Tracing The Roots Of Mathematics Anxiety Through In-Depth Interviews With Preservice Elementary Teachers

Tracing The Roots Of Mathematics Anxiety Through In-Depth Interviews With Preservice Elementary Teachers

Karen M. Trujillo

Through administration of the Revised Mathematics Anxiety Rating Scale (R-MARS) to 50 preservice elementary teachers, the five most mathematically anxious were identified. Each of the five identified participants was interviewed with regard to her mathematics experiences in elementary school, high school, college, and family setting. Their perceptions as to the causes of their specific anxieties about mathematics were expressed. Their future plans to deal with their anxieties about teaching mathematics when they join the teaching profession were also voiced. Negative school experiences, lack of family support, and general test anxiety were trends found within the backgrounds of the participants. Despite their current apprehensions regarding the study and teaching of mathematics, most of the subjects were very confident and optimistic as to the possibility of setting aside their fears in order to develop into effective teachers of mathematics themselves.

Over the past 25 years, mathematics anxiety has become a very popular research topic for both mathematics educators and educational psychologists. Mathematics anxiety has been defined as a state of discomfort which occurs in response to situations involving mathematical tasks which are perceived as threatening to self esteem (Cemen, 1987). In turn, these feelings of anxiety can lead to panic, tension, helplessness, fear, distress, shame, inability to cope, sweaty palms, nervous stomach, difficulty breathing, and loss of ability to concentrate (Cemen, 1987; Posamentier & Stepelman, 1990, p. 210). Although only a small proportion of persons suffer from a propensity to experience this condition, it is important to recognize how it can lead to a very debilitating state of mind. Those persons with severe cases of mathematics anxiety are limited in college majors and career choices. There is a particular concern in the case of elementary teachers, because it is has been reported that a disproportionately large percentage experience significant levels of mathematics anxiety (Buhlman & Young, 1982; Levine, 1996). This leads to doubts as to their potential effectiveness in teaching mathematics to young children (Trice & Ogden, 1986).

According to Hadfield and McNeil (1994) the causes of mathematics anxiety can be divided into three areas: environmental, intellectual, and personality factors. Environmental factors include negative experiences in the classroom, parental pressure, insensitive teachers, mathematics presented as rigid sets of rules, and nonparticipatory classrooms (Dossel, 1993; Tobias, 1990). Intellectual factors include being taught with mismatched learning styles, student attitude and lack of persistence, self-doubt, lack of confidence in mathematical ability, and lack of perceived usefulness of mathematics (Cemen, 1987; Miller & Mitchell, 1994). Personality factors include reluctance to ask questions due to shyness, low self esteem, and viewing mathematics as a male domain (Cemen, 1987; Gutbezahl, 1995; Levine, 1995; Miller et al., 1994).

Many researchers attempt to trace the evolution of mathematics anxiety among high school and college students back to their elementary school classroom experiences. When early school experiences get the blame for mathematics anxiety, the elementary teacher is usually labeled as the responsible party. Mathematically anxious teachers are said to pass their anxieties on to their students (Buhlman & Young, 1982). They are also often doubted as to their effectiveness as teachers of mathematics (Hadfield & McNeil, 1994; Kelly & Tomhave, 1985). According to Brush (1981), mathematically anxious teachers tend to use more traditional teaching methods, such as lecture, and concentrate on teaching basic skills rather than concepts. This is contrary to the current movement toward teaching mathematical concepts and problem solving through cooperative learning and projects (National Council of Teachers of Mathematics, 1989). It is certainly agreed upon by most educators that elementary school teachers are at a disadvantage if they possess mathematics anxiety, and to admit their fears and attempt to overcome them would not only be in their best interest, but also be in the best interest of their students.

Although prevention is the most desirable solution for mathematics anxiety, this is not a possibility for many mathematically anxious elementary teachers already in place. However, in looking for solutions and potential interventions, a thorough investigation of teachers’ and preservice teachers’ perceived causes of their own mathematics anxiety could help to build a theory as to future prevention. Also, through exploration of their own backgrounds, preservice teachers may perhaps identify and confront their own personal levels of mathematics anxiety prior to entering the classroom as teachers.

