Factors affecting the academic achievement in socioeconomically disadvantaged students Makalenin Türkçe Başlığı: Sosyoekonomik açıdan dezavantajlı öğrencilerde akademik başarıya etki eden faktörler Yazar(lar):

Bu calismanin amaci, PISA 2012 uygulamasinda dusuk sosyoekonomik altyapidan gelen ogrenciler arasinda matematik performansi bakimindan yuksek ve dusuk basari gosteren ogrencilerin basarilarina etki eden faktorleri degerlendirmektir. Arastirmanin evreni, PISA 2012 degerlendirmesinin yapilacagi tarih itibariyle 15 yasinda olan ogrencilerden olusmaktadir. Turkiye ornekleminde, 12 istatistiki bolge biriminden 57 il ve toplam 170 okuldan 4848 ogrenci yer almistir. Bu Calismaya, Turkiye ornekleminde ekonomik, sosyal, kulturel durum indeksine gore en alt %33.00’luk dilimde olan ogrenciler dâhil edilmistir. Arastirma, sosyoekonomik bakimdan dezavantajli olup matematikte dusuk basari gosteren 218, yuksek basari sergileyen 173 ogrenci ile yurutulmustur. Ogrenci ozellikleri ile matematik basarisi arasinda yurutulen yapisal esitlik modeli sonucunda okula yonelik tutum degiskeninin, dusuk basarili grupta pozitif ve manidar bir yordayici oldugu gorulmustur. Yuksek basarili grupta matematige yonelik duyussal ozellikler performansin pozitif yonde aciklayicisi iken, okula yonelik tutum matematik basarisinin negatif aciklayicisi durumundadir. Bu sonuclar, ogrenci basarilari arasindaki farka yonelik egitim yatirimlarinin yeniden gozden gecirilmesine ve basarida en fazla artis yaratacak olan alanlara kaynak aktarilmasina olanak saglayacaktir.


