Effect of math-specific self-efficacy on math literacy: Evidence from a Greek survey

Abstract

Prior research has suggested a strong link between student-level psychological constructs such as self-efficacy and achievement in academics. In this study, we looked at the relationship between math self-efficacy and mathematics literacy using a large-scale survey from Greece. Our analytical results show that there is a strong association between math self-efficacy and math literacy among Greek high school students, and that this association persists even after controlling for student-level differences such as age, grade, gender, parental education, parental occupation, family wealth, cultural possessions, and availability of educational resources at home, and school-level differences such as school type, school size, student–teacher ratio, and school-level socioeconomic status.

Keywords

Mathematics self-efficacy literacy Program for International Student Assessment multiple regression

Background

Self-efficacy is a measure of an individual’s perception of own ability to complete a specific task or to accomplish a certain goal. According to Bandura’s (1988) social cognitive theory, self-efficacy can play an important role in determining how an individual perceives and approaches various tasks and goals. Individuals with high levels of self-efficacy approach problems as tasks that must be mastered while those with low self-efficacy see them as hurdles to be avoided (Bandura, 1998). Thus, self-efficacy does not only play an important role in identification of initial goals but also influences the level of motivation towards accomplishing those goals (Bandura, 1993). Bandura’s (1998) social cognitive theory has some overlap with Vygotsky's well-known concept of zone of proximal development from the latter’s sociocultural theory of cognitive development, in the notion that human beings learn from their environments including experiences of others around them (Vygotsky, 1978). Bandura has additionally argued that differences in self-efficacy can result in fundamental differences in how individuals view the world around them. Those with high self-efficacy generally believe that they have a higher degree of control over their lives and what actions they take and choices that they make directly affect their lives. On the other hand, individuals with low self-efficacy generally believe that such actions and choices have little effect on events in their lives and that the course that their lives take falls more or less outside their personal control (Bandura, 2001). Some studies, such as Judge et al. (2002), have asserted that psychological constructs such as generalized self-efficacy, self-esteem, neuroticism, and locus of control, in fact, measure the same underlying factor and are thus highly related concepts. Other studies have highlighted the importance of variables related to self-efficacy such as perseverance, confidence, and motivation (Boaler, 1998; Dweck, 2007). For example, the effect of stereotyping in math education has been shown to have a negative effect on a student’s confidence. Similarly, when students make mistakes and do not have adequate teacher support, they may develop a fixed mind-set and equate their mistakes with their lack of ability in problem-solving (National Association of Mathematics Advisers (NAMA), 2015). Such fixed mind-sets can permanently hinder learning and have long-term consequences (Boaler, 2013; Dweck, 1986).

Prior research has suggested that in an educational context a student’s self-efficacy may be task- or goal specific (Chiu and Xihua, 2008; McConney and Perry, 2010). This means, for instance, that an individual’s self-efficacy in achieving learning goals in mathematics may have different determinants as compared to that student’s self-efficacy in achieving learning goals in reading. Such differences can arise due to the different nature of the two subjects, leading to differences in corresponding tasks to be completed and goals to be accomplished. Thus, when examining the effect of self-efficacy on performance in a certain subject, self-efficacy specific to that subject should be employed as opposed to a general measure of self-efficacy (Pajares and Miller, 1994). For example, when looking at mathematics achievement, self-efficacy is a student’s self-perceived confidence to complete certain mathematical tasks that are considered essential for such achievement.

In context of academic performance, as a prerequisite for many natural science disciplines such as physics, computer science, and engineering, the subject of mathematics tends to enjoy a special attention (Akinwunmi et al., 2014; Tularam, 2010). The learning of mathematics relies heavily on fluency, reasoning, and problem-solving skills. These three dimensions interact with each other and need to be developed in tandem, with metacognitive abilities and psychological constructs such as self-efficacy and self-regulation playing a prominent role in order for learning to be effective (Kramarski and Mevarech, 2003; Robbins, 2011; Zimmerman, 2000). In order to see how self-efficacy affects academic performance in mathematics, it is important to use a math-specific measure of such self-efficacy (Pajares and Miller, 1994). In this context, math performance can be either thought of as math achievement or math literacy. Although most self-efficacy-related empirical research tends to use these measures as substitutes (e.g. Cheema and Galluzzo, 2013; Martin and Veiga, 2010), they are not the same. For example, math achievement focuses on the knowledge that a student has acquired through formal schooling, while literacy measures the student’s ability to use that knowledge in order to solve everyday problems in mathematics. What is important, however, is that prior studies have shown self-efficacy to be an important determinant of math performance regardless of how it is defined (Hacket and Betz, 1989; Multon et al., 1991). Recent research has suggested that in the U.S., math-specific self-efficacy can explain as much as one-fifth of the total variation in individual math performance over and above that attributable to demographic differences (Kitsantas et al., 2010, 2011). Although this hints at a strong relationship, there is evidence in the literature that the nature of this association may not be the same across cultures (Bandura, 2002; Klassen, 2004), thus necessitating a separate examination for each country. An examination of nature and causes of such country-level differences is important because the determinants of academic performance vary across countries. For example, in some countries, academic performance is seen as largely being individual-centered with school-level differences playing a very small role in its variation, while in others between-school differences may be more important (Reynolds et al., 2002). As a result of such differences in the determinants of academic performance are not identical across countries. In countries where academic performance tends to be determined by student-level characteristics, demographic differences such as gender, parental education, socioeconomic status (SES), etc. play a relatively more important role, as opposed to school-level characteristics such as school type, student–teacher ratio, school SES, etc. (Chatterji, 2005; Reynolds et al., 2002). Stobart (2005) suggests that even after controlling for individual- and school-level characteristics, issues such as equity and fairness in assessment can distort observed relationships among variables of interest. Thus, for instance, a student with a high level of self-efficacy may perform poorly on a mathematics test simply because the test items may be set in a socioeconomic or cultural context that is foreign to the student. An examination of such factors usually cannot be accomplished without relying on large-scale samples. Results based on such samples are readily generalizable to large populations and thus tend to have national relevance.

