Does formal teacher competence matter for students’ mathematics achievement? Results from Swedish TIMSS 2019

ABSTRACT

Research has accumulated on the effects of teachers on student achievement, especially in mathematics. However, empirical evidence regarding the impact of formal teacher competence indicators presents a mixed picture. This study explores the influence of educational level, subject – and grade-specific specialization, teaching experience, and professional development as indicators of formal teacher competence on student mathematics achievement in grade 4 in Sweden. Utilizing data from TIMSS 2019, the study employs confirmatory factor analysis and multilevel structural equation modeling to also test a latent model of formal teacher competence. Results reveal a positive relationship between formal teacher competence and students’ mathematics achievement, even after controlling for students’ socio-economic status and immigration background. Additionally, selection effects were found, suggesting that students in classrooms with a more advantaged composition had more competent teachers. The study underscores the need for an equitable distribution of qualified teachers across schools, highlighting implications for teacher specialization and allocation.

KEYWORDS:

• Teacher competence
• subject-specific specialization
• teaching experience
• mathematics achievement
• SES

Introduction

The concept of teacher quality is multifaceted, lacking a universally agreed-upon definition (Darling-Hammond, 2021). One primary challenge is distinguishing between teacher quality and teaching quality. Teacher quality typically refers to measurable factors such as certification, test scores, and degrees, which are seen as predictors of success in classrooms (Goe, 2007). Conversely, teaching quality pertains to the actual practices and performance of teachers within classrooms, irrespective of their formal qualifications (Goe, 2007; Seidel & Shavelson, 2007). These definitions are often intertwined, leading to assumptions that teacher quality automatically guarantees teaching quality, or that teaching quality is solely a result of teacher quality. However, several researchers point out that high-quality teaching is more complex than that; it is rooted in a knowledge base that combines understanding of content, pedagogy, and knowledge of learners (Darling-Hammond, 2021; Shulman, 1987).

Nevertheless, the interest in the impact of teacher quality indicators such as certification, experience, and professional development on student learning is still subject to significant interest in research (Goe, 2007; Kyriakides et al., 2020; Scheerens, 2013), likely due to its policy implications. If certified or more specialized teachers significantly impact student learning, there are strong incentives for investing in teacher education. Although research suggests substantial differences in teacher effectiveness (Hattie, 2009; Kyriakides et al., 2013; Nye et al., 2004), the relationship between teacher qualifications and student achievement has shown inconsistency or, to some extent, weak predictive effects (e.g., Blömeke & Olsen, 2019). Many studies have traditionally focused on a limited set of teacher variables (see, for example, Goe, 2007), which limits a comprehensive exploration that goes beyond observable characteristics. Teacher quality is likely a latent trait shaped by factors such as teacher education, specialization, professional development, and experience. Within the teacher workforce, the variation in these aspects is generally large. For instance, in Sweden, student teachers have received varying training over the years and are specialized for different educational levels, with different subject specializations. However, despite these differences in training, they still teach the same subjects and grade levels (Furuhagen et al., 2019). Yet, few studies recognize the large variation among teachers and thus do not consider teacher quality indicators together as a latent trait. However, it could be hypothesized that such a trait exists and may have a more significant impact on student learning than individual characteristics.

In this study, we investigate aspects of teacher quality in terms of formal competence as reflected by their teacher training and pedagogical knowledge acquired not only during teacher training but also through years of teaching experience. However, it is important to note that teacher competence is understood as a multidimensional construct, encompassing not only formal qualifications such as specialized subject matter (content) knowledge, but also encompassing more generic pedagogical knowledge and skills applied in teaching practice (Blömeke, 2017; Blömeke et al., 2020; Blömeke et al., 2022; Shulman, 1987). These dimensions are, however, beyond the scope of measurement in this study.

Indicators of formal teacher competence

Research has shown the importance of ensuring highly competent teachers for all students, especially in mathematics (Clotfelter et al., 2007; Darling-Hammond, 2000, 2017; Rosas & Campbell, 2010) and for students from disadvantaged home backgrounds (Allen & Sims, 2018). A vast body of research has arrived at conflicting and inconclusive results of which teacher qualifications are of greatest importance for student achievement in mathematics (Coenen et al., 2018; Goe, 2007; Wayne & Youngs, 2003). However, one aspect of teacher quality where consensus across studies has emerged is the impact of teachers possessing degrees in mathematics, appropriate certifications, and potentially higher levels of mathematical coursework on student achievement in mathematics (Goe, 2007). Nevertheless, teachers develop their formal competence in several ways; through their teacher education, by means of professional development and through experience.

Teacher degrees and subject-matter specialization

In the case of mathematics teachers, their formal level of education, including Master and subject-related degrees, certification, and subject specializations can be regarded as indicators of formal teacher competence. These indicators are presumed to deliver the profession-specific knowledge and subject matter knowledge necessary for meaningful mathematics teaching (Coenen et al., 2018; Gustafsson & Nilsen, 2016) promoting student outcomes (Baumert et al., 2010; Blömeke et al., 2016; Coenen et al., 2018; Hill et al., 2019; Kunter et al., 2013; Lee & Lee, 2020; Toropova et al., 2019). However, the extent to which these qualifications translate into improved student achievement is a much-debated issue within educational research.

While some research emphasizes the importance of teachers possessing a Master’s degree, a large body of research suggests that the effects of Master’s degrees on student achievement is either negligible or marginal at best (e.g., Clotfelter et al., 2007; Coenen et al., 2018; Goe, 2007). Moreover, the value of a Master’s degree appears to vary depending on whether it is a subject-specific degree or not. Studies indicate a more favorable relationship between student achievement and teachers holding a Master’s degree in mathematics and/or in science (Blömeke et al., 2016; Coenen et al., 2018; Gustafsson & Nilsen, 2016; Harris & Sass, 2011), implying that subject-specific expertise may play a role in teaching quality (Baumert et al., 2010; Campbell et al., 2014; Hill et al., 2019; Norton, 2019). Additionally, teachers with more mathematical coursework tend to possess higher levels of pedagogical content knowledge which is suggested to influence student achievement (Baumert et al., 2010; Hill, 2007; Hill et al., 2019). Further, strikingly little research has investigated the relation between primary school teachers with a Master’s degree and the performance of primary school students (Croninger et al., 2007).

