Towards quality and equitable education in South Africa: Unpacking the relationship between teacher factors, students’ socioeconomic background and mathematics achievements

ABSTRACT

This study sought to understand the relationship between teacher factors, students’ socioeconomic background and mathematics achievements in South African context. This study contributes to educational quality and equity research in South Africa. Applying a two-level structural equation modelling technique, a sample of 334 mathematics teachers and 12,514 students from 292 schools in South Africa grade 9 (TIMSS) 2015 was used. The results revealed that teacher qualification and characteristics and instructional quality do not affect student mathematics achievement, once the student’s family SES and classroom SES compositions were taken into account. The classroom SES composition explained almost 80% of the cross-classroom differences in mathematics achievement differences in South Africa, indicating a high level of socio-economic segregation between classrooms in mathematics achievement. A tentative explanation might be that qualified and experienced teachers are more likely to be self-selected to schools and classes where the best students are. Moreover, since student’s achievement level is related to their socio-economic background. High achieving schools and classrooms very often are also with students of a higher level of SES. Thus, in South Africa, the teacher effects are confounded with SES composition effect. These results are discussed, and policy implications and practice recommendations of the findings are suggested.

KEYWORDS:

• South Africa
• TIMSS 2015
• quality education
• equity
• teachers
• students

Introduction

Education is of important benefits for the development of both individuals and society as a whole. It associates with qualified workforce and economic growth, social mobility, higher adult numeracy and literacy levels, and better health and wellbeing. Therefore, improving educational quality and providing education for all is of growing interest worldwide and have become the most desirable goals stated in their policy documents in all educational systems (Van Damme & Bellens, 2017). They are also deemed relevant as two dimensions of effectiveness in education (Creemers & Kyriakides, 2010; Nachbauer & Kyriakides, 2019). This is evident by, for example, the Strategic Framework for Education and Training of the European Union (European Commission, 2016) and the law of No Child Left Behind Act (NCLB) of 2001 in the USA, and the National Development Plan 2030 for South Africa. Quality and equity, as outcomes of an education system, imply that schools or education system of a country (e.g. South Africa) should evenly distribute the benefits of education among all students. There should not be any barriers to access and participation in education. Moreover, the expected outcomes of students from education should not be affected by their socioeconomic status (SES) or other backgrounds, such as gender, ethnicity, or religion (e.g. Takyi et al., 2019).

Unfortunately, ensuring all learners to have the equitable opportunity and quality in education remains a challenge in many educational systems (Gorard & Smith, 2004; Van Damme & Bellens, 2017). It was observed in the Trends in International Mathematics and Science Study that the mathematics score for grade 8 students improved in many countries. Still, the achievement gaps concerning socioeconomic and ethnic background also have increased significantly (I.V.S. Mullis et al., 2016). South Africa, for example, although the government promotes a solid legal policy for the right and accessibility to education for everyone, irrespective of gender or ethnicity, a proper mechanism for the effective fulfilment of the quality and equity in education is still lacking. Inequity in achievement has increased in South African schools in recent years (Frempong et al., 2011; Spaull, 2019). The South African learners performed significantly worse in TIMSS achievement, compared to all other developing countries in the study (Howie & Pietersen, 2001; Reddy et al., 2019). The average mathematics achievement in TIMSS 2015 in South Africa is 372, far below the international mean of 500 points. This indicates great challenges in education quality provision (Alex & Juan, 2017; Arends et al., 2017; Frempong et al., 2011; Sayed & Ahmed, 2011; Visser et al., 2015). Howie and Pietersen (2001) found that among the various factors (i.e. SES, age, attitude towards mathematics and language) that were examined, social economic status of students had the most significant influence on students’ mathematics achievement. Moreover, in a more recent study by Reddy et al. (2019), the researchers found that there is an unequal distribution of available resources and learning activities in learners’ homes, with learners in fee-paying schools enjoying higher levels of resources and home educational activities.

To achieve their educational goals of high performance and high equity, South African will need high-quality teaching for every student. Teacher and teaching quality have consistently been found to be substantial for student’s academic achievement and well-being (Canales & Maldonado, 2018; Slater et al., 2012; Wayne & Youngs, 2003). However, despite the substantial evidence that teachers matter in student learning, there remains no agreement as to which teacher quality is most consequential for student achievement (Canales & Maldonado, 2018; Gustafsson, 2003; Rivkin et al., 2005)

Reviews of the studies investigating the effects of teacher education, certification, and years of formal teaching experience on student outcomes have been conducted (Darling-Hammond, 2000, 2014; Goe, 2007; Wayne & Youngs, 2003). In essence, several teacher characteristics seem to be consistently cited as important teacher input that may contribute to explaining variation in teacher “effects” affecting student achievement. Much research has focused on investigating the influence of a particular aspect of teacher quality, for example, teacher education or certification on student outcomes. However, very little evidence exists on the relationship between instructional quality and student’s mathematics achievement conditioned on student’s family socioeconomic background and teacher’s qualification.

Moreover, most of the research in this area has centred on individual countries, such as the United States (Goe, 2007); Nordic region (Blömeke et al., 2016; Nilsen & Gustafsson, 2016) mostly with TIMSS 2007 and 2011 dataset; and Germany (Atlay et al., 2019). Only a few came from developing countries (e.g. South Africa included; Frempong et al., 2011; Sayed & Ahmed, 2011; Visser et al., 2015). There is no previous attempt observed to investigate these attributes in TIMSS 2015 in South Africa. Therefore, Sayed and Ahmed (2011) highlighted that quantitative evidence is not enough in South Africa. Previous studies in South Africa like Howie and Pietersen (2001) largely focused on students’ characteristics, which limit our understanding of the impact of teacher qualification and characteristics, teacher instructional quality on student learning outcomes. This study combines teachers’ and students’ characteristics to provide broader understanding of the factors that influence students’ mathematics achievement in South Africa.

Aim and relevance of the study

The current study is from a larger dissertation, which investigated the relationship between teacher qualification and characteristics, teacher instructional quality, students’ family socioeconomic background, and student mathematics achievement with the South Africa data from TIMSS 2015. It can be hypothesized that teacher qualification (indicated by teacher experience, formal education, and teacher major or specialization), teacher instructional quality, and classroom SES composition have significant effects on ninth graders’ mathematics achievement in South Africa, after taking into account students’ SES. The study may promote a precise explanation for variation in teacher effectiveness and student achievement, in terms of teacher characteristics and their classroom practises, conditioning on student’s family SES background. Given this, we anticipated that this study would lead to findings and conclusions that provide policy implications and practice recommendations that are useful for improving mathematics education in South Africa.

