Attitudes and Beliefs Toward Mathematics for Elementary Pre-service Teachers

US-China Education Review B, ISSN 2161-6248 September 2014, Vol. 4, No. 9, 616-626 D DAVID PUBLISHING Attitudes and Beliefs Toward Mathematics for Elementary Pre-service Teachers Yea-Ling Tsao Minnesota State University Mankato, Mankato, USA The purpose of this study was to explore pre-service elementary teachers attitudes/beliefs toward mathematics learning. Sixty elementary pre-service teachers who were enrolled in a mathematics content course for elementary school completed Fennema-Sherman Mathematics Attitudes Scales (FSMAS) to measure their attitudes and beliefs toward mathematics. The FSMAS subscale data on the mean scores of the Confidence in Learning Mathematics Scale, Mathematics Anxiety Scale, Effectance Motivation Scale, and Mathematics Usefulness Scale were 2.87, 3.17, 3.26, and 3.55 respectively. The participants had a mean composite survey score of 3.21 on the 5-point Likert scale, with a score of 1 representing the most negative attitude, a score of 3 representing a neutral position, and a score of 5 representing the most positive attitude. Therefore, the mean composite score that reflected attitudes was just above the neutral position. Unfortunately, many pre-service elementary teachers in the study did not exhibit positive attitudes toward mathematics learning. The lowest mean score for attitudes was the Mathematics Anxiety Scale in learning mathematics at 2.87. This result indicates that the sample of pre-service elementary teachers appear to have stronger anxiety toward themselves and mathematics learning. The correlations among the four subscales were all statistically significant (p < 0.001). Recommendations for exposing pre-service teachers to positive attitudes and beliefs about mathematics are discussed. Keywords: mathematics anxiety, effectance motivation, mathematical beliefs, pre-service teachers Introduction The research into how students attitudes affect learning of mathematics-related subjects has been one of the core areas of interest by mathematics educators. Some researchers reported that attitudes can be learned and that teachers can encourage and influence students to like mathematics. Many believe that in order to teach mathematics well, one needs to have a positive attitude toward the subject, and that the task of improving the attitudes toward mathematics of future elementary teachers begins at the university. The critical role of attitude is well recognized in advancing mathematics education, particularly that improving the attitudes toward mathematics of pre-service elementary teachers is an important concern for university education courses in order to facilitate positive mathematics attitudes in future elementary students (Sherman & Christian, 1999). This leads to the conclusion that it is important for teachers across all levels of mathematics instruction to exhibit positive attitudes and beliefs in order to allow their students to develop positive attitudes and beliefs toward mathematics. Unfortunately, this is not always the case. Many studies have considered the mathematics attitudes of teachers and some studies have indicated that negative attitudes were possessed by pre-service Yea-Ling Tsao, Ph.D., professor, Department of Mathematics and Statistics, Minnesota State University Mankato.

