Introduction

Do you like mathematics? Chances are your immediate response was a negative one. Research has shown that mathematics anxiety has been a common topic among educators (Bursal & Paznokas, 2006; Reys, 1995; Singh, Granville, & Dika, 2002; Thompson, 1992; Zettle & Raines, 2002). Mathematics anxiety has it roots in teaching and teachers (Tobias, 1998; Vinson, 2001; Widmer & Chavez, 1982) and has been tied to poor academic performance of students, as well as to the effectiveness of early childhood/elementary teachers (Bush, 1989; Hembree, 1990). The beliefs that pre-service teachers hold are very similar to those held by severely mathematics anxious people in mathematics anxiety clinics (Bursal & Paznokas, 2006; Tooke & Lindstrom, 1998). Pre-service teachers have poorer attitudes toward mathematics than the general college population (Emenaker, 1996), and have greater mathematics anxiety when the subject either is, or is perceived to be, under evaluation (Wood, 1988).

A significantly larger percentage of pre-service teachers were reported to experience higher levels of mathematics anxiety than were other undergraduate university students (Bursal & Paznokas, 2006; Harper & Daane, 1998; Hembree, 1990; Kelly & Tomhave, 1985). Mathematics anxiety has an effect on learning, and may perhaps be a greater block to mathematics learning than supposed deficiencies in our school curricula and teacher preparation programs (Martinez, 1987). This is cause for alarm, considering that teachers who possess higher levels of mathematics anxiety may unintentionally pass on these negative feelings to their students (Wood, 1988).

Limited research exists regarding the effectiveness of a mathematics methods course in reducing the mathematics anxiety levels among pre-service teachers (Bursal & Paznokas, 2006; Williams & Ivey, 2001; Zettle & Raines, 2002). This study was conducted to add to this body of knowledge and will identify mathematics anxiety and the research of mathematics anxiety regarding instruction and pre-service teachers. It will also highlight the methods used in the study and changed levels of pre-service teachers’ mathematics anxiety after participation in a mathematics methods course and provide a discussion and summary of the study’s conclusions.

Mathematics Anxiety Defined

For many, mathematics anxiety is a feeling of helplessness, tension, or panic when asked to perform mathematics operations or problems. It has been described as an “I can’t syndrome,” a feeling of uncertainty, of not being able to do well in mathematics or with numbers (Tobias, 1998). Bursal and Paznokas (2006) and Gresham (2004) present it as a lack of applied understanding and/or an irrational dread of mathematics, often leading to avoidance of the subject. Mathematics anxiety is a state of discomfort which occurs in response to situations involving mathematical tasks which are perceived as threatening to self esteem, and can often create a negative attitude toward the subject (Burns, 1998; Zettle & Raines, 2002). In turn, these feelings of anxiety can lead to fear, distress, shame, inability to cope, sweaty palms, nervous stomach, difficulty breathing, and loss of ability to concentrate (Burns, 1998; Bursal & Paznokas, 2006; Dutton & Dutton, 1991; Hembree, 1990). Richardson and Suinn (1972) say mathematics anxiety is a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations. In each of these definitions, mathematics anxiety is considered to be specific to mathematics instruction and mathematics related activities so deliberative in nature that it can interfere with mathematics performance and inhibit subsequent learning (Burns, 1998; Bursal & Paznokas, 2006; Gresham, 2004; Hembree, 1990; Kelly & Tomhave, 1985; Tobias, 1998; Zettle & Raines, 2002).

Mathematics Anxiety and Instruction

Many studies now show that too many students in the United States have a moderate level of procedural knowledge of mathematics and an even lower level of conceptual knowledge (Vinson, 2001). Therefore, mathematics power is diminished and mathematics anxiety is increased. Several common instructional teaching techniques cause mathematics anxiety, such as assigning the same work for everyone, teaching the textbook problem by problem, insisting on only one correct way to complete a problem, lecturing, concentrating more on basic skills rather than concepts, and devoting more time to seatwork, and whole class instruction (Furner & Berman, 2005; Tobias, 1998). These “traditional” ways of teaching can be the cause of mathematics anxiety.