Introduction
It is important for individuals to have a secure future for both themselves and society.However, some individuals have complications in their lives making it more difficult to achieve success.For example, being socio-economically disadvantaged is a determinant of not only the access to education, but also the educational success (ERG, 2014;Tansel, 2002).Many studies show a strong nexus between socioeconomic indicators such as the educational status of parents or the household income and the learning outcomes of students.These studies report the possibility of coming from a lower socioeconomic status is higher for students with low success (Acemoğlu & Pischke, 2001;Baker, Goesling, & LeTendre, 2002;Chevalier & Lanot, 2002;Davis-Kean, 2005;Konstantopoulos, 2006;Köse, 2007;OECD, 2007;2011;Şirin, 2005).
While the studies conducted highlight the determinative role of socioeconomic characteristics on academic achievement, a subset of students shows remarkable success despite their disadvantaged socioeconomic status.For example, one out of every three students from disadvantaged families in OECD countries overcomes their socioeconomic status and show a great success.This ratio is over 60.00% in OECD countries such as Korea and Hong-Kong-China.However, the ratio is lower in Canada, Finland, Japan, and Spain where 35.00% of the disadvantaged students are high-achieving students (OECD, 2011).Approximately one million students (6.40%) n the 2012 Programme for International Student Assessment (PISA) succeeded despite the difficulties from their socioeconomic status.This ratio was 7.20% for Turkey in the PISA 2012, which was higher than the OECD average (OECD, 2013).
These students are able to succeed better than anticipated despite the difficulties such as low socioeconomic status and poor environmental conditions (OECD, 2011).In the literature, they are called dauntless students (Masten, 2001), resilient students (Dinçer & Oral, 2013), and disadvantaged highachieving students (OECD, 2011).Despite the various risk factors that may cause students to fail in school, the surprising academic achievement is called academic resilience.Academic resilience can be developed through reducing risk factors, enriching protective factors, and increasing the effectiveness of protective factors (Krovetz, 1999).However, some risk factors are a basis for many problems.Being disadvantaged socioeconomically is among such risk factors.A low socioeconomic status can lead to the lack of requirements needed to maintain a healthy lifestyle as well as to the insufficiency in meeting basic needs.This situation usually depends on the quality of the environment.Therefore, a low socioeconomic status is a critical and general risk factor for students (Brackenreed, 2010).
The negative consequences of a risk factor can be eliminated by either directly removing the risk itself or developing protective factors (Tiet & Huizinga, 2002).According to Krovetz' theory of resilience, protective factors can be related to the individual or the society (Krovetz, 1999).In this case, academic resilience is not just about the individual's own characteristics.It is influenced by the individual's social and physical environment and shaped through the interaction of the individual and exogenous factors (Johnson, 2008;Masten, 2001;Toland & Carrigan, 2011;Wasonga, 2002).
According to the literature, economically disadvantaged students' goals, their expectations for the future (Krovetz, 1999), their thoughts of a successful future, and their belief in successfully fulfilling responsibilities increase their chance of success compared with their socioeconomically advantaged peers (Fallon, 2010;OECD, 2011).Self-confidence, motivation, the skill of goal setting, and stress management are among the determinants of academic resilience (OECD, 2011).In addition, qualified school and education services, positive perceptions towards schools and teachers, the social support provided by parents and peers (Bernand, 2004;Foster, 2013), and the duration of education at the school (OECD, 2011) are listed among the effective factors.
The skills that have lasting impacts on academic performance are not specific to particular individuals.These characteristics can be developed through constructing supportive environments (Masten, 2001).As a result, researchers from around the world as well as from Turkey have conducted studies focusing on students coming from a disadvantaged socioeconomic status with relatively high success (Alva, 1991;Arastaman & Balcı, 2013;Arnold, 2003;Borman & Overman, 2004;Dinçer & Oral, 2013;Foster, 2013;Gizir & Aydın, 2009;Gonzalez & Padilla, 1997;Morales, 2008;OECD, 2011;Wasonga, 2002;Waxman, Padron, Shin, & Rivera, 2008;Yavuz, 2015;Yılmaz-Fındık & Kavak, 2013).However, the studies about the disadvantaged high-achieving students in Turkey are not sufficient.One of these studies reported a positive relationship between academic resilience and the positive perception of academic competence, high expectations, feeling hopeful about the future, and positive peer and school relationships (Gizir & Aydın, 2009).Another study indicated students' academic resilience varies according to gender, geographical region, type of program and school, and status of having a preschool education.The results of this study revealed that the insufficient number of teachers negatively affects students' academic resilience and factors such as discipline in the school, quality of educational materials, and student-teacher relationship increase students' academic resilience (Dinçer & Oral, 2013).Arastaman and Balcı (2013) found that academic achievement and absenteeism predict academic resilience at a low level.They also determined that perceived parent and peer support is an important predictor of academic resilience.According to another study, cognitive flexibility and perceived social support predict academic resilience, whereas gender and attachment to the school do not (Yavuz, 2015).
In Turkey, some studies focused on low socioeconomic status based on the region of the school and were conducted only in particular provinces (Arastaman & Balcı, 2013;Gizir & Aydın, 2009).Therefore, the generalizability of these studies is limited.Moreover, some were based on the PISA 2009 data (Dinçer & Oral, 2013;Yılmaz-Fındık & Kavak, 2013).The PISA is conducted every three years to measure the life skills of students in mathematics, reading, and science and each session concentrates on one of these fields.The reading field in the PISA 2009 and the mathematics field in the PISA 2012 were investigated in detail.Turkey's mathematics average is less than other fields in almost all PISA reports.Turkey performed below the average among both OECD and all participating countries in mathematical literacy (MEB, 2015).Considering the students' distribution according to their competence level, the percentage of students below the second level in the mathematics test was higher than the percentage in the fields of reading and science.However, the second level in PISA is regarded as the basic competence level and students below this level do not possess the necessary skills for active participation in social life (MEB, 2015;OECD, 2011;2013).In this regard, it is of critical importance to determine the factors contributing to the high performance of the socioeconomically disadvantaged high-achieving students in the mathematics field.Therefore, data that eliminates the effect of socioeconomic status on academic achievement need to be generated.This can make it possible to determine appropriate investment areas in education, and as a result, students' achievement affected by this risk can be enhanced.
Thus, this study investigates socioeconomically disadvantaged students based on the PISA 2012 data to determine how high-achieving students differ from low-achieving students from similar socioeconomic status examining the roles of affective characteristics towards mathematics, teachers, and the school in student achievement.In line with the determined general aim, an answer to the following question was sought: 1) Do the disadvantaged high-and low-achieving students' affective characteristics towards mathematics, anxiety towards mathematics, and affective characteristics towards the school and teacher explain their mathematical literacy performance?

