The importance of teachers’ pedagogical-psychological teaching knowledge for successful teaching and learning

ABSTRACT

Effective teacher education is expected to ensure that future teachers acquire professional knowledge that is relevant for coping successfully with the requirements of their teaching practice. To strengthen evidence-based teacher education, we need to better understand which teacher education outcomes are predictive for high-quality instruction and student learning. This study hence investigates the impact of teachers’ pedagogical-psychological teaching knowledge (PPTK) on student’s perception of instructional quality and students’ achievement in mathematics. The study is based on longitudinal data of 28 early career primary school teachers and their students (n = 509). The results indicate PPTK as a significant predictor for students’ perception of teachers’ classroom management as well as teachers’ quality of explaining. PPTK and teachers’ cognitive activation as perceived by students are significant predictors for students’ mathematics achievement. These results emphasize the importance of PPTK for successful learning processes in mathematics in primary school. The findings are discussed regarding their relevance for the effectiveness of teacher education.

KEYWORDS:

• Early career teachers
• pedagogical-psychological teaching knowledge
• instructional quality
• mathematics achievement
• primary school

Theoretical background

Effective teacher education is expected to ensure that future teachers acquire professional knowledge that is relevant for coping successfully with the requirements of their teaching practice. A central aspect of classroom environments is multidimensionality, which is characterized by multiple simultaneous and dynamic processes during teaching (Doyle, 1986). This multidimensionality is not least due to diverse learners, various activities and different aims. Teachers require specific professional competences to deal with this diverse setting and implement high-quality instruction which is important for students’ learning success (e.g. Charalambous, 2019; Hattie, 2010; Kyriakides et al., 2009; Lipowsky, 2006; Seidel & Shavelson, 2007; Wayne & Youngs, 2003). Of special importance here, is pedagogical competence, the aspect of professional competence which comprises general pedagogical knowledge (GPK) as well as the skill to transform knowledge into performance (situation-specific skills). GPK, along with content knowledge (CK) and pedagogical content knowledge (PCK), is one aspect of professional knowledge that is particularly relevant for teaching and is, therefore, frequently examined (Baumert & Kunter, 2006, 2011; Depaepe et al., 2020; Guerriero, 2017; Kaiser & König, 2019; Shulman, 1986). GPK refers to the planning and implementation of teaching and includes content areas such as efficient classroom management or subject-independent knowledge of student learning processes (Brühwiler et al., 2017; Lenske et al., 2016; Voss & Kunter, 2011; Voss et al., 2015).

Research findings indicate that it cannot necessarily be assumed that the pedagogical knowledge at the end of teacher education correlates with effective practice in the classroom (Blömeke et al., 2020; Brühwiler et al., 2017; Cauet et al., 2015; König et al., 2021). Novice teachers commonly face difficulties in the transition phase from teacher education to teaching. They struggle to apply acquired knowledge in the classroom (Doyle, 2006; Wanzare, 2007), which highlights the necessity for a broader perspective on professional knowledge and a deeper understanding of teacher transition from theory to practice (König et al., 2024). Research has determined that expert teachers’ classroom performance is aided both by theoretical (‘knowing, how … ’) and practical knowledge (‘knowing, what … ’) (Bromme, 2001; Voss et al., 2015) as well as situation-specific skills (Blömeke et al., 2015; Leinhardt et al., 1995).

Situation-specific skills include noticing, interpreting and decision-making in specific classroom situations (Blömeke et al., 2015). Noticing relevant situations which call for knowledge-based reasoning, is often seen as belonging to the umbrella concept of ‘professional vision’ (Seidel & Stürmer, 2014) or ‘noticing’ (König et al., 2022), which does not typically include the aspect of decision-making.