The purpose of the present study was to implement an in-depth exploration of the early school mathematics experiences of highly mathematically anxious preservice elementary teachers. We hoped to identify commonalties between the various participants in relation to their negative emotions pertaining to mathematics, their early school and home experiences in mathematics, and how they planned to overcome their mathematics anxiety upon entering their own classrooms as instructors.

Background of Researchers

It is customarily expected that in reporting a qualitative research study the backgrounds of the researchers be described, so that readers are informed as to any potential biases in data collection or analysis, which should be minimized through triangulation (Bogdan & Biklen, 1998, p. 33-36; Krathwohl, 1993, p. 328). The two authors of this study are both mathematics educators. One author holds a doctorate in education, is an associate professor of mathematics education, and research methods at a Research I land grant institution, and has 15 years public school mathematics teaching experience. His interest in mathematics anxiety came about through several years of contact with prospective and inservice elementary school teachers who often have difficulty in developing effective mathematics instruction due to negative attitudes towards mathematics itself. His beliefs with regard to the emergence of mathematics anxiety relate to the theory that personality type and cognitive style are key factors, more so than negative mathematics experiences in the company of teachers, parents, and peers.

The other author recently completed a doctorate in education, with an emphasis in mathematics education, and has four years of public school teaching experience. Her interest in mathematics anxiety emerged from her classroom experiences with her students at the secondary level. Her interest in carrying out this study also resulted from her recent focus on in-depth interviewing as a qualitative research technique. Her prior beliefs with regard to the emergence of mathematics anxiety relate to the theory that the tone of early personal experiences in mathematics in and out of the classroom are key factors in the development of ones ultimate attitude toward mathematics, with teachers, parents, and peers exerting major influences.

Method

During the fall semester, 1995, the Revised Mathematics Anxiety Rating Scale [R-MARS] (Plake & Parker, 1982) was administered to 50 students in the elementary mathematics methods classes at a land grant institute in the southwestern U.S. The R-MARS contains 24 questions, each to be rated by the respondent on a 1 – 5 Likert scale. The test items consist of statements that describe situations requiring mathematical thought or tasks, and are rated as to the degree of anxiety that the respondent perceives she/he would experience in the given situations. The test items were developed from the 98 item Mathematics Anxiety Rating Scale, (Richardson & Suinn, 1972), with which it correlates at a level of .97 (Plake & Parker, 1982). The test-retest reliability for the parent instrument has been shown to range from .78 to .85 and internal consistency has been reported as .97 (Hannafin, 1985). Possible scores range from 24 to 120. The higher the score, the higher the level of mathematics anxiety. Six of the 49 participants scored above 100 points on the profile. These six students were then asked to participate in an in-depth interview to explore their individual experiences related to mathematics anxiety. One of the six potential subjects did not wish to participate, while the other five agreed to be interviewed by one of the researchers.

The interviews were all conducted by a single researcher, one of the two authors, and were recorded on audio tape. They were open ended in format, not consisting of a specific list of questions. However, there was an attempt to direct the discussion toward the subjects’ general feelings toward mathematics, their early school experiences in mathematics, and their plans for coping when they were to take charge of their own elementary school classrooms. A modified version of the Seidman indepth interviewing technique was employed (Seidman, 1991), which suggests that several categories or themes usually emerge from an analysis of the communications of the participants. While Seidman recommends three separate 90-minute interviews in order to insure the establishment of sufficient rapport with the participants, our technique collapsed the processes of building rapport and information gathering into a single interview session. The interviewer also attempted to adhere to the more generally accepted guidelines for the conduction of research interviews (Gall, Borg, & Gall, 1996, p. 318). Confidentiality was assured, rapport was built, benefits of the interview were explained, simple probes were used rather than cross-examining, hinting, or leading questions, and threatening topics were either avoided or approached in a very delicate manner.

