Translating the Children’s Anxiety in Math Scale to Turkish for Use with Turkish Children

Math anxiety has become problematic for Turkish students and is thought to be a major cause of low math performance on national and international exams. As Turkey attempts to gain entry to the European Union, it is imperative that the Turkish educational system make efforts to decrease students’ math anxiety. Turkish researchers lack an appropriate scale to assess math anxiety in their students, however, particularly in their primary grade students. This study attempts to remedy that by translating the Children’s Anxiety in Math Scale to Turkish and assessing its psychometric properties. After translation, data were collected from 1587 children in grades 1-5 in Turkey; results of an exploratory factor analysis revealed both a three-factor and a one-factor solution. Confirmatory factor analysis suggest that the one-factor solution fits the data best. Suggestions for future research and applications are included.


INTRODUCTION
In an effort to gain membership into the European Union and its standards and norms, Turkey has implemented a campaign involving numerous social and political reforms [1], the most impactful of which can be seen in Turkey's educational system. There have been shifts in Turkey's curriculum, educational practices, materials, and activities, as well as other components of learning environments. For instance, the national curriculum has shifted from behaviorist teaching approaches to more student-centered cognitive and constructivist approaches that focus on the applicability and practicality of knowledge [2].
Other than curricular changes, the Turkish Education System has been subjected to additional reform with the implementation of national and international exams. This reform is ongoing, but the most impactful change felt throughout Turkey is the implementation of a student selection examination in order to pass on to secondary education. In the Turkish Education System (MEB), the compulsory education period was raised to 12 years in 2012. This system was defined as four years in primary school, four years in secondary school, and four years in secondary education [3]. In 2013, after implementing the 12 years compulsory education system, students were required to pass the Transfer from Elementary Education to Secondary Education (TEOG) examination to move on to secondary school [4].
Unfortunately, based on results from the 1999-2007 Trends in International Mathematics and Science Study (TIMMS) [5,6] and the Program for International Student Assessment (PISA) 2003-2006-2009-2012 exam results [7,8], it was discovered that Turkish students have lower overall success on international exams than other countries and OECD countries. More specifically, it has been observed that Turkish students have lower success on the math subset of both national exams applied in Turkey and international exams applied in other countries. Turkish students also show lower overall success in mathematics when compared to students in other countries [9][10][11][12][13][14][15][16].

Math Success and Math Anxiety
According to PISA 2003 results [10,11], one of the four factors affecting the math success of Turkish students' on the PISA exam is that students have math anxiety, or the "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" [17]. In school settings, math anxiety can lead to an extreme avoidance of anything math related, including performing math problems, speaking in math classes, enrolling in math classes, and pursuing college degrees or jobs in STEM (science, technology, engineering, and mathematics) fields [18][19][20]. While there are environmental influences and individual differences, math anxious individuals typically perform more poorly on math problems and have lower overall final grades in math courses than their non-math anxious peers [21,22]. Turkish students have been found to experience math anxiety at higher levels than other OECD countries, and this anxiety is one of the most important affective characteristics influencing their math success [10,23,24].
While math anxiety is known to be a serious problem in Turkish students, Dede [25] suggests that no sufficient Turkish math anxiety scales have been developed to measure the math anxiety of primary school students. After investigating math anxiety scales that were developed in Turkey and/or adopted to Turkish, most were found to be developed for teaching candidates and not students [26][27][28][29][30][31] [38] to Turkish, which is the scale that is most often used to measure math anxiety in primary students. While the MARS-E is a frequently used and adequate scale, there are three major problems with it that cause concern. First, as Ashcraft and Moore [39] point out, it is a dated measure. Second, it was developed for use with upper elementary students, not students in primary grades. Third, and perhaps most importantly, it uses numeric Likert-type response options for children; this type of response option relies on the ability to conceptually represent emotions as numbers, a skill that is difficult for children [40]. To remedy these problems, Jameson [22] developed the Children's Anxiety in Math Scale (CAMS) which uses facial image response options, was developed with the purpose of capturing math anxiety in children as young as primary grades, and is more up-to-date than previous scales. The CAMS has a solid factor structure and excellent internal consistency, as well as good validity as shown through correlation with math performance [22]; further, it has been effectively used with children as young as kindergarten [41]. Because the CAMS better fits the needs of researchers and educators in Turkey, the purpose of the current research is to translate the CAMS to Turkish and evaluate the factor structure and reliability of the translated version.

Translation Process
A panel was assembled to translate the CAMS. The panel consisted of seven members: three with doctorate degrees in mathematics education, two with doctorate degrees in English language education, and two experts in educational sciences and evaluation and assessment. Prior to the panel session, which was to be held for the translation of the scale, the original form of the scale was given to each member, and they were asked to independently translate the items of the scale from English to Turkish. When the panel assembled, the translation was carried out using a backtranslation technique: each item was read aloud in English, matched to its literal Turkish equivalent, translated back into English, and then re-translated into Turkish. This process was repeated until a consensus among the members of panel was met concerning the appropriate translation of each item.
The final form of the scale consisted of two sections that were identical with the original scale: the first included demographic information, and the second featured the identical facial expressions found in the original scale (see Appendix). The translated version of the CAMS can be found in the appendix.