Literature review

The relation of teacher quality and student achievement

A number of studies have found a relation between an aspect of teacher qualification, teacher instructional quality, and student outcomes. Blömeke et al. (2016) analyzed the grade 4 data in TIMSS 2011 using a multilevel structural equation modeling technique (MSEM) and noted that teacher qualification was significantly related to instructional quality and student achievement, while student achievement was not always predicted by instructional quality. They also found an average effect size, estimated around, which is a notable effect in the study. The significance of teacher qualifications varies across countries around the world, suggesting that the relationship between teacher qualification, instructional quality, and student achievement needs to be further investigated. Similarly, Blömeke and Olsen (2019) investigated the effects of teacher quality on the fourth and eighth-grade student’s mathematics and science achievement in 5 countries using TIMSS 2011 data. They also found an average effect size estimated around for the relationship between teacher qualification, instructional quality, and student achievement. These authors mentioned that little consistent patterns within countries existed regarding instructional quality as predictors. These studies have found little evidence for the significant effect of instructional quality on achievement. This may be due to the varying operationalization of instructional quality (Akiba et al., 2007; Luschei & Chudgar, 2011). Also, Scherer and Nilsen (2016) and Blömeke et al. (2016) who examined the consistency of relations between teacher qualification, instructional quality, and student achievement warned against quick generalization.

Teacher qualifications

As observed by Goe (2007), the evidence for teacher qualifications indicated by teacher experience, teacher education, certification, and test scores are significantly related to student academic achievement. In these premises, the study only focused on two aspects of teacher qualifications, namely: teacher experience and education. These are further discussed below.

Teacher experience

Teacher experience is usually measured by the number of years of service. In the studies examining the effects of teacher experience on student’s learning outcomes (e.g. Nye et al., 2004), a positive impact is often found, i.e. the longer the in-service years of teachers, the better their students’ achievement is (e.g. Wayne & Youngs, 2003). Using 50-state data from the National Assessment of Educational Progress (NAEP) mathematics and reading test scores, it was found that the effects of teacher experience on student achievement differ, depending on the degree of teacher effectiveness (Darling-Hammond, 2000).

Also, researchers such as Akiba et al. (2007) corroborated the importance of teacher experience relating to grade four and eight mathematics teachers across different TIMSS cycle. Interestingly, some studies have contended that experience matters most in the first year (Rivkin et al., 2005), some have said after the first few years (Nye et al., 2004), some pointed out 3 years (Akiba et al., 2007), others have claimed 4 or 5 years (Goe, 2007), and still, others have mentioned 10 years (Papay & Kraft, 2015; Wiswall, 2013). The evidence that experience effect seems to level off after five years has found support in previous research (e.g. Darling-Hammond, 2000). Still, some researchers have put forward that teachers reach a certain peak in their careers, particularly 19 years after which their contribution to student achievement declines (Toropova et al., 2019). The Trends in International Mathematics and Science Study (TIMSS), for example, have shown that teachers of mathematics in grade 8 who teach mathematics have on average 15.77 years of experience.

Teacher confidence

Confidence is defined as one’s perception of self-regarding achievement in school (Reyes, 1984, p. 559). For example, it reflects a teacher’s sense of personal ability in successfully completing a specific activity. It is worth noting that the belief that an individual can organize and execute a particular activity is often discussed under the heading of self-confidence or self-efficacy (Bandura, 1997). Teacher’s confidence, as one of the important characteristics, plays a crucial role in student achievement. It has commonly been stated that the influence of teachers’ confidence levels contributes to student performance. It was observed that teachers’ self-confidence in their teaching skills is not only related to their professional behaviour but also with students’ performance and motivation (Bandura, 1997; Henson, 2002). Other researchers (Klassen & Tze, 2014; Klassen et al., 2011; Tschannen-Moran et al., 1998) have concluded that the teachers’ self-confidence is a vital aspect of teacher competence that influence teachers’ instructional practices. These findings were also supported by Beswick (2007).

Instructional Quality (InQua)

Apart from teacher qualifications such as teacher experience and education that have proven to be paramount to student’s achievement in a range of studies, quality of teaching also matters for student educational outcomes. Instructional quality is a construct that reflects the features of teachers’ teaching practices well known to be positively associated with student outcomes, both cognitive and affective ones (p. 5, Nilsen et al., 2016). The definition focuses on the measures of the classroom process concerning student outcomes. Some studies reported that constructs about teacher instructional practices had shown more significant relationships with teacher self-efficacy, especially at the primary school level (Toropova et al., 2019). Further, instructional quality is presumed to be an important aspect of an individual teacher’s characteristics (Bellens et al., 2019). While there is agreement among researchers on the three global dimensions of instructional quality, there remains some concern from other studies. Surprisingly, researchers within the same strand of research found clarity of instruction (CI) as the fourth dimension of instructional quality (Nilsen et al., 2016). Also, there is a similar pattern of contradictory research, which places emphasis on four dimensions of instructional quality (Blömeke & Olsen, 2019). One could argue that the field of measuring instructional quality is disintegrated or perhaps fragmented (Bellens et al., 2019). Instructional quality has been observed as best indicators of examined teaching practices (Blömeke & Olsen, 2019) and traditionally assessed through students, teachers, researchers, and/or external observers (Toropova et al., 2019).

Student background and their academic achievement in an international perspective

Educational equity is measured by, for instance, the effect of students’ socioeconomic background (SES) on their achievement and the gap in outcomes between low- and high-SES schools and students. Therefore, one frequently used component is the strength of the SES factor when predicting achievement (Akiba et al., 2007; Yang-Hansen & Gustafsson, 2004).

Admittedly, SES is commonly conceptualized as the relative position of an individual or family within a hierarchical social structure, based on their access to, or control over wealth, prestige, and power (Gustafsson et al., 2018; Mueller & Parcel, 1981). Research shows that SES is typically measured by parental education levels, parental occupation prestige, and family income (Caro & Cortés, 2012; Yang-Hansen & Gustafsson, 2004). Yang-Hansen (2003) identified various aspects of the SES, and they related differently to student learning outcomes.

However, there is no consensus on how to measure SES. Moreover, different explanations and operationalization procedures exist depending on what one wants to measure. For example, some studies used the number of books at home as a single SES indicator. PISA studies compute the index ESCS to measure student’s family economic, social, and cultural status and are a combination of the highest level of parent education, highest parental occupational position, cultural possessions, and home possessions. TIMSS studies also created a home educational resources (HER) index, which is measured by different educational aids from student questionnaire. As part of the discourse, SES operationalization procedures may relate to data availability. However, a number of studies have indicated that the number of books at home is a useful indicator of SES (Sirin, 2005; Yang-Hansen et al., 2014) and has made valuable contributions to educational research (Caro & Cortés, 2012). However, it was also shown that books at home mainly capture the cultural capital component of SES (Sirin, 2005; Yang-Hansen, 2003; Yang-Hansen & Gustafsson, 2004). Further, Yang-Hansen (2003) revealed that the cultural capital component of SES is the most important component relating to student outcomes.

It has frequently been asserted that a perfectly equitable education system would reflect students’ achievement unrelated to their socioeconomic status (SES). The bottom line of concern is that educational inequities related to socioeconomic status (SES) are unfair and that they can be measured through the relationship between students’ family socioeconomic background and student achievement. Previous research has confirmed that student socioeconomic status (SES) significantly affects student achievement (Yang-Hansen & Gustafsson, 2016). Further, the effect of four meta-analyses, based on 499 studies (957 effects) on socioeconomic status (SES), found an effect size, which has a notable influence on student achievement (Hattie, 2008). It is worth noting that Hattie (2008) defined the effect size as follows: small, medium, and large. This implies that what is really necessary when judging educational outcomes is the size of the effects. Similarly, White’s (1982) meta-analysis revealed that the aggregated effect of socioeconomic status (SES) was at the school level, whereas the effect was at the individual student level. As Sirin pointed out in 2005, the relationship between SES and mathematics achievement was estimated in a study by J. E. Gustafsson (1998) who found that in most countries, the effect of individual background factors on student achievement was relatively stable over time. However, in the case of South Africa, other studies indicate that students are segregated by SES in South African schools. Thus, the effect of SES on students’ achievement level has been observed in high achieving schools (Frempong et al., 2011).