This paper aims to examine the situation-specific skills (interpretation and decision-making) of GPK and its relationship with instructional quality and students’ achievement in mathematics. In contrast to Shulman (1986, 1987) who focuses more narrowly on pedagogical knowledge as a method of teaching and classroom management, the psychological component of student learning is more strongly considered (see also Baumert & Kunter, 2006). In the following, the term pedagogical-psychological teaching knowledge (PPTK) is explicitly used when referring to the knowledge-based, situation-specific skills of GPK and the pedagogical as well as the psychological aspects.The present paper addresses the question of how teachers’ PPTK impacts students’ perception of three aspects of instructional quality (classroom management, cognitive activation and quality of explaining) and students’ mathematics achievement.

Previous findings from the study underlying the present contribution, showed that PPTK does not increase during the first three years on the job (Affolter et al., 2017). To strengthen evidence-based teacher education, we have to better understand which teacher education outcomes are predictive of high-quality instruction and student learning. There is a need for better understanding of the complex relation between PPTK, instructional quality, and student achievement, which is still seen as a black box due to the lack of empirical evidence (Blömeke et al., 2022).

Teachers’ professional knowledge and its relevance for instructional quality as well as students’ achievement

Teachers’ professional competence comprises disposition (knowledge and motivational-affective aspects) as well as situation-specific skills (Blömeke et al., 2015). The more recent models of professional competences including situation-specific skills highlight their importance for the transformation of knowledge into effective practice (Blömeke et al., 2015; Depaepe et al., 2020; Krauss et al., 2020). It is assumed, that teachers need situation-specific skills to transform their knowledge into practice (Blömeke et al., 2015; Depaepe et al., 2020; Krauss et al., 2020; Ulferts, 2019). Figure 1 is an adapted model of teacher professional competences according to Blömeke et al. (2015) focusing on GPK.

Figure 1. Teacher professional competence model focusing on GPK (Brühwiler & Hollenstein, 2021).

Teachers’ professional knowledge is considered to be an essential prerequisite for planning challenging, varied and motivating learning opportunities, as well as for student outcomes (Baumert et al., 2010). It is assumed that teachers’ professional knowledge (and the quality of their instruction) influences students’ learning outcomes (Terhart, 2012). In recent years, an increasing number of studies have been conducted to investigate the impact of professional knowledge on instructional quality and student achievement at lower secondary level (Förtsch et al., 2016; Keller et al., 2017; Kirschner et al., 2017; König et al., 2021; Lenske et al., 2016; Mahler et al., 2017; Sadler et al., 2013).

However, the findings for primary schools are still weak (Fauth et al., 2019; Lange et al., 2015). To date, for example, in terms of mathematics at primary level, the following empirical findings can be summarized: Hill et al. (2005) showed that primary school teachers’ mathematical content knowledge (MCK) had a positive effect on student achievement during one school year. However, the results of the study should be interpreted with caution. The measurement of MCK used also relates to mathematical pedagogical content knowledge (MPCK). Rowan et al. (2002) found that a high level of MCK can negatively influence the learning process among primary school students if there is a lack of MPCK and GPK. However, they did not measure teachers’ MCK with a standardized test instrument but rather did so distally based on the teachers’ university degree in mathematics (bachelor’s vs. master’s degree). Their assumption was that teachers with a high level of MCK would find it difficult to prepare appropriate mathematical content for the target level and explain it to learners in a simplified way (Rowan et al., 2002; Zumwalt & Craig, 2008).

Successful student learning processes are influenced not only by subject-related knowledge but also by GPK. The importance of GPK has been confirmed by several studies: according to a study by König et al. (2012), higher GPK test performance correlates with a better self-assessment of future primary school teachers’ teaching competences. Brühwiler (2014) has shown that highly adaptive teaching competence (an aspect of GPK) among primary school teachers correlates positively with higher instructional quality (e.g. higher student participation, better explanation, less teaching pressure). Furthermore, instructional quality has been found to mediate a positive effect on student achievement in a series of teaching lessons on a given topic (Brühwiler, 2014). Few studies focus on the influence of GPK on students’ learning outcome in primary school. Muntoni et al. (2020) investigated the teacher expectations of 50 teachers and their influence on mathematics achievement (N = 796 primary school students) in addition to teachers’ pedagogical knowledge. However, no significant relationship between GPK and students’ achievement was demonstrated.