ATTITUDES AND BELIEFS TOWARD MATHEMATICS 617 teachers specifically (Davies & Savell, 2000; Grootenboer, 2002; Tsao, 2004). In addition, many pre-service teachers have been found to have negative attitudes toward mathematics that had developed when they were students, thus continuing a negative cycle (Arp, 1999). As a mathematics educator, the researcher found that some pre-service student teachers have developed negative attitudes toward mathematics because of their weak mathematical background, their experiences with mathematics, lack of support from their families, and effect of their previous mathematics classes. A belief about the usefulness of mathematics is another important attitudinal variable to consider. Since mathematics is not easy for most people to learn, it is reasonable to question making the effort if one does not believe in its utility. Some students believe that mathematics is a difficult subject because of the experiences they had during their early school days. Some of these students continue to have difficulties with the mathematics content course during college. The beliefs a person holds about his/her ability to do mathematics, about the nature of mathematics, and about problem-solving are dominant forces in shaping that person s behavior while engaged in work on a mathematical task. This study was undertaken in an attempt to understand the mathematics beliefs held by pre-service teachers; understanding teaching from a teacher s perspective has enriched the understanding of learning from a student s perspective. Through research on teachers attitudes and beliefs about mathematics and mathematics teaching and learning, teacher educators can learn how best to address these issues. This research would help teacher educators explicitly address specific aspects of dispositional issues in mathematics content courses for teaching, which could in turn have the potential to support their learning of mathematics. Further, it describes how this can provide an opportunity to incorporate program changes that could provide pre-service teachers with an opportunity to gain positive attitudes toward mathematics. There are two research questions that will be answered in the study: 1. What are the attitudes and beliefs toward mathematics of pre-service elementary school teachers entering an introductory mathematics methods course? In particular, how do pre-service teachers score on each of the four attitudinal components being measured: Confidence in Learning Mathematics Scale, Mathematics Anxiety Scale, Effectance Motivation Scale, and Mathematics Usefulness Scale? 2. What are the relationships among the four measures of attitude toward mathematics for pre-service elementary teachers? Background of the Study According to the National Council of Teachers of Mathematics (1989), a mathematical disposition refers to a tendency to think and act in positive ways (p. 233). Damon (2005) stated dispositions as traits or characters that lead a person to follow certain choices or experiences. Damon viewed dispositions as having a major impact on who we are and who we become. As students, pre-service elementary teachers dispositions with respect to mathematics warrant considerable attention, as those dispositions can influence the nature of the mathematical knowledge they develop while enrolled in a teacher preparation program. Fennema and Sherman (1976) pointed out that a person s attitude toward mathematics was critical for deciding to take mathematics and to learn it. This is true not only in high school, but in college. Many pre-service teachers are afraid to take math courses and when forced to do so, do not do well, even though they may earn good grades in other courses. For example, considering pre-service elementary teachers who tend to

618 ATTITUDES AND BELIEFS TOWARD MATHEMATICS experience math anxiety when engaging mathematical tasks, they may avoid the perceived source of that anxiety, and consequently, not take advantage of the opportunity to learn mathematics offered by the task at hand. Research on elementary teachers attitudes toward mathematics has shown that these teachers have relatively negative attitudes toward mathematics; pre-service elementary teachers have been shown to have the most negative attitude toward mathematics when compared to all other college majors (Hembree, 1990). Attitude toward mathematics is no doubt a complex idea that interacts with other important belief structures of a teacher. Research on attitudes toward mathematics is associated with research on beliefs, anxiety, and efficacy toward mathematics (Beswick, 2006; Beswick & Dole, 2001; McGinnis, Kramer, Shama, Graeber, Parker, & Watanabe, 2002). Efficacy has also been shown to be related to attitudes toward mathematics (Randhawa, Beamer, & Lundberg, 1993). Furthermore, attitudes toward mathematics have been shown to be negatively correlated with anxiety toward the subject (Brady & Bowd, 2005). In a previous research, which explored elementary students beliefs about the usefulness of mathematics, Kloosterman and Cougan (1994) concluded that primary students did not have a sincere belief that mathematics was useful. Other researchers have investigated the correlation between beliefs about usefulness and achievement in mathematics and found a positive relationship between these variables (Iben, 1991; Midgley, Feldlaufer, & Eccles, 1989). The findings of this study strongly