Research Design
The study was designed as descriptive survey study because it describes an existing situation.In the descriptive survey model, the individual or object of descriptive survey studies is described in its own condition without any attempt to change or influence it (Karasar, 2009).

Study Group
Students below the age of 15 who participated in the PISA 2012 in Turkey constituted the universe of the study.The Turkey sample in the PISA 2012 consisted of 4848 students from 170 schools in 57 different provinces.The participants were selected through stratified random sampling, which represents 12 statistical regions.This study followed the method in the OECD's (2011) report titled "Against the Odds" to select the disadvantaged high-and low-achieving students in Turkey's sample.In order to identify the disadvantaged students, the students in the lowest 33.00% according to the index of economic, social, and cultural status (ESCS) were considered.The achievement status of the students in the lowest 33.00% according to the ESCS index were grouped as follows: The lowest 33.00% according to the average mathematics score are identified as low-achieving students, the highest 33.00% are identified high-achieving students, and the middle 33.00% are mid-achieving students.In addition, 66 mid-achieving students who were above the OECD average (448) were included in the group of students in the highest 33.00% in order to reach a sufficient sample number for analysis.This shift between groups did not change the results since there was not a statistically significant difference between these 66 students and the high-achieving students in terms of mathematical achievement.In addition, the 25.00% or 33.00% cut-off points were referenced when identifying disadvantaged high and lowachieving students.Another way to group students was by achievement according to the PISA's six competency levels.Because the number of disadvantaged high-achieving students significantly decreased with these cut-off points, this method was not preferred in the analysis.The cut-off points were defined as 25.00% and 33.00% in the academic achievement distribution and the analysis were repeated for justification.The results did not reveal any qualitative or quantitative differences.After excluding the missing variables from the analysis, the study included 218 students in the low-achieving group and 172 students in the high-achieving group.The two groups were compared in terms of achievement in order to identify the most apparent differences.
The sample size of structural equation model (SEM) studies has been the topic of many studies.The required sample sizes for Confirmatory Factor Analysis (CFA) model and simple or complex SEM models vary.Various factors such as the number of indicators, factors, and latent variables can influence the sample size (Muthen & Muthen, 2002).In many studies, the analyses compatible with a normal distribution and maximum likelihood prediction with 10 individuals per variable were included in the model as ideal.In other words, for a 10-variable model, there is a need for 10 individuals per variable, so there must be at least 100 people in the analysis (Bentler & Chou, 1987;Kline, 2005).Similarly, when there is no missing variables and the data is appropriate for a normal distribution, having a 150-person sample size is considered to be sufficient (Anderson & Gerbing, 1984;Muthen & Muthen, 2002).It is emphasized that when the number of indicators in a factor is too high, the sample size can be decreased (Muthen & Muthen, 2002).The general opinion about sample size in SEM studies is that 200 participants are enough (Jackson, 2001).In multiple group studies, Kline (2005) stated that having 100 individuals in each group is enough.In this study, the number of successful students in the disadvantaged group could not reach 200; however, it did exceed 150.The model was implemented on the large samples randomly selected according to the PISA Turkey data, and the model was confirmed with its form in this study.Therefore, the sample size was considered to be sufficient by the researchers; however, though it should be noted as a limitation.

Data Collection
In the study, the form B data that provides the most information about student characteristics was used to describe the structural model depending on the number of students accessing the item.The data about students' affective characteristics such as their interest in mathematics, motivation level, self-perception, statements such as teachers' behaviors in the classroom in learning-teaching process, and sense of belonging to the school are collected through the student survey (MEB, 2015).The data collected from each country was brought together in the OECD database.The responses to these statements were accessed through the codes posted on the OECD website.