Several past empirical studies have looked at the relationship between math-specific self-efficacy and math achievement using nationally representative samples from inside and outside the U.S. For example, using a U.S. sample of 4784 students nested in 264 schools, Kitsantas et al. (2011) looked at the effect of data aggregation and disaggregation on the relationship between math self-efficacy and math achievement. Their results were based on aggregated and disaggregated ordinary least squares (OLS) multiple regression equations, and hierarchical linear models (HLMs), and indicated that regardless of the analytical method used, self-efficacy consistently came out as a major predictor of math achievement, with a one standard deviation (SD) increase in math self-efficacy being associated with anywhere between two-fifths and one-half of an SD increase in math achievement. This study controlled for demographic differences such as age, gender, race, and SES at both student and school levels. In a related study, Kitsantas et al. (2010) used a nationally representative sample of 5200 high school students from the U.S in order to examine how the relationship between math self-efficacy and math achievement was moderated by the amount of time spent on math homework. Their results were based on OLS multiple regression and multivariate analysis of variance (MANOVA), and indicated that although the effect of amount of time spent on math homework was small and there was no interaction effect between math self-efficacy and the amount of time spent on math homework, math self-efficacy managed to explain as much as 20% of the total variation in math achievement after controlling for individual student differences such as gender, race, amount of time spent on math homework, and availability of math-related educational resources at home. This study did not include any school-level variables, and its results were generalizable only to the U.S. population.

McConney and Perry (2010) used a nationally representative sample of 12,500 15-year-old students from 320 schools in Australia in order to investigate the relationship between SES and academic achievement as moderated by math-specific self-efficacy and reported that within both low and high socioeconomic groups, students with high self-efficacy outperformed their low-efficacy counterparts by as much as one full SD on math achievement. Their results had important Australia-specific implications, such as the effect of school SES on math achievement is strongest for students who have low SES but high self-efficacy, and weakest for those with high SES but low self-efficacy.

Using a multilevel mediation model, Yıldırım (2012) investigated, among other variables, the relationship between math self-efficacy and math achievement in a nationally representative sample of 4855 Turkish high school students. Her findings suggested the existence of a strong relationship between math self-efficacy and math achievement. Ignoring the effect of any other variables, math self-efficacy explained approximately 21% of the variation in math achievement. After controlling for gender and SES, math self-efficacy and math anxiety together accounted for approximately 16% of the total variation in math achievement. These reported percentages are low relative to those from comparable U.S. samples (Kitsantas et al., 2010; Malpass et al., 1999).

In addition to these examples of nationally representative survey-based studies, several recent small-scale empirical studies have also reported evidence of a strong relationship between math self-efficacy and math achievement. For example, using a sample of 144 primarily Asian American students, Malpass et al. (1999) showed that self-efficacy had a strong effect on math achievement. Ignoring the effect of any other variables, math self-efficacy explained approximately 32% of the variation in math achievement in this sample. In a similar but comparative study of Taiwanese (n = 188) and U.S. (n = 107) students, Chen and Zimmerman (2007) found significant differences in self-efficacy, math performance, and the association among these variables between these two groups of students. More specifically, they found that on average Taiwanese students had higher math self-efficacy and exhibited superior math performance, with American students reporting their self-efficacy less accurately as compared to their Taiwanese counterparts. Although such small-scale studies are important, as these two examples show their findings have very limited application because they are based on very small samples (Chen and Zimmerman, 2007, n = 295; Malpass et al., n = 144) and because the analytical models considered in these studies do not account for important school-level differences (this latter limitation being a function of the former). In addition to the effect of self-efficacy, past research has identified individual-specific factors such as gender, race, SES, parental education, etc., and school-specific variables such as school type (private, public), school SES, school climate, student–teacher ratio, etc. as important determinants of mathematics performance, factors that have the potential to modify the relationship between self-efficacy and math performance. A detailed discussion of these factors is beyond the scope of this paper. For examples of published literature reviews, we refer the readers to Harris and Herrington (2006) for race, Haynes et al. (1997) for SES, Hembree (1990) and Ma (1999) for anxiety, Martin and Veiga (2010) for parental education, Zimmerman and Kitsantas (2005) for self-efficacy, and Carbonaro (2006) and Heyneman (2005) for school type and student–teacher ratio. Inclusion of such student- and school-specific factors in empirical models of student performance is important in order to avoid a specification bias (Gujarati, 2003).

In context of the relationship between self-efficacy and academic performance using large-scale surveys, the case of Greece is interesting for several reasons. First, large-scale assessments such as the Program for International Student Assessment (PISA) have received attention in Greek media and political forums, where low scores of Greek students relative to other OECD countries have been seen as a source of concern (Anagnostopoulou et al., 2010). Second, despite this attention, there remains a significant lack of empirical research based on nationally representative samples that can help shed more light on the nature and causes of low performance among Greek students (Apostolopoulos et al., 2008). Given the importance of self-efficacy as a determinant of mathematics performance, an empirical study of this relationship with findings generalizable to a large segment of Greek student population can thus be invaluable toward understanding the variation in student math performance.