The investigation was phenomenological by design, in that it attempted to understand the mathematics experiences of the participants from their own perspectives, to understand their resultant beliefs, and to understand how those beliefs may have affected their present attitude toward mathematics teaching and learning. The goal was to find the meanings of the experiences to the participants, not to the researcher (Leedy, 1997, pp. 161-162). A phenomenological approach assumes that there will ultimately be some invariable element that is common among the perceived experiences (Tesch, 1994, p. 147).

All of the participants in the study were female, two Hispanic and three Anglo. The three Anglo women were traditional students ranging in age from 21 to 25. For purposes of this study they are referred to as Jane, Sandy, and Veronica. The two Hispanic women were returning students, one age 40 and the other age 33. For the purposes of this study they are referred to as Nora and Oralia. All five participants were pursuing degrees and certification in elementary education. Each interview lasted approximately one hour, although due to time constraints, a second interview was required for one of the participants.

Results

The first step of the data analysis process was the transcription of all audio recorded interviews to typewritten text. Both researchers then read all transcripts with an eye for a means of organizing small units of analysis into specific categories. As suggested by Lofland and Lofland (1984), categories were derived that could be used to organize data with regard to themes such as personal meanings (philosophies, rules, norms), events, interactions between persons, social roles, and interpersonal relationships. Although categories were developed, it was more themes and patterns that were sought in the final analysis. After conferring together, the researchers initially developed a set of 8 categories of the respondents’ statements. The transcripts were then read again, and an attempt to place all statements into the categories resulted in an expansion to 10 categories with the “school experiences” category being expanded into three separate school levels. The final 10 categories were: view of mathematics, self concept in mathematics, elementary school experiences, secondary school experiences, college experiences, examples of good mathematics teachers, examples of bad mathematics teachers, family influences, math test anxiety, and plans for teaching children mathematics. Both authors then independently identified trends within each category through extraction of the ideas incorporated in the various statements. As previously stated, the goal was to summarize the personal perceptions of the individuals, rather than to gain support for a specific hypothesis in relation to their personal experiences. A synthesis of the findings then resulted in a condensation into the five general areas that follow. It was intended that independent analyses of data by the two authors prior to their collaboration on the final interpretation would serve as some measure of triangulation.

Self Perceptions Related to Mathematics Anxiety

Oralia’s perceptions of the reasons for her mathematics anxiety are multifaceted. She attributes her difficulty to her personality, her lack of solid foundation in mathematics, and her learning style. She explains as follows:

I love math, but nobody ever had the patience to teach it to me. In

elementary, I was a slow learner and I wouldn’t ask questions because I was

afraid of the humiliation. It is hard to learn if you are unhappy, so I

lack the basic foundations. I can’t learn if you just tell me. You have to

show me and in math nobody ever did that.

However, it is important to note that even though Oralia has had a history of negative experiences in mathematics, she took algebra I, algebra II, and geometry in high school and passed all classes with a B average. She attributes her success in these classes to “hard work and a lot of extra time”. She commented that “I would go for help in the morning, and at lunch, and my teachers were there. The teacher’s attitude is very important.”

Nora tended to attribute her success to the instructor and the way mathematics was taught to her. She describes her experiences:

As long as it makes sense, I’m O.K. If I see things as a whole, I get

overwhelmed. If it is in pieces, then it is O.K. I am a concrete thinker. I

always attribute my success to the instructor. In 111 the teacher

humiliated me in front of the whole class and reminded me of high school. I

resented the class and didn’t try very hard. In 114, I did great because

[my teacher] made me feel confident so I could do it.

For Jane there were also a number of problems, including teacher personality, lack of basic skills, and the means of introduction of the material. Her comments included:

It depended on the teacher. I needed to know why and nobody could answer. I

was taught in a step by step fashion and I don’t think that way. If I was

taught overall concepts, holistically, maybe it would have been better. I

also never memorized the basic formulas and concepts, so every time I take

a test I have to relearn concepts like percentages and stuff.