Pilot Study
To ensure that the administration of the scale was fluid as well as to ensure the understanding and appropriateness of the items, a pilot study was conducted at four different primary and one middle schools with 150 students using the Turkish version of the CAMS (T-CAMS). Teachers of each classroom (i.e., four primary teachers and one middle math teacher) were asked to be active participants in the administration by communicating with students and providing feedback to the researcher on the administration process. The procedure was also video recorded with permission whenever possible. After the pilot study, the panel assembled once more with the teachers involved in the pilot study. The video recordings and the feedback from the teachers were shared with the members of the panels. Based on this evidence and the feedback from the teachers, the items of the scale and the administration process were revaluated and altered by decreasing the language difficulty to ensure full comprehension of each item. Once this modification was complete, the final form of the scale was developed.

Data Collection
Once the scale was finalized, schools were selected to be included in data collection to assess the psychometric properties of the T-CAMS. Schools were selected based on their ability to accurately reflect the Turkish population in terms of socioeconomic levels. Seven primary schools and three middle schools were selected for the final scale implementation. Both primary and middle schools were selected as the original CAMS was administered to children in grades 1-5 in the United States, which equates to both primary and middle school grades in Turkey. Data were collected from a total of 1587 children in grades 1-5. Effort was made to sample approximately equal numbers of children from each grade level, as well as to equally sample girls and boys. The majority of students came from homes in which their father worked and their mother stayed home (N= 982; 61.9% of sample). The most common profession for the fathers of the sample participants was tradesman (N=267; 16.8% of sample) and for the working mothers of the sample participants was teacher (N=162; 10.2% of sample). See Table 1 for all demographic information. Following standard procedures, Institutional Review Board approval, parental permission, and child assent were collected prior to data collection.
Implementation of the T-CAMS paralleled the standard English-language administration by providing each student with a paper copy of the demographic sheet and the facial images scale. Items were verbally administered to all participants, beginning with two non-math practice items to ensure children understood how to respond to each item and concluding with the full 16-item T-CAMS. Data collection times ranged from 15 minutes (for secondary students) to 45 minutes (for the youngest primary students) and occurred over a three-month period by one researcher.

RESULTS
Please see Table 2 for descriptive statistics for the T-CAMS.

Exploratory Factor Analysis (EFA)
With a subset of 500 participants from the total data set, an exploratory factor analysis (EFA) was run with all 16 items of the T-CAMS (see Table 3). Values of the Kaiser-Meyer-Olkin measure of sampling adequacy (KMO = .911) and Bartlett's test of sphericity (χ 2 = 6259.053, df =120, p < .0001) met the necessary assumptions for conducting the EFA using maximum likelihood method. Because there are likely correlations among various anxiety factors, we chose the oblique Promax rotation. The initial EFA solution contained three factors with eigenvalues exceeding the standard 1.0 value, and these three factors explained 47.94% of the variance. Examination of the scree plot suggested that all three of these factors were providing meaningful contributions to the factorial structure. The first factor included 11 items (eigenvalue 5.004), the second included three items (eigenvalue 1.55), and the third included two items (eigenvalue 1.112). Internal consistency estimates of the first factor revealed high reliability (coefficient alpha = .856), but estimates of the second and third factor were quite low (coefficient alpha = .448 and .266 respectively).
Because the second and third factor appeared questionable in the T-CAMS, items on those factors were removed from the analysis, and an EFA with varimax rotation was conducted (See Table 4). This EFA revealed a one-factor solution (eigenvalue 4.59) accounting for 41.81% of the variance. A correlation between students' scores on the full-scale (16-item) and shortened 11-item version of the T-CAMS was high and significant (r = .951, p < .0001), showing that the shortened version could be considered an equivalent measure, with a more clear internal structure. These results were invariant across gender and grade in school.