supported a positive relationship between the perceived level of teacher support and students beliefs about the usefulness of mathematics. Raymond (1993) found that teachers mathematics teaching practices did not always match their mathematics attitudes. Understanding where one s attitudes and beliefs come from and the relationship between these attitudes and teaching practices can help teachers identify and resolve conflicts between the two. Mathematics teachers beliefs in their efficacy to teach mathematics had an effect on their students; students in the classes of teachers with a positive sense of efficacy in teaching were more likely to believe that they were performing better in mathematics than students in the classes of teachers with a lower sense of efficacy in teaching mathematics (Midgely et al., 1989). Often, teachers must compromise between attitudes and actual classroom practice causing them to move down in their list of hierarchical attitudes until the problem in the classroom is resolved. This leads to the conclusion that it is important for teachers across all levels of mathematics instruction to exhibit positive attitudes and beliefs in order to allow their students to develop positive attitudes and beliefs toward mathematics. The researcher adopted the Fennema-Sherman Mathematics Attitudes Scales (FSMAS) (Fennema & Sherman, 1976) to evaluate student mathematics attitudes, because the impact of FSMAS has been felt widely in all research on attitudes toward mathematics in mathematics education research over the last three decades (Mcleod, 1994; Tapia & Marsh, 2004). This publicly available attitude test consists of nine domain specific tests which reflect attitudes about learning mathematics; these tests may be used as separate tests or in any combination. This study used four of the domain scale tests: Confidence in Learning Mathematics Scale, Mathematics Anxiety Scale, Effectance Motivation Scale, and Mathematics Usefulness Scale. The domain scales are identified and described as follows: 1. The Confidence in Learning Mathematics Scale is intended to measure confidence in one s ability to learn and to perform well on mathematical tasks. The dimension ranges from a distinct lack of confidence to definite confidence;

ATTITUDES AND BELIEFS TOWARD MATHEMATICS 619 2. The Mathematics Anxiety Scale is intended to measure feelings of anxiety, dread, nervousness, and associated bodily symptoms related to doing mathematics. The dimension ranges from feeling at ease to those of distinct anxiety; 3. The Effectance Motivation Scale in mathematics is intended to measure effectance as applied to mathematics. The dimension ranges from lack of involvement in mathematics to active enjoyment and the seeking of challenge. The scale is not intended to measure interest or enjoyment of mathematics; 4. The Mathematics Usefulness Scale is designed to measure students beliefs about the usefulness of mathematics currently and in relationship to their future education, vocation, or other activities (Fennema & Sherman, 1976). Methodology Participants Sixty pre-service elementary teachers who were enrolled in a mathematics methods course for elementary teachers at a midsized university in the Southern Minnesota were participants for the study. It involved two different sections of the course with the same mathematics instructor who was also the researcher. Instrument The researcher administrated the FSMAS (Fennema & Sherman, 1976), which were designed to evaluate student mathematics attitudes. This publicly available attitude test consists of nine domain specific tests which reflect attitudes about learning mathematics; these tests may be used as separate tests or in any combination. This study used four of the domain scale tests: Confidence in Learning Mathematics, Mathematics Anxiety, Effectance Motivation, and Mathematics Usefulness. These four tests, consisting of 12 questions per test, offered a 48-item test. This test was randomly generated by a computer program for a cumulative test. Table 1 shows three items. Table 1 Sample of FSMAS Statement Circle choice I usually have been at ease during math tests. A B C D E I do as little work in math as possible. A B C D E Taking mathematics is a waste of time. A B C D E The Fennema-Sherman tests use a Likert-type scale wherein the subjects respond on a scale of 1 to 5, to their degree of agreement with the statement. A score of 5 is given to the response that is hypothesized to have a more positive relation to learning mathematics. Scores of each domain scale and the cumulative score of all domains indicate student attitudes toward learning mathematics. A high score represents a positive attitude toward learning mathematics. The FSMAS were also used to assess pre-service elementary teachers attitudes toward mathematics; the split-half reliabilities reported by Tsao (2004) for four scales measures ranged from 0.87 to 0.93. The alpha reliability coefficient was 0.96 for the current study. Procedure The main purpose of this study was to examine the beliefs of pre-service elementary teachers toward mathematics and explore pre-service teachers score on each of the four attitudinal components being

