Mathematics anxiety and mathematical self-concept: Considerations in preparing elementary-school teachers

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1 SOCIAL BEHAVIOR AND PERSONALITY, 2009, 37(5), Society for Personality Research (Inc.) DOI /sbp Mathematics anxiety and mathematical self-concept: Considerations in preparing elementary-school teachers Mine Isiksal Middle East Technical University, Ankara, Turkey Joanne M. Curran SUNY Oneonta College, Oneonta, NY, USA Yusuf Koc Indiana University Northwest, Gary, IN, USA Cengiz S. Askun Middle East Technical University, Ankara, Turkey The purpose of this study was to explore the effects of type of educational system and years spent in teacher education programs on preservice teachers mathematics anxiety and mathematical self-concept scores. The sample consisted of 234 American and 276 Turkish early childhood and elementary school preservice teachers. The Abbreviated Mathematics Anxiety Scale (AMAS; Hopko, 2003) was used to measure how anxious preservice teachers feel during a specific mathematics related event. In order to measure the mathematical selfconcept of preservice teachers, the Experience with Mathematics Questionnaire (EMQ; Gourgey, 1982) was used. Regarding the effect of the educational system, results revealed that while the American preservice teachers had significantly higher anxiety scores, Turkish preservice teachers had significantly higher self-concept scores. Results supported previous findings emphasizing the negative relationship between mathematical anxiety and mathematical self-concept. Keywords: self-concept, mathematics anxiety, preservice teacher education, education systems. Mine Isiksal, PhD, Faculty of Education, Middle East Technical University, Ankara, Turkey; Joanne M. Curran, PhD, Division of Education, SUNY College at Oneonta, Oneonta, NY, USA; Yusuf Koc, PhD, School of Education, Indiana University Northwest, Gary, IN, USA; Cengiz S. Askun, PhD, Middle East Technical University, Ankara, Turkey. Appreciation is due to anonymous reviewers. Please address correspondence to: Yusuf Koc, School of Education, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA. Phone: ; Fax: ; ykoc@indiana.edu 631

2 632 Mathematics anxiety and mathematical self-concept Over the past decade, research studies on affective variables have received increased attention within the fields of psychology and education (Murphy & Alexander, 2000; Pintrich, 2000). Educational psychologists have been interested in determining the nature of the relationship between affective variables and academic achievement (Cokley, 2000; Lent, Brown, & Gore, 1997). Mathematics anxiety (Hembree, 1990; Ma, 1999) and academic self-concept (Manger & Eikeland, 1998; Marsh, 1994) are two of these variables which are also the focus of the present study. In particular, the purpose of this study was to explore the effect of the type of educational system and the number of years spent in teacher education programs on preservice teachers mathematics anxiety and mathematical self-concept scores. Anxiety is a complex construct that has been defined in a number of ways (Fennema & Shermann, 1976). Spielberger (1972) discussed two general types of anxiety: state anxiety and trait anxiety. State anxiety is the unpleasant emotional state or condition which is characterized by activation or arousal of the autonomic nervous system (p. 482). State anxiety is dependent on time and situation, and is aroused when a person perceives a situation to be dangerous. Trait anxiety, on the other hand is described as relatively stable individual differences in anxiety proneness (Spielberger, 1972) and does not depend on time or situation. Mathematics anxiety is a form of state anxiety as it is aroused in situations involving mathematics. In a recent study, learning math anxiety (LMA), anxiety about the process of learning, and math evaluation anxiety (MEA), more directly related to testing situations, were acknowledged as critical elements of mathematics anxiety (Hopko, 2003). Baloglu and Kocak (2006) stated that situational, dispositional, and environmental factors are three sources of mathematics anxiety. Situational factors are external and dispositional factors are internal and related to personality. In addition, environmental factors are defined as individuals attitudes, prior perceptions and experiences (Baloglu & Kocak, 2006). Similarly, McLeod (1994) found that students construct anxieties about the subject in a similar way that they form identities, and there are many individual and environmental influences that cause anxieties to develop. Elementary mathematics classes can be considered to be the beginning point of mathematics anxiety (Harper & Daane, 1998), directly linked to prior experiences at the elementary and secondary school levels (Jackson & Leffingwell, 1999). Those experiences could lower confidence in one s own mathematics ability, leading to students avoiding mathematics by the time they get to secondary school (Harper & Daane, 1998). Math anxious people may avoid mathematics classes and mathematics-related activities. Mathematics anxiety is a critical factor not only for student learning (Hembree, 1990; Ma, 1999), but also for teachers effectiveness in teaching. Vinson (2001) noted that teachers who experience