Context

South Africa’s educational reforms envision educational policies. The country has seen a proliferation of educational policies in the post-apartheid South Africa education system (e.g. Sayed & Ahmed, 2011) and triggered significant adoption of “inclusive” education (Frempong et al., 2011). The proliferation of these policies was intended to enhance quality education for all students regardless of their background characteristics. Nevertheless, the quality of South African’s educational system has remained low and characterized mainly by inequality of educational opportunities (Spaull, 2013b). Two schooling systems can be seen in the South African education system. According to Spaull (2013b), the smaller wealthy population, which is better performing, provides students with required skills, and another for a larger and poor population, which is low-performing and poorly equipped to provide students with the knowledge they should be acquiring at school. Besides, in many countries of which South Africa is of no exception, where educational achievement remains strongly linked to family background, education may be attributable to reinforcing inequalities. South Africa is almost experiencing a highly unequal school system (Spaull, 2019). Therefore, learning that takes place in schools may be unequal due to student background characteristics, and this may as well limit students’ abilities. Moreover, it has become increasingly clear that inefficiencies and teacher quality in South Africa have been noted as a determining factor that is key to underachievement in education quality. The most striking example of this is that South Africa’s primary school-level mathematics teachers are least knowledgeable in sub-Saharan Africa. Therefore, many of these mathematics teachers, who serve poor and rural communities, have below basic levels of content knowledge. In several cases, these teachers cannot answer the questions their students are required to answer based on the curriculum (Spaull, 2013b, p. 8). These issues needed policy attention to improve teacher quality, and also, as the main route to addressing instructional quality in South Africa.

Research questions

Using data from TIMSS 2015, this study investigated the following research questions in terms of teacher qualification and characteristics and their classroom practises, conditioning on student’s family socioeconomic background to fulfil the aim.

1. Is there any relationship between teacher qualification, teacher characteristics, instructional quality, and classroom SES composition, and student mathematics achievement for South African ninth graders?

2. To what extent do the teacher qualification and characteristics, instructional quality, and classroom SES composition affect ninth graders’ mathematics achievement in South Africa?

3. Is SES the strongest predictor of South Africa's grade nine student’s achievement?

Method

Sample and Sampling Strategy in TIMSS 2015

TIMSS employs a two-stage stratified sample design or cluster sampling design for students in eighth grade. First, samples of schools are drawn as a first stage, which may be stratified. The second stage consisted of intact classrooms of students selected from each of the sampled schools (Joncas & Foy, 2010). This means that students are not sampled individually at the second stage of sampling but rather TIMSS select intact classrooms, as TIMSS has a focus on curriculum-based assessment. In the case of South Africa, the same sampling procedure was applied to ensure the sample is representative of its population. First, the sampling process entailed sampling a list of schools stratified by school type (public and independent), province, and language of instruction, followed by randomly selecting a class within the sampled school, after which intact classes participated in the survey. Further, participating countries are met with the minimum requirement of sampling 150 schools and a student sample of at least 4000. However, in a situation where a country’s class size is smaller or not more than 30 students per school than expected, countries were advised to sample more schools or more classrooms per school to align with the minimum target of sample size 4000. Along with these, to ensure an acceptable response, experts from the National Research Coordinators put in place a minimum student response or participation rates of 85%, while 50% or less are deemed to be not desirable and could lead to exclusion from the study. Approximately, the South African TIMSS sample consisted of 334 mathematics teachers and 12,514 students from 292 schools. Consequently, these samples were nationally representative of all grade 9 students in South Africa, with an average age of 15.7 years (LaRoche & Foy, 2016).

Matrix Sampling

In TIMSS, a single precise estimate for a student is not possible. Therefore, the dependent variable, which is the overall mathematics achievement for each student, is represented by five plausible values, BSMMAT01 to BSMMAT05. The plausible values are set to have a mean of 500 and a standard deviation of 100 (Mullis et al., 2012).

However, plausible values cannot be recognized as individual test scores, instead of as a measure of population performance. For instance, individual scores are not reported in TIMSS, but the assessment only estimates population parameters. According to Wu (2005), plausible values are a representation of “the range of abilities that an individual might reasonably have based on their responses to test items” (p. 115). Plausible values have been successfully used to describe the performance of a population or to estimate population characteristics compared with simple point estimates of abilities (Wu, 2005).

Variables and Measures

The primary variables of interest were the student achievement scores in mathematics, student’s family background variables, three teacher qualification variables, as well as variables indicating teacher characteristics (e.g. teacher confidence) and instructional quality from the 2015 TIMSS.

Student outcome: mathematics achievement (BSMMAT01 to BSMMAT05)

Mathematics achievement measured by the five plausible values¹ (BSMMAT01 to BSMMAT05) is used to describe students’ mathematics competence level in South Africa in TIMSS 2015. The five plausible values were used as the endogenous variables (dependent variables) in this thesis. With regards to TIMSS 2015 international report, a set of four international benchmarks was provided for countries with considerable descriptive of what students know based on their mathematics scores (Mullis et al., 2016). Students with score points between 400 and 475 are classified as low proficiency level, score points between 475 and 550 are intermediate achievement level, and score points from 550 to 625 are regarded as high proficiency and scores above 625 points as proficiency at an advanced level. As presented in the descriptive statistics table of mathematics achievement variable, Table 1 shows that the valid sample size of N = 12,514. It should be pointed out that the average students’ performance for South Africa is below the international benchmark. The average mathematics performance is 372 points, which is far below the international mean (set at 500 points). It can also be seen that there is some variability in their abilities in different achievement scores presented in Table 1 when taken into account the mean and standard deviation of achievement scores. Since the five plausible values of mathematics achievement were estimations of population values, given all available information of achievement test as well as from student contextual questionnaires, the mean for these PVs are not exactly the same, and variation can be observed in both mean and SD values. Therefore, the current analyses use all five plausible values as recommended, which provides more precise estimations of the population parameters.

Table 1. Descriptive statistics of the dependent variable “BSMMAT01 to BSMMAT05”

Plausible Values	Variables Labels	N	Mean (M)	Standard Deviation (SD)
BSMMAT01	1st Plausible Value Mathematics	12,514	371.42	81.73
BSMMAT02	2nd Plausible Value Mathematics	12,514	370.90	82.13
BSMMAT03	3rd Plausible Value Mathematics	12,514	369.67	82.89
BSMMAT04	4th Plausible Value Mathematics	12,514	369.24	82.56
BSMMAT05	5th Plausible Value Mathematics	12,514	369.88	83.10

The model estimations were run five times separately for each PV five mathematics achievement scores, and the results of the five analyses generated a single value by averaging the estimated parameter or statistics. By doing so, the measurement error can be correctly estimated to ensure valid statistical inferences (Rutkowski et al., 2010).