Effective teachers of mathematics know that they must follow the modes of learning as presented by Bruner so students are provided with concrete experiences that form the basis of pictorial and symbolic mathematics learning (Vinson, 2001). Therefore, Bruner’s mode of instruction was used as the instructional foundation for this study. Bruner’s theoretical framework based upon cognitive structure, is that learning is an active process in which learners construct new ideas of concepts based upon their current or past knowledge. For example, the concept of prime numbers appears to be more readily grasped when the students, through construction, discover that certain handfuls of beans cannot be laid out in completed rows and columns. Such quantities have either to be laid out in a single file or in an incomplete row-column design in which there is always one extra or one too few to fill the pattern. It is easy for the student to go from this step to the recognition that a multiple table, so called, is a record sheet of quantities in completed multiple rows and columns. Here is factoring, multiplication, and primes in a construction that can be visualized (Bruner, 1961). Using this constructivist approach, the goal of instruction is to help learners develop learning and thinking strategies, focus on the individuals’ active construction of knowledge, and facilitate learning by encouraging active inquiry.

Perhaps one of the enduring merits of Bruner’s work is its equal attention to theorizing not only about how students learn but also about how to shape instructional practices to encourage such learning. Students learn most about a particular subject when they learn how to “[obtain] knowledge for oneself for use of one’s own mind” (Bruner, 1961, p. 22, quoted in Driscoll, 1994). Problem-based learning offers one of the best ways of facilitating students’ discovery learning, Bruner claimed, because it provides students with both the guided practice in inquiry and the “cognitive conflicts” through which students expand their conceptual frameworks (Dricsoll, 1994). Bruner would probably say that some students do not succeed in college curricula because (1) the subjects they are expected to master are not being offered in an appropriate mode of representation for all students and (2) different ways of knowing and learning often do not facilitate student learning equally well in formal instructional settings. Bruner’s theories provide educators with useful ways of thinking with greater complexity about how students learn and how best to offer instruction, involving the use of concrete material, semi-concrete or pictorial activities, and by exploring new ways to attack problems symbolically (Driscoll, 1994).

Effective mathematics instruction will prevent the development of or reduce mathematics anxiety (Seymour, 1996; Tobias, 1998). According to qualitative interviews with teachers across the United States, effective mathematics instruction is “learning in action” (Vinson, 2001, p. 91). Tobias (1998) suggested that “learning in action” is using activities such as problem solving activities, simulations, discoveries, challenges, and games. This non-traditional approach to teaching can reduce mathematics anxiety (Hembree, 1990; Tobias, 1998). Other strategies to reduce mathematics anxiety include establishing a supportive classroom, using manipulatives to bridge from concrete to abstract, using a variety of techniques, and addressing students’ attitudes towards mathematics (Taylor & Brooks, 1986). Further, it has been suggested that professors who teach college courses for pre-service teachers should themselves incorporate the strategies as defined by the National Council of Teachers of Mathematics (2000) (See Appendix A for NCTM Strategies). One commonality was found among programs reporting a reduction in mathematics anxiety. Material was introduced slowly, the instructor assumed no prior mathematical knowledge, and students were encouraged to discuss their own thought processes in learning (Wood, 1988). The most successful programs were those featuring teachers who attempted to change the way mathematics was perceived and learned and through changes in instructional strategies (Bursal & Paznokas, 2006; Teague & Austin-Martin, 1981; Wood, 1988).

Mathematics Anxiety and Pre-Service Teachers

How then does the aforementioned affect pre-service teachers? Research has shown that a disproportionately large percentage of pre-service teachers experience significantly high levels of mathematics anxiety (Battista, 1990; Burns, 1998; Bursal & Paznokas, 2006; Gresham, 2004; Kelly & Tomhave, 1985; Singh et al., 2002; Sloan, Daane, & Giesen, 2002; Sovchik, Meconi, & Steiner, 1981; Vinson, 2001; Zettle & Raines, 2002). This leads to doubts as to their potential effectiveness in teaching mathematics to children (Burns, 1998; Sovchik, 1996). Several educators agree that teachers transmit their avoidance and fear of mathematics to their students (Furner & Berman, 2005; Hembree, 1990; Kelly & Tomhave, 1985; Lazarus, 1974; Sloan et al., 2002; Tobias, 1998; Vinson, 2001; Zettle & Raines, 2002). The instruction of mathematics seemed to play a critical role in shaping one’s attitudes toward mathematics (Jackson & Leffingwell, 1999). Mathematics anxiety is directly related to perceptions of one’s own mathematical skill in relation to skills in other subject areas and with negative attitudes towards mathematics (Wright & Miller, 1981). In other words, negative attitudes toward mathematics can produce negative results in mathematics thus creating mathematics anxiety (Vinson, 2001).