School Experiences Related to Mathematics

All of the participants recalled struggling in elementary school, except Sandy. Jane was one of the only Anglo children in a Navajo school. All of the children thought she was smart and she had a very high self concept of her intelligence. This concept began to deteriorate after many episodes like the one she described here:

I remember getting a lower grade than this boy on a test. He was shocked

and he made me feel bad. I ended up in special education for a while

because I had problems with organization. I slipped through the cracks all

through school.

Veronica recalled a very rigid elementary school experience:

There was a lot of drill and repetition and no hands on. There were so many

rules and a lot of memorization. I was not confident in math and I was

afraid to get the wrong answer. There was so much pressure and only one

right way. I felt isolated and alone when I didn’t understand.

Nora and Oralia had similar experiences. Both felt isolated in elementary school. Nora did not speak English when she started school and her problems were compounded because her family frequently relocated. She did not remember having many close friends and was often afraid of being held back. Oralia said that she was teased and bullied a lot in elementary school, and had several traumatic experiences. She described elementary school as follows:

I was degraded in elementary school. I was labeled early as a slow learner.

I was too shy to ask questions because kids are mean when you don’t

understand. Everything was rushed and nobody wanted to take the time to

teach me. One teacher can scare you and you carry that all through school.

It makes you timid.

Even though most of the participants experienced some negativity at an early age, their mathematics anxiety seemed to become magnified in junior high and high school. Each of these women had at least one mathematics class in high school that was very detrimental to the development of their mathematics skills. Sandy described her geometry teacher as follows. “She was old. She knew her subject, but she couldn’t teach it. She was nervous and insecure and would get shocked by everything. She was always nagging and no fun.”

Jennifer described one of her teachers in a similar way:

He would go to conferences and get all excited, but nothing would change.

We were in rows, we did homework, turned it in, and would take a test. I

always wanted to know “why?”, and he would never answer me. He would say

“Just do it.” He didn’t connect with us, and if we had trouble, we couldn’t

go in for help.

Nora went to a very small school, and there was only one mathematics teacher. She took one year of mathematics and was so intimidated that she went no further until she attended college over twenty years later. She recalled her experience in high school:

He was a redneck, loud and intimidating. And, he would make fun of the

kids, and even hit them with his ring. I was afraid and I never spoke up. I

loved science, but I was told that I had to be good in math, so I didn’t

pursue that either.

Veronica described her geometry teacher in much the same way as the others.

He wouldn’t explain or answer questions. He scared me and it was a

turn-off. He was negative, old, strict, and he would yell. He would lecture

and then sit down at his desk. He didn’t want to deal with us on a

one-to-one basis, so we would reach out to each other.

Oralia had three very good teachers in high school, but when she tried to enroll in calculus as a senior she was asked to drop the class after failing the first test. She described her experience as follows. “He made me feel stupid. Some learn faster and I learn slower, but it doesn’t mean I can’t learn the same stuff. I ended up taking a general math class.”

Even though all of these individuals had negative experiences, most of them eventually had at least some positive experiences in mathematics at either the secondary or the college level. Oralia described her algebra teacher as “fun”. “He answered all of my questions, put in extra time before school and at lunch, and I was not afraid to ask [questions in class] because he would quiet down the teasers.”

Veronica described one of her better teachers as follows. “He would joke around and he could relate to us. He would explain real slow and would take time. I wasn’t afraid to ask questions. The class was relaxing and fun.”

At the college level both Jane and Nora had positive experiences. Jane described her first college instructor as “very relaxed and kick back”. “There was no threat. He was patient and answered ‘Why?'” Nora described her first college instructor in the following way: “She always had a good attitude. She could explain and demonstrate at the same time. She would make sure everyone understood before going on. She did not overwhelm us.”

In college, all of the women in this study were exposed to mathematics in a very different light in their mathematics methodology courses and in their “mathematics for teachers” courses, which are required for all elementary majors. Veronica’s description is representative of the group:

It was hands-on. I learned different techniques. It was the first time I

realized how math could be taught. We used manipulatives, games, blocks,

and geometrical shapes. We worked in groups, and for word problems we

learned how to picture it and write things down.