Data Analysis
In the data analysis, the premises were checked and the data was organized to be appropriate for the analysis.The scales related to the characteristics of the students were examined through CFA.The variables to be included in the student characteristic model were determined and the consistency of the model with the whole data was confirmed through CFA.The invariance of the model in high or low success groups was investigated through the multiple group CFA.In order to reveal the relationships between student characteristics and mathematics achievement, the SEM in LISREL 8.80 program was used.
Studies investigating the achievements of disadvantaged students have mostly used Linear Regression Analysis.In traditional regression models, the measurement errors in the independent variable are ignored.At this point, the regression results may not be sufficiently explanatory.The SEM includes the measurement errors in the observed variables (dependent or independent) and the direct or indirect influences of variables in the process of analysis.Therefore, this enables to obtain values for testing, prediction, or development of complex models (Kline, 2005;Raykov & Marcoulides, 2006).Similarly, these relationships can be revealed visually with the help of path diagrams.On the other hand, when the regression coefficients are compared between groups, SEM is preferred instead of Regression Analysis because it enables keeping the errors, factor loadings, and correlations between factors of the observed coefficients under control.

The analysis of premises:
The data were analyzed with SPSS 20.00 in terms of lost value and normality.Because it may lead to changes in the results of the analyses, first the missing variables were investigated.In the sample from Turkey, the students belonging to the disadvantaged group that did not answer the student survey were excluded from the analysis as missing variables.The remaining 391 values were analyzed for any outliers with one variable.The items that exceeded the calculated z value ± 3.00 were excluded from the analysis.
Because the SEM is a multivariate analysis, the cleanness from multivariable surplus values was tested by calculating the Mahalanobis Distance.These distances revealed a chi-square distribution whose degree of freedom is the sample size and, when p<.00, they prove multivariable outlier observations (Kline, 2005;Stevens, 2009).The results revealed the data did not have multivariate outliers; therefore, it was not possible to test the multivariate normality assumption since it requires many linear combinations in SEM.Therefore, a univariate normality analysis for each observed variable is recommended (Weston & Gore, 2006).To decide whether the values are normal, the kurtosis and skewness values for each independent variable used in the study and the ratio of their mean scores to their standard deviation (dependent change coefficient) were considered.The results revealed the variables were suitable for normal distribution.When regression analysis was conducted on the variables to be considered for the SEM, their tolerance values were at the desired level with Variance Inflation Factor (VIF) values being far below 10, and Condition Index (CI) values being under 30.These results suggest there was not a multiple linkage problem between the items (Büyüköztürk, 2010;Gujarati, 2004;Kline, 2005;Stevens, 2009).