Greenwood (1984) and others (Burton, 1984; Clute, 1984; Downie, Slesnick, Stenmark, & Hall, 1983; Tobias, 1998) contended that the root of some mathematics anxiety lies in how one is taught mathematics. This is particularly significant since teachers are inclined to teach just as they were taught (Furner & Berman, 2005). A possible solution to the problem may lie in the preparation of teachers of school mathematics. This solution supported by Bursal and Paznokas (2006), Stodolsky (1985), Tooke and Linstrom (1998), and Vinson (2001) indicated that the nature of instruction itself seems a powerful source in shaping later attitudes, expectations, and conceptions of learning.

Research Involving Mathematics Anxiety

Bursal and Paznokas’ (2006) study showed that over half of the 65 pre-service teachers involved had mathematics anxiety. Scholfield (1981) linked negative teacher attitudes about mathematics to mathematics anxiety. Negative attitudes toward mathematics and mathematics anxiety influence how often mathematics is used, as well as the willingness to pursue advanced work in mathematics, and even the choice of prospective occupations (Dutton & Dutton, 1991). Negative attitudes toward mathematics and mathematics anxiety can produce negative results in mathematics due to the reduction of effort expended toward the activity, the limited persistence one exerts when presented with an unsolved problem, the low independence levels one is willing to endure, and whether or not a certain kind of activity will even be attempted (Burns, 1998; Cruikshank & Sheffield, 1992; Hembree, 1990; Post, 1992; Vinson, Sloan, Haynes, & Brasher, Gresham, 1998).

Particular groups of students have higher mathematics anxiety levels (Battista, 1990; Bursal & Paznokas, 2006; Hembree, 1990). Female students and students who have previously received lower than expected or lower than average scores in mathematics classes have tended to have higher levels of mathematics anxiety (Battista, 1990; Betz, 1978; Bursal & Paznokas, 2006; Calvert, 1981). Studies have consistently shown that elementary education majors have the highest or one of the highest levels of mathematics anxiety (Hembree, 1990; Kelly & Tomhave, 1985; Vinson, 2001).

Kontogianes (1974) found that a self-paced program in which pre-service teachers participated in lectures, group sessions, and individualized tutoring from the professor, positively affected the pre-service teachers’ mathematics anxiety, achievement, retention, and attitude. Sovchik et al. (1981) found a reduction in mathematics anxiety among pre-service elementary teachers after participating in a mathematics methods course which implemented concrete manipulatives, open discussions, and student journal logs. Chapline’s (1980) study indicated a reduction of mathematics anxiety after inductive approaches to problem-solving, test preparations designed to reduce mathematics anxiety, and student logs of attitudes and perceptions were used.

Effective teaching of mathematics should place emphasis on manipulatives and authentic learning situations that mimic situations of dealing with mathematics (Dutton & Dutton, 1991; Vinson, 2001). Studies by Bursal and Paznokas (2006), Hembree (1990), Tobias (1998), and Vinson (2001) found that pre-service teachers’ mathematics anxiety levels are significantly reduced when an emphasis was placed on understanding. The use of manipulatives and concrete materials in the classroom could eliminate mathematics anxiety in students (Thompson, 1992).

As indicated, many studies have reported success in reducing mathematics anxiety in pre-service teachers. This study compared the pre- and postlevels of pre-service teachers’ mathematics anxiety and found a reduction in mathematics anxiety among those pre-service teachers. It implemented many of the same strategies found in the studies mentioned such as using concrete manipulatives, journal logs, and discussions. However, it differs from other studies in that pre-service teachers actively participated in their own teaching experiences throughout the duration of the mathematics methods course. In addition, it involved six different course sections over a 4-year time period and involved a larger sample size. The results provide insight into the durability and effectiveness of teacher training programs that emphasize manipulatives and other strategies to help reduce mathematics anxiety in pre-service teachers.

