Each statement on the checklist related to experiences in mathematics or mathematics classes. Students were asked to agree or disagree with each statement. If they agreed with the statement, they then indicated whether they believed that factor had caused them to experience any math anxiety. The instrument was administered during the first week of the semester.

Methods Course Reflection (MCR). To ascertain what influences the methods course had on anxiety, the 7-item

MCR was given the last week in the semester. This instrument was designed by the researchers to determine the influence on math anxiety of (a) working with a partner, (b) working in cooperative learning groups, (c) working with small groups or in centers, (d) using manipulatives, (e) doing problem solving activities, (f) writing about mathematics in journals, and (g) doing fieldwork in a local school during the math methods course.

In teroiews. Eleven students were selected to be interviewed because they exhibited the

greatest differences between their MARS pretest and posttest scores. Six of the students had a decrease in math anxiety while five had an increase. The students were asked to explain how the methods course influenced their levels of math anxiety and what past experiences led to their math anxiety. The interview data were analyzed using a grounded theory approach to develop topics (Bogdan & Biklen, 1992).

Results The results of the analysis of variance measuring the differences between the

pretest and posttest MARS showed a significant difference (F = 16.76, df = 1, P < .OS). By the end of the mathematics methods course, the level of math anxiety of the preservice elementary teachers was lowered significantly from the level of math anxiety at the beginning of the course. However, not all students experienced a decrease. Forty-four of the students showed a decrease, while nine exhibited an increase.

The results of the FIMA instrument indicated that each factor on the survey concerning past experiences in mathematics had a direct influence on the math anxiety of at least one subject. The foremost factor for 75% of the students was word problems. For 6O%, math anxiety was caused by: (a) an emphasis on the right answers and the right method, (b) fear of making mistakes, and (c) frustration at the amount of time it took to do word problems. At least half of the students indicated additional reasons for their math anxiety: (a) an emphasis on timed tests, (b) feeling dumb when unable to solve a mathematics problem, and (c) having no confidence in their mathematics ability.

32

The MCR survey showed what aspects of the math methods course influenced the math anxiety of the students. Sixty percent indicated that the following factors decreased their math anxiety: (a) working with a partner, (b) working in cooperative learning groups, (c) working with small groups or in centers, (d) using manipulatives, (e) writing about mathematics in journals, and ( f ) doing fieldwork in a local elementary school. The other factor, doing problem solving activities, showed a decrease in math anxiety for 41% of the students, but an increase or no change in the other 59%.

The interviews yielded more specific information about past experiences which led to math anxiety and the influence of the methods course. The responses to the interview question about past influences causing math anxiety yielded four topics: (a) specific math content, (b) teacher instruction and attitude, (c) specific episodes in math classes, and (d) aspects not directly related to the math classroom.

The math content causing anxiety ranged from topics introduced in the elementary school, such as multiplication and long division, to high school content, most notably, geometry. Teacher instruction and attitude caused anxiety in some students. One student said, Math was never fun; it was structured, time consuming, and boring. Some students indicated that teachers taught content quickly, then assigned homework without adequate explanation. One student relayed that her teacher told her she would just be one of those people who would never get math. Teachers also were the cause of most of the specific math episodes that caused anxiety in students. Most of the episodes related involved the student being embarrassed by the teacher for giving an incorrect answer or for feeling stupid when asking a question. Other episodes involved studying for and taking tests. Tests tended to increase anxiety and cause some students to become real nervous. There were some aspects that were not directly related to the math classroom that caused anxiety. These included a slowness for learning, dyslexia, never being able to balance a checkbook, thus bouncing checks frequently, and parental pressure to do well in mathematics.

The responses to being asked about methods course influences divided into two topics: the way the course was taught and field experiences. The students stressed math anxiety was lessened when instructors talked to them instead of lectured to them. The students also liked doing something with manipulatives as opposed to sitting and taking notes since the manipulatives enabled them to see math and better understand how it works. Two students stated that initially the use of manipulatives increased their math anxiety because they were unfamiliar with the materials and methodology. However, after experiencing several weeks with different materials, math became much easier with the manipulatives and their anxiety decreased. Anxiety also decreased when students were allowed to work together. One student said she thought it helped to talk togethersince someone else might explain it differently than the instructor. When working problems in groups, the students no longer felt isolated. Another student indicated I found when I explained the problem to my partner or group, I understood it

33

better. Another factor that helped to decrease math anxiety was that the instructor allowed them to work math problems in more than one way. A game atmosphere was beneficial to one student who indicated that during this time she was more relaxed and felt it was more acceptable if she messed up.