The analysis of student surveys:
In this study, the variables in the PISA student survey thought to explain mathematics achievement were analyzed using the CFA to determine their factor structures.The factors revealed from the confirmation of the model-data compatibility characteristics in the student survey are presented in Table 1.
The mathematics anxiety scale was confirmed as a two-factor form.The anxiety sub-dimension consisted of five items and their factor loadings ranged between .46 and .76.The factors loadings in the sub-dimension of belief in becoming unsuccessful in mathematics ranged between .41 and .63.Following CFA, the values of RMSEA=.06,χ2/df=2.27,CFI=.96,GFI=.95, and SRMR=.04NNFI=.95 were obtained.Students' characteristics towards schools consisted of three dimensions: learning outcomes, learning activities, and belonging to the school.The sub-dimension of learning activities consisted of four items: Schools' role in preparing students for the university, providing a good occupation opportunity, difficulty of studying, and providing a good graduation score.The factor loadings of the items ranged between .68 and .72.The learning outcomes sub-dimension consisted of four items and their factor loadings ranged between .26 and .68.The sub-dimension that measures students' sense of belonging to the school includes nine items.The factor loadings in this dimension were between .41 and .62.The CFA results confirmed a three-factor form.Following CFA, the values of RMSEA=.09,χ 2 /df=3.51,CFI=.92,GFI=.87, and SRMR=.07NNFI=.91 were obtained.Teacher characteristics consisted of five factors that are teacher support, teacher-student relation, teacher-directed instruction, formative assesment, and student orientation as a result of CFA.The teacher support factor consisted of four items.The factor loadings of the items ranged between .50 and .74.The sub-dimension of teacher-student relations consisted of five items and their factor loadings ranged between .30and .69.The sub-dimension of student orientation was tested with four items in five stages.The factor loadings of the items ranged between .55 and .59.The sub-dimension of formative assesment consisted of four items and their factor loadings ranged between .50 and .67.Teacher directed instruction behavior consisted of five items and their factor loadings ranged between .57and .61.Following CFA, the values of RMSEA=.04,χ 2 /df=1.63,CFI=.97,GFI=.92,SRMR=.05, and NNFI=.97 were obtained.The fit indices of the model indicated that the teacher characteristics were confirmed as a five-factor form in both groups.
Constructing the model: At this stage, the invariance of the model of the students' characteristics towards mathematics was first investigated.Measurement of invariance means the relationship between the latent and observed variables were found to be the same between the groups (Widaman & Rice, 1997).It is advised that the individuals in different groups should have equal probability of getting a particular point when measured in terms of the same characteristic.If the groups have the same actual score, the observed scores should be the same (Collins & Lanza, 2010;Wu, Li, & Zumbo, 2007).At this point, the scale does not provide any advantage for one of the groups.
One of the most common and accepted techniques for examining the measurement invariance is the Multiple Group Confirmatory Factor Analysis (MG-CFA) as it is a powerful and versatile approach.In this analysis, the parameters obtained from the models, in which the parameters are released between the groups, and from the model, in which the parameters are restricted, were compared gradually and tested in four stages that are configural, scalar, powerful, and strict invariance (Meredith, 1993).Once an invariance phase was reached, the other was conducted.
Configural invariance means the factor structure does not vary among groups (Vandenberg & Lance, 1998).Configural invariance is provided when fit indices are in the acceptable range and the next stage, scalar invariance, can be investigated.In order tohave the same values between groups, the factor loadings of the model are limited (Cheung & Rensvold, 2000).The hypothesis that the regression constant does not vary between groups is tested at the powerful invariance.At the stage of strict invariance, the variance regarding the regression surplus was restricted to be equal among groups (Wu et al., 2007).