Student background variables

In this study, based on the available information in TIMSS 2015, the student’s responded number of books in the home (BOOKS), number of home study support (HSS), and parents’ highest education level (PEDU) are used as proxies for socioeconomic status (SES) background at the individual (within) level. The aggregated values of these individual proxies are used as indicators of classroom socioeconomic composition at the classroom (between) level.

The indicator of BOOKS contains the information on students’ estimated number of books in the home (see, Table 2), provided by students. This information is retrieved from the student questionnaire. The question contains five response categories: (1) None or very few (0–10) books); (2) Enough to fill one shelf (11–25 books); (3) Enough to fill one bookcase (26–100 books); (4) Enough to fill two bookcases (101–200 books); (5) Enough to fill three or more bookcases (more than 200; Martin et al., 2016). In Table 2, the mean and standard deviation of these variables are presented. The mean value describes the central tendency, and the standard deviation indicates a measure of spread or variation of a set of the data value around its mean value. The low standard deviation indicates that the data closely cluster to the mean or average (Bland & Altman, 1996). Further, the indicator HSS was computed based on student responses concerning the availability of home resources study supports such as internet connection, own room or both. Similarly, information concerning the parents’ highest education level (PEDU) was derived from responses to the student questionnaire and was captured by five response categories: University or higher, post-secondary but not University, upper secondary, lower secondary, some primary, lower secondary, or no school. The mean and standard deviations for the three indicators as a proxy for SES are presented in Table 2 below.

Table 2. Descriptive statistics for student-estimated number of books in the home, the number of home study support, and parents’ highest education level

Indicator/ item	Question/ Variable labels	Mean	Standard Deviation
BOOK	About how many books are there in your home? (Do not count magazines, newspapers, or your school books)	1.89	.99
HSS	Number of Home Study Supports	1.22	.73
PEDU	Parents’ Highest Education Level	3.18	1.69

The choice of the derived indicators of SES stems from the lowest percentage of missing values in these indicators: 1.1% in students’ estimated number of books at home (BOOKS), 3.4% in the number of home study support (HSS), and 5.1% in parents’ highest education level (PEDU). Furthermore, the number of books at home is well established as a good measure of student background.

Teacher background variables

Teacher experience, education, and major

The variable of BTBG01 contains the information on teacher experience. Teacher experience is commonly used to represent the total number of years the teacher reported teaching (see, Table 3). Also, to measure the level of formal education completed by teachers, the item, BTBG04 was used. This item, BTBG04 contains information about teachers’ degrees from teacher education. Further, teachers were asked to rate their major or main area of study. The item, BTDM05 reflects whether teachers’ main area of study was either mathematics or mathematics education. The three indicators BTBG01, BTBG04, and BTDM05 to teacher qualification variables with their mean and standard deviation are represented in Table 3 below.

Table 3. Descriptive Statistics for number of years of teacher experience, teacher degree, and teacher major (manifest variables)

Indicator	Question/ Variable labels	Response categories	M	SD
BTBG01	Number of years of experience	Reported in whole number	13.73	9.77
BTBG04	Level of formal education completed/ Teacher degree	Did not complete upper secondary, upper secondary, post-secondary, non-tertiary, short-cycle tertiary, bachelor’s or equivalent, master’s or equivalent, Doctor or equivalent	4.67	.68
BTDM05	Major	Focus on either mathematics major OR mathematics education	3.84	1.04

Teacher Confidence in Mathematics

In recent cycles in TIMSS, the measure of teacher self-efficacy in mathematics included items in the “confidence in teaching mathematics scale”, (hereafter referred to as TCM) that could be related to aspects of Bandura’s theoretical foundation for the self-efficacy construct (I. Mullis et al., 2009). The items in the teacher confidence in mathematics scale or index TCM scale are presented in Table 4. Teachers of mathematics in the South African sample report above-average levels of self-confidence in all aspects. Mean confidence levels appear to be nearly the same across the dimensions, except for the somewhat lower mean for teacher confidence for providing challenging tasks for the highest achieving students, and also for improving the understanding of struggling students.

Table 4. Descriptive Statistics for Teacher Confidence in Mathematics

Indicator/ item	Question/ Variable labels	Response categories	M	SD
BTBM17A_R	Inspiring students to learn mathematics	Very high, high, medium, low	3.52	.596
BTBM17B_R	Showing students a variety of problem solving strategies		3.40	.596
BTBM17C_R	Providing challenging tasks for the highest achieving students		3.01	.804
BTBM17D_R	Adapting my teaching to engage students’ interest		3.25	.656
BTBM17E_R	Helping students appreciate the value of learning mathematics		3.41	.649
BTBM17F_R	Assessing student comprehension of mathematics		3.20	.686
BTBM17G_R	Improving the understanding of struggling students		3.04	.722
BTBM17H_R	Making mathematics relevant to students		3.26	.641
BTBM17I_R	Developing students’ higher-order thinking skills		3.10	.726

Instructional quality as assessed by teachers

TIMSS teacher background questionnaire included several aspects relating to instructional quality (Blömeke et al., 2016). These aspects relate to form a latent variable of instructional quality (hereafter referred to as InQua). Mathematics teachers in the South Africa sample reported high levels of linking new content to students’ prior knowledge. They also rated students completing a challenging exercise that required them to go beyond the instruction relatively low (see, Table 5).

Table 5. Descriptive statistics for instructional quality as assessed by teachers

Indicator/ item	Question/ Variable labels	Response categories	M	SD
BTBG14A_R	Relate the lesson to students’ daily lives	Every or almost every lesson, about half the lessons, some lessons, never	3.12	.842
BTBG14B_R	Ask students to explain their answers		3.30	.800
BTBG14C_R	Ask students to complete challenging exercises that require them to go beyond the instruction		2.90	.864
BTBG14D_R	Encourage classroom discussions among students		3.14	.843
BTBG14E_R	Link new content to students’ prior knowledge		3.62	.593
BTBG14F_R	Ask students to decide their own problem-solving procedures		2.97	.836
BTBG14G_R	Encourage students to express their ideas in class		3.35	.758

Validity and reliability

To evaluate the reliability of the indicators of a theoretical concept and to measure internal consistency of a composite scale, Cronbach’s alpha () is used. A coefficient of 0.70 has often been regarded as an acceptable threshold for reliability; however, between 0.80 and 0.90 inclusive and above is preferred based on the psychometric quality of scales (Cronbach, 1951).

In this study, the α coefficient was between 0.80 and 0.91, indicating a high reliability of all the composite scales (George & Mallery, 2003). Cronbach’s alpha reliability coefficient is presented in Table 6 below. The index of TCM shows high internal consistency of the coefficient of teacher confidence (Cronbach’s .91). This means that about 91% of the variance in the teacher confidence scores is reliable. Therefore, only 9% is due to error variance. This presupposes that the TCM is measured with good reliability and low error. The same applies to the index of InQua, with Cronbach’s .80, indicating the reliability for the InQua is very high. The error variance is estimated at 20%.