3 Mathematics anxiety and mathematical self-concept 633 mathematics anxiety may promote the early development of mathematics anxiety in their students. Swetman, Munday, and Windham (1993) found that elementary school teachers who experienced higher levels of mathematics anxiety spent less time on planning mathematics-related activities and dedicated fewer hours to mathematically related activities than did the teachers with lower anxiety levels. In this study, we sought to understand how two environmental factors, type of educational system and years spent in teacher education programs, affect preservice teachers mathematics anxiety and mathematical self-concept levels. Reyes (1984) defined confidence in mathematics as a particular component of self-concept that is specific to mathematics (p. 559). Thus, confidence in mathematics or self-concept specific to mathematics is related to one s perception of self regarding achievement in school (Reyes, 1984). Mathematics self-concept refers to perceptions of one s ability to learn and perform tasks in mathematics, one s confidence in being able to learn mathematical new topics, and how interested one is in pursuing mathematical ideas (Reyes, 1984, p. 560). In the literature, a negative relationship between mathematics anxiety and math achievement among elementary and secondary students (Hembree, 1990; Ma, 1999) and significant positive correlation between mathematics self-concept and mathematics achievement (Manger & Eikeland, 1998; Marsh, 1994) have been reported. In a meta-analysis, Hembree found that positive attitude toward mathematics was consistently related to lower mathematics anxiety. More particularly, Hembree mentioned a strong negative relationship between math anxiety and enjoyment of mathematics, as well as self-confidence in the subject. At postsecondary levels, similar kinds of relationships have been found, but the relationships were weaker compared to those at middle and high school (grades 5-12) levels (Hembree, 1990). In a recent study, Brady and Bowd (2005) conducted a study with 238 preservice teachers from elementary teacher education programs (grades 1 through 8). The findings of the survey study indicated that preservice teachers confidence in teaching mathematics was related to two factors: mathematics anxiety and prior mathematics learning experiences at elementary and secondary levels. More specifically, level of mathematics anxiety was found to be negatively correlated with level of confidence in teaching mathematics, and level of enjoyment of mathematics in elementary and secondary schools was positively related to level of confidence in teaching mathematics (Brady & Bowd, 2005). In a similar study, Bursal and Paznokas (2006) investigated the relationship between preservice elementary teachers math anxiety and confidence levels in teaching mathematics and science. Their results revealed that preservice teachers with low levels of math anxiety are more confident about teaching elementary mathematics and science compared to their peers who have higher levels of math anxiety. Our review of the literature indicates that most of the previous research

4 634 Mathematics anxiety and mathematical self-concept on mathematics anxiety and self-concept involved elementary through high school students, with less information available for college-age samples. We hypothesize that undergraduate students experience during their university years has an influence both on their cognitive and affective development. Thus, in this study, we aimed to examine the differences between third and fourth year preservice teachers mathematics anxiety and self-concept scores. In addition, Brady and Bowd (2005) mentioned that more emphasis should be placed on the relationship between preservice teachers experiences and affective variables involving attitudes toward mathematics, mathematics anxiety, and confidence in mathematics. Moreover, although a large research tradition has developed around mathematical anxiety and self-concept in many countries, less has been done to analyze cross-national differences. Affective variables, including mathematics anxiety and mathematical self-concept, might be shaped by the education system and should be carefully examined in different countries with diverse educational backgrounds. Additionally, as Baloglu and Kocak (2006) concluded, there is little agreement in the literature with regard to the effect of environmental sources of anxiety. Also, little is known about the relationship between self-concept and quality of instruction. Our review of the research literature indicated that researchers have not studied the relationship between these two variables. In an earlier survey study with 120 elementary and secondary teachers, Guskey (1988) found a strong, statistically significant relationship between teachers self-concept about teaching and their attitudes toward the implementation of changes in instructional practices. Therefore, Guskey reported that teachers with strong confidence in their teaching abilities were more receptive to the implementation of instructional innovations. However, we do not know much about the relationship between self-concept and quality of instruction. In relation to this, we aimed to answer the following research questions: 1. Is there a significant difference in mathematics anxiety and the mathematical self-concept scores of Turkish and American preservice elementary school teachers? 2. Is there a significant difference in mathematics anxiety and mathematical self-concept scores with respect to number of years spent in college? 3. Is there a significant relationship between mathematics anxiety and the mathematics self-concept scores of college students? The organization and curriculum of teacher education programs vary across the states in America, but most teacher education programs require preservice teachers to be qualified in similar areas, including content, curriculum, pedagogy, special education, and school community. High school graduates are admitted to teacher education institutions on the basis of satisfactory GPA and SAT scores. At the end of their second year, students with acceptable course grades are allowed