The comments from the students whose math anxiety increased centered around their beliefs that they lacked mathematics knowledge prior to the course. One student said she realized she needed a better grasp of mathematics in order to teach it to children one day. Another student indicated he did not feel comfortable being watched by someone (either the instructor or others in the group) when working a problem. A third comment centered around journal writing as one student indicated that writing in the math journal made him really nervous because he could not explain the math in words, he could only do the algorithms he was taught.

The field experience helped to reduce math anxiety in most students. Some students commented that after using manipulatives to teach children, they realized how successful concrete materials could be in teaching and learning mathematics. They also found that elementary children seemed to learn from each other and liked to work together to arrive at a solution. However, some students indicated the field experience caused them anxiety. One student said he had anxiety because you really have to understand it to teach it. Anxiety increased in another student when her cooperating teacher watched her teach.

After the data were collected, math anxiety was discussed with the students. Many of the students were amazed at the similarities of negative experiences in mathematics. A discussion ensued about how their own anxiety levels could easily be assimilated by their elementary students if they were not careful in their instruction. Small groups brainstormed about the things they could and should do as teachers to help alleviate math anxiety in the classroom.

The data suggested to the methods course instructors that problem solving was still a main factor creating math anxiety in many students. The instructors discussed ways of infusing less threatening activities in class, while still maintaining the integrity of the course. In addition, since geometry was found to be the content area associated with the most amount of anxiety, it was decided to enhance that area for the next semester.

Discussion The findings suggest that math anxiety still persists in many future elementary

classroom teachers. The cause of this anxiety has begun, many times, in elementary school. Often the anxiety has been created by the classroom teacher. If future elementary teachers understand what caused their own anxiety they may be better able to promote an atmosphere that helps inhibit math anxiety in children.

Many of the causes of math anxiety have stemmed from rigid and structured classroom instructional practices. Students have often felt under pressure to do

34

math in an allotted amount of time and to do it the "right" way. There frequently have been embarrassing situations where teachers have made an example of a student for the way a question was asked or problem was answered. Students have been made to feel "stupid or dumb" in front of the class. There has been undue teacher emphasis on tests and grades that has produced much anxiety in students.

The overwhelming factors causing math anxiety in the preservice teachers appeared to be word problems and problem solving. Preservice teachers need to learn more creative ways of presenting problem solving activities to children in a manner that will be motivating. These need to be real-life problem situations in which children are interested. If problem solving is presented in rigid textbook form, it will only cause more math anxiety among students. Since problem solving is a known factor causing math anxiety, methods course instructors must make certain they present problem solving activities in a non-threatening environment.

The math methods course can have a significant impact on helping future teachers learn to cope with their own anxiety and learn how to teach mathematics to children in ways that limit anxiety. Methods courses should emphasize working together, using manipulatives, writing about mathematics, and having extensive fieldwork experiences. In addition, the course needs to help students reflect on their own past math experiences and anxiety levels to enable them to create less anxious and more positive mathematics classrooms in the future. By sharing experiences and discussing the implications, students can begin to realize how important the attitude of the teacher is in reducing math anxiety in the classroom.

Prospective teachers need to be aware of factors that cause math anxiety and not contribute to them. If the Standards are to be implemented in classrooms, the anxiety factors must be eliminated in order for the Standards to succeed. By reducing math anxiety in the classroom, we can hope to create a new generation of students who believe in and are confident in their ability to do mathematics. However, the future elementary teacher holds the key to establishing this anxiety-free mathematics classroom environment.

Norma Wynn Harper is an Assistant Professor in the Departments of Education and Mathematics at Judson College. Her research interests include mathematics across the curriculum, multiple intelligences, and learning styles.

C.J. Daane is a Professor in Teacher Education at the University of Alabama. Her research and teaching interests include elementary mathematics education, mathematics curriculum, student teaching and university-school collaboration.