Teaching experience

Teaching experience is one of the widely used indicators of teacher competence, yet it remains a subject of considerable debate among scholars. While many studies operate under the assumption of a linear relationship between teacher experience and student outcomes, others adopt categorical variables to account for heterogenous effects across different teacher experience levels. Some studies differentiate between the initial years of experience and subsequent ones, while others propose a curvilinear relationship (Toropova et al., 2019). Regardless of the method adopted, the results are inconclusive. While some studies have documented positive associations between teachers’ years of experience and student achievement (Clotfelter et al., 2010; Coenen et al., 2018; Hill et al., 2019; Lee & Lee, 2020)., other studies have found that teaching experience has moderate or little (e.g., Shuls & Trivitt, 2015), or no contribution to student achievement (e.g., Gustafsson & Nilsen, 2016). However, recent findings suggest that teacher experience continues to contribute to student achievement throughout a teacher’s career (Coenen et al., 2018), instead of merely, as some research has reported, the first (up to about five) years (Clotfelter et al., 2010; Goe, 2007). Further, in mathematics it is demonstrated that students with higher mathematics achievement are taught by more experienced teachers (Blömeke et al., 2016; Blömeke & Delaney, 2012; Hill, 2007).

Professional development

In most educational systems, a variety of professional development activities for teachers exist, differing in layout, content, and time (Blömeke et al., 2016; Kennedy, 2016). However, teachers’ professional development (PD) is an area that has received less attention within the research domain of teacher and teaching quality. Few studies have investigated its impact on teaching quality, with little evidence linking it to improved student outcomes (Kirsten et al., 2023; Muijs et al., 2014). However, some studies suggest that teachers’ participation in PD activities can improve their teaching quality (e.g., Blömeke et al., 2016), especially when they integrate new learning into existing practice (Timperley et al., 2007). In the case of mathematics, PD has shown a positive relationship with students’ mathematics achievement (Gustafsson & Nilsen, 2016) and is suggested to improve teachers mathematical knowledge, if focused on content and formative assessment (Hill et al., 2019). Some studies, like that of Jacob et al. (2017), found evidence of a positive relation between PD activities and teachers’ mathematical knowledge but did not observe effects on teachers’ instructional practices or student outcomes for elementary school students. Additionally, recent research, which included countries participating in TIMSS from 2003 to 2019, indicated even a small negative effect of professional development on student performance in mathematics and science (Kirsten et al., 2023).

Further, research shows that greatest outcomes of PD are achieved when approaches are tailored to address particular challenges or solving specific problems related to student engagement, learning and well-being (Muijs et al., 2014). Additional research is required in this domain to better understand how PD influences teacher and teaching quality.

Teacher education in Sweden

In Sweden, almost 90% of teachers have a teacher education, but there is great variation in the type of training these teachers have depending on when they were educated (see Table 1). For example, 1970s teacher education reforms were connected to the development of a nine-year comprehensive school. During this period, a coherent teacher education was implemented, with common courses for student teachers but also subject and subject block specializations for different stages in primary and secondary school. Primary and secondary school teacher education was divided into three-year stages with different levels of teacher competencies: primary school (grades 1–3), upper primary school (grades 4–6), and lower secondary school (grades 7–9). Then, in the late 1980s, a specialized teacher education for mathematics and science and Swedish and social sciences/languages was introduced for primary and secondary school (grades 1–7 and 4–9 respectively), which prepared teachers with different levels of subject matter knowledge and pedagogical content knowledge for the different grade levels. A few years after the turn of the millennium, this education was discontinued in favour of a more generalized primary school teacher’s degree (grades 1–5/6), with several subject options to choose from. This teacher education prepared the primary level teachers to teach most of the subjects covered in the syllabus, however, without a requirement of a specialization in either mathematics or reading for these grades. Another change was a subject-specific secondary school teacher’s degree (grades 6–9) where teachers usually became specialized in two to three subjects (Furuhagen et al., 2019; Persson, 2008; SOU 2008:109).

Table 1. Teacher education categories in primary school 1972 – today.

Years	Teacher category
1972–1988	Lower primary teacher grades 1–3
	Upper primary teacher grades 4–6
1988–2001	Mathematics and sciences grades 1–7
	Swedish and social sciences grades 1–7
	Mathematics and sciences grades 4–9
	Swedish and another language grades 4–9
	Social sciences grades 4–9
2001–2011	Teacher degree Earlier grades 1–5/6
	Teacher degree Later grades 6/7–9
2011–	Lower primary teacher Preschool class – grade 3
	Upper primary teacher grades 4–6

Further reforms have been carried out to change teacher training in recent past. These include a lower primary and upper primary teacher degree with mandatory subject specializations in reading and mathematics for all primary teachers, as well as more homogeneous subject choices in relation to grade level intended to be taught. This typically implies that Swedish teachers today have varying degrees of expertise and specialization, i.e., relevant education for teaching the actual subject and grade. Sweden has recently also faced teacher sorting, meaning that more qualified teachers tend to work in schools with higher student achievement and with a more homogeneous socio-economic and linguistic background (e.g., Hansson & Gustafsson, 2016; Holmlund et al., 2020). Simultaneously, Sweden has faced increasing performance gaps between schools and different student groups (Yang Hansen & Gustafsson, 2016, 2019). Furthermore, the reforms implemented in the Swedish education system in the 1990s transformed the highly centralized Swedish education system into a system characterized today by decentralization, privatization, and marketing. These reforms in turn led to the introduction of free school choice together with a voucher system, allowing parents to select schools for their children, resulting in an increased number of independent schools run with public funding (Lundahl, 2002). In the wake of these reforms, performance gaps between schools and groups of students have successively increased (Yang Hansen & Gustafsson, 2019), as has the sorting of teachers across different schools (Hansson & Gustafsson, 2016).