5 Mathematics anxiety and mathematical self-concept 635 to enter the teacher education program. It is worth noting that it is not a highly competitive system to be admitted into. In Turkey, teacher education institutions offer regular four-year college degrees with a teaching license. The institutions admit their students via a nationwide university entrance exam. It is a highly competitive exam with questions covering various areas: mathematics, science, social sciences, and the Turkish language. Students who are admitted to the teacher education programs take theoretical and practical courses in three major areas: content, teaching as a profession, and general education (Isiksal, Koc, Bulut, & Atay-Turhan, 2007). Method Participants The data were collected from a convenience sample of 234 American and 276 Turkish early childhood and elementary school preservice teachers. The American sample consisted of 121 (51.7%) junior and 113 (48.3%) senior students, and 222 (94.9%) of them were female. Regarding the ethnic backgrounds of the American preservice teachers, 225 (96.2%) were Caucasian; 4 (1.7%) Asian; 3 (1.3%) African American; 1 (0.4%) Hispanic; and 1 (0.4%) identified other. In total, the American sample consisted of participants who were undergraduate students in two different state universities; one in the South-east and the other in the North-east of the country. Thus, we concluded that participants were drawn from a variety of socioeconomic levels. The American participants do not have a content major prior to taking the teacher education programs. They take 2-3 mathematics courses prior to entering the school of education programs. They also take one mathematics teaching methods course during their teacher education programs. It is a prerequisite of only one of these universities for preservice teachers to take two more courses concerning mathematics teaching and learning in elementary schools. In both universities, the participants have the option to major in mathematics, but most of them choose not to do so. It is assumed that the American sample represents students in similar teacher education programs in early childhood and elementary education. The Turkish sample consisted of 276 preservice teachers. Of these, 88 (31.9%) were junior and 188 (68.1%) were senior students, and 181 (65.6%) were female. Representing a variety of socioeconomic levels, no ethnic differences were observed among Turkish participants. Participants were preservice teachers enrolled in early childhood or elementary education programs from two state universities in South-west Turkey. Content majors, e.g., mathematics, are not offered prior to the teacher education programs. Both early childhood and elementary education preservice teachers take one mathematics teaching methods course. In addition to the teaching methods course, those majoring in

6 636 Mathematics anxiety and mathematical self-concept elementary education take basic level mathematics courses. All teacher education programs follow the same curriculum approved by the Turkish Higher Education Council (Isiksal et al., 2007), thus, our sample is representative of the majority of the teacher education programs in the country. Instruments The Abbreviated Mathematics Anxiety Scale (AMAS; Hopko, 2003) was used to measure how anxious preservice teachers felt during a specific mathematics-related event (e.g., when taking an examination in a math course). The AMAS is measured on a 5-point Likert type scale ranging from 1 = low anxiety and 5 = high anxiety, and consists of 9 items. The construct validity of the instrument was obtained from a sample of 1,239 undergraduate students by using explanatory factor analysis. Results yielded a strong internal consistency and good convergent/divergent validity (Hopko, 2003). In terms of internal consistency, Cronbach s alpha was calculated to be.82 for American and.83 for Turkish samples, respectively. In order to measure the mathematical self-concept scores of preservice teachers, the Experience with Mathematics Questionnaire (EMQ; Gourgey, 1982) was administered to participants. The EMQ was designed to measure preservice teachers attitudes, beliefs, and feelings about their ability to learn mathematics (e.g., I have a good mind for mathematics). The EMQ consists of 27 items, and responses are made on a 5-point Likert-type scale ranging from 5 = strongly agree to 1 = strongly disagree. Gourgey (1982) reported an internal consistency level of.96 using 92 graduate and undergraduate students in a statistics course. The Cronbach s alpha for this study was calculated to be.96 for the American and.91 for the Turkish samples, respectively. After obtaining permission from the developers of the instruments to use the scales in the current research study, the questionnaires were translated and adapted for Turkish preservice teachers. To address content validity concerns, two education professors compared the original and translated versions, and the questionnaires were iteratively revised until 90% agreement was reached between the two professors. Results A Multivariate Analysis of Variance (MANOVA) was conducted to determine the effect of the differences in educational system and university grade level on preservice elementary teachers mathematics anxiety and mathematical selfconcept scores. Preliminary assumption testing was conducted to check for normality, linearity, univariate and multivariate outliers, homogeneity of variancecovariance matrices, and multicollinearity assumptions. Results revealed no