Table 6. The reliability coefficient for instructional quality (InQua) and teacher confidence in mathematics (TCM)

Scale	Indicators	Cronbach’s alpha
InQua	BTBG14A_R, BTBG14B_R, BTBG14C_R, BTBG14D_R, BTBG14E_R, BTBG14F_R, BTBG14G_R	.80
TCM	BTBM17A_R, BTBM17B_R, BTBM17C_R, BTBM17D_R, BTBM17E_R, BTBM17F_R, BTBM17G_R, BTBM17H_R, BTBM17I_R	.91

Analytical process

In this study, we used two-level structural equation modelling (SEM) as the main analytical method to answer the research questions. As it was mentioned above, TIMSS comes to terms with hierarchically structured data with students nested within the classroom level. In the analysis using a multilevel approach, the weighting factor must be applied for each hierarchical level appropriately. In this study, because of the two-stage cluster sample design of TIMSS, weight for student and teacher effect at the classroom level were used in the analysis to account for bias in the parameter estimates or unequal probability of students and classroom being selected. As recommended by Rutkowski et al. (2010), weights at the student level are a product of student weight and student weight adjustment. At the classroom level, weights are a product of class weight, a class weight adjustment, a school weight, and a school weight adjustment.

The analysis was performed using Mplus V. 8.3. In a stepwise manner, first, path analysis using latent variables or unobserved measurement models employing CFA was formulated. Next, with the help of structural equation modelling, the relationship between variables of interest was specified accordingly. A latent measurement model of teacher instructional quality and perhaps, teacher confidence in mathematics was formulated at only the classroom level. This means that the teacher’s effects were modelled at the teacher level since teacher variation is only at the teacher level. Also, the individual (student) level was modelled at both the individual (student) level and teacher level, which means that individuals’ variation was decomposed at both levels. As the focus of this study was on the relations between teacher qualification and characteristics, teacher instructional quality, and student mathematics achievement, the researcher is interested in the aggregated level of students’ family socioeconomic background. Students shared teaching and learning-related factors or common characteristics within the same classroom, and classroom level is necessary when considering such a group-level construct (Lüdtke et al., 2009).

The student background variables were created (PEDU, BOOKS, and HSS), designed to reflect parents’ highest education level, number of books in student’s home and the number of home study support, and teacher background variables (T_EXP, T_EDU, T_Major, InQua, TCM) to explain variation in achievement. Student’s family SES and classroom SES composition were taken into account. Other variables are distinguished into simple and complex scale. The simple scale including items like teacher experience, teacher education, and teacher major or specialization. The complex scale is defined by observable (manifest) items and constructed using procedures that encompass a variety of factors. Items are recoded, including teacher instructional quality (BG14A_R, BG14B_R, BG14C_R, BG14D_R, BG14E_R, BG14F_R, and BG14G_R) and teacher confidence in teaching mathematics (BM17A_R BM17B_R BM17C_R BM17D_R BM17E_R BM17F_R BM17G_R BM17H_R BM17I_R).

The study makes use of a two-level model analysis. The final model was used to investigate the relationship between teacher qualification, teacher characteristics, instructional quality, and classroom SES composition, and student mathematics achievement for South African ninth graders. To investigate the extent to which teacher qualification and characteristics, instructional quality, and classroom SES composition has a significant effect on ninth graders’ mathematics achievement in South Africa, the same “model” was estimated. Finally, the two-level model was estimated to investigate if SES is the strongest predictor of South Africa grade nine students' achievement.

Results

In the following, measurement models are formulated and evaluated. Results of structural models and parameter estimates are presented.

Measurement model of teacher instructional quality

Confirmatory factor analysis (CFA) was conducted to test the measurement properties of teacher instructional quality (InQua) using Mplus. Since this construct was assessed by teachers, the measurement model of teacher instructional quality is at the aggregated level. Table 7 showed that all the model fit indices were at the acceptable level, which implied that the one-factor model fits the data very well. Chi-square value χ2 (14) 22.865 is not significant, with 0.0625, indicating that the model implied variance-covariance matrix is not significantly different from the observed variance-covariance matrix from the data. SRMR = .029. Furthermore, the Comparative Fit Index (CFI) is 0.980, and the Tucker-Lewis Index (TLI) is 0.970. Root Mean Square Error Approximation (RMSEA) of 0.044 satisfies the acceptable threshold of less than 0.08. Both CFI and TLI are greater than the cut-off value of 0.95, but in some cases, 0.90 is acceptable, since chi-square is too sensitive to sample size (Hair et al., 2006).

Table 7. The model fit indices of teacher instructional quality (InQua) and teacher confidence in teaching mathematics (TCM)

Parameters	χ2	df	CFI	TLI	RMSEA	SRMR
InQua	22.865	14	0.980	0.970	0.044	0.029
TCM	57.826	27	0.969	0.959	0.060	0.035

Figure 1 shows the standardized factor loadings and residuals of the measurement model of InQua. A standardized factor loading is between plus and minus one and can be interpreted as the regression coefficient of the indicator, say Q14a, on the latent variable, InQua. The factor loadings in Figure 1 range from .46 for indicator Q14a (Relate the lesson to students’ daily lives) to .68 for indicator Q14b (Ask students to explain their answers), all being significant and positive. These model results confirmed that only a single dimension, i.e. teacher’s instructional quality can be identified by the seven indicators. In other words, the indicators properly capture the underlying construct of teacher instructional quality (InQua). Hence, this result exhibited good construct validity of InQua.

Figure 1. The measurement model of teacher instructional quality (InQua).

Measurement model of teacher confidence in mathematics

Further, confirmatory factor analysis (CFA) was performed to test the measurement property of teacher confidence in mathematics (TCM) using Mplus. Since this construct was assessed by teachers, the measurement model of teacher confidence in mathematics is at the aggregated level. Table 7 exhibited that all the model fit indices were at the acceptable level, which implied that the one-factor model fits the data very well. However, the chi-square value χ2 (27) 57.826 is significant, with = .0005, since χ2 is known to be too sensitive to the sample size (Hair et al., 2006). SRMR = .035. Moreover, the Comparative Fit Index (CFI) is .969, and the Tucker-Lewis Index (TLI) is .959. Root Mean Square Error Approximation (RMSEA) of .060 satisfies the recommended level of acceptable fit of less than .08. Both CFI and TLI are greater than the cut-off value of 0.95, but in some cases, .90 is acceptable, since chi-square is found to be too sensitive to the sample size (Hair et al., 2006).

Figure 2 shows the standardized factor loadings and residuals of the measurement model of TCM. A standardized factor loading is between plus and minus one and can be interpreted as the regression coefficient of the indicator, say Q17a, on the latent variable, TCM. The factor loadings in Figure 2 range from .60 for indicator Q17a (inspiring students to learn mathematics) to .82 for indicator Q17I (developing students’ higher-order thinking skills), all being significant and positive. These model results confirmed that only a single dimension, i.e. teacher’s confidence in mathematics, can be identified by the nine indicators. In other words, the indicators properly capture the underlying construct of teacher confidence in mathematics (TCM). Hence, this result demonstrated good construct validity of TCM.Structural models

Figure 2. The measurement model of teacher confidence in mathematics (TCM).