Taken together, these reforms create a promising backdrop for investigating teacher effects in the Swedish context. While prior studies paid great attention to the relationships between teaching qualifications and student achievement in primary and secondary school (Baier et al., 2019; Baumert et al., 2010; Baumert & Kunter, 2013; Blömeke et al., 2016; Kunter et al., 2013), research has not accumulated the same amount of evidence regarding the relationship between various combinations of teachers’ subject-specialization and student achievement – particularly in the primary school years (Croninger et al., 2007; Depaepe et al., 2013). In addition, few studies have focused on the matching between teachers’ formal training and the subject and grades taught. A recent study found, however, that teachers’ specialization is of importance for primary students’ performance in reading (Myrberg et al., 2019). However, there have been limited studies on teacher effects in mathematics in Sweden, despite the fact that teacher effects tend to have a greater impact on students’ mathematics achievement (e.g., Nye et al., 2004).

Aim

The current study investigates the importance of several teacher competence indicators on mathematics achievement in fourth grade using TIMSS 2019 data. Moreover, we formulate a latent variable representing teacher competence, which captures a wider spectrum of formal competence for teaching mathematics in grade 4. More specifically, the research questions are:

• What measures of teachers’ formal competence, in terms of formal level of education, subject-specific specialization, teaching experience, and professional development are related to students’ mathematics achievement in grade 4?

• How is teachers’ formal competence, formulated as a latent construct, related to students’ mathematics achievement in grade 4?

• How is teachers’ formal competence distributed with respect to classroom composition in terms of students’ socio-economic and language background?

Methods and data

The data in the present study was retrieved from the official website of Trends in International Mathematics and Science Study, TIMSS, (https://timssandpirls.bc.edu). TIMSS is one of the International large-scale assessments (ILSA), conducted by the International Association for the Evaluation of Educational Achievement (IEA). TIMSS assesses mathematics and science achievement for fourth and eighth grade students. TIMSS is conducted on a four-year cycle, with its first assessment in 1995, and the latest in 2019. In the present study, we use Swedish data from 2019. In Sweden, a total of 145 schools, 194 teachers, and 3965 students in grade 4 participated in TIMSS 2019 (The Swedish National Agency for Education, 2020).

Variables

The current study uses information from the student, teacher, and parent/home questionnaires. In the next sections, the variables are presented, starting with the teacher variables.

Teacher variables

In line with previous findings and theory, we selected a set of indicators of teacher competence to be tested on student mathematics achievement in grade 4. More specifically, specialization during teacher training, teaching experience, professional development activities, and formal educational level were selected. We used these variables for separate regression analyses as well as indicators of teacher competence in a latent variable. Some demographics of the participating teachers are presented in Table 2. The demographics show that the teacher sample is relatively representative of the Swedish teacher population. Statistics from Statistics Sweden (Statistics Sweden, 2020) show that the proportion of teachers who are younger than 40 is a little over 30% of the teaching staff, which also corresponds to the proportion in the TIMSS study, and that just over 30% of teachers are between 40 and 49 years of age. Further, 75% of primary school teachers in 2019 were women (Statistics Sweden, 2020). In the TIMSS data, the figure is 70.3%. However, 10% of the information is missing. In addition, the proportion of teachers in Sweden who have a teaching degree towards primary school also corresponds relatively well to the proportion with a teaching degree in the TIMSS data (see Table 2). The response rate in the TIMSS study for these demographics varied between 85.4% and 90.0%.

Table 2. Demographics of participating teachers in TIMSS 2019.

	N	Percent
Gender female	2786	70.3
Teacher age
Under 25	43	1.1
25–29	459	11.6
30–39	692	17.5
40–49	1372	34.6
50–59	700	17.7
60 or more	303	7.6
Years been teaching
Less than 4	880	22.2
5–7	580	14.6
8–14	694	17.5
15–21	660	16.6
22+	656	16.5
Education primary	3120	78.7
Education secondary	492	12.4
Major mathematics	2216	55.9
Specialization mathematics	2816	71.0

Specialization: One important indicator of teacher competence is the degree of specialization relevant for teaching mathematics at the primary school level (“Spec”). It is a composite variable derived from several questions in the teacher questionnaire.

First, to identify uncertified teachers, we used the information about majors (TG5A) but also a previous question regarding post-secondary education (TG4). Teachers without teacher certification were assigned code 0. Second, we reviewed the different combinations of specializations that teachers reported and recoded them according to relevance for teaching mathematics to grade 4 students. We assigned code 1 to teachers that had a certification, but no specialization related to mathematics.¹ Further, teachers with a specialization in science (related to mathematics) were coded 2. Teachers with mathematics specialization but who also had a specialization in other subjects were coded 3. Teachers with a focused specialization, i.e., in mathematics or mathematics and science were coded 4.

Furthermore, if teachers had an education towards primary school, as indicated by question TG5A, they got an extra credit point (some teachers had relevant specialization but had only teacher education for secondary school). Thereby, we retrieved a variable with six categories (0–5). This variable was labeled “Spec” in our analyses (Figure 1). Teachers who answered this question thus have a major in education and one or more specializations.

Figure 1. Specialization for teaching primary mathematics.

Teaching experience: Years of teaching experience is another variable of interest, widely cited in previous research as related to teacher effects (e.g., Coenen et al., 2018). In the current sample, teachers were generally experienced with on average over 13 years of teaching experience (M = 13.08, SD = 10.67). In addition to a continuous variable measuring teaching experience (“Yrs’), we also binned the variable (“Yrs_cat”) into five relatively equal-sized groups to be used in the analyses. This was made to allow for categorical latent variable modeling in a further step.

Professional development: Next, we selected a variable concerning teachers’ professional development. Teachers were to consider seven different professional development activities, in which they had been involved in the past two years. These were (1) mathematics content, (2) mathematics pedagogy/instruction, (3) mathematics curriculum, (4) integrating technology into mathematics instruction, (5) improving students’ critical thinking or problem-solving skills, (6) mathematics assessment, and (7) addressing individual students’ needs. The response categories were coded 0 = No and 1 = Yes. A sum was calculated based on these seven variables and a new variable (“Pro_dev”) with five categories was created, where “0” indicated no professional development content in the past two years, “1” indicated one content area/context, “2” two content areas/contexts, “3” three content areas/contexts, and “4” indicated four to seven content areas/contexts. The frequency of participation in professional development is presented in Table 3 below.

Table 3. Frequencies of professional development in the past two years.