The examples of empirical studies provided earlier in this section indicate not only that the relationship between math achievement and math self-efficacy is important and can differ between countries but also that, given the potential existence of strong moderating effects, any analytical study examining the relationship between these two variables must adequately control for individual- and school-level characteristics. In this study, we investigate the relationship between math self-efficacy and math literacy using a large-scale survey from Greece. To our knowledge, no prior study has investigated this relationship for the high school student population in Greece and given cross-country differences in educational systems, findings from other countries may not be relevant or fully applicable to Greece (e.g. Chen and Zimmerman, 2007; McConney and Perry, 2010). Our study bridges this gap by specifically linking the variables of interest to a Greek population. By relying on recent data, this study provides information about our variables of interest that is current for Greece. The specific research questions that this study examines are: (1) is there a relationship between math self-efficacy and math literacy? and, if such relationship exists then, (2) does it persist after controlling for important student- and school-level differences?

Method

Sample and participants

We extracted student- and school-level data from the PISA (OECD, 2012, 2014b) student and school data files. PISA is an international assessment of literacy of 15-year-old students in areas such as mathematics, reading, and science that is overseen by the OECD and administered by national educational authorities across 65 OECD and non-OECD participant countries. In addition to the assessment component, PISA contains separate surveys for students and school administrators who collect a variety of information covering background characteristics, beliefs, attitudes, and perceptions about various topics of interest (OECD, 2013). PISA has a three-year assessment and survey cycle with one of the three literacy areas, mathematics, reading, and science being the focus in a given survey year. The focus area for 2012 was mathematics, and results from this assessment/survey cycle were made available by OECD in December 2013. PISA samples are nationally representative and are selected using a two-stage process in which schools across the entire country are randomly selected in stage 1 using a stratified design. This is followed by a random selection of students within each selected school in the second stage. The next PISA assessment with focus on mathematics will take place in 2021.

For the purposes of this study, we extracted the sample of all students from Greece who responded to items forming the math self-efficacy scale and who had valid values for all other variables of interest in this study. This resulted in an overall sample of 2748 students from 142 schools, of whom 51% (n = 1403) were girls and 49% (n = 1345) were boys. All of the students in our sample were 15 years old with variation in age measurable in months and all were enrolled in grade 10. A majority of these students attended public schools (n = 2540, 92.4%), while the rest attended private schools (n = 208, 7.6%). About nine-tenths of funding for public schools came from the government (M = 88.57%, SD = 12.82%) with the rest accounted for by private sources and minor student fees. For private schools, almost all funding came from student fees (M = 98.0%, SD = 2.12%) with the balance attributable to private sources. School size ranged from 20 to 1172 students (M = 286.05, SD = 159.91), while student–teacher ratio at school ranged from 1.09:1 to 34.47:1 (M = 9.13, SD = 3.40).

Measures

Math literacy

The main objective of the math literacy assessment in PISA is to determine the readiness of students who are about to approach the end of their compulsory schooling in coping with math-related challenges that they are expected to face in their everyday lives after leaving school. In this respect, PISA does not measure the extent to which students have mastered math skills at school, but rather it focuses on measuring what students are capable of doing with what they have learned (OECD, 2012). This is different from achievement that focuses on the measurement of knowledge that has been accumulated during time spent at school. PISA procedures for ensuring that this measure has construct validity are very comprehensive and involve expert panels and extensive pilot testing of mathematics assessment items in participating countries before the final set of items is fielded (OECD, 2012).

The math literacy assessment in PISA 2012 was based on multiple-choice, open-ended, and fill-in-the-blank type items with scores for each individual student reported as a set of five plausible values. While actual test items are not released by PISA, sample items are available that can be examined in order to form an overall idea about what is measured by an assessment of math literacy (OECD, 2014a). A sample item included, “Mount Fuji is only open to the public for climbing from 1 July to 27 August each year. About 200,000 people climb Mount Fuji during this time. On average, about how many people climb Mount Fuji each day?” Response choices for this item were A (340), B (710), C (3400), D (7100), and E (7400). More sample items for mathematics assessment are available at OECD (2006b). The plausible values for a student represent random draws from the posterior distribution of all scores that can be reasonably assigned to that student (Mislevy, 1991; Mislevy et al., 1992). The plausible value approach allows explicit modeling of uncertainty associated with measuring a true score (Wu, 2005). The method of dealing with multiple plausible values is the same as that for dealing with multiple imputation estimates as outlined by Rubin (1987), which involves repeating statistical analyses separately with each plausible value and then calculating a weighted average of parameter estimates and their standard errors. In order to avoid artificially reducing the variability in parameter estimates, plausible values should not be averaged, rather the analyst should either choose one of those values for analysis or, as stated earlier, repeat the calculations as many times as there are plausible values (Brown and Mickleright, 2004; Von Davier et al., 2009). In this study, we have followed the former approach. We note that each plausible value vector is a measure of the same unidimensional math literacy construct for students included in our sample.

The student math literacy scores were reported in PISA 2012 as standardized values with a mean of 500 and an SD of 100 for OECD countries. Since our sample includes students from Greece only, we rescaled these scores to have a mean of 0 and an SD of 1 in our sample. The inter-plausible value correlations ranged between .89 and .90 (p < .001 for all r; M = .89, SD = .003) suggesting a very high degree of substitutability among the five values. Given such high associations, we elected to use one plausible value for analysis. For this purpose, we randomly chose one of the five available plausible values and used it for all statistical analyses. After standardization the mean literacy, score ranged between −3.25 and 3.16 (M = 0, SD = 1) for the 2748 students in our sample. A histogram of the distribution of student mathematics literacy in our sample is presented in Figure 1.

Figure 1.

Histogram of student mathematics literacy score in the Greek portion of PISA 2012 sample (n = 2748).