The Study

Research Investigation

This study investigated early childhood/elementary pre-service teachers’ levels of mathematics anxiety. It also examined whether pre-service teachers’ mathematics anxiety can be reduced after participation in a mathematics methods course. The research was conducted during different sections of fall and spring semesters over 4 years.

Subjects

The subjects were 246 junior early childhood/elementary education pre-service teachers from a large southeastern university who were enrolled in a mathematics methods course focusing on methods for teaching elementary mathematics. The participants were overwhelmingly female (237 out of 246); therefore no attempt was made to differentiate results by gender. The subjects were working toward a K-6 endorsement in early childhood/elementary education from the state. They had a weekly practicum experience in the schools throughout the semester. All subjects had completed at least two university mathematics courses and one elementary mathematics content course. Students were informed both verbally and in writing that their participation in the study was completely voluntary and would not influence their grade in the course.

Data Collection

The Mathematics Anxiety Rating Scale (MARS) was used as the quantitative instrument for this study. Developed by Richardson and Suinn (1972), the 98-item, self-rating Likert-type scale may be administered either individually or to groups. Each item on the scale represents a situation which may arouse mathematics anxiety by indicating “not at all,” a little,” “a fair amount,” “much,” or “very much.” The statements describe everyday life and academic situations requiring mathematical thought or tasks and are rated as to the degree of anxiety that respondents perceived they would experience in the given situations (See Appendix B for MARS Statement Examples). The MARS has been demonstrated to be a valid test (p < .001) with which it correlates at a level of .97. The test-retest reliability for the instrument has been shown to range from .78 to .85 and internal consistency has been reported as .97. Possible scores range from 24 to 120. The higher the score, the higher the level of mathematics anxiety.

Procedures

Pre-service teachers were given the MARS pretest on the first day of class for the semester. Bruner’s model of instruction was also introduced. During the mathematics methods course, pre-service teachers participated in discussion sessions, journal writing, teacher directed large and small group activities, literature based mathematical activities, student group presentations involving hands-on manipulatives, implementation of hands-on approaches to teaching mathematic content that involved them with the use of various concrete materials commonly utilized in mathematics teaching, and a 12-week field experience practicum in the K-6 classroom (6-weeks in the K-2 grades and 6 weeks in the 3–6 grades). During the field experience practicum, each pre-service teacher taught four or more lessons involving the use of concrete manipulatives and the integration of literature in the mathematics curriculum. The field experience was supervised by both a university faculty member and the pre-service pupil’s full-time teacher. Pre-service teachers were required to write detailed lesson plans describing all their planned instructional activities for the field experience practicum. They were also required to keep journal logs of their thoughts and processes during the 12-week teaching experience and during the semester long methods course. During the last week of the semester, pre-service teachers were given the MARS as a posttest.

The qualitative methods of the study included informal observations of pre-service teachers during the methods course taught for the semester, questionnaire-guided narrative interviews, informal discussions, and informal interviews that were either initiated by the pre-service teacher during or after class or by the professor (the researcher in this study). The interviews were usually in response to questions by pre-service teachers regarding their own personal concerns, experiences, background, assignments, and mathematical teaching practices. However, pre-service teachers were asked specific interview questions throughout the research period (See Appendix C for Interview Questions). Field notes and audio recordings of interviews and discussions were used and analyzed and decoded for emerging themes.

Results

The pretest MARS score was subtracted from the posttest MARS score for each to reveal to difference score (see Table I). A positive difference score meant that the pre-service teacher’s mathematics anxiety actually increased during the semester. A negative score meant that the pre-service teacher’s mathematics anxiety decreased by that much. Table I shows the raw score means by group (semester). This table reveals that the greatest difference in change scores from pretest to posttest existed between Fall-03 (−18.13) and Fall-05 (−49.40). This means that the average reduction of mathematics anxiety was significantly greater in the Fall-05 semester than in Fall-03 semester. A possible reason for this could be that Fall-03 semester was the professor’s first semester to teach at that particular college. In addition, it was the professor’s first time to teach a larger class population size. Table II provides the t-test comparisons of pretest and posttest raw scores by semester.