Professional development content area/context	Frequency	Percent
0 None	1269	32.0
1 Content area	765	19.3
2 Content areas	545	13.7
3 Content areas	114	2.9
4–7 Content areas	740	18.7
Total	3433	86.6
Missing	532	13.4
Total	3965	100

Formal level of education: Next, we used an item about “Formal level of education completed” (Table 4) which essentially refers to ISCED levels and is obtained directly from the teacher questionnaire. The response options ranges from 1 (No formal education) to 7 (Doctoral or equivalent level of education). All teachers in our data had completed Upper Secondary education but no one had Doctoral or equivalent level of education. Notably, 9.0% of the students had teachers with less than Bachelor’s level of education, 59.6% had teachers with Bachelor’s level, and 10.0% had teachers with Master’s level of education.

Table 4. Level of formal education completed.

	N	Percent
Did not complete upper secondary education	0	0
Upper secondary education	126	3.2
Post-secondary, non-tertiary education	29	0.7
Short-cycle tertiary education	221	5.6
Bachelor’s or equivalent level	2365	59.6
Master’s or equivalent level	395	10.0
Doctoral or equivalent	0	0
Missing	829	20.9
Total	3965	100

Covariates

When examining teacher effects on student achievement in a cross-sectional setting, it is vital to control for initial differences in the outcome variable. Sometimes we may suspect that other variables, such as students’ immigration background, may influence the relationship we want to investigate. For this reason, to determine the effectiveness of a teacher and to control for selection effects, we add the influence of covariates, such as immigration background, into the regression between our independent variables and dependent variable. Typically, the covariates and independent variables are let to correlate with each other.

In this study, we control for effects related to student background through information on students’ socio-economic status (SES) and language/immigration background, using the variables “The number of books at home” (“Books’) and “Language spoken at home” (Lang) (see Table 5). Educational research has employed a diverse range of socioeconomic status (SES) indicators, as highlighted by White (1982). Sirin’s (2005) perspective emphasizes the importance of considering several factors in SES conceptualization, including (a) the unit of analysis for SES data, cautioning against assumptions at the student level when using aggregated data; (b) the type of SES measure, recognizing its influence on relationships with student outcomes; (c) the range of the SES variable, with a note on the potential limitations of dichotomous variables; and (d) the source of SES data, acknowledging the dependence on student family background, age, and achievement level for data accuracy.

Table 5. Descriptive statistics of Lang, Books, and Math_ach.

Variable name	Label	N	Minimum	Maximum	Mean	SD
Lang	Often speak Swedish at home	3857	1	4	1.59	0.85
Books	Number of books in your home	3841	1	5	2.99	1.22
Math_ach	Mathematics achievement	3965	260.78	755.35	521.23	73.28

In large-scale assessments of student achievement, the number of books in a student’s home is commonly used as a proxy for SES (Mullis et al., 2009; Wiberg & Rolfsman, 2023). Despite its historical recognition as a valuable measure of student background (Schütz et al., 2008), concerns have arisen about its validity. Engzell (2021) urges caution in relying solely on the number of books at home as an SES indicator due to potential underreporting by low-achievers and the endogeneity of parental input, which may introduce an upward bias.

Nevertheless, this indicator has undergone extensive testing in international research over several decades (Hanushek & Woessmann, 2011). For the purposes of this study, the variable is especially important at the aggregated level, where it serves as a measure of classroom composition. At the classroom level, the included variables require high data coverage to serve as indicative of classroom composition. However, parental occupation and education, which are reported by the parents themselves, contain a large number of missing values in the Swedish TIMSS data (>20%). Consequently, when books are used alongside a measure of the language spoken at the student’s home, it can be considered suitable for fulfilling its intended purpose. Nevertheless, we conducted sensitivity analyses with a composite of books, occupation, and education, and the results were largely the same. The relationship between teacher competence and student achievement decreased slightly. However, this composite was somewhat biased in nature because students with a high number of books also had parents that responded to their questionnaire to a higher extent.

“The number of books at home” (“Books”) is measured with five categories ranging from 1 (None or very few books) to 5 (Enough to fill three or more bookcases). 33.0% of students report having less than 25 books at home. “Books” is used as a proxy for student socio-economic background at the individual level and as an indicator of classroom socio-economic composition at the classroom level.

Further, the student reported “Language spoken at home” (Lang) serves as a proxy of immigration background at individual level and as an indicator of immigrant composition at the classroom level. “Language spoken at home” has four categories ranging from 1 (I always speak Swedish at home) to 4 (I never speak Swedish at home). 10.9% of the students were born in another country, however, only 2.1% of students report they never speak the language of test at home and 16.1% of the students report they sometimes speak another language at home.

TIMSS does not have test information on students’ prior achievement in mathematics. However, parents are asked a battery of questions regarding students’ literacy and numeracy skills and activities before school start. We used this information to formulate a proxy variable for students’ prior achievement. This variable was used to control for students’ prior achievement when examining the relationship between teacher competence and student achievement. Ten items from the Home (parents) questionnaire, out of which seven items regarded how well the student could do different levels of reading and writing and three items regarded basic mathematical skills before the child began primary/elementary school, were of interest. The seven reading and writings skill items ranged from 1 (Very well) to 4 (Not at all). These were reverse recoded to match the coding of the mathematics items, which was the opposite (1 =  Not at all to 4 = Very well). However, only three of the items, with most variation in responses, were finally chosen for the final analysis (Table 6). A sum variable (Early_litnum) was created with these three items. The response rate for the items varied between 81.3% and 81.6%.

Table 6. Descriptive statistics of parent’s reported student skills before starting primary school.

	N	Minimum	Maximum	Mean	SD
Read sentences	3234	1	4	2.56	1.01
Write words	3245	1	4	2.98	0.89
Write numbers	3224	1	4	2.90	0.92

Outcome variable

From students, we retrieved information about their achievement in mathematics (Math_ach). TIMSS employs a complex matrix-sampling design, where each student only answers a part of the total item pool and different booklets. However, TIMSS provides standardized mathematics achievement scores on a continuous scale (Martin et al., 2020). Based on Item Response Theory (IRT), achievement results for all students are placed on a common scale, even though they have not taken all the test-items. Because plausible values are imputed scores selected from a conditional distribution, IEA follows Rubin’s (1987) advice to repeat the process several times so that the uncertainty of the imputation process can be quantified. This results in five plausible values for each student. As recommended by, for example, Rutkowski et al. (2010) estimates should be calculated using each of the five plausible values, and eventually averaging the results from the five runs.