Relations between teacher qualification and characteristics, instructional quality, classroom composition, and student mathematics achievement

Considering the above latent variable models of InQua and TCM as classroom-level construct which yielded substantially better fitting model and higher validity, the researcher can now have more confidence to test the hypothetical model. The interrelationship among these latent variables and student mathematics achievement was simultaneously examined at student and teacher levels in a two-level structural model, controlling for the socioeconomic status of students at both levels. The structural model at the teacher level was constructed so that teacher instructional quality (InQua), teacher confidence (TCM), and three teacher qualifications (TQ) variables, namely, teacher experience, their formal education, and teacher major or specialization, are interrelated and affecting mathematics achievement, after taking into account the variation of the classroom SES composition and student’s SES at the respective levels. Student mathematics achievement scores (i.e. all five plausible values) was used as the dependent variables in the model. At the individual level, only the relationship between student’s family socioeconomic status and their mathematics achievement was tested.

The model structure was portrayed in Figure 3.

Figure 3. The hypothetical model with the relations between three teacher qualification and characteristics (TCM), instructional quality (InQua), student and classroom SES composition, and mathematics achievement (M_ACH).

Model fit of the final structural model for South Africa

In a further step, a structural model for the South Africa sample was constructed to assess whether the parameter estimates to be analysed are valid and reliable. It is critical that the parameters to be analysed should be providing reliable estimates. To conduct a two-level analysis, Mplus was used to run the (same) model structure five times based on the five plausible values generated for each student. In this way, Mplus does a calculation for the final parameter estimate of the standard error for the target parameters. The option for the evaluation in Mplus was TYPE = TWOLEVEL; ESTIMATOR = MLR functions in ANALYSIS command together with CLUSTER = IDTEACH; WEIGHT = HOUWGT (house weight); and BWEIGHT = MATWGT teacher weight). My reasoning here of incorporating house weight and teacher weight at individual and teacher levels is to properly adjust the standard error due to the clustered sampling strategy. Moreover, each classroom may not only have one teacher, and a teacher may not only teach one classroom, with the teacher weight, we also can adjust the teacher-classroom one-to-one match.

Results showed that the two-level model estimates had a satisfactorily good fit to the data. The chi-square test associated with the mean and standard deviations were χ2 (215) = 347.576, SD = 6.295, and χ2 is derived by the formula χ2 = mean/degree of freedom. When the value is less than 5, it is regarded as substantially good fit chi-square estimates. The formula holds if and only if the model is run five times, as mentioned before. Thus, the χ2 satisfies the goodness-of-fit. Moreover, the measure of fit indices with regards to the mean and standard deviations are CFI (M = 0.930, SD = 0.003); RMSEA (M = 0.007, SD = 0.000), within-level SRMR (M = 0.013, SD = 0.003) and between-level SRMR (M = 0.058, SD = 0.000). These fit indices were found to exhibit an exceptionally good fit to the data. Further, it can be observed that the standard deviation for RMSEA is very small, almost close to zero, which means that all the 5 times estimation or the number of successful computations from different plausible values provide an equally good fit. Similarly, the SRMR value at the individual level is good, and there is almost no variation at the between levels, indicating an excellent model fit. Hence, this model is valid and reliable for two-level modelling (Refer to Table 8 for more detail).

Table 8. Model fit indices for the final structure model (two-level model)

Fit Indices			Mean	Standard deviation
Chi-square (χ2)			347.576	6.295
df	215		-	-
CFI			0.930	0.003
RMSEA			0.007	0.000
SRMR			0.013 (Within-level)	0.003 (Within-level)
			0.058 (Between-level)	0.000 (Between)

Reporting results for interclass correlation (ICC)

The research questions in the study are focused on how teacher-related factors affect student achievement. In the two-level structure equation model, only the student and teacher levels are simultaneously analysed in the analysis. Taking advantage of two-level analysis, the intraclass correlation coefficients were examined. To perform two-level modelling, an important aspect is to determine whether the between teacher-level effects were reliable for the purpose of the study’s variables. Two-level modelling is usually required when the intraclass correlation coefficient is .05 or higher (Muthén, 1994). However, when the ICC is less than .05, two-level modelling will not be warranted. This is usually the case when the between-group variability is not present.

As is shown in Table 9, the intraclass correlation coefficient varies between .09 and .62. About 9.4% of the between-classroom variation in the parent’s highest level of education is due to the fact that students are sorted into different classrooms. 15.8% of the between-classroom variation in the number of books at home and 16.2% of the between-classroom variation in the home study supports is due to students going to different classrooms. Concerning student mathematics achievement, different classroom belongingness explains 62.3% of between-classroom differences in mathematics achievement. In other words, 62.3% of the variance in mathematics test scores in TIMSS 2015 across different classrooms is explained by the classroom effects. The phenomenon of classroom effects could mean that different teachers teach different classrooms or with different students’ family background composition, classroom learning culture, etc. The proportion of variance of the mathematics achievement shows a measure of the extent to which the classrooms are segregated in terms of student achievement. The main argument is that students going to different classrooms should achieve equally, but the ICC coefficient for between-classroom differences were very high, indicating classroom segregation indicator in South Africa.

Table 9. Estimated Intraclass correlation coefficients of the latent variable indicators

CLUSTER	AVERAGE CLUSTER SIZE	BSMMAT	PEDU	BOOKS	HSS
326	38.172	0.623	0.094	0.158	0.162

R-Square

Generally, the R-square of the estimates from the model provides information about the proportion of the variation in each of the dependent variables that are accounted for by the independent variables. Since SES significantly affects mathematics achievement, it is important to examine if differences in mathematics achievement are explained by this model. R-square, in other words, is the percentage of the explained variance in the outcome variable by the model. The final model (Figure 3) can explain almost 80% of the variation in mathematics achievement across different classrooms.

Parameter estimates

Corresponding to the research questions formulated in the previous section, the main results are presented. Table 10 and Table 11 show both the direct and indirect effects of the interplay among factors depicted in the constructed structural model, respectively (see, Figure 3).

Table 10. Standardized direct effects in the final model

Parameter Estimate	Factor loading	Standard Error* (S.E.)	P-value
Within level
SESW effect on BSMMAT	0.073	0.030	0.014
Between level
Teacher qualification effects on mathematics achievement
BTBG01 effect on BSMMAT	0.032	0.047	0.498
BTBG04 effect on BSMMAT	0.076	0.045	0.093
BTDM05 effect on BSMMAT	0.006	0.044	0.895
Teacher qualification effects on instructional quality
BTBG01 effect on INQUA	−0.148	0.070	0.034
BTBG04 effect on INQUA	−0.026	0.064	0.690
BTDM05 effect on INQUA	0.018	0.072	0.802
Classroom student’s SES composition effect on class-level factors
SESB effect on BSMMAT	0.874	0.032	0.000
SESB effect on INQUA	0.014	0.079	0.862
SESB effect on TCM	0.022	0.079	0.778
SESB effect on BTBG01	0.007	0.085	0.935
SESB effect on BTBG04	0.098	0.059	0.096
SESB effect on BTDM05	−0.019	0.080	0.809
Interrelationship among teacher-related factors and mathematics achievement
INQUA effect on BSMMAT	−0.085	0.077	0.267
TCM effect on BSMMAT	0.018	0.081	0.825
TCM effect on INQUA	0.713	0.051	0.000
Correlation among teacher-related factors
BTBG01 correlates with TCM	0.014	0.086	0.871
BTBG04 correlates with TCM	−0.067	0.061	0.274
BTDM05 correlates with TCM	0.051	0.077	0.508
BTBG04 correlates with BTBG01	−0.158	0.080	0.048
BTDM05 correlates with BTBG01	0.038	0.099	0.701
BTDM05 correlates with BTBG04	0.220	0.108	0.041