In the model invariance test, the differences between the CFI values obtained in the progressive models were investigated (Cheung & Rensvold, 2002;Hu & Bentler, 1998).Because this difference was between the range -.01≤∆CFI≤.01, the model invariance was ensured (Cheung & Rensvold, 2002;Wu et al., 2007).Once the student characteristics model was invariant in the sub-groups, the structural model was established by adding the mathematical performance as the second level latent variable.SEM are a comprehensive statistical technique used to test the models involving the hypotheses regarding the casual and correlational relationships between the observed and unobserved (latent) variables (Hu & Bentler, 1995).The theoretical structural model intended to be established by adding mathematical literacy performance is shown in Figure 1.The constructed structural model was compared by limiting factor loadings, correlations between factors, and error variances between high-and low-achieving groups.The ranges of χ 2 /df<3.00,CFI and NNFI>.90,GFI>.85,RMSEA<1.00, and SRMR<.08 were considered in the analysis of model-data consistency (Hu & Bentler, 1995;Tabachnick & Fidell, 2001).

Results
In this part of the study, the measurement model was tested in terms of the model-data consistency in all data and sub-groups through CFA prior to the analysis of the structural model.Fit statistics regarding the measurement model are presented in Table 2.The invariance of the confirmed measurement tool in high-and low-achieving groups was investigated using MG-CFA.The fit statistics obtained at the invariance stages are presented in Table 3.As seen in Table 3, the model of students' characteristics towards mathematics met the configural invariance and each factor structure was the same in the achievement groups (χ2=3.02,RMSEA=.10,CFI=.90).Because the differences between CFI values obtained in the stages of scalar, powerful, and strict invariance were within the acceptable range, the structured model met the full invariance conditions in the low-and high-achieving groups.As a result, measurement model can be used in examining the structural model in order to measure the variables related to mathematical literacy in high-and low-achieving groups.
In the study, a structural model was constructed in order to determine the variables related to the mathematical performance in the disadvantaged high-and low-achieving groups by constraining factor loadings, the correlations among factors, and the error variance.The values kept constant in both groups have yellow arrows.Because the relationship between students' characteristics in each group and the mathematical performance vary between groups, the arrows are blue and the obtained regression indices are different in the groups.The standardized regression indices (beta) and fit indices are presented in Table 4 and the values according to the achievement groups are displayed in Figure 2.
As seen in Table 4, the χ 2 /df and RMSEA values were calculated as χ 2 /df =2.37 and RMSEA=.08.Values of CFI=.90 and NNFI=.90 indicated that the model structured between students' characteristics and the mathematical performance was acceptable.When the standardized indices were examined, the standardized factor loadings were obtained as .28 and .87 between the affective characteristics towards mathematics and the observed variables and .44 and .92 between the anxiety variable and the observed variables.The factor loadings between the variable of the attitude towards the school and the observed variables ranged between .60 and .75.The factor loadings between the latent variable of teacher characteristics and the observed variables were between .52 and .86.In the literature, the standardized value criterion is accepted as low when it is .10,medium when approximately .30, and good when it is .50and above (Şimşek, 2007).The t values obtained in the structural model in Figure 2 reveal the variables of the affective characteristics towards mathematics (t=2.41) and the attitude towards the school (t=-3.58)and they were the variables that significantly explained the mathematical literacy performance of the disadvantaged high-achieving students in Turkey.Students' affective characteristics towards mathematics were a positive predictor of student performance.A unit increase in the affective characteristics created an increase of .26units in their mathematical performance.The attitude towards the school was a negative predictor of the student performance.A unit increase in the attitude towards the school decreased the student performance by .38 units.The anxiety towards mathematics (t=-.02) and teachers' characteristics (t=-.77) did not have a significant effect on student performance.
According to Figure 2, only the variable of the attitude towards the school (t=2.19) was a positive predictor of the mathematical literacy performance in the low-achieving group.This variable created a .20-unitincrease in the mathematics performance.The variables of the affective characteristics towards mathematics (t=-.79),anxiety (t=.74), and teacher characteristics (t=-1.49)did not have significant effects on student performance.