Data analysis

The main method of analysis is multilevel Structural Equation Modeling (SEM) with latent variables. The study relies on two-level regression to account for potential cluster effects (students’ achievement scores nested within classrooms) that are due to the hierarchical nature of the data (e.g., Hox, 2002). The student house weight (“HOUWGT”) was used to account for the stratification on both levels, student and class level. The set of observed teacher competence indicators (formal educational level, subject specialization, teaching experience, and undertaken professional development activities) were used as measures of a latent variable, Teachers’ formal competence (TCH_COMP) for teaching primary school mathematics, which was subsequently related to the outcome variable in structural models (Kline, 2016). This latent variable defines a construct which is not directly observable through single indicators, and is useful when theoretical constructs, such as teacher competence, are operationalized. Another feature of latent variables is that they are free from measurement error, since the unique part of the variance is separated from the unexplained part (Kline, 2016). Two-level modeling was used to account for potential cluster effects in the SEM. Robust maximum likelihood (MLR) was used as the main estimation method. Ordinal variables were treated as continuous as the variables have at least five categories (Muthén, 1984; Robitzsch, 2020). Missing data was handled by full information maximum likelihood (FIML). The analyses were conducted using SPSS version 28 (IBM Corp., 2021) and Mplus version 8 (Muthén & Muthén, 2017/2017).

For models that were not fully saturated we investigated recommended model fit indices (χ², RMSEA, SRMR, CFI, TLI) to evaluate the hypothesized model against the observed data (Hu & Bentler, 1999).

Procedure

The model building was a stepwise procedure. In the first step, as our interest concerns the impact of different teacher qualifications, two-level regression analyses were conducted for each independent teacher variable separately and the outcome, student mathematics achievement. In further models, the independent teacher variables were used together in a two-level multiple regression.

Next, latent measurement models were formulated using multilevel confirmatory factor analysis (CFA). In a third step, the latent teacher competence variable was related to student achievement in mathematics in multilevel SEM, thereby investigating a more comprehensive spectrum of formal teacher competence.

The equation model Student Achievement is a function of the variables tested in model 4 (Table 8) where u_0j and e_ij are the residuals accounting for unobserved and unexplained variation in achievement at student level: $\mathrm{Student}\mathrm{Achievemen}{t}_{0j}={\gamma }_{00}+{\gamma }_{10}\mathrm{SES}+{\gamma }_{20}\mathrm{Lang}+{\gamma }_{01}\mathrm{TCH}\mathrm{\_COM}{P}_j+{\gamma }_{02}\mathrm{ClassSE}{S}_j+{\gamma }_{03}\mathrm{ClassLan}{g}_j+u_{0j}+e_{\mathrm{ij}}$

It should be noted that a latent factor can be modeled with either continuous or categorical indicators, or a mix of both (Muthén, 1983, 1984). Irrespective of how indicators of the measurement model are defined, the interpretation of the results is the same. Measurement models with both continuous and categorical treatment of the indicators were compared (CFA1 – CFA3 in Appendix 2). The model where the indicators were defined as categorical (CFA3) resulted in stronger factor loadings than in the measurement model with “Formal”, “Spec”, and “Yrs” as continuous indicators (CFA1). This measurement model had better AIC and BIC measures than CFA1 and CFA2 (where the binned “Yrs_cat” was used instead of the continuous “Yrs”). Despite the better fit of CFA3, we opted to use CFA1 (Figure 2) for two primary reasons. First, some of the variables are more reasonably treated as continuous (experience, specialization) (Robitzsch, 2020). Second, CFA1 provides the most conservative estimates, as well as goodness-of-fit indices in the structural model, which prevents an overestimation of our results. Although CFA3 produces larger effects in later models where control variables are included, this is partly because latent aggregation for our controls is not available in Mplus for this model.

Figure 2. Measurement model of latent mathematics teacher competence on between level.

Note: Coefficients are significant at p < .001.

The measurement model and the final structural model are presented in the Results section (Figures 2 and 3) together with tables of estimates of correlations and multilevel SEMs (Tables 7 and 8).

Figure 3. Relations between mathematics teacher competence for primary school and student achievement.

Note: The relations between mathematics teacher competence for primary school and student achievement, controlled for student SES and immigrant background/classroom composition at the individual/classroom level.

Table 7. Means, standard deviations and correlations for dependent variable and independent variables at classroom level.

	1.	2.	3.	4.	5.	6.	7.	8.
1. Formal	1.00
2. Pro_dev	0.13	1.00
3. Yrs	0.13	−0.10	1.00
4. Spec	0.33	0.05	0.18	1.00
5. Math_ach	0.08	0.04	0.11	0.12	1.00
6. Lang	0.00	0.05	−0.05	−0.06	−0.19	1.00
7. Books	0.07	0.03	0.09	0.10	0.44	−0.30	1.00
8. Early_litnum	0.06	−0.02	0.03	0.10	0.33	0.05	0.09	1.00
M	4.93	1.54	13.07	3.10	523.10	1.58	3.94	2.72
SD	0.78	1.80	10.67	1.38	72.70	0.84	1.14	0.75

Table 8. Relationships between student mathematics achievement and formal teacher competence for primary school.