König and Kramer (2016) as well as Seidel and Stürmer (2014) have developed video-based procedures to capture teachers’ knowledge in a contextualized way. Early contextualized instruments that have been developed show that these tests do not necessarily have to be more closely related to classroom activities, as they tend to test cognition rather than performance (Blömeke et al., 2014; Kulgemeyer & Riese, 2018). Nevertheless, certain initial successes show a significant correlation (Blömeke et al., 2022; Brühwiler et al., 2017) and emphasize the importance of situation-specific skills for high-quality instruction and students’ achievement (Blömeke et al., 2022; König et al., 2021). Overall, however, only a few have verified the predictive validity of the test instruments (Brühwiler et al., 2017; Lenske et al., 2016). Research results show that it cannot necessarily be assumed that pedagogical knowledge as a disposition correlates with effective practice in the classroom (Brühwiler et al., 2017; Cauet et al., 2015). In a previous study, the authors showed a significant positive relation between teachers’ PPTK and students’ mathematics achievement (Hollenstein et al., 2019).

Instructional quality and its importance for successful learning in the classroom

In the aforementioned studies, different aspects of instructional quality are considered. In the majority of cases, the characteristics once described as basic dimensions in the German-speaking context, such as classroom management, student support and cognitive activation (Praetorius et al., 2018), were examined as mediators and viewed as generic aspects of instructional quality. Effective classroom management is considered a substantial determinant of successful teaching (Doyle, 2006; Helmke, 2017). Cognitive activation seems to be important for student learning, whereas the support that students receive relates to students’ interest in mathematics (Klieme et al., 2001). However, current studies also focus on cognitive support, which appears to be particularly relevant for science (Kleickmann et al., 2020). The quality of teacher explanations (as one option of providing cognitive support) also appears to be significant, especially in the subject of mathematics. To date, the quality of teacher explanations has been studied mostly in relation to science and less as regards mathematics. In science, teacher explanations are very important, but also very difficult to measure (Kulgemeyer & Riese, 2018). For example, attempts are made to filter out the variety and quality of explanations by means of lessons videography and observation grids (Geelan, 2013; Wittwer & Renkl, 2008). Within the framework of teachers’ professional knowledge, various studies have given rise to teacher explanations. For example, Rowan et al. (2002), Brühwiler (2014) and Kulgemeyer and Riese (2018) found that the quality of teacher explanations (as one aspect of instructional quality) relates to professional knowledge. The ability to provide high-quality explanations can be important for successful learning processes among students and comprises the ability to prepare content competently in a way that is appropriate for the target group, as well as to convey knowledge in an understandable way (Brühwiler, 2014; Eder & Mayr, 2000). The ability to provide high-quality explanations means that the teacher plans the lesson in such a way as to make it comprehensible, clear and motivating (Eder & Mayr, 2000). To do this, teachers not only need CK and PCK but also GPK (cf. for physics teachers see Kulgemeyer & Riese, 2018).

Consequently, classroom management and cognitive activation, as well as the quality of teachers’ explanation can be important for students’ mathematics achievement.

Research questions and hypotheses

The foregoing literature review indicates that there are few empirical findings relating to the impact of teachers’ PPTK on teaching and on students’ learning outcomes at primary level, in particular (Fauth et al., 2019; Lange et al., 2015). The aim of this paper is to empirically test relations between the PPTK and students’ perceptions of three aspects of teachers’ instructional quality (classroom management, cognitive activation and quality of explanation) and students’ mathematics achievement. Specifically, the following research questions are of interest:

1. What is the impact of primary teachers’ PPTK on student perceptions of (a) classroom management, (b) cognitive activation and (c) quality of explanation in mathematics lessons?