Math self-efficacy

This scale measures a student’s perception of own efficacy in completing math-related tasks. The scale had eight underlying items with Cronbach’s alpha of .83 in our sample. The inter-item correlations ranged between .13 and .73 (M = .38, SD = .11). A sample item included, “How confident do you feel about having to do the following calculation: Calculating how many square meters of tiles you need to cover a floor?” The response categories for each item were 1 (very confident), 2 (confident), 3 (not very confident), and 4 (not at all confident). The scale was inverted, so that higher scores on the scale are representative of higher self-efficacy. Responses from the eight self-efficacy items were combined into a weighted likelihood estimate (WLE) using an item response theory (IRT) model based on Warm (1989) that was adapted for PISA (OECD, 2006a). The value for math self-efficacy scale in our sample ranged between −3.54 and 2.36 (M = 0, SD = 1).

Student-specific controls

We used student-specific variables in order to control for between-student differences in our analysis. These variables include gender, parental education, parental occupation, family wealth, cultural possessions, and availability of educational resources at home.

Gender: This is a nominal variable that takes a value of 0 for boys and 1 for girls. Thus, the reference category is boys.

Parental education: This variable equals the higher of the number of years of schooling for a student’s father or mother. In our sample, this variable ranged between 3 years and 17 years (M = 14.06, SD = 2.94). Standardized values of this variable ranged between −3.77 and 1.00 (M = 0, SD = 1).

Parental occupation: The index of parental occupation is based on the International Socio-Economic Index of Occupational Status (ISEI) developed by Ganzeboom et al. (1992) and adapted for the PISA student questionnaire. In our sample, the value of this index ranged between 11.01 and 88.96 (M = 49.31, SD = 22.94) before standardization and between −1.67 and 1.73 (M = 0, SD = 1) after standardization. Higher values on this index represent more prestigious occupations.

Family wealth: This variable indexes a student’s family wealth based on student’s access to resources such as a personal room, availability of internet at home, and household ownership of items such as dishwasher, DVD player, etc. The value of this index ranged between −5.83 and 3.84 (M = 0, SD = 1) in our sample.

Cultural possessions: This variable indexes cultural resources such as classical literature, books of poetry, and works of art possessed by a student’s family. This is a standardized variable and in our sample, and the value of this index ranged between −1.51 and 1.27 (M = 0, SD = 1).

Home educational resources: This variable indexes the educational resources available to a student at home and is based on the student’s access to resources such as a study desk, a computer that can be used for school work, a dictionary, educational software, etc. The value of this index ranged between −4.01 and 1.32 (M = 0, SD = 1) in our sample.

In addition to the aforementioned student-specific controls, our sample automatically controlled for age and grade as all students were 15-year-old and enrolled in grade 10.

School-specific controls

We used school-specific variables in order to control for between-school differences in our analysis. These variables include school SES, school size, school type, and student–teacher ratio at school.

School SES: This variable is the average SES level of all students in a school. As a standardized variable, school SES has a mean of 0 and an SD of 1. In our sample, school SES ranged between −2.91 and 2.70.

School size: This is the total school population that comprises of total number of boys and total number of girls enrolled in a school. This variable was also standardized and ranged between −1.66 and 5.54 in our sample (M = 0, SD = 1).

School type: This is a categorical variable that takes a value of 0 for private schools and a value of 1 for public schools. Thus, the reference category is private school. A public school is defined as any school managed directly or indirectly by a government department or agency, while private schools are those that are directly or indirectly managed by private bodies and include those run by private businesses, churches, and other nongovernmental organizations (OECD, 2011).

Student–teacher ratio at school: This variable is the ratio of total number of students to total number of teachers at school. The ratio was standardized to have a mean of 0 and SD of 1 and ranged between −2.37 and 7.46 in our sample.

Analytical method

We used both bivariate and multivariable methods in order to examine the relationship of math literacy scores with math self-efficacy, and student and school characteristics. For bivariate analysis, we used zero-order Pearson product moment and point biserial coefficients of correlation in order to test for significant associations. For multivariable analysis, the nested structure of our data makes multilevel modeling methods such as HLM, an attractive choice (intraclass correlation coefficient (ICC) = 0.39). However, we note that the number of students sampled from some schools included in our data set was as small as two which is not sufficient for HLM purposes. As an alternative, we chose OLS multiple regression for our multivariable analysis. Since this method has the potential to produce inflated standard errors, we encourage the readers to pay careful attention to clinical significance by looking at effect sizes rather than relying on statistical significance alone. We estimated three nested multiple regression models where math literacy score was the dependent variable, and student characteristics, school characteristics, and self-efficacy were predictors. Model 1 included only student-level predictors, Model 2 included both student- and school-level predictors, and Model 3 included all predictors from Model 2 in addition to self-efficacy and its corresponding two-way interactions with other predictors. This approach allowed us to separate the unique contribution of student characteristics, school characteristics, and self-efficacy towards explaining the variation in math literacy scores. The three regression models are given by expressions (1) to (3).

Y_{i} = β_{0} + \sum_{j = 1}^{6} β_{j} X_{ij} + ɛ_{i}

(1)

Y_{i} = λ_{0} + \sum_{j = 1}^{6} λ_{j} X_{ij} + \sum_{k = 1}^{4} γ_{k} Z_{ik} + ν_{i}

(2)

Y_{i} = π_{0} + \sum_{j = 1}^{6} π_{j} X_{ij} + \sum_{k = 1}^{4} τ_{k} Z_{ik} + π_{7} {SE}_{i} + \sum_{j = 1}^{6} δ_{j} (SE \times X_{j})_{i} + \sum_{k = 1}^{4} θ_{k} (SE \times Z_{k})_{i} + ψ_{i}

(3)

where Y_i is the math literacy score of student i; β’s, λ’s, γ’s, π’s, τ’s, δ’s, and θ’s denote regression coefficients; X’s denote J = 6 student-level control variables; Z’s denote K = 4 school-level control variables; and ɛ, ν, and ψ are student-specific error terms.