Outcome	Predictor	Model 1	Model 2	Model 3	Model 4
Mathematics achievement
Within	Books		.30*** (.02)		.29*** (.02)
	Lang			-.11*** (.02)	-.06* (.02)
Between	TCH_COMP	.51*** (.10)	.21* (.11)	.35*** (.10)	.21* (.10)
	Books		.74*** (.07)		.58*** (.09)
	Lang			-.59*** (.07)	-.26** (.08)
	TCH_COMP with Lang			-.20 (.12)	– .20 (.12)
	TCH_COM with Books		.33*** (.11)		.34** (.11)
ICC		0.185	0.186	0.186	0.185
R^2w			.09*** (.01)	.01** (.00)	.09*** (.01)
R^2b		.26* (.13)	.70*** (.06)	.55*** (.08)	.74*** (.06)
χ^2 (df) (SD)		2.33 (2)	3.77 (4)	5.66 (4)	6.40 (6)
RMSEA (SD)		.01 (.00)	.00 (.00)	.01 (.00)	.00 (.00)
CFI (SD)		.99 (.01)	1.00 (.00)	.99 (.00)	1.00 (.00)
TLI (SD)		.98 (.03)	1.00 (.00)	.97 (.01)	1.00 (.00)
SRMRw (SD)		.00 (.00)	.00 (.00)	.00 (.00)	.00 (.00)
SRMRb (SD)		.03 (.00)	.04 (.00)	.04 (.00)	.04 (.00)

Notes: Standardized estimates at the within/between level.

*Coefficients are significant at p < .05.

**Coefficients are significant at p < .01.

***Coefficients are significant at p < .001. Clusters N = 224, average cluster size = 17.70.

Results

First, we tested the teacher competence indicators on student achievement one-by-one and thereafter we determined which ones were the most influential. In a later step, we operationalized the construct of teachers’ formal competence via a latent variable. Additionally, we controlled for the covariates previously described in the method section.

What teacher competence indicators influence math achievement?

We ran multilevel regressions with teacher competence indicators as independent variables and student mathematics achievement as a dependent variable. Regression estimates for single predictors revealed that all formal teacher competence indicators except “Pro_dev” had a significant relationship to student mathematics achievement (β_Formal= .21 (.06), β_Spec= .23 (.08), β_Yrs= .26 (.08), β_{Yrs_cat}= .30 (.08), and β_{Pro_dev}= .07 (.07)). Teaching experience appears to be the strongest predictor when introducing all indicators in a multiple regression. Other indicators even become non-significant. The standardized beta estimates, p-values, and amount of explained variance of predictor variables are presented in Appendix 1.

Teacher competence as a latent construct

The regression analyses suggested that several of the indicators, when used as single predictors, may be of importance for student achievement. It is reasonable to assume that some teachers have more or less of the desired characteristics. In order to encapsulate a more comprehensive range of teacher quality indicators and to better operationalize the concept of formal “teacher competence” we formulated a latent variable (TCH_COMP).

We tested several competing measurement models by means of CFA with the indicators “Formal”, “Spec, “Yrs”, “Yrs_cat” and “Pro_dev” in different combinations. However, in line with previous analyses, “Pro_dev” was found not to be of importance. The factor loading was non-significant and “Pro_dev” was therefore excluded from further analyses. Because the measurement model with three indicators was “just-identified” it fitted the data perfectly.

The relationship between teachers’ formal competence and student mathematics achievement

The structural model aimed to estimate the relations between the independent latent teacher variable (TCH_COMP) and the dependent variable, student mathematics achievement (Math_ach) as depicted in Figure 3. The result revealed strong effect of .51 (p < .001) for the latent teacher competence factor. Thus, a considerably stronger effect than for any of the indicators alone (Table 8).

Considering student classroom composition

In a further step, to control for classroom composition, proxies for students’ socio-economic background (Books) and immigrant background (Lang) were introduced and treated as within – and between-level covariates. These variables were first entered in the models one at a time (Models 2–3 in Table 8) and thereafter together. Finally, a proxy for prior achievement level (reading, writing, and mathematics) of the child before school start (Early_litnum) was entered, together with SES and Lang.

After controlling for student SES, the regression coefficient for TCH_COMP decreased (β = .21) but was still significant at p < .05 (Model 2 in Table 8). This suggests that teacher competence still has an influence on student achievement when the school composition is set to be the same. However, the more advantaged schools in terms of students’ SES background have a higher proportion of teachers with relevant competence for teaching mathematics in primary school, indicated by the significant relationship between TCH_COMP and SES (r = .33 (.11), p < .001). Further, on the individual level a positive significant relationship of .30 between SES and Math_ach was found. The relationship between SES and Math_ach on the between level was even stronger at .74, suggesting large achievement differences between classrooms of high and low socio-economic composition. Classes with higher student SES composition perform better.

After controlling for student immigration background (Model 3 in Table 8), the regression coefficient for TCH_COMP also decreased somewhat (β =  .35), while a negative relationship on both levels exists (within β = −.11 and between β = −.59). This suggests that individuals with different language background than Swedish perform lower in mathematics. When a classroom is composed by a higher proportion of students with different language backgrounds, achievement differences become more pronounced. We did, however, not observe any significant relationship between TCH_COMP and Lang.

Notably, the effects of TCH_COMP remained even when controlling for SES and Lang together, at .21 (p < .05) (Model 4 in Table 8). Further, student socio-economic background has a more pronounced influence on Math_ach on the individual level (SES β = .29 (.02), p < .001) than student immigration background (Lang β = −.06 (.02), p < .05). These relationships are even stronger at the between level. The issue of school segregation will be discussed in the next section. Another finding is that the relation between TCH_COMP and SES was still significant (SES r = .34 (.11), p < .01).

Moreover, we added a proxy for students’ prior achievement levels (Early_litnum). However, as the ICC suggested no between class variation it was only inserted on the within level. There was also an issue of multicollinearity as Early_litnum was highly correlated with SES and Lang on the between level. Early_litnum had a significant relation with student achievement on the within level at .33 (p < .001), an effect that went beyond the socio-economic effects. This variable is therefore promising when it comes to explaining individual differences in achievement. However, the effect of TCH_COMP became non-significant even though the size of it remained the same as in the previously mentioned model (Model 4). Further, all models except the model where Early_litnum was included had good model fit. For this reason, our best and final model includes only the covariates SES and Lang (Model 4 in Table 8).

Discussion

The discussion focuses on (a) the measures and modeling of teachers’ formal competence for teaching mathematics in primary school, (b) the contribution of teachers’ formal competence to student achievement in mathematics, and (c) the distribution of teachers’ formal competence.