620 ATTITUDES AND BELIEFS TOWARD MATHEMATICS measured: Confidence in Learning Mathematics, Mathematics Anxiety, Effectance Motivation, and Mathematics Usefulness. On the first day of the mathematics content class, these pre-service teachers were given the FSMAS to evaluate student mathematics attitudes in August 2013. Each domain scale consists of 12 statements, six worded positively and six worded negatively. A score of 5 is given to the response that is hypothesized to have a more positive relation to learning mathematics. Mean scores and standard deviations will be calculated. Correlation analysis was performed using the Statistical Package for Social Science (SPSS). Scores of each domain scale and the cumulative score of all domains indicate student attitudes toward learning mathematics. Results and Discussion Table 2 displays the mean scores and standard deviations on the FSMAS by subscales for the 60 participants. The participants had a mean composite survey score of 3.21 on the 5-point Likert scale, with a score of 1 representing the most negative attitude, a score of 3 representing a neutral position, and a score of 5 representing the most positive attitude. Therefore, the mean composite score reflected attitudes were just above the neutral position. Unfortunately, many pre-service elementary teachers in the study did not exhibit positive attitudes toward mathematics learning. Table 2 Means of Subscale, Overall Mean, and Standard Deviation of FSAMS (N = 60) Subscale Quantity Mean (M) Standard deviation (SD) Mathematics Anxiety 12 2.87 0.65 Confidence in Learning Mathematics 12 3.17 0.65 Effectance Motivation 12 3.26 0.57 Mathematics Usefulness 12 3.55 0.62 Total scale 48 3.21 0.61 The FSMAS subscale data on the mean scores of the Confidence in Learning Mathematics Scale, Mathematics Anxiety Scale, Effectance Motivation Scale, and Mathematics Usefulness Scale were 2.87, 3.17, 3.26, and 3.55 respectively. Previous studies have shown that many pre-service elementary school teachers have negative attitudes toward mathematics (Cornell, 1999; Hungerford, 1994; Philippou & Christou, 1998). This study supports these findings. The lowest mean score for attitudes was the Mathematics Anxiety Scale in learning mathematics at 2.87. The Mathematics Anxiety Scale is intended to measure feelings of anxiety, nervousness, and associated bodily symptoms related to doing mathematics. Higher scores reflect lower level of mathematics anxiety. This result indicates that the sample of pre-service elementary teachers appear to have stronger anxiety toward themselves and mathematics learning. Examples of these included Math does not scare me at all, I almost never have gotten shook up during a math test, and It would not bother me at all to take more math courses. Examples of those who marked agree indicating a favorable attitude were: Mathematics makes me feel uneasy and confused and Mathematics usually makes me feel uncomfortable and nervous. Pre-service teachers experience higher levels of mathematics anxiety than other university undergraduate students (Hembree, 1990; Gresham, 2007), with the incidence of mathematics anxiety significantly higher among elementary education students (Swars, Hart, S. Z. Smith, M. E. Smith, & Tolar, 2007). This math anxiety often passes on to the elementary students they teach (Middleton & Spanias, 1991). Research has

ATTITUDES AND BELIEFS TOWARD MATHEMATICS 621 identified reasons for pre-service teachers experiencing mathematics anxiety: past experiences of failing mathematics (Bekdemir, 2010); teaching practices associated with negative attitudes toward mathematics (Swan, 2004); and students experiences during their own primary school education (Uusimaki & Nason, 2004). Multiple factors impact mathematics anxiety, which include tying instruction to the exact procedures in the textbook, timed tests, hostile teacher behavior, embarrassing students in front of peers, only accepting one method of solving a problem, and lack of differentiation based on student needs (Jackson & Leffingwell, 1999; Swars, 2006). Vinson (2001) found that exploring the conceptual content in meaningful ways with manipulatives before learning the procedural aspects of mathematics reduced the mathematics anxiety among pre-service teachers. Thus, pedagogical strategies used by mathematics teachers are critical in developing confident students without mathematics anxiety. Fennema and Sherman (1976) defined that confidence in learning mathematics is confidence in one s ability to learn mathematics and to perform well in situations involving mathematics. Pre-service elementary teachers confidence in their ability to learn mathematics had a mean score of 3.17, which was just above the neutral position. The result confirms that the lack of confidence in mathematics is related to the actions of pre-service elementary teachers (Soodak & Podell, 1996). Examples of questions with a favorable attitude, from the confidence level form, were Generally, I have felt secure about attempting mathematics and I am sure I could do advance work in mathematics. The mean scores for the two items were 3.01 and 2.89 respectively. Research also found that teachers who had been identified as having low self-confidence in mathematics attributed this feeling to negative experience in school mathematics (Relich, 1996). An answer of disagree on six negatively stated comments indicated a favorable attitude. Examples of this include I am no good in math and I do not think I could do advanced mathematics. Both of these items appear to indicate low self-confidence. If a pre-service elementary teacher s confidence in mathematics is low, he/she tends