Confirmatory Factor Analysis (CFA)
Data from the remaining 1087 participants were used for the confirmatory factor analysis. These students completed the T-CAMS at the same time as the EFA sample, but they were not included in those analyses.
The purpose of the CFA was to estimate the fit of two alternative models generated in the EFA. The two models in review were (a) the original 16-item three-factor scale, and (b) a one-factor 11-item math anxiety scale.
To conduct the CFA, the AMOS statistical package was used employing maximum likelihood analysis. Overall, the indicators for goodness of fit for the data demonstrated that the one-factor 11-item math anxiety scale fits the data slightly better than the original 16-item three-factor scale (see Table 5). Given the different lengths of the scales for these two CFA solutions, the AIC and BIC indicators hold merit in making the final judgment of model fit.  .662 -.049 .016 When I think about doing math, I feel: .640 -.127 .068 Compared to other school subjects, math makes me feel: .621 -.018 .094 When I solve math puzzles, I feel: .530 -.138 .151 When the teacher calls on me to answer a math problem, I feel: .597 .037 -.259 If I have to add up numbers on the blackboard in front of the class, I feel: .561 .284 -.318 Thinking about working on math in class makes me feel: .702 -.227 .076 Working on math at home makes me feel: .725 -.191 .125 When my teacher says that he or she is going to give me a math problem on the blackboard, I feel: .684 .053 -.236 When I know that my class will be working on math at school, I feel: .603 -.241 .225 When I know that I am going to have a math test, I feel: .670 -.041 -.023 When I have a hard math question, I feel: .399 .655 -.085 When I am working on math problems that are difficult and make me think hard, I feel: .446 .595 -.098 When I make a mistake in math, I feel: -.151 .354 .609 When the teacher gives the class a math problem I don't understand, I feel: . 185 .498 .521 When the teacher is showing the class how to solve a math problem, I feel: .  .666 When I think about doing math, I feel: .647 Compared to other school subjects, math makes me feel: .627 When I solve math puzzles, I feel: .536 When the teacher calls on me to answer a math problem, I feel: .605 If I have to add up numbers on the blackboard in front of the class, I feel: .547 Thinking about working on math in class makes me feel: .715 Working on math at home makes me feel: .741 When my teacher says that he or she is going to give me a math problem on the blackboard, I feel: .688 When I know that my class will be working on math at school, I feel: .619 When I know that I am going to have a math test, I feel: .688 Eigenvalue 4.599 Coefficient alpha .856 Taking into consideration the minimal differences in the models, the stronger internal consistency in the shorter scale, the acceptable fit for the 11item scale, and the interest in maintaining parsimony with the construct of math anxiety, the selection of the 11-item version is most desirable for future uses with the T-CAMS.

DISCUSSION
The purpose of the current study was to translate the English Children's Anxiety in Math Scale [22] to Turkish and to assess the psychometric properties of the T-CAMS. The results of this study confirmed that the T-CAMS was a reliable and valid measure of math anxiety in the Turkish sample. The adaptation process provided evidence to support using this scale and also revealed a new factor structure that promotes the use of a shorter form.
Though Jameson's [22] original Englishlanguage scale purported a 16-item three-factor conceptualization of math anxiety, the current model did not provide support for breaking the math anxiety construct into subcomponents such as math error anxiety, math performance anxiety, and general math anxiety. The CAMS includes items that measure these various proposed separate factors, but the current data maintain a strong fit with the single-factor model. Naturally, further research comparing the single-factor and multi-factor models directly is warranted to establish that the findings in this study are accurate with other samples. Adaptation to Turkish of additional math anxiety scales (or using already existing translated math anxiety scales) could be necessary to cross-validate the findings. One of the major areas in which Turkish students have difficulties in math compared to other countries participating in the PISA 2012 exam is problem solving [7,8]. The two items that were most factorially conflicted were related to problem solving (i.e., Q8: When the teacher is showing the class how to solve a math problem, I feel:, and Q13: When the teacher gives the class a math problem I don't understand, I feel:), suggesting that Turkish students may perceive problem solving to be a construct separate from mathematics.
Further, examining the items that did not load well and were dropped from the 16-item scale shows that four of the five items are related to completing math that is difficult or prone to errors. It is possible that the factor termed "math error anxiety" on the English version of the CAMS is not a construct present in Turkish students. It is also possible that this error anxiety is a component of Turkish students' self-efficacy in mathematics as opposed to their anxiety in mathematics. Ruzgar, Sokmen, and Boynak [42] state that there is a lot of pressure placed upon Turkish students from a young age to score well in mathematics and sciences so that they enter a strong elementary school and increase their chances of acceptance to a competitive university. One would then expect that Turkish students would have high math error anxiety, but the T-CAMS did not indicate that. Additional research should explore this discrepancy to uncover the specific nature of this factor in Turkish students.

CONCLUSION
In conclusion, the current research provides a valid and reliable measure of Turkish primary students' math anxiety. The establishment of a consistent and equivalent Turkish-language version of the CAMS provides a valuable tool for conducting valid cross-cultural research on math anxiety. This is of particular import for Turkish researchers, as recent multi-national educational assessments have identified that Turkish students experience high math anxiety. In addition to creating and validating the T-CAMS, the results of this research have prompted reevaluation of the English language version of the CAMS, with preliminary analyses demonstrating that a shortened version of the English CAMS is also a preferred solution for measuring math anxiety in English-speaking elementary students. Further work on validating the CAMS is currently ongoing as we establish the optimal shortened version in both English-and Turkish-speaking samples.