The measures, modeling, and contribution of teachers’ formal competence for teaching mathematics in primary school

In a first step, we created a variable indicating teachers’ subject-specific specialization for primary mathematics teaching with the information on majors and different specializations during teacher training. Next, we explored the influence of several teacher competence indicators; formal level of education, subject-specific specialization, teaching experience, and professional development, using two-level regression analyses. It was found that the frequency of professional development activities related to mathematics teaching was not associated with student achievement while formal level of education, subject-specific specialization, and teaching experience had moderate effects. Although previous research has indicated a link between teachers’ professional development activities and student achievement (Johansson et al., 2022; Kennedy, 2016), it is worth noting that our measure of professional development, which aggregates participation in various mathematics teaching-related activities, did not predict student achievement. Previous research has produced somewhat disparate results concerning the relationship between participation in professional development activities and student achievement; this finding aligns with studies using similar sources and operational definitions (Kirsten et al., 2023). Interestingly, we observed a negative correlation between teaching experience and professional development, indicating that the more experienced teachers were engaged in professional development activities to a lower degree than less experienced teachers. It appears reasonable that teachers who feel the need of professional development undertake it to a larger degree. However, these teachers might not necessarily be the ones with the highest competence. On the other hand, recent research has shown that teachers with higher prerequisites in terms of grade point average tend to engage in professional development to a higher degree (Johansson et al., 2022). Further investigations of professional development as an indicator of teacher competence are needed.

Based on the remaining indicators of teachers’ formal competence, a latent teacher competence variable was created which was then related to student mathematics achievement. Our results emphasize the importance of content knowledge in mathematics, particularly specialization in both mathematics and science, in primary school education to enhance student achievement in mathematics. Furthermore, we demonstrate a significant effect of the latent construct of formal teacher competence on student achievement, even if the effect decreased somewhat when classroom composition in terms of SES and language background was taken into account. The concept of formal competence implies that a composite measure of qualifications could potentially encompass a more comprehensive range of teacher quality.

Teachers’ knowledge of the content and how to best teach this content to students improve over time and influence how teachers act adaptively and flexibly in their teaching. However, most teachers of primary mathematics in Sweden (Ebbelind, 2020; SOU 2008:109) like in most parts of the Western world (e.g., Australia, United Kingdom, United States of America, New Zealand (Norton, 2019)) are not specialized teachers in mathematics. These teachers rather hold a generic teacher education, and they teach a range of subject disciplines in primary school grade levels. Due to the Swedish educational reforms of the 1980s, when a specialized teacher education towards mathematics and science for primary and secondary school was introduced, teachers were mainly prepared with subject matter knowledge and pedagogical content knowledge for the different grade levels. In 2001, these teacher education programs were discontinued in favor of a more generalized primary school teacher degree, which however was later changed to include compulsory training in reading and mathematics with a focus on subject matter knowledge and pedagogical knowledge (Ebbelind, 2020; SOU 2008:109). These differences in teacher education likely resulted in teachers with different levels of subject-specific and grade-specific competence, impacting their knowledge, instruction and ultimately influencing student learning and achievement.

While this study may not directly measure teachers’ pedagogical content knowledge (Shulman, 1987), it does underscore the importance of specialization in mathematics for student achievement in mathematics. The Swedish teacher training, with its current emphasis on grade – and subject-specific orientation, prioritizes the development of teacher students’ subject matter knowledge, curriculum understanding, and PCK. Nevertheless, our findings underscore the intricate nature of teacher quality and formal competence, acknowledging that it may not solely encompass subject-specific knowledge but could also involve grade specific knowledge (Cohen et al., 2018; Hill et al., 2019). This suggests the need for more refined measures of formal characteristics in further research. Moreover, in line with previous research in the field of mathematics, this study’s findings confirm that formal level of education and teaching experience significantly influence primary students’ mathematics achievement (Clotfelter et al., 2007; Coenen et al., 2018).

In addition, teacher competence in Sweden appears to be unevenly distributed across schools, contributing to differences in achievement for different student groups when classroom composition in terms of SES and language background are taken into account. This brings us to discuss the distribution of this competence.

The distribution of teachers’ formal competence

In Sweden, attainment differences have increased steadily since the early 1990s primarily due to increased school segregation and free school choice (Yang Hansen & Gustafsson, 2016). The relationships found in this study between socio-economic and language/immigration background and mathematics achievement, on individual and on classroom level, are thus in line with prior research showing that students’ socio-economic background is important for students’ academic outcomes (e.g., Gustafsson et al., 2013; Sirin, 2005; Yang Hansen & Gustafsson, 2019).

Teachers with higher formal level of education completed, a specialized mathematics and science education aimed at primary school and with more experience are to a higher degree found in schools with a higher student SES composition. They are found in classes where students perform better. Teacher competence is thus not distributed in a compensatory manner to classrooms with disadvantaged students, resulting in reduced equality in conditions for teaching and learning. The results, however, demonstrate that a considerable part of the effect of teacher competence remains, even when controlling for SES and language/immigration background, despite the fact that highly competent teachers tend to work in classes where students perform better and have a more advantaged background.

The results further demonstrate that quality and equity in education are intertwined (Kyriakides et al., 2020). Equality, in the sense that all students, regardless of conditions must have the same opportunity to meet teachers with adequate competence in mathematics is lacking in Swedish primary school. Lower degrees of competence can have many implications. Teacher competence matters for students’ school performance, especially in schools where compensatory efforts are necessary. Pedagogical segregation with respect to teacher competence can imply less progression for students in need of support, as well as segregation in achievement between schools, which from both an individual and societal perspective is a problem for the Swedish school. The distribution of teacher competence must be further investigated and extended to include city versus rural schools as well as publicly versus privately run schools.

Limitations

Our study focused particularly on a set of indicators of formal competence and its relationship with student achievement. Teacher competence has been defined in various ways, from possessing subject matter expertise and achieving high grades to being supportive, or enthusiastic in the classroom. These definitions primarily focus on individual qualities that are assumed to impact student learning but may not necessarily be linked to student achievement or to specialized teaching training. Given the complex nature of teacher knowledge (Shulman, 1987) and competence (Blömeke, 2017; Blömeke et al., 2020), assessing effects of formal competence based solely on students’ achievements might be limited. Shulman (1986, 1987) further emphasized that effective teaching resides at the intersection of content and pedagogy, underlining the importance of looking beyond content knowledge when investigating what matters for student achievement. Additionally, previous research suggests that the effect of teacher quality on student achievement is mediated via teaching quality (e.g., Blömeke et al., 2016). While international large-scale assessments encompass observations of teacher behaviors in classrooms through student-reported ratings of teaching behavior, these ratings encounter challenges due to their reliance on indirect measures rather than direct observations of teachers’ actual behaviors (Johansson & Myrberg, 2019). To address this issue in future research, it is imperative to incorporate direct classroom observations of teachers’ behaviors, thereby ensuring more precise explorations of teacher and teaching quality (Praetorius et al., 2018). Consequently, we urge future research to explore the relationships between teacher competence indicators and other outcomes, as well as the relationships between teacher behavior in classrooms and different student outcomes (Muijs et al., 2014).