Family Influences on Mathematics Attitude

None of the participants had a great deal of support in mathematics at home. Veronica’s father passed away when she was seven years old, and her mother was not very good at mathematics. She remembered her home experiences:

She [Mom] would drill us over and over on times tables until we just got

sick of it. She would try to help with algebra by reading the book, but

sometimes it didn’t work, so I would go to an aunt. She did talk to my

teachers and then they would put in the effort.

Sandy attributed most of her mathematics anxiety to her father as evident when she said:

I would ask him questions and he would get frustrated and annoyed. I would

get nervous and intimidated. He still puts me on the spot. We have a great

relationship except when it comes to math. I get reduced to 15 years old. I

guess he has a lot to do with the way I feel about math.

Both of Jane’s parents were educators, but she recalled her mother being uncomfortable with mathematics. She described her parents’ attitude when she started getting low grades in mathematics: “When I started having trouble they were supportive, but also disappointed and embarrassed. It made me feel incompetent.”

Oralia and Nora had very similar experiences with their parents. Both recalled feeling isolated when they would have homework. They were both the oldest child and their parents were unable to help them beyond basic mathematics. However, it is interesting to note that their own children now excel in mathematics.

Mathematics Test Anxiety

Mathematics anxiety for all of the participants became most evident when they described how they felt during timed mathematics activities, such as testing situations. Even though some described having some anxiety with other types of tests, mathematics tests seemed to be where their feelings of anxiety were magnified. Veronica described her syndrome of mathematics test anxiety:

I blanked out during an accounting test in high school. I couldn’t answer

any of the questions. I was devastated, embarrassed, and scared. I couldn’t

recall anything. I had to leave and go back later to finish. Now I get

nervous and paranoid. I worry about failing. I get an upset stomach and I

always think I’m going to blank out again.

Jane also had a history of mathematics test anxiety, as evidenced by her comments:

I like math, but I freak on tests. I get low scores due to mechanical

errors. After 12 years of low scores, you get a complex and think you’re

dumb. During a test I get in a frenzy. I go fast, then slow, and then I

just can’t think. For 111, the final was fifty percent of the grade and it

was comprehensive. I had notes, but I couldn’t find anything. I got frantic

and gave up. It was defeating. I just shut down and couldn’t remember

anything.

Sandy described herself taking a mathematics test in the following way:

If I know it, I’m fine. If I am timed, I get nervous and forget everything.

I do the ones I know, but then I get stressed that I’m not thinking fast

enough and forget. I worry about finishing, and I can’t remember it even if

I do know it. It is horrible. I get nervous just thinking about it.

Oralia expressed the most severe mathematics test anxiety in the group. Her problem came to light with a discussion of standardized tests such as the Pre-Professional Skills Test (PPST), which is required for admittance into the teacher education program. In fact, she never passed the mathematics portion of the PPST. She instead completed an extra mathematics class which was offered to her by the college of education as an alternative to satisfy the requirement. She described her view as follows:

I panic if I’m timed. You are just setting me up to fail. If you tell me I

can take all the time I want, but I can only miss five, I can’t do it. I

just panic and get a stomach ache. I don’t have good foundations so I have

to relearn the concepts. I get frustrated and scared and I don’t remember.

It is embarrassing. [Standardized tests] determine everything and prove

nothing. You are telling me that I am not qualified to be a teacher because

of a few questions on a math test? That makes me so mad. I know I’m not

going to pass the NTE [National Teachers Examination], it is like a self

fulfilling prophecy with me.

Future Plans for Teaching Mathematics to Children

As stated earlier, one of the main concerns of this study pertains to how the mathematics anxiety of preservice teachers carries over into their own classrooms. We suggested that teachers who suffer from high levels of mathematics anxiety may not be very effective in their own mathematics instruction. To be more specific, it has been conjectured that they tend to teach mathematics in a very traditional format, which is not in accordance with the latest standards. These particular participants, however, indicated that they plan to be much more progressive in their future mathematics instruction. When asked how they planned to teach mathematics, the responses were very promising.