Table 11. Standardized total and specific indirect effects estimated in the structural model

Relations	Total Indirect effects (Z-effects)*	**P-value
Total indirect effect of SESB on mathematics
BSMMAT—SESB	0.006 (0.587)	0.557
The specific indirect effect of SESB on mathematics via teacher-related factors
BSMMAT—BTBG01—SESB	0.000 (0.003)	0.935
BSMMAT—BTBG04—SESB	0.007 (0.006)	0.192
BSMMAT—BTDM05—SESB	0.000 (0.001)	0.918
BSMMAT—INQUA—SESB	−0.001 (0.007)	0.870
BSMMAT—TCM—SESB	0.000 (0.002)	0.859
BSMMAT—INQUA—BTBG01—SESB	0.000 (0.001)	0.936
BSMMAT—INQUA—BTBG04—SESB	0.000 (0.001)	0.731
BSMMAT—INQUA—BTDM05—SESB	0.000 (0.000)	0.851
BSMMAT—INQUA—TCM—SESB	−0.001 (0.005)	0.786

*Z-effect is the ratio of the estimate or regression coefficient and standard error, (i.e. Z_value = estimate/ standard error) and when is 1.96, then the effect is significant. The estimates reflect the regression weight or the strength of the relationship between variables.

** P-value is significant at .05.

Research Question one

Is there any relationship between teacher qualification, teacher characteristics, instructional quality, and classroom SES composition, and student mathematics achievement for South African ninth graders?

No significant direct relationship between the teacher background indicators (experience, education, and major), and teacher confidence, teacher instructional quality, and classroom average mathematics achievement was found. As seen in Table 10, the p-values of the effects of almost all teacher-related factors are greater than .05. Further, student-level SES has a statistically significant relationship with students’ mathematics achievement with the path coefficient of 0.073 (.014.05). The classroom SES composition has a very strong statistical relationship with average mathematics achievement with a regression coefficient of 0.874, p05. While in the correlation part, teacher confidence was significantly positively related to teacher instructional quality.05, meaning that teachers with higher levels of confidence offered a higher quality of instruction, as needed by their students. Teacher’s years of working affected teacher’s instructional quality negatively (−.15, p .034). No significant indirect effects were found of SESB on classroom average mathematics achievement, as presented in Table 11.

Research Question Two

To what extent do the teacher qualification and characteristics, instructional quality, and classroom SES composition affect ninth graders’ mathematics achievement in South Africa?

With regards to the findings of RQ 1, as mentioned before, Figure 3 (see Table 10) graphically showed the model at the classroom level chosen to answer RQ2. Since the analyses of research RQ 1 reveals no significant association between teacher qualification and characteristics, teacher instructional quality, and mathematics achievement, it follows that the effects of the three teacher qualification variables on student average achievement were not significant, and estimated at _exp = 0.032 (p = 0.498.05;_edu = 0.076 (p = 0.093.05) and _major = 0.006 (= 0.895.05) (i.e. with extremely very small effect, not differ from zero). In terms of teacher confidence, a non-statistically significant effect on mathematics exists, estimated at 0.018, = 0.82.05), indicating that teacher confidence does not impact achievement. For instructional quality, the results exhibited regression weights of _INQUA −0.085 (= 0.267.05), which means that the regression weights of teacher instructional quality have a negative impact on mathematics achievement. Also, results reveal the regression weight of SES_B = 0.874.05, and a significant effect is due to SES composition in terms of student achievement. Taking into account the RQ 2, the size of the effects of the relationship between teacher qualification, and characteristics, teacher instructional quality, and classroom SES composition do not influence ninth graders’ mathematics achievement in South Africa. However, the classroom SES composition is the only variable significantly attributable to mathematics achievement variation in South Africa.

Research Question one

Is SES the strongest predictor of South Africa's grade nine student’s achievement?

Socioeconomic status is a significant predictor at the individual student level with the effect size (0.07, p = .014), but SES is a statistically significantly strong predictor at the classroom level (0.879, p .05). Returning to the intra-class correlation coefficient estimated at 62.3% in Table 9 above, it can be seen that classroom composition in terms of SES is very high taking into account this estimate. Almost 80% of the classroom-level variance of the mathematics achievement was explained by the classroom SES composition. High variation across classrooms in South Africa exists, which indicates that if a student has a better condition of SES, the student in question tends to have a higher level of mathematics achievement or go to a better classroom. Therefore, SES composition is a strong predictor of South Africa grade nine student’s achievement.

Discussion

South Africa is a country of higher classroom segregation. South African students show a huge achievement variation in mathematics in the ninth grade in TIMSS 2015. South African’s highly achievement inequitable environment provides unique insights into understanding the relationship among factors that are known to contribute to achievement differences in mathematics. This study developed a hypothetical model to examine the relationship between teacher qualification and characteristics, teacher instructional quality, students’ family socioeconomic background, and student mathematics achievement with the South Africa data from TIMSS 2015. This study examines whether it can be hypothesized that aspects of teacher quality and classroom SES composition have a significant effect on ninth graders’ mathematics achievement in South Africa. Also, whether SES is the strongest predictor of South Africa grade nine students' achievement.

In this context, the results of the study revealed no significant relationship between teacher qualification and characteristics, teacher instructional quality, and student’s mean mathematics achievement. Teachers with experience, a degree, and who majored in mathematics had no significant relationship with student mathematics achievement. In terms of teacher’s experience, the results of the study are concordant with previous research, which points out that the relationship between student achievement and teacher experience is non-statistically significant (Nilsen & Gustafsson, 2016). The study results suggest that the effect of teacher experience on student achievement is not deterministic in South Africa. No relationship was found between teacher experience, teacher education, and teacher major or specialization. Besides, when examining the relationship between teacher experience and teacher education, it was found that the teacher’s experience was negatively correlated with teacher education, and the effects were not significant. Undeniably, the idea that teachers with experience cease to contribute to student mathematics achievement is not in agreement with other research (Akiba et al., 2007).

With regards to teacher confidence in teaching mathematics, the results of the study suggest, however, that it is not deterministic with student achievement in mathematics. Still, when examining the effects of teacher confidence in teaching mathematics, no significant effect from SES is possible. As demonstrated by the study results, teacher confidence in teaching mathematics does not show any significant direct or indirect effects on classroom average mathematics achievement. These findings also contradict those found by Bandura (1997) and Henson (2002), who found the relationship between teacher self-confidence and mathematics ability. When it comes to the effects of teacher confidence on instructional quality, it appears significantly strong, as revealed by the study results, which means that teachers with higher levels of confidence offered a higher quality of instruction. This result corresponds with previous studies (Klassen & Tze, 2014; Klassen et al., 2011; Tschannen-Moran et al., 1998) which have shown that teacher confidence influences teacher’s instructional practices.