Table I Mathematics Anxiety Raw Score Means
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Table II t-Test Comparisons of Pretest and Posttest Raw Scores by Semester
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Discussion and Summary

After comparing group means for the pretest and posttest scores, it was found that the overall pre-service teachers’ mathematics anxiety was reduced (p < .001). In addition, pretest and posttest raw score differences were highly significant. Although the gain for Fall-03, Spring-04, and Spring-05 semesters were not as great the Fall-04, Fall-05, Spring-06 semesters, there was a change indicating a reduction in students’ mathematics anxiety.

Informal interviews, questionnaire-guided narrative interviews, discussions, and journal logs indicated the emergence of several themes. These included: (a) attributing the reduction in their mathematics levels to the use of manipulatives implemented throughout the course, (b) the personality of the professor and inviting environment as produced by the professor, and (c) the use of journal writing used throughout the study. Students were specifically asked what they felt contributed to their decrease in mathematics anxiety. Two hundred thirteen students attributed their mathematics anxiety reduction to the methodology and the use of concrete manipulatives provided in the course to teach the subject content. Eleven students attributed their lowered mathematics anxiety levels to the enthusiasm of the professor in teaching the subject content and inviting atmosphere of the course. Sixteen students thought their mathematics anxiety levels were reduced by a combination of implemented methods including the methodology and use of concrete manipulatives used throughout the course, the professor’s enthusiasm and excitement toward teaching the mathematics content including the inviting atmosphere of the mathematics classroom as produced by the professor, and journal writing. Students commented on how the use of journal writing throughout helped them work through their mathematics anxiety while both teaching students in their practicum and taking the methods course. Many students commented that they finally “understood concepts such as fractions, decimals, percents, probability and statistics, and algebra when the topics were presented in a concrete and practical format”. Others commented that mathematics was now less “foreign” to them, noting that perceptions of their abilities to understand mathematics concepts were now enhanced. The most unanimous and interesting comment was that they felt as though their mathematics anxiety could have been prevented in elementary school, if they had received instruction of mathematical concepts through the use of concrete manipulatives.

Six students experienced an increase or no change in mathematics anxiety. During interviews, questionnaire-guided narrative interviews, and discussions, students revealed that they preferred doing mental math or working with others to solve problems. They indicated more stress and lack of understanding in working with manipulatives since they had never been introduced to them before. They implied they were unfamiliar with and intimidated by the manipulatives. Therefore, they struggled with learning mathematics at the same time they were learning to use manipulatives. Students also commented on the difficulty they experienced to integrate both mathematics and literature in their lesson planning. Although students were given access to literature, websites, and book lists, they expressed hardship in finding literature appropriate for the skill they were teaching and with the grade level in which they were assigned. Another rationale for their increased mathematics anxiety included the course requirement of teaching lessons implementing manipulatives utilizing both whole and small group instruction. For many students, this was their first methods course and only experience teaching a mathematics lesson before a group of students.

Conclusion

Educators do have an impact upon their students’ mathematics anxiety levels (Emenaker, 1996; Gresham, Vinson, Haynes, Brasher, & Sloan, 1998). The quality of mathematics instruction in the elementary schools depends on the preparation of pre-service early childhood/elementary teachers of mathematics (Battista, 1990). Bruner’s modes of learning, with emphasis on the use of manipulatives and concrete learning of the mathematical content, journal logs, small and whole group instruction and presentations, literature based activities, and practicum experiences during the mathematics methods course were implemented in this study. The concrete experiences helped the pre-service teachers have a better understanding of the procedural purposes and mathematical concepts. As per student interviews the use of manipulatives aided the pre-service teachers in learning how to teach mathematics.

Limited research exists regarding the effectiveness of a mathematics methods course to identify and reduce mathematics anxiety in pre-service teachers (Bursal & Paznokas, 2006; Williams & Ivey, 2001; Zettles & Raines, 2002). The findings in this study support Vinson’s (2001) study in which pre-service teachers’ mathematics anxiety levels were reduced after using manipulatives and Bruner’s framework throughout a mathematics methods course. During this study, mathematics anxiety levels of early childhood/elementary pre-service teachers were reduced as indicated by pre–post results, interviews and journal logs. Through interviews and informal discussions, pre-service teachers indicated a greater understanding of mathematics concepts and procedures. The results of this research study can help bridge the gap in the existing research and influence the way future teachers are trained to teach mathematics. Understanding mathematical content and its presentation will help pre-service teachers teach their students effectively, thus preventing or reducing mathematics anxiety in their future students.