2. What is the impact of primary teachers’ PPTK and the three aspects of instructional quality on students’ mathematics achievement?

According to the theoretical framework, a correlation is likely to be found between PPTK and instructional quality (Brühwiler, 2014; Brühwiler et al., 2017; Rowan et al., 2002). The highest positive impact of PPTK is assumed to relate to classroom management, because the other two aspects of instructional quality (cognitive activation and explaining quality) also require MCK. Additionally, a positive impact of PPTK on students’ mathematics achievement is assumed (Brühwiler, 2014; Fauth et al., 2019; Hill et al., 2005; Lange et al., 2015).

Method

Sample and study design

The data in the present study were based on the longitudinal study, Outcome of Teacher Education, supported by the Swiss National Science Foundation. Conceptually and methodologically, this study followed the international teacher education study (Teacher Education and Development Study: Learning to Teach Mathematics; Tatto et al., 2012). The longitudinal study tracked (pre-service) teachers from the beginning of their teacher training until their third year of employment. These teachers began their studies as primary school teachers at a university of teacher education in Switzerland in 2008, and they graduated in 2011. This article focuses on the participants’ third year in the profession (school year 2013/2014). 28 primary school teachers (3^rd grade: n = 6; 3^rd/4^th grade: n = 2; 4^th grade: n = 2; 4^th/5^th grade: n = 2; 5^th grade: n = 5; 5^th/6^th grade: n = 3; 6^th grade: n = 8)¹ participated along with their students (N = 509; 3^rd grade: n = 130; 4^th grade: n = 71; 5^th grade: n = 134; 6^th grade: n = 174). At the beginning of the school year, the teachers were assessed in PPTK. Students’ mathematics achievement was captured with a standardized mathematics test at the beginning and end of the school year. At the end of the school year, the students also answered questions on instructional quality.

Due to the longitudinal study design, it cannot be ruled out that the analysis was based on a positive selection of the sample. A total of 40 percent of the teachers at the end of their teacher training took part in the surveys during their third year on the job, 29 percent could not be located at the time. The majority of the remaining teachers (31 percent) did not participate due to lack of time (15 percent) while others did not provide a reason (8 percent). In some individual cases, teachers were unable to participate because they were abroad at the time of the survey (2 percent), had unpaid leave (2 percent) or were absent for a longer period due to illness (2.5 percent). Others (1.5 percent) had not worked as a teacher after their studies, for example, because they had begun a master’s degree at lower secondary level. When comparing the means of PPTK at the end of teacher training (the means of the teachers who participated during their third year in the profession vs. the means of the teachers who did not participate) there is no significant difference in PPTK (t(151) = −.105, p = .917). This could indicate that it is not a positive selection, at least with regard to the professional knowledge of the teachers.

Instruments

Pedagogical-psychological teaching knowledge (PPTK)

A recently developed test for PPTK within the [name of the study] framework was used to record contextualized teachers’ general pedagogical-psychological knowledge. PPTK comprising six text vignettes was used to describe difficult situations in the classroom and was designed to elicit teaching knowledge in the following areas: attribution theory, didactics (transfer and forms of representation), self-regulated learning (metacognition), self-concept, problem-solving behaviour and the culture of mistakes (Brühwiler et al., 2017; see Figure 2). The aim of the PPTK was to capture knowledge-based situation-specific skills (especially interpretation and decision-making). An analysis of the test measuring PPTK followed a quasi-pair comparison with expert answers analogous to the ‘Würzburger Lesestrategie-Wissenstest’ (Schlagmüller & Schneider, 2007).² The maximum score possible for the 27 items was 54 points. On average, the teachers achieved M = 46.11 points (SD = 3.83; min. = 33; max. = 51). The internal consistency was satisfactory (α = .76).

Figure 2. Example item of PPTK; Aera attribution theory.