not to enroll in additional college mathematics courses. The mean score of the Effectance Motivation Scale in learning mathematics was 3.26. The Effectance Motivation Scale is the subject s active involvement or lack of involvement in solving mathematical problems. With respect to mathematics, effectance motivation indicates the extent to which an individual seeks enjoyment and challenges in mathematics for its own sake, and is therefore motivated intrinsically to pursue it (Fennema & Sherman, 1976; Frary & Ling, 1983). The lack of perseverance, motivation, and involvement in problem is a cause for concerns. Examples of these responses included I like math puzzles and When a question is left unanswered in math class, I continue to think about it afterward. The mean scores for these two items were 2.79 and 3.11 respectively. As Fennema and Sherman (1976) discussed, pre-service elementary teachers focalization on exploration with confidence is lower partially due to the lack of encouragement of students to focus on problem-solving skills. How long a person goes on trying and how much frustration he/she can tolerate will depend on the degree of confidence he/she brings to the learning skills initially. Examples of those who marked disagreement indicating a favorable attitude were I would rather have someone give me the solution to a difficult math problem than to have to work it out for myself and I am challenged by math problems, I cannot understand immediately. A person s success will depend partly on how long he/she perseveres. A good level of initial confidence can lead to later success. However, lack of confidence will have the opposite effect. Furthermore, low math-anxious students liked mathematics and expressed that mathematics was like a puzzle or like an adventure and while high math-anxious students expressed dislike and lack of motivation for the subject (Byrd, 1982).

622 ATTITUDES AND BELIEFS TOWARD MATHEMATICS The mean score of the Mathematics Usefulness Scale in learning mathematics was 3.55. This represents attitudes that are somewhat positive, indicating that they had only moderately positive attitude scores about usefulness of mathematics currently and in relationship to their future education, vocation, or other activities. Examples of these included I will need mathematics for my future work, Mathematics is a worthwhile and necessary subject, and I study mathematics because I know how useful it is. The mean scores for the items were 4.05, 3.70, and 3.68 respectively. Perceived usefulness means viewing the knowledge gained in the subject as usable beyond the situation in which the learning occurred (Bruner, 1966; Elliot, 1986). Moreover, Elliot (1986) viewed perceived usefulness of mathematics as the extent to which students perceive the usefulness of mathematics in achieving short- or long- term goals. For instance, successful completion of a particular mathmatics course could be a short-term goal, while finding a worthwhile career for which mathematics is needed could be a long-term goal. Previous research has found that students who perceive the utility of studying mathematics will tend to perform better in the subject (McLeod, 1989). Contrariwise, students who fail to see the practical or future utility in studying mathematics tend to enroll less often in higher-level math courses, perform less well in math courses, or find math less interesting than other courses. This drop in the perception of usefulness is in line with the teachers. Table 3 displays Pearson Correlation Coefficient between the subscales of FMAS. Pearson correlations were calculated among the four subscales, which are presented in Table 3. The correlations among the four subscales were all statistically significant (p < 0.001). There appears to be a significant relationship between mathematics anxiety and self-confidence in mathematics, perceived usefulness of mathematics, and effectance motivation in mathematics in pre-service teachers. Conversely, pre-service teachers with low mathematics anxiety may claim to possess high self-confidence in mathematics and to perceive high usefulness of mathematics and high effectance motivation in mathematics. Table 3 Pearson Correlation Coefficient Between the Subscales of FSMAS Mathematics Anxiety Confidence in Learning Effectance Motivation Mathematics Usefulness Mathematics Mathematics Anxiety 1.000 - - - Confidence in Learning 0.825 * Mathematics 1.000 - - Effectance Motivation 0.702 * 0.825 * 1.000 - Mathematics Usefulness 0.498 * 0.378 * 0.457 * 1.000 Note. * p < 0.001. The link between self-confidence in mathematics and mathematics anxiety is quite evident in the result of research. Essentially, situations in which people have low self-confidence in their abilities are more likely to cause anxiety (Atkinson, 1988). Ernest s (2004) failure cycle suggested that both mathematics anxiety and a lack of self-confidence in one s mathematics abilities originate from repeated failure in mathematics. The findings of this present study support Swars et al. s (2007) investigations of pre-service teachers mathematics anxiety and mathematical beliefs. The pre-service teachers had strong mathematical beliefs and felt less anxious about mathematics. Hendel (1980) noted that participants in a mathematics anxiety reduction program consistently rated their abilities in mathematics as poor, indicating low self-confidence in their mathematics abilities.