In order to aid interpretation, all continuous independent variables were standardized to have M = 0 and SD = 1 in our sample. It should be noted here that although such transformation affects parameter estimates and their standard errors, however, since it is a linear transformation, it has no effect on coefficients of correlation, R² values, and the results of tests of hypotheses (Cohen et al., 2003). We examined the distribution of each variable included in the analysis in order to ensure that the interpretation of z-scores remained valid and was not affected by the presence of outliers. For each multiple regression model, all relevant variables were entered simultaneously in the regression equation. We evaluated assumptions underlying multiple regression, examined the residuals for randomness, and computed R² values to assess adequacy of fit (Tabachnick and Fidell, 2007). Unless indicated otherwise, all tests of hypotheses were evaluated at the 5% level of significance. We used normalized sampling weights and performed all computations with SPSS 22.0. All effect size interpretations are based on guidelines recommended by Cohen (1992).

Results

Bivariate results

Descriptive statistics for math literacy and its determinants are presented by gender and by school type in Table 1. The Pearson correlations for math literacy and its determinants are presented in Table 2. Since gender and school type are dichotomous variables, any correlation involving these determinants is a point biserial correlation estimate.

Table 1.

Descriptive statistics for math literacy score and its predictors by gender by school type.^a

	Boys			Girls
Variable	n	M	SD	n	M	SD
Public schools
Math literacy score	1244	0.04	1.04	1296	−0.14	0.93
Cultural possessions	1244	−0.12	1.00	1296	0.02	0.99
Family wealth	1244	∼0	0.98	1296	−0.12	0.95
Home educational resources	1244	−0.04	1.01	1296	−0.04	0.99
Parental education	1244	0.02	0.98	1296	−0.12	1.02
Parental occupation status	1244	−0.03	0.97	1296	−0.09	1.00
School SES	1244	−0.17	0.88	1296	−0.11	0.87
School size	1244	∼0	0.91	1296	−0.03	1.00
Student–teacher ratio at school	1244	−0.07	0.90	1296	0.06	1.08
Math self-efficacy	1244	0.09	1.06	1296	−0.17	0.90
Private schools
Math literacy score	101	0.74	1.00	107	0.49	0.96
Cultural possessions	101	0.71	0.97	107	0.30	1.01
Family wealth	101	0.70	0.87	107	0.85	0.76
Home educational resources	101	0.70	0.72	107	0.64	0.63
Parental education	101	0.40	0.82	107	0.77	0.82
Parental occupation status	101	0.39	0.94	107	0.48	0.80
School SES	101	0.69	1.02	107	0.73	1.24
School size	101	0.18	1.43	107	0.22	1.46
Student–teacher ratio at school	101	0.02	0.95	107	0.06	1.05
Math self-efficacy	101	1.74	0.82	107	1.64	0.89

SES: socioeconomic status.

Note: n = 2748.

All continuous variables are standardized with M = 0 and SD = 1 for the overall sample.

Table 2.

Pearson product moment coefficients of correlation for math literacy, student and school characteristics, and math self-efficacy.

	r^a
Variable	1	2	3	4	5	6
1. Math literacy score	—
2. Cultural possessions	.25***	—
3. Gender^b	.09***	−.08***	—
4. Family wealth	.14***	.22***	.05**	—
5. Home educational resources	.27***	.35***	∼0	.32***	—
6. Parental education	.28***	.33***	.07***	.28***	.23***	—
7. Parental occupation status	.35***	.34***	.02	.28***	.22***	.60***
8. School SES	.42***	.35***	−.03	.30***	.27***	.42***
9. School size	.07***	.07***	.01	.05**	.04*	.10***
10. School type^b	.18***	.17***	∼0	.20***	.12***	.19***
11. Student–teacher ratio at school	.10***	.10***	−.06**	.04*	.09***	.07***
12. Math self-efficacy	.49***	.25***	.14***	.17***	.24***	.20***
	7	8	9	10	11	12
7. Parental occupation status	—
8. School SES	.47***	—
9. School size	.07***	.21***	—
10. School type	.22***	.48***	.06**	—
11. Student–teacher ratio at school	.08***	.19***	.60***	.01	—
12. Math self-efficacy	.24***	.24***	.05**	.14***	.08***	—

SES: socioeconomic status.

Note: n = 2748.

Effect size interpretation: r = .10, small; r = .30, medium, r = .50, large.

Reference category is male for gender and private for school type.

p < .05; **p < .01; ***p < .001.

Figures in Table 1 suggest that both boys and girls in private schools tend to have higher means on all 10 continuous variables as compared to their public counterparts. On the other hand in general, with few exceptions, within each school type, the difference between boys and girls seems to be small and bidirectional on the 10 continuous variables. These figures give the overall impression that there is no systematic difference between boys and girls in terms of means on included variables. However, there is a systematic difference on those same variables between private and public schools, where students in private schools tend to have higher literacy scores, higher self-efficacy, parents with more education and higher occupational status, more cultural possessions, family wealth, and home educational resources, and their schools tend to have higher SES, and larger student populations.