Note: Checked boxes = classified by the experts as the best solution

Student perceptions of classroom management, cognitive activation and quality of explanation

At the end of the school year, the students completed a questionnaire on their perceptions of the three aspects of teachers’ instructional quality: (1) classroom management, (2) cognitive activation and (3) quality of explanation. Students were asked to classify the statements using a four-point Likert scale ranging from 1 ‘not true at all’ to 4 ‘completely true’. The items were taken from validated instruments used to measure the quality of teaching specifically in young children from grade 2 onwards (Dubberke et al., 2008; Institut für Qualitätsentwicklung, 2010). In some cases, the items are partially adapted or supplemented for use in the present study (reflecting the language ability and age of the children). Care was taken to ensure that the items were very short and concise.³ Table 1 represents an overview of the three dimensions with item examples and descriptive statistics.

Table 1. Three dimensions of instructional quality with item examples and descriptive statistics.

Scale (number of items)	Item examples	m	sd	min	max	ICC1	ICC2
Classroom management (3)	Our mathematics teacher is immediately aware, if we are not paying attention.	3.19	.61	1.00	4.00	.15	.76
Cognitive activation (8)	When we start a new topic, our mathematics teacher asks what we already know about this topic.	2.94	.52	1.00	4.00	.11	.68
Quality of explanation (4)	Our mathematics teacher is able to teach us a great deal.	3.29	.63	1.00	4.00	.23	.85

Students’ achievement in mathematics

At the beginning and end of the school year, the students’ mathematics achievement was measured using part of a standardized mathematics test. This test is specifically designed to correspond to each class level in German-speaking Switzerland. The four tests cover 30–70 class-specific mathematics tasks in the areas of arithmetic, geometry, algebra, calculus and stochastics. The test has the advantage of reference values based on a representative sample for each class level (Moser, 2003). In addition, the language complexity of the tasks is reduced and adapted to the reading competence of younger students. Nevertheless, the test also has a limitation. No IRT scaling across class levels was possible due to the lack of anchor items. To merge the tests, test values within the same class levels were z-standardized across both measurement time points for each student. These values were then merged across the class levels to form one variable for each student and measurement time point. The variable expresses how the students’ mathematics achievement is relative to that of other students at the same class level. The mean value at the beginning of the school year was transformed to m = 500, with a standard deviation of sd = 100. For descriptive statistics, see Table 2.

Table 2. Descriptive statistics and internal consistency of students’ mathematics achievement test separated by class.

		Beginning of school year			End of school year
	n	m	sd	Cronbachs α	m	sd	Cronbachs α
3^rd year	130	496	96	.67	607	122	.73
4^th year	71	508	109	.82	615	122	.88
5^th year	134	497	95	.77	595	123	.77
6^th year	174	501	102	.94	611	124	.87
Total	508	500	100	—	608	123	—

Control variable

To control the possible effects of students’ social background on mathematics achievement, the students’ social background was included in the analyses as a control variable. Social background was recorded using the student questionnaire. In order to keep the questionnaire as short as possible, the social background index consisted of two indicators: parents’ educational attainment [measured with the six-level International Standard Classification of Education (UNESCO, 2012)] and possession of books (an aspect of cultural capital). The second aspect was assessed based on the number of books at home, with six answer categories ranging from 1 (‘0 to 10 books’) to 6 (‘more than 500 books’). The index on social background consists of the two indicators of the highest level of school or educational attainment of the students’ parents and the number of books at home, which is a short form of the ESCS, broadly recorded in PISA and highly correlated with it (at least in Swiss data) (r > 0.90). The social background index was formed from a main component analysis of the two items and was z-standardized (for this sample: M = .12; SD = 0.81).