Veronica: I don’t want to stress rules so much. Let kids invent new ways to

do problems. They need visual aids to let them see. I want to bring in

stuff to measure and for fractions and word problems. Some things have to

be memorized, but you can make it a game and have hands-on. I want it to be

fun where there is interaction between students and the smarter kids are

helping the slower ones. I want to be positive, encouraging, and open for

questions. It is important to be relaxed and to praise students. I used to

be paranoid about teaching, but not now. I always thought I would be thrown

in without preparation, but I can read and prepare before teaching. I’m not

worried.

Oralia: Teaching math doesn’t scare me. I can handle it. I want a lot of

communication. I want to expose them and give them a good foundation. I can

bring in people who use math and let the kids ask them questions. We could

read math and make it realistic so that they know they need it.

Nora: You have to be careful of how kids feel. I want to try as many

different approaches to make them understand. I won’t allow other kids to

ridicule them. I learned from my bad experiences. Manipulatives are

excellent because you can see it and see how it applies.

Sandy: I can teach elementary without fear. I can prepare the day before.

I’m worried about getting up there and not knowing. I don’t want to scare

kids. I want to answer their questions and not tell them “Just do it”, like

I was told. Before I teach, I will find the best way to present it, and if

I don’t know the answer, I will find it. I want my class to be

constructivist with a lot of interaction between students. I want learning

centers and groups, a positive learning environment, so they are not

scared. After the first year, it will be O.K.

Jane: I want to use manipulatives and connect them with concepts early on.

Writing is important because it completes the learning cycle. Kids can

communicate their ideas by writing, talking, and interaction. I want to use

computer programs that are fun and challenging. If a kid gets the concept

and is making mechanical errors, tell him the concept is O.K. If you don’t

tell him, he thinks the whole idea is wrong and it makes it confusing. I am

excited, but it is scary because I have a lot to learn.

Conclusions and Discussion

The findings in this study are varied with regard to individual differences in environmental factors and how the participants responded emotionally and intellectually to these factors. However, there are many similarities among the experiences of the participants. First, all of them had several negative experiences in the mathematics classroom. Secondly, none of them had very much positive support at home. And thirdly, all of them suffer from severe mathematics anxiety. Despite these disadvantages, all of them plan to employ the constructivist and developmental methods they learned in their college mathematics methods classes in order to make mathematics meaningful to their own students.

If we were to propose a theoretical model for the causes of mathematics anxiety, the data collected in the present study indicates negative classroom experiences in mathematics and lack of support at home combined with an anxiety toward testing will yield a mathematically anxious individual. Of course this model cannot be generalized beyond the participants in this study at this point. Each participant’s story reflects only her own life experiences. However, it is noteworthy that the commonalties found among the participants in this study can also be found in the literature (Hadfield & Foss, 1993; Miller & Mitchell, 1994).

Prevention of mathematics anxiety for those who have not yet manifested its symptoms apparently requires more positive classroom experiences early on, and a decisive effort by parents to build a home environment supportive of mathematical ideas, applications, and conversations. For adult preservice elementary teachers who already possess significant levels of mathematics anxiety, other solutions must be considered.

Mathematics anxiety reduction clinics have been reported to be successful in several previous studies (Hembree, 1990; Kostka & Wilson, 1986; Sime et al., 1987). Though the results are mixed, and the benefits have not yet been shown through longitudinal studies to necessarily be long lasting, the evidence that special programs can be successful in the reduction of mathematics anxiety is convincing (Wood, 1988). The most effective programs typically focus on study skills to build confidence, combined with relaxation techniques to reduce the physiological aspects of the anxiety (Bander, Russell, & Zamostny, 1982). Key components also usually include verbal and written communication and role playing to assist participants in confronting their negative assumptions about mathematics and in becoming aware of similar experiences of others. These activities are followed by visualizations of the replacement of negative experiences and negative self talk with positive visualizations, and then a commitment to changes in behavior, which include asserting oneself in class when concepts are not well explained or understood (Foss & Hadfield, 1993). It would be advantageous for all mathematically anxious elementary teachers to have the luxury of attending such clinics, on an ongoing basis. However, their limited availability is prohibitive in most settings.