Figures in Table 2 show associations among math literacy and its predictors with effect sizes ranging from small to large. This interpretation is adapted from Cohen (1992) who classified correlation-based effect size estimates for r = .10, .30, and .50 as small, medium, and large, respectively. Math literacy had a significant relationship with all 11 predictors, with the highest associations observed for self-efficacy, r = .49 (large effect), p < .001, school SES, r = .42 (large effect), p < .001, and parental occupation status, r = .35 (medium effect), p < .001, suggesting that in a bivariate context, these variables individually account for 24%, 18%, and 12% of the total variation in math literacy. To summarize, the correlation matrix presented in Table 2 shows the strongest association of math literacy, our dependent variable, with math self-efficacy, our primary independent variable.

Multiple regression results

Multiple regression results for Models 1 and 2 are presented in Table 3, and results for Model 3 are presented in Table 4.

Table 3.

Multiple regression models predicting literacy in mathematics from student and school characteristics.

					95% CI
Predictor	b	SE(b)	t	p	Lower	Upper
Model 1
Student effects
Cultural possessions	0.09	0.02	4.76	<.001	0.05	0.13
Gender^a	−0.20	0.03	−5.71	<.001	−0.27	−0.13
Family wealth	−0.03	0.02	−1.72	.086	−0.07	0.00
Home educational resources	0.18	0.02	9.56	<.001	0.14	0.22
Parental education	0.07	0.02	3.29	<.001	0.03	0.12
Parental occupation status	0.25	0.02	11.20	<.001	0.20	0.29
Model 2
Student effects
Cultural possessions	0.05	0.02	2.60	.009	0.01	0.09
Gender	−0.23	0.03	−6.80	<.001	−0.29	−0.16
Family wealth	−0.06	0.02	−3.47	<.001	−0.10	−0.03
Home educational resources	0.15	0.02	8.23	<.001	0.11	0.19
Parental education	0.03	0.02	1.33	.184	−0.01	0.07
Parental occupation status	0.16	0.02	7.15	<.001	0.11	0.20
School effects
School SES	0.33	0.02	14.71	<.001	0.28	0.37
School size	−0.05	0.02	−2.58	.010	−0.10	−0.01
School type^a	0.12	0.07	1.66	.097	−0.02	0.26
Student–teacher ratio at school	0.06	0.02	2.80	.005	0.02	0.10

CI: confidence interval; SES: socioeconomic status.

Note: n = 2748. R² is .18 and .25 for models 1 and 2, respectively.

Reference category is male for gender and private for school type. ΔR²= 0.07, p < .001.

Table 4.

Multiple regression model predicting literacy in mathematics from student and school characteristics, and math self-efficacy.

					95% CI
Predictor	b	SE(b)	t	p	Lower	Upper
Model 3
Student effects
Cultural possessions	−0.01	0.02	−0.32	.752	−0.04	0.03
Gender^a	−0.11	0.03	−3.52	<.001	−0.17	−0.05
Family wealth	−0.07	0.02	−4.16	<.001	−0.10	−0.04
Home educational resources	0.10	0.02	5.96	<.001	0.07	0.13
Parental education	0.02	0.02	1.10	.272	−0.02	0.06
Parental occupation status	0.12	0.02	5.84	<.001	0.08	0.16
School effects
School SES	0.29	0.02	14.17	<.001	0.25	0.33
School size	−0.05	0.02	−2.71	.007	−0.09	−0.01
School type^a	0.20	0.07	2.91	.004	0.07	0.34
Student–teacher ratio at school	0.05	0.02	2.53	.012	0.01	0.09
Math self-efficacy	0.37	0.06	5.97	<.001	0.25	0.49
Interaction effects
Math self-efficacy × cultural possessions	−0.02	0.02	−0.90	.371	−0.05	0.02
Math self-efficacy × gender^a	0.08	0.03	2.49	.013	0.02	0.14
Math self-efficacy × family wealth	−0.04	0.02	−2.70	.007	−0.08	−0.01
Math self-efficacy × home educational resources	∼0	0.02	−0.27	.791	−0.04	0.03
Math self-efficacy × parental education	0.02	0.02	0.92	.360	−0.02	0.06
Math self-efficacy × parental occupation status	0.05	0.02	2.36	.018	0.01	0.09
Math self-efficacy × school size	0.03	0.02	1.60	.111	−0.01	0.07
Math self-efficacy × school SES	0.03	0.02	1.56	.120	−0.01	0.07
Math self-efficacy × school type^a	−0.02	0.06	−0.37	.712	−0.15	0.10
Math self-efficacy × student–teacher ratio at school	−0.04	0.02	−2.37	.018	−0.08	−0.01

CI: confidence interval; SES: socioeconomic status.

Note: n = 2748. R²= .38.

Reference category is male for gender and private for school type. For Models 2 and 3, ΔR²= 0.13, p < .001.

Model 1

This model predicted the effect of six student-level predictors on math literacy. With the exception of family wealth, b = −0.03, p = .086, all other predictors had a significant effect on math literacy, p < .001. A 1 SD increase in cultural possessions, home educational resources, parental education, and parental occupation status, was associated with an increase in math literacy of 0.09, 0.18, 0.07, and 0.25 SDs, respectively, after controlling for all other predictors in the model, p < .001. The difference in mean literacy between boys and girls was significant with boys outperforming girls by 0.20 SDs after controlling for all other predictors in the model, p < .001. This model explained slightly under one-fifth of the total variation in math literacy, R²= .18, p < .001. In summary, results for Model 1 suggest that in general student-level factors play an important role in explaining variation in math literacy.