It is also worth noting that the effectiveness of teachers may be contextual and contingent on the student population they engage with. While previous research using secondary data has often used socioeconomic status and immigration background to explain and control for differences in student achievement (e.g., Toropova et al., 2019), this approach provides only partial insight into the factors that determine student success. Connecting prior achievement data with ILSA data could reveal more nuanced insights into teacher effectiveness (Caro et al., 2018). By doing so, we could discern various facets of teacher quality and identify the key qualifications that contribute to student achievement. This approach could also shed light on whether teachers could compensate for differences stemming from different student characteristics and home background. As a result, it is often challenging to find positive effects of more qualified or competent teachers, leading prior research to question the relevance of teacher education (e.g., Chingos & Peterson, 2011). However, successful school systems emphasize the existence of a distinct body of knowledge that every teacher should have, and that it is a part of teachers’ competence to effectively address different students’ individual learning needs (Darling-Hammond, 2021).

Regarding the TIMSS data, it is important to acknowledge its limitations as it provides only a snapshot of relationships at a certain period of time, thereby making it challenging to draw causal inferences using this data. The lack of longitudinal data as well as the lack of prior achievement of students prevents us from interpreting observed associations with student achievement as causal effects (Caro et al., 2018). Additionally, since students are sampled, and their respective teachers are administered a questionnaire, teacher-level inferences may not be appropriate. However, the teacher demographics of this study suggest that this sample is representative for the entire population, indicating good alignment with the larger teacher population. Nevertheless, despite its limitations, cross-sectional data can still be valuable for studying changes over time in both student and teacher characteristics, generating new hypotheses, and facilitating in in-depth studies (Gustafsson, 2018). Furthermore, these characteristics can be influenced by various educational policy instruments, making the trends and changes in the data interesting from a policy development perspective. However, connecting these findings to register data would yield even more valuable insights.

Further, it is essential to consider the potential influence of previous teacher quality on the achievement of grade 4 students. Unfortunately, information on how long the teachers have taught the students is not available in TIMSS data. PIRLS offers this information, making it a potential resource for future comparative studies. Despite these limitations, our findings can still provide valuable insights that may inform the future development of measures and dimensions of teacher competence for primary school using ILSA data.

Disclosure statement

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

Additional information

Notes on contributors

Mari Lindström

Mari Lindström is a PhD student in Education at the Department of Education and Special Education at the University of Gothenburg. Her research interests include teacher education, teacher knowledge and competence, and student achievement in mathematics and science.

Stefan Johansson

Stefan Johansson is associate professor in Education at the Department of Education and Special Education, University of Gothenburg. His research interests center on the measurement of formal teacher competence and its effects on student achievement. Much of his previous research has used international large-scale assessment data to address these issues.

Linda Borger

Linda Borger is a senior lecturer at the Department of Education and Special Education at the University of Gothenburg, Sweden. Her primary research interests include educational assessment and measurement, large-scale assessment, and test development and validation.

Notes

1 TIMSS provided a question (TG5B) about just that: “If your major or main area of study was education, did you have a in any of the following?”. Response options were “Mathematics”, “Science”, “Language of test/reading” and “Other subject”.

Appendix 1

Standardized regression coefficients, p-values, and explained variances of regression analysis for variables predicting student mathematics achievement.

Table

Outcome	Predictor	Regression 1	Regression 2	Regression 3	Regression 4	Regression 5	Regression 6	Regression 7	Regression 8	Regression 9
Mathematics achievement
Within
Between	Formal	.21*** (.06)					.10 (.08)	.09 (.08)	.14 (.08)	.13 (.08)
	Spec		.23** (.08)				.17 (.10)	.16 (.10)	.17 (.09)	.16 (.09)
	Yrs			.26** (.08)			.26**(.09)		.19* (.09)
	Yrs_cat				.30*** (.08)			.25**(.09)		.21** (.09)
	Pro_dev					.07 (.07)	.09 (.07)	.08 (.07)
ICC		0.188	0.184	0.183	0.183	0.184	0.193	0.193	0.190	0.190
R^2		.05 (.03)	.05 (.04)	.07 (.04)	.09 (.05)	.005 (.01)	.15** (.06)	.14* (.06)	.12* (.05)	.12* (.05)
AIC (SD)		35539.10 (38.33)	44893.70 (40.78)	39284.13 (42.45)	39280.23 (42.63)	38131.97 (38.40)	33171.38 (41.49)	33172.47 (41.42)	34833.64 (41.26)	34832.54 (41.36)
BIC (SD)		35550.59 (38.33)	44918.84 (40.78)	39308.74 (42.45)	39304.84 (42.63)	38156.46 (38.40)	33213.25 (41.49)	33214.34 (41.42)	34869.82 (41.26)	34868.72 (41.36)

*Coefficients are significant at p < .05.

**Coefficients are significant at p < .01.

***Coefficients are significant at p < .001.

Appendix 2

Confirmatory factor analysis with teacher indicators.

Table

Level	Indicator	CFA1	CFA2	CFA3^a
Between	Formal	.53*(.15)	.51* (15)	.64* (.22)
	Spec	.67* (.15)	.53* (.12)	.78* (.17)
	Yrs	.28* (.06)
	Yrs_cat		.41* (.09)	.69* (14)
AIC		2622.242	1904.403	1670.021
BIC		2677.862	1960.971	1770.585

Note: Clusters N = 224, average cluster size = 17.70.

*Coefficients are significant at p < .001.

^a All indicators are treated as categorical.