A second solution would be to simply not require mathematically anxious elementary teachers to teach mathematics. Instead, allow them to concentrate on the teaching of other content areas where they have more confidence and expertise. Many mathematics educators are proponents of the placement of mathematics specialists in all elementary schools (Miller, 1992). There are currently some colleges of education that offer master’s degrees with specialties in elementary mathematics education for those who wish to seek employment as mathematics specialists. The districts that can afford specialists have met with some degree of success. Some schools even have a separate mathematics laboratory complete with classroom sets of manipulatives so that each class within the school can relocate to the lab on a rotating schedule, with a permanent mathematics specialist on hand to direct the instruction (Tankersley, 1993). This could definitely help to insure the quality of mathematics instruction, but the plan is not financially feasible for most school districts. Neither the additional personnel nor the classroom space is available.

A third, and probably the most practical solution, is to provide elementary mathematics methods courses and professional development opportunities that reduce mathematics anxiety through the development and delivery of cutting edge lessons in mathematics for elementary school children. Effective mathematics methodology courses tend to improve not only methodology as such, but also mathematics content and conceptual understanding, while reducing mathematics anxiety (Levine, 1996; Nilssen, Gudmundsdottir, & Wangsmo-Cappelen, 1995; Rasch, Finch, & Williams, 1992). When activities are designed for students to address affective issues in mathematics, methodology courses tend to show marked improvement in attitudes toward mathematics (D’Emidio-Caston, 1993). Mathematics methods courses and professional development workshops must of course incorporate activities that build a depth of conceptual understanding, require mathematical reasoning, provide connections within mathematics, and address these concerns through a problem solving approach (National Council of Teachers of Mathematics, 1989). Hands-on materials and cooperative learning projects are often the vehicle for incorporating such strategies. Workshops with these approaches are currently available to elementary teachers nationwide at centrally located sites (Burns, 1993). Prospective and inservice teachers that build a depth of conceptual understanding in effective methodology courses typically experience at least some degree of reduction of their anxieties about teaching mathematics, as they build a sense of preparedness.

All of the prospective elementary teachers in this study had environmental, cognitive, and personality factors that contributed to their levels of mathematics anxiety. They all had negative classroom experiences and minimal family support, they all suffered from mathematics test anxiety, and they all had fears in regard to teaching mathematics themselves. Although the intentions of the present study were simply to find the roots of mathematics anxiety among five specific preservice teachers, it is encouraging to find that they all are aware of their negative feelings toward mathematics, and they are all determined to prevent the passage of their negative feelings on to their own students. This provides a basis for the assertion that their university mathematics methods course had a positive impact on their attitude. The awareness of their situation, and the willingness to confront it indicates the promise of effectiveness in their future mathematics teaching career. However, a follow-up study will be necessary if we are to determine whether or not these teachers actually will realize their intentions of overcoming their anxiety toward mathematics. It could be the case that their initial spark of enthusiasm and optimism will not be matched by actual performance.

In summary, it is the opinion of the authors that although we cannot expect every teacher to love mathematics, we can encourage every teacher to become aware of her/his level of mathematics anxiety so that it can be addressed and hopefully reduced. An in-depth look at one’s own negative prior experiences can often help to set a more positive direction for future encounters. As a matter of fact, clinics for mathematically anxious college students have been shown to be reasonably effective in the reduction of mathematics anxiety (Foss & Hadfield, 1993). By controlling their anxiety, in consort with the implementation of cutting edge conceptual mathematics lessons, the majority of the more determined teachers will be able to effectively teach their students mathematics, and the importance of mathematics, with a positive attitude, in a rich learning environment.

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KAREN M. TRUJILLO AND OAKLEY D. HADFIELD New Mexico State University Las Cruces, New Mexico

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