Model 2

This model predicted the effect of six student-level determinants and four school-level determinants on math literacy. For the set of student-level variables, the signs and magnitudes of parameter estimates were similar to those in Model 1, but the pattern of significance was slightly different. With the exception of parental education, b = 0.03, p = .184, all other predictors had a significant effect on math literacy, p < .01. A 1 SD increase in cultural possessions, home educational resources, and parental occupation status, was associated with an increase in math literacy of 0.05, 0.15, and 0.16 SDs, respectively, p < .01, while a 1 SD increase in family wealth was associated with a decrease in math literacy of 0.06 SDs, p < .001, after controlling for all other predictors in the model. The difference in mean literacy between boys and girls was again significant with boys outperforming girls by 0.23 SDs after controlling for all other predictors in the model, p < .001.

For the set of school-level variables, a 1 SD increase in school SES and student–teacher ratio at school was associated with an increase in math literacy of 0.33 (p < .001) and 0.06 (p = .005) SDs, respectively, while a 1 SD increase in school size was associated with a decrease in math literacy of 0.05 SDs (p = .010), after controlling for all other predictors in the model. The difference in mean literacy between private and public was not significant, b = 0.12, p = .097. This model explained about one-quarter of the total variation in math literacy, R²= .25, p < .001, suggesting that school-level predictors explained an additional 7% of the total variation in math literacy over and above that accounted for student-level predictors, ΔR²= 0.07, p < .001. In summary, results for Model 2 suggest that in general both student and school level factors play an important role in explaining variation in math literacy.

Model 3

This model retained all variables from Model 2 but added self-efficacy and all possible two-way interactions between self-efficacy and other predictors to the regression equation. Estimation results suggest that after self-efficacy was included in the model, among the student-level predictors, the partial effect of cultural possessions (b = −0.01, p = .752) and parental education (b = 0.02, p = .272) on math literacy was statistically not significant. All remaining student-level predictors had a significant effect on math literacy with a 1 SD increase in home educational resources and parental occupation status associated with an increase in math literacy of 0.10 and 0.12 SDs, respectively, p < .001, while a 1 SD increase in family wealth was associated with a decrease in math literacy of 0.07 SDs, p < .001, after controlling for all other predictors in the model. With all else in the model held constant, the difference in mean literacy between boys and girls was again significant with boys outperforming girls by 0.11 SDs after controlling for all other predictors in the model, p < .001.

For the set of school-level predictors, with all else held constant, school SES and student ratio had a significant and positive effect on math literacy with a 1 SD increase in these variables associated with an increase in math literacy of 0.29 and 0.05 SDs, respectively, p < .05. A 1 SD increase in school size was associated with a decrease in math literacy of 0.05 SDs, p = .007. The difference in mean literacy between private and public school students was significant, b = 0.20, p = .004, with public school students outperforming their private school counterparts after controlling for all other variables in the model.

The partial effect of math self-efficacy on math literacy was large and significant with a 1 SD increase in such efficacy associated with a 0.37 SD increase in math literacy, p < .001. Of the 12 possible two-way interactions involving math self-efficacy, only 4 were statistically significant, p < .05. The self-efficacy × gender interaction effect suggested that the effect of self-efficacy on math literacy differed significantly between boys and girls, b = 0.08, p = .013. After taking this interaction into account, a 1 SD increase in self-efficacy was associated with an increase in math literacy of 0.45 SDs for girls as compared to 0.37 SDs for boys suggesting that improvements in self-efficacy were associated with a relatively better math literacy performance in girls. The self-efficacy × family wealth interaction effect suggested that the effect of self-efficacy on math literacy varied with family wealth, b = −0.04, p = .007. Substituting family wealth values of M − 1 SD, M, and M + 1 SD, for low, medium, and high family wealth, a 1 SD increase in self-efficacy caused math literacy to increase by 0.41 SDs when family wealth was low; by 0.37 SDs when family wealth was medium; and by 0.33 SDs when family wealth was high. Thus, an increase in family wealth weakened the positive association between self-efficacy and math literacy.

The self-efficacy × parental occupation status interaction effect suggested that the association between self-efficacy and math literacy varied with parental occupation status, b = 0.05, p = .018. Substituting parental occupation status values of M − 1 SD, M, and M + 1 SD, for low, medium, and high parental occupation status, a 1 SD increase in self-efficacy was associated with an increase in math literacy of 0.32 SDs when parental occupation status was low; 0.37 SDs when parental occupation status was medium; and 0.42 SDs when parental occupation status was high. Thus, an increase in parental occupation status augmented the positive association between self-efficacy and math literacy. The self-efficacy × student–teacher ratio interaction effect suggested that the association between self-efficacy and math literacy varied with student–teacher ratio at school, b = −0.04, p = .018. Substituting student–teacher ratio values of M − 1 SD, M, and M + 1 SD, for low, medium, and high student–teacher ratio, a 1 SD increase in self-efficacy was associated with an increase in math literacy of 0.41 SDs when student–teacher ratio was low; 0.37 SDs when student–teacher ratio was medium; and 0.33 SDs when student–teacher ratio was high. Thus, an increase in student–teacher ratio weakened the positive association between self-efficacy and math literacy.

A visual presentation of the four significant interaction effects of model 3 is provided in Figures 2 through 5. In order to aid interpretation and comparison, all figures have identical variables and scales on the vertical and horizontal axes. This model explained about two-fifths of the total variation in math literacy, R²= .38, p < .05, suggesting that math self-efficacy and its interactions with other variables explained an additional 13% of the total variation in math literacy over and above that accounted for by other student and school-level variables, ΔR²= 0.13, p < .001. In summary, results for Model 3 suggest that self-efficacy is an important predictor of math literacy even after controlling for student- and school-level effects.

Figure 2.