ATTITUDES AND BELIEFS TOWARD MATHEMATICS 623 In addition, Bulmahn and Young (1982) found that pre-service teachers who do not enjoy mathematics in the broad sense from its logical beauty to real-life applications identified mathematics as their worst subject among the courses they were expected to teach when they become an elementary teacher. Research recommended that pre-service teachers participation in mathematics methods courses reduces their mathematics anxiety level (Gresham, 2007; Harper & Daane, 1998; Tooke & Lindstrom, 1998). Mathematics educators also need to develop pre-service teachers motivation toward mathematics. It is important to help pre-service teachers understand the role mathematics plays in fields that they might find interesting or challenging, so that they will be more motivated to take more upper-level mathematics classes. Helping pre-service teachers realize these types of connections between the mathematics they are learning in school and its applications in their future classroom is also strongly encouraged by the reform movement. Conclusion One quality that an elementary pre-service teacher should possess is positive attitudes and beliefs toward mathematics. The results revealed that the participants had a mean composite survey score of 3.21, the mean composite score reflected attitudes that were just above the neutral position. Unfortunately, many pre-service elementary teachers in the study did not exhibit positive attitudes toward mathematics. The lowest mean score for attitudes was the Mathematics Anxiety Scale in learning mathematics at 2.87. This result indicates the sample of pre-service elementary teachers appear to have stronger anxiety toward themselves and mathematics learning. To resolve mathematics anxiety, teachers need to have positive experiences with mathematics, see the purpose behind the mathematics they are teaching, write about mathematics, use manipulatives, work in groups, and have field experiences teaching mathematics (Perry, 2004; Tsao, 2004; Swars, 2006). It would be useful to survey pre-service students as they progress through their four-year teaching degree to see if anxiety toward mathematics lessens as they prepare to embark on their career as a teacher. If the anxiety did not diminish, it would be recommended that pre-service teachers with low mathematical self-efficacy seek support from a mentor. The correlations among the four subscales were all statistically significant (p < 0.001). The results indicate that anxiety has the power to influence other aspects as self-confidence in mathematics, perceived usefulness of mathematics, and effectance motivation in mathematics. This situation makes one to think that it is important especially for elementary school pre-service teachers, where they should develop their attitudes toward mathematics. It should be provided for pre-service teachers that they should appreciate the importance of mathematics for the life and they should also understand that mathematics is a universal language. Numerous studies have revealed that pre-service teachers beliefs could be influenced by teacher education programs (Beswick, 2006; Swars et al., 2007). Yet, for change possibly to occur, pre-service teachers must reflect on their beliefs (Philipp, 2007). If beliefs are established through classroom experiences (De Corte, Op t Eynde, & Verschaffel, 2002), then pre-service teachers naive mathematical beliefs might be recognized, challenged, and reflected upon in the classroom environment. Changes in mathematical beliefs have shown in method courses for elementary pre-service teachers and mathematics method courses should be taught in a more constructivist manner in order for the pre-service teachers possibly to develop beliefs that are consistent with the reform ideals of the National Council of Teachers of Mathematics principles and standards (Hart, 2002; Tsao, 2004).

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