On the other hand, the absence of a relationship between teacher instructional quality and average student mathematics achievement was less anticipated, as previous research has indicated that teacher instructional quality is positively related to academic achievement (Nilsen et al., 2016). However, in the South African context, the relationship between teacher instructional quality and classroom average mathematics achievement is not significant. Somewhat surprisingly, the results also indicated that the effects of teacher instructional practices on student’s average mathematics achievement were rather weak. In other words, teacher instructional practices cannot be determined as a result of the student’s average mathematics achievement.

Indeed, findings of the study demonstrated only a direct significant effect from classroom SES composition to student average mathematics achievement. This finding also points out that individual-level SES significantly affects student mathematics achievement. The strength of the effects was not strong at the student level, but at the classroom level, it is really strong. These results are in agreement with previous research that found significant effects of SES on student achievement (Yang-Hansen & Gustafsson, 2016). Taking the analysis one step further, what is really affecting achievement is because of classroom segregation, which means that student mathematics achievement differences depend on classroom SES composition. In South Africa, the dominant contribution to achievement differences is student SES and classroom SES composition, other factors like teacher qualification, teacher confidence, and teacher instructional quality do not matter very much. As mentioned above, apart from student SES and classroom SES explaining variations in mathematics achievement, other mechanisms like aspects of teacher quality, are not deterministic in terms of achievement differences. The findings indicated that more than half of the total variation in South Africa students’ mathematics achievement can be attributed to classroom differences, of which the differences in classroom SES composition were found to be the major explanatory factor. The between-class differences in mathematics achievement may be further explained by other classroom and/or school-level factors, such as uneven distributions of the physical and human resources of different kinds, where public classrooms or schools have less resources compared to their private counterpart. This is an important equity issue to be examined in the further study of South Africa data.

In view of the much stronger influence of student SES and classroom SES composition in South Africa, the education system is relatively ineffective because the country is highly segregated in terms of the mechanisms of SES and reduces equity and is being reflected in classrooms and schools. These mechanisms responsible for the student SES and classroom SES composition are alarming and deserve the attention of further research. Essentially, student SES and classroom SES composition may not only attributable to variations in achievement and student SES characteristics of the classroom’s student intake but also to physical resources-related characteristics (e.g. school-building conditions, library materials, access to computers and flushing toilet, etc.) that vary across classrooms are captured by the classroom SES effect.

The question ought to be how we can best ameliorate the impact of students’ SES background characteristics on mathematics achievement, rather than eradicate it. Deliberation of targeted provisions of physical resources may, therefore, be a better alternative to classrooms in respect of improving access to good equitable and quality education in the South African context. Because educational researchers have argued that inadequate physical educational infrastructures and teaching and learning resources (Adane, 2013) have adverse effect on academic achievements of students. Equitable distribution of physical educational resources is imperative for improving academic achievements of students regardless of their socioeconomic background.

Limitations, conclusion, and implications for policymakers, students, teachers, and educational researchers

The current study aimed to investigate the relationship between aspects of teacher quality, classroom SES composition, and student mathematics achievement. One possible limitation is the use of the cross-sectional design of the South African TIMSS study, which makes it possible for a correlational conclusion to be made rather than for example, drawing causal relations between classroom SES composition and classroom average mathematics achievement. Notwithstanding the study provides valuable findings. The study findings are as follows: First, results demonstrate no significant relationship between teacher qualification and characteristics, teacher instructional quality, and student average mathematics achievement. Second, findings indicate that individual student-level SES significantly affects mathematics achievement. However, classroom-level SES composition strongly affects classroom average mathematics achievement. Third, teacher characteristics (teacher confidence) were positively related to teacher instructional quality. However, teacher characteristics and teacher instructional quality had no relationship to the classroom average mathematics achievement. Fourth, teacher experience, teacher level of formal education, and teachers who focus on either mathematics or mathematics education had no association with the classroom mean mathematics achievement.

SES strongly appears to be a dominant contribution to achievement differences between classrooms in South Africa. SES may not only capture the socio-economic conditions of the classroom but also variations in physical resources across classrooms with different SES effects. The analysis from South African TIMSS 2015 data highlights the view that the quality and equity of education can be achievable through an increase in school physical resources.

The findings of this study have influential implications, in particular, for policymakers, students, teachers, and educational researchers. Interventions that aim to improve educational quality and equity in terms of mathematics achievement cannot be solely aimed at the human resource-related factors (e.g. teacher qualification, teacher instructional quality, and teacher confidence). The findings point to the greatest need to consider physical resources as an enriching tool for improving educational quality and equity rather than just any of the human resource-related factors. Therefore, there should be equitable distribution of physical resources within the educational system in South Africa. Students must be made aware of the effects of these physical resource-related factors on their achievement to compensate for any deficiencies.

Also, the findings generally point to the importance of reducing socioeconomic inequity conditions in societies for the sustainability of educational and economic outcomes. Moreover, efforts to reduce socioeconomic inequities in societies will be benefited given its positive and significant effect on mathematics achievement.

South Africa is one of the growing economies on the African continent. Therefore, greater efforts rest on the national Department of Basic Education and the Provincial Education Departments to design and implement cost-effective interventions to target students and classrooms in SES disadvantaged. To this end, South Africa can achieve the Sustainable Development Goals (SDGs) as documented in the National Development Plan of 2030.

The evidence from these findings suggests that increasing classroom physical resources in the education sector is one way to enhance student learning and achievement in South Africa. A greater collaboration of school physical resources should be pursuing by the Department of Basic Education and should be considered as a better school condition to improve student learning and achievement. On the basis of these findings, some far-reaching practice recommendations can be attributable to teachers of mathematics and school principals regarding their daily work. The findings seem to reveal that the classroom SES composition is the strongest factor for measuring inequity in educational outcomes. High classroom SES effect on achievement is a segregation measure and would not be recommended. However, if schools can work against school segregation, and mathematics teachers and school principals can establish networks with other schools and try to help each other to reduce the segregation that will further be helpful to reduce educational inequality.

Further research

The student’s SES effect on their mathematics achievement may differ across different schools. It may thus be interesting and important to estimate such a random slope model to investigate the compensatory effect.

Acknowledgements

We would like to thank Dr. Kajsa Yang-Hansenfor the great support and diligent guidance towards this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors have no funding to report.

Notes on contributors

Ernest Mensah

Ernest Mensah is currently admitted into the PhD in Education program at Indiana State University, USA. He obtained his Master of Science with a major in Education with Specialization in Educational Research at the Göteborgs universitetsbibliotek, Sweden. His research interest is in improving mathematics achievements of students.

David Baidoo-Anu

David Baidoo-Anu is a PhD in Education Candidate at the Faculty of Education, Queen’s University in Kingston, Ontario Canada. He earned his Master of Philosophy in educational measurement and evaluation from the University of Cape Coast-Ghana. Previously a part-time lecturer at Presbyterian University College- Ghana, his enormous interest in research, particularly classroom assessment coupled with his experience directed him to the Queen’s Assessment and Evaluation Group (AEG). He believes that if classroom assessment is appropriately used, it has the power to support equitable access to education and propel learning forward for diverse students. David’s current research focuses on classroom assessment cultures.