7 Mathematics anxiety and mathematical self-concept 637 violations on normality, linearity, and homogeneity of variance assumptions. In addition, a moderate strength correlation (r = -.52, p =.00) between mathematics anxiety and self-concept scores was in evidence for multicollinearity. The descriptive statistics of Turkish and American preservice teachers mathematics anxiety and self-concept scores by the year they are at in their program are summarized in Table 1. Table 1 Descriptive Statistics for Turkish and American Students with Respect to AMAS and EMQ Country Year M SD Total N Mathematics USA Junior anxiety Senior as measured Total by the AMSA Turkey Junior Senior Total Self-concept USA Junior as measured Senior by the EMQ Total Turkey Junior Senior Total The results indicate that both the effect of the differences in the educational system (Wilks Lambda =.92, F(2, 505) = 21.6, p =.00) and the effect of years spent in college (Wilks Lambda =.98, F(2, 505) = 5.3, p =.00) on combined scores of mathematics anxiety and mathematics self-concept are statistically significant. A univariate Analysis of Variance (ANOVA) was conducted as a follow-up to reveal the effect of each independent variable on each dependent variable separately. The results showed that there was a significant effect on preservice elementary teachers mathematics anxiety in relation to the differences in the educational system (p =.00) in that American preservice teachers had significantly higher scores on the Abbreviated Mathematics Anxiety Scale (M = 22.9, SD = 5.7) than their Turkish counterparts (M = 18.6, SD = 6.7). Results also revealed that there is a significant effect of years spent in college on anxiety scores (p =.01) where junior preservice teachers had higher anxiety scores (M = 21.9, SD = 6.3) compared to seniors (M = 19.6, SD = 6.7). On the other hand, there was no significant effect of the differences in educational system and years spent in college interaction on preservice teachers mathematics anxiety scores. In other

8 638 Mathematics anxiety and mathematical self-concept words, the effect of the differences in educational system did not depend on years spent in college, where both junior and senior American preservice teachers had higher anxiety scores compared to junior and senior Turkish preservice teachers. Results revealed small effect sizes in that eta square (η 2 ) values showed that 8% of the variance in mathematics anxiety was explained by differences in the educational system, 1% by years spent in college, and 1% by the differences in the educational system and years spend in college interaction. In Figure 1, the relationships among differences in the educational system, years spent in college, and mathematics anxiety are given. Figure 1: Relationship between mathematics anxiety scores and differences between educational systems. From Figure 1, it can be seen that American preservice teachers had higher mathematics anxiety scores compared to Turkish participants both in their junior and senior years of university education. The junior American and Turkish preservice teachers also had higher mathematics anxiety scores compared to their senior partners. While the gap between junior and senior preservice teachers anxiety scores was small in the American sample, the difference was relatively larger in the Turkish sample. In terms of mathematical self-concept scores, Turkish preservice teachers (M = 101.9, SD = 14.9) gained significantly higher scores on the mathematical self-

9 Mathematics anxiety and mathematical self-concept 639 concept scale (p =.00) compared to their US counterparts (M = 96.2, SD = 20.5). However, results revealed no significant difference on mathematical self-concept scores (p =.7) between juniors (M = 98.9, SD = 18.3) and seniors (M = 99.5, SD = 17.5). In addition, results revealed no significant effect of the differences in the educational system and years spent in college interaction on preservice teachers mathematical self-concept scores. Similar to the anxiety scores, eta square (η 2 ) values revealed small effect sizes where 3% of the variance in mathematical self-concept scores was explained by differences in the educational system, 1% by years spent in college, and 1% by the differences in the educational system and years spend in college interaction. In Figure 2, the relationships among differences in the educational system, years spent in college, and mathematical self-concept scores are given. Figure 2: Relationship between mathematics self-concept scores and differences between educational systems. From Figure 2, it can be seen that Turkish preservice teachers had higher mathematical self-concept scores compared to their American counterparts in both their junior and senior years of university education. The junior American and Turkish preservice teachers had higher mathematics anxiety scores compared to their senior partners. However, the gap between junior and senior preservice teachers self-concept scores were very small among the participants from both nations.