35

Appendix A

Factors Influencing Mathematics Anxiety

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

I rarely had the opportunity to work in groups, so I felt isolated in math class.

I felt math was not useful.

I lacked an understanding of the vocabulary used in math.

I found word problems to be difficult.

There was an emphasis on drill and practice.

There was an emphasis on the right answers and the right method.

There was an emphasis on timed tests.

I rarely had the opportunity to work with manipulatives or concrete materials.

I felt as if I could not keep up with other students in math.

I felt math classes did not relate math to the real world.

I felt helpless in problem solving.

I lacked an understanding of the material.

I lacked an interest in math.

I had a fear of making mistakes.

I felt insecure and inferior when it came to math.

I felt dumb when I was unable or slow to solve a math problem.

I felt I was just not good at math.

My mother or father was not good in math.

I felt that males were better then females in math.

I was not confident in my math ability.

I knew I could never work hard enough to do math well.

There was an emphasis on memorizing rules and applying those rules.

I felt frustrated at the amount of time it took to work problems.

I had previous math teacher(s) demonstrate negative attitudes toward math.

I had bad experiences with past math teachers.

I had embarrassing or negative experiences in past math classes.

36

References

Ball, D. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449-465.

Bogdan, R. C., & Biklen, S. K. (1992). Qualitative Researchfor Education (2nd ed.). Boston: Allyn and Bacon.

Buerk, D. (1985). The voices of women making meaning in mathematics. Journal of Education, 167 (3), 59-70.

Bush, W. S. (1989). Mathematics anxiety in upper elementary school teachers. School Science and Mathematics, 89,499-509.

Dodd, A. W. (1992). Insights from a math phobic. Mathematics Teacher, 8L 296-298.

Dutton, W. H. (1951). Attitudes of prospective teachers toward arithmetic. Elementary School Journal, 51,84-90.

Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? Arithmetic Teacher, 37 (5), 10-12.

Hadfield, 0. D., & Lillibridge, F. (1991). A hands-on approach to the improvement of rural elementary teacher confidence in science and mathematics. Nashville, TN: Annual National Rural Small Schools Conference. (ERIC Document Reproduction Service No. ED 334082).

Two-Year College Mathematics Journal, 11 (3), 174-188.

preservice elementary teachers. Arithmetic Teacher, 32 (5), 51-53.

attitudes in preservice teachers. Arithmetic Teacher, 31 (2), 8-9.

Teacher, 31 (6), 5456.

education. Phi Delta Kappan, 74 (7), 548-558.

Hilton, P. (1980). Math anxiety: Some suggested causes and cures: Part 1.

Kelley, W. P., & Tomhave, W. K. (1985). A study of math anxiety/avoidance in

Larson, C. N. (1983). Teacher education - techniques for developing positive

Lester, F. (1984). Preparing teachers to teach rational numbers. Arithmetic

Merseth, K.K. (1993). How old is the shepherd? An essay about mathematics

Morris, J. (1981). Math anxiety: Teaching to avoid it. Mathematics Teacher, 74,

National Council of Teachers of Mathematics. (1995). Assessment standardsfor

National Council of Teachers of Mathematics. (1991). Professional standards

National Council of Teachers of Mathematics. (1989). Curriculum and

Reyes, L. H. (1984). Affective variables and mathematics education. The

Richardson, F.C., & Suinn, R.M. (1972). The MARS: Psychometric Data.

Stodolsky, S. S. (1985). Telling math: Origins of math aversion and anxiety.

Tobias, S. (1988). Dealing with math/science blocks. Liberal Education, 74 (2),

413-417.

School Mathematics. Reston, VA: Author.

for teaching mathematics. Reston, VA: Author.

evaluation standards for school mathematics. Reston, VA: Author.

Elemenfay School Journal, 84,558-580.

Journal of Counseling Psychology, 19 ,551-554.

Educational Psychologist, 20,125-133.

20-23.

37

Tobias, S. (1978). Overcoming math anxiety. New York: W.W. Norton and

Tobias, S., & Weissbrod, C. (1980). Anxiety and mathematics: An update.

Widmer, C. C., & Chavez, A. (1982). Math anxiety and elementary school

Company, Inc.

Harvard Educational Review, 50 (l), 63-70.

teachers. Education, 202 ,272-276.

38