Visual representation of the effect of math self-efficacy on math literacy with separate lines for boys (solid line) and girls (dotted line), with dotted reference lines drawn at mean values of plotted variables. Quantities on both axes have standard deviation units.

Figure 3.

Visual representation of the effect of math self-efficacy on math literacy with separate lines for low (dotted line), medium (solid line), and high (solid bold line) parental occupation status, with dotted reference lines drawn at mean values of plotted variables. Quantities on both axes have standard deviation units.

Figure 4.

Visual representation of the effect of math self-efficacy on math literacy with separate lines for low (dotted line), medium (solid line), and high (solid bold line) family wealth, with dotted reference lines drawn at mean values of plotted variables. Quantities on both axes have standard deviation units.

Figure 5.

Visual representation of the effect of math self-efficacy on math literacy with separate lines for low (dotted line), medium (solid line), and high (solid bold line) student–teacher ratio at school, with dotted reference lines drawn at mean values of plotted variables. Quantities on both axes have standard deviation units.

The R² values of .18, .25, and .38 from Models 1, 2, and 3 translate into effect size estimates, f ²= .22, .33, and .61, which can be classified as medium, large, and large, respectively (Cohen, 1992).

Discussion

Prior research has suggested a strong link between student-level psychological constructs such as self-efficacy, and academic achievement. In this study, we looked at the relationship between math self-efficacy and mathematics literacy using a large-scale survey from Greece. Our specific research questions were (1) Is there a relationship between math self-efficacy and math literacy? and, if such relationship exists then, (2) does it persist after accounting for individual- and school-level characteristics. In order to answer these questions, we employed both simple bivariate methods and a multivariable scheme of hierarchical regression models. Our analytical results showed that there is a strong association between math self-efficacy and math literacy among Greek high school students and that this association persists even after controlling for student- and school-level characteristics. In addition to self-efficacy, availability of home educational resources, parental occupation status, school SES, school type, and student–teacher ratio had a positive association with math literacy, while gender, family wealth, and school size had a negative association with such literacy. In this respect, our findings tie in with those reported by past research such as Cheema and Galluzzo (2013) for gender, Caldwell (2010) and Levy (2012) for school type, and McConney and Perry (2010) for variables such as parental education, family wealth, etc. that are related to SES. These findings have several implications.

First, self-efficacy was strongly and positively associated with math performance both before and after controlling for demographic differences. By itself, self-efficacy accounted for anywhere between 13% (with covariates) and 24% (without covariates) of the total variation in math performance. These estimates are not as high as for some other countries such as the U.S. (e.g. Kitsantas et al., 2010), but still, represent medium-to-large effect sizes. An implication for empirical analysts here is that any serious modeling of math performance of Greek high school students should not omit self-efficacy. Such omission has the potential to cause a specification error that in turn can lead to inaccurate estimation of parameter estimates and their standard errors.

Second, we found evidence of a significant interactive effect of gender, parental occupation, family wealth, and student–teacher ratio on the relationship between math self-efficacy and math performance. For each covariate, an increase in self-efficacy was associated with an increase in math performance at all levels of that covariate, with a faster rate of increase observed for girls, students associated with high parental occupation status, low family wealth, and low student–teacher ratio. The implications of these observed interactions are that: (1) If school resources for addressing gender achievement gap due to differences in psychological perceptions are scarce and a choice has to be made about their allocation, then our findings suggest that girls should be given preference over boys because the marginal rate of return from investing such resources in girls exceeds that of boys (these findings are in contrast to those from other countries, e.g. Cheema and Galluzzo (2013) who did not find a significant interaction between gender and self-efficacy for U.S. 15-year-old students); (2) although an increase in self-efficacy is associated with an increase in performance at all levels of parental occupation status, as self-efficacy improves the literacy gap between low and high groups based on parental occupation status also increases. This finding is in line with prior studies that have positively associated SES with academic performance (e.g. Martin and Veiga, 2010). There is little that school administrators can do to change social norms and perceptions about status of various occupations; however, they can use this information to divert school resources in order to further improve self-efficacy and performance of students who come from relatively low occupational status families; (3) since improvements in self-efficacy were associated with an increase in math literacy at a faster pace for students who belonged to low-wealth families as compared to those who came from high-wealth families, an administrator interested in reducing the math literacy gap between low and high-wealth students should focus on improving self-efficacy of the latter group (our finding is in line with prior research (McConney and Perry, 2010) when we consider the fact that family wealth is one component of SES); and (4) low student–teacher ratio has a stronger effect on the positive relationship between self-efficacy and performance as compared to a high ratio. This finding is in line with past research such as Lubienski et al. (2008) and makes intuitive sense because when a teacher has fewer students to work with, that teacher can devote more individual time to them which in turn is expected to raise self-efficacy and performance.

Although our statistical procedures revealed several important relationships between math literacy and its predictors, the findings of this study are applicable only to the target population of Greek students considered in this study. Generalizations to other samples in Greece or other countries thus may not be relevant. Another limitation of our study is that student responses to self-efficacy items were based on self-report and not on direct observation. Any bias in those responses thus becomes an inherent weakness of the data subsequently used for statistical analyses. Finally, we note that many of our results, including those related to interactions between self-efficacy and control variables, were highly significant. This is expected when the sample size is large because standard errors of most parameter estimates are inverse functions of sample size. For this reason, wherever applicable, readers should pay careful attention to reported effect sizes. For any researchers interested in extending this line of research, we suggest replication of our study with samples from other populations both inside Greece and from other countries. Other possible extensions of this study include adding additional predictors in the analysis, evaluating sensitivity of observed results to method of analysis, and replicating our method using alternative constructions of math self-efficacy.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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