10 640 Mathematics anxiety and mathematical self-concept Lastly, in order to investigate the relationship between mathematics anxiety and the mathematical self-concept scores of college students, correlation analysis was performed. Results indicated that there is a significantly negative correlation (r = -.53, p <.05) between math anxiety and self-concept scores where students who have higher self-concept scores have lower math anxiety scores. Discussion and Conclusions In this research study, the effect of type of educational system and years spent in college on preservice teachers mathematics anxiety and mathematical self-concept scores were investigated. In addition, the relationship between anxiety and self-concept scores was investigated. Regarding the effect of which educational system the participants were in, results revealed that while the American pre-service teachers had significantly higher anxiety scores, Turkish pre-service teachers had significantly higher self-concept scores. In addition, there was a significant negative correlation between math anxiety and selfconcept scores. Our results support the previous findings reporting the negative relationship between math anxiety and mathematical self-concept scores (e.g., Brady & Bowd, 2005; Bursal & Paznokas, 2006). The above differences between the American and Turkish preservice teachers could be explained by a variety of factors however, we believe that the university entrance exam in Turkey accounts for a large amount of the mean difference in the mathematics anxiety and self-concept scores. As in Japan (Judson, 1999), Turkey has a highly competitive university entrance exam. Graduates of all high schools are eligible to take the entrance exam and each year approximately 1.5 million students do so. Only about 15% of them gain scores high enough to enter four-year regular university programs. Due to this competitive environment, Turkish students have private lessons or tutoring as early as the elementary grades. During this preparation period for the university entrance exam, students learn various strategies to approach multiple choice problems and take hundreds of multiple choice practice tests. In addition, students are required to have a high degree of familiarity with mathematics regardless of the major they plan to take in college. They put in a lot of effort preparing for the exam, particularly the mathematics section. As Baloglu and Kocak (2006) suggested, previous experience in school mathematics beginning from elementary grades and involvement in mathematics-related environments (McLeod, 1994) could be reasons for the lower math anxiety scores gained by the Turkish preservice teachers. As a result, in order to gain a successful grade in the highly competitive university entrance exam and be accepted into a university program, adequate preparation, including the control of anxiety is necessary. This could explain why Turkish preservice teachers math anxiety scores were significantly lower

11 Mathematics anxiety and mathematical self-concept 641 than their American counterparts. Similarly, the higher self-concept scores gained by the Turkish participants might be due to their extensive preparation for the university entrance exam and gaining entrance to the university. In terms of American universities, the entrance requirements for college vary and the SAT examinations do not carry the same weight as those of the Turkish entrance examinations. For instance, for the American sample in this study, scores on the math section of the SAT were at average level, 532 out of 800. These scores indicate a basic level of competence in mathematics (Dorans, 2002). In addition, in America, lack of mathematically-based skills remains socially acceptable, unlike lack of efficacy skills (Kloosterman, 1997). These, among others, could be why American preservice teachers have higher anxiety and lower self-concept scores compared to their Turkish counterparts. Results also revealed that senior preservice teachers have lower math anxiety scores compared to the junior preservice teachers in both educational systems. The nature of pedagogical courses in both countries, especially the method used to teach courses, may be one of the reasons for such a difference. Senior preservice teachers mastery experiences during methods courses and student teaching, where they devote more class time to mathematical activities and learn new approaches to teaching, could positively affect Turkish and American preservice teachers competence in mathematics and lower their anxieties (Peressini, Borko, Romagnano, Knuth, & Willis, 2004). Teacher educators expect that practical experience will encourage students to reflect on their classroom experiences in the context of the conceptual framework of their teacher education program. This context assists students in interpreting their experiences and identifying themselves as teachers of mathematics. Their success in interpreting these experiences will improve their competence and sense of control in the classroom and reduce math anxiety. Future studies could examine how different educational systems may affect math anxiety and self-concept scores of junior and senior undergraduate students. There are a few limitations that should be taken into account by future researchers: This sample was restricted to four universities in two countries, so this study could be replicated with broader samples for generalization. In addition, although the universities were somewhat similar in terms of academic quality, some environmental or demographic factors such as individuals attitudes, prior perceptions, socioeconomic level, age, and gender could not be controlled within the scope of this study. Thus, further studies should be carried out to better understand the effect of specific environmental and personality-related factors on preservice teachers math anxiety and self-concept scores. In addition, some research studies have emphasized that mathematics anxiety and self-concept are not constructs dependent on a single factor (Marsh, 1992). Further research could be performed to reveal individual differences on affective variables such

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