Discussion, Conclusion & Implementation
The results revealed that the variables of the affective characteristics towards mathematics and the attitude towards the school were the variables that explain the mathematics achievement of socioeconomically disadvantaged high-achieving students.The mathematics anxiety and teacher characteristics did not have a significant role in the mathematics performance of the students in this group.Only the variable of the attitude towards the school had a significant effect on the mathematics achievement of the socioeconomically disadvantaged low-achieving group.The anxiety towards mathematics, affective characteristics towards mathematics, and teacher characteristics did not have significant effects on the mathematics achievement of the students in this group.

High-Achieving Group
Low-achieving Group Figure 2.The relationship between mathematical performance and students' characteristics according to achievement groups.
The first result of the study indicated that the mathematics achievement of the disadvantaged highachieving students is positively affected by students' affective characteristics towards mathematics.The literature describes negative attitudes towards mathematics as one of the reasons for failure in mathematics.Self-perception and self-confidence are listed among the important variables related to mathematics achievement (Demir, Kılıç, & Ünal, 2010;Johnson, 2000;Lee & Stankov, 2013;Linnakyla & Malin, 2008;Tapia & Marsh, 2000;Yenilmez & Özabacı, 2003).In this regard, this result is consistent with the literature.While many studies have supported this evidence, some studies have found that there is not a significant relationship between the affective characteristics and the achievement or proposed high attitude towards low achievement.Peker and Mirasyedioğlu (2003) indicate that even though approximately 70.00% of the students failed the mathematics course, they have positive attitudes towards mathematics.In this study that categorized the students' mathematics performance as low, medium, and high competence level based on the PISA 2012 Turkey data without a socioeconomic differentiation, it was determined that the affective characteristics towards mathematics did not have an explanatory effect on student performance.When considered with the competency levels, this variable was found to be a significant explanatory predictor of the student performance at a low level (MEB, 2015).Therefore, this result is consistent with the general tendency in the literature.However, this result should be regarded with the knowledge that this study was limited to the socioeconomically disadvantaged students and the anxiety and affective characteristics towards mathematics are measured with a limited number of items in the PISA.The insufficient number of participants and items and the possibility of perceptions and tendencies to come to the forefront in the responses to the items might have led to these results.
Another significant result of the present study is that students' attitudes towards the school significantly predicted mathematics performance in both high-and low-achieving groups.This variable positively explained student performance in the low-achieving group and increased the performances by .29-units;yet, it negatively explained student performance in the high-achieving group.On the other hand, the study conducted by Borman and Overman (2004) investigating reasons of failure in mathematics for students from low socioeconomic status reported positive attitudes towards the school as one of the most important characteristics of high-achieving students.Another study highlighted that the disadvantaged high-achieving students establish stronger connections with the school and attach more value to the school compared to the low-achieving ones (Gonzales & Padilla, 1997).While there were some studies asserting that positive attitudes towards school do not affect achievement (Adıgüzel & Karadaş, 2013;Yavuz, 2015), the general tendency in the literature is that it improves achievement (Cheng & Chan, 2003;Ford & Ill, 2008;Lamb & Fullarton, 2002;Malindi & Machenjedze, 2012;OECD, 2003;Tatar, 2006).In fact, the academic achievement of a student who does not like the school and does not like going to the school cannot be expected to be the same as the academic achievement of a student who likes the school, enjoys going to the school, and cares about the school.Therefore, the reverse relationship between the socioeconomically disadvantaged high-achieving students with these variables is noteworthy.The positive attitudes towards school consitute a protective factor (Maddox & Prinz, 2003) and this serves as a bridge between student-school and student-achievement for disadvantaged students (Ungar & Liebenberg, 2013).Therefore, as the students' positive attitudes towards the school increases, their level of academic resilience (Malindi & Machenjedze, 2012) and academic achievement (OECD, 2003) increase and the dropout rates decrease (Orfield, 2004).Considering this and the related results from this study, the socioeconomically disadvantaged highachieving students can show a high performance independent from their attitudes and sense of belonging towards the school.
Another result revealed that teacher characteristics are not a significant predictor in both high-and low-achieving groups.The PISA national final report indicated that teacher characteristics are a significant predictor at the low and medium competency levels.According to this report, a unit increase in teacher characteristics corresponds to a .17-unitdecrease in student performance at the low competency level and a .10-unitincrease at the medium competency level.Even though both studies were based on the PISA 2012 data, this study was conducted with the students in the lowest 33.00% in terms of socioeconomic status and the lowest and highest 33.00% in terms of achievement.Therefore, the study groups of the two studies are different, which may cause the contradiction in the results.Other studies on this issue emphasized the crucial effect of teacher characteristics on students' academic resilience (Benard, 1997).The achievement gap between students with low and high income is largely closed by qualified teachers (Borman & Kimball, 2005;Dünya Bankası, 2011).However, teachers' effect on students' achievement can differ from school to school (Konstantopoulos, 2009) and teachers' effect on students' achievement decreases in the schools with low socioeconomic status (Ferguson, 1998).It is more likely for students from a low socioeconomic status to receive their education in schools from teachers with lower qualifications and experience (Ferguson, 1998;Krei, 1998;Langford, Loeb, & Wyckoff, 2002).For this reason, this result can indicate the absence of teachers who can protect, raise, and support students against the negative effect of parents and the environment in the schools in which the socioeconomically disadvantaged students receive their education or students.Alternatively, students may not have the perception that their teachers have such qualifications.Considering this possibility and the results of this study, providing a positive change in teacher characteristics in Turkey can also lead to an increase in the mathematics achievement of the socioeconomically disadvantaged high-achieving students and improve the academic resilience of the low-achieving students in the same socioeconomic status.
The limitations of the study should be considered when discussing the results of the study.This study was conducted with the students in the lowest 33.00% according to the socioeconomic index and in the lowest and highest 33.00% according to the mathematics score average on the PISA 2012.Therefore, it was not possible to increase the sample size.This situation may have influenced the generalizability of the study.The variables that can be constantly scored were included in the study since the sample size was not very large.Mathematical literacy can be influenced by other factors than discussed.However, this study focused on the affective characteristics that can reveal students' academic resilience.
In this part of the study, some suggestions are provided based on the results: 1) Considering the effect of affective characteristics towards the lessons on the academic achievement of the disadvantaged high-achieving students, preventive guidance practices that develop students' self-control, improve students' self-esteem and self-respect, and encourage students to develop positive attitudes towards lessons are vital.
2) Apart from the individual support, support programs can be developed that provide teachers to support students and establish relationships with students based on commitment and trust in order to increase and strengthen teachers' support for students.
3) Further studies can investigate the reasons for the negative relationship between the attitudes towards the school and the academic achievement of the socioeconomically disadvantaged highachieving students.

Figure 1 .
Figure 1.The model established theoretically between student characteristics and mathematics achievement.

Table 1 .
The Factors towards Student Characteristics that Explain Mathematics Achievement of Turkey in the PISA 2012 and the Observed Variables.

Table 2 .
Fit Statistics Regarding the Measurement Model.

Table 3 .
The Fit Statistics Obtained at the Invariance Stages According to Achievement Groups.

Table 4 .
The Indices of Structural Equation Model Between Students' Characteristics and MathematicsAchievement.