Data analysis

To examine the effect of teachers’ professional knowledge on the three aspects of teachers’ instructional quality (as perceived by students) and students’ mathematics achievement, regression and mediation models (random intercept models) were specified using Mplus 7.0 (Muthén & Muthén, 2019). The calculated models were generated manifestly at class level due to the sample size. The sample size with N = 28 corresponds only slightly to the lower limit (N = 30) for the use of multi-level analyses (Maas & Hox, 2005). Nevertheless, it was necessary to consider the hierarchically nested data structure in the analyses. The intraclass correlation (ICC₁) of student-perceived quality of explanation and students’ mathematics achievement exceeded the critical value of 10% (Lüdtke et al., 2009).

The statistical parameters were estimated using the Full Information Maximum Likelihood Method (FIML; Schafer & Graham, 2002; a total of 6.04% missing values).

Results

The impact of PPTK on students-perceived instructional quality

The first research question deals with the effect of PPTK on three aspects of teachers’ instructional quality, as perceived by students.

Table 3 shows the effect of PPTK on student-perceived instructional quality aspects. The findings indicate a significant positive impact of PPTK on student-perceived classroom management (β = .28; p = .098) and on quality of explanation (β = .30; p = .055). A positive relation, although not significant is seen between PPTK and students-perceived cognitive activation (β = .25; p = .247).

Table 3. Effect of PPTK on student-perceived instructional quality.

	Student-perceived classroom management	Student-perceived cognitive activation	Student-perceivedquality of explanation
	M1 β (SE)	M2 β (SE)	M3 β (SE)
Student level
Students’ social background	−.08(.05)	−.07(.04)	−.08(.04)^(*^)
Class level
Aggregated students’ social background	−.03(.26)	−.02(.27)	.03(.20)
PPTK	.28(.17)^(*^)	.25(.21)	.30(.15)^(*^)
Explained variance at student-level (R^2within)	1%	1%	1%
Explained variance at class-level (R^2between)	8%	6%	9%

Notes: PPTK: pedagogical-psychological teaching knowledge; Sample: class level N = 28; student level N = 509; random-intercept-model; M1: dependent variable = student-perceived classroom management; M2: dependent variable = student-perceived cognitive activation; M3: dependent variable = student-perceived quality of explanation; coefficients are standardised.

⁽*⁾p < .10.

The impact of PPTK on student-perceived instructional quality, and students’ mathematics achievement

Eight random intercept models were specified to investigate the impact of PPTK on students’ mathematics achievement. The null model showed that according to the ICC₁, 15% of the variance in students’ mathematics achievement was due to differences between classes. The results of these analyses (see Table 4) show that students’ mathematics achievement at the beginning of the school year and their social background account for 59% of the variance at student level and 96% of the variance at class level (M1). In addition to these two important predictors, a significant positive effect on class level was found between student-perceived cognitive activation (M3: β = .19; p = .062) as well as PPTK (M5: β = .23; p = .004). No significant effect is indicated between student-perceived classroom management (M2) and teachers’ quality of explanation (M4).

Table 4. Impact of teachers’ PPTK and student-perceived instructional quality on students’ mathematics achievement.⁴

	Students’ mathematics achievement t2
	M1 β (SE)	M2 β (SE)	M3 β (SE)	M4 β (SE)	M5 β (SE)	M6 β (SE)	M7 β (SE)	M8 β (SE)
Student level
Students’ mathematics achievement t1	.74 (.02)***	.74(.02)***	.73 (.02)***	.74 (.02)***	.73 (.02)***	.73 (.02)***	.73 (.03)***	.73 (.02)***
Students’ social background	.10 (.03)**	.09(.03)**	.09 (.03)**	.09 (.03)**	.10 (.03)**	.09 (.03)**	.09 (.03)**	.09 (.03)**
Student-perceived classroom management		−.03 (04)				−.01 (.04).
Student-perceived cognitive activation			-.07 (.04)*				-.07 (.04)^(*^)
Student-perceived quality of explanation				.01 (.03)				.01 (.03)
Class level
Aggregated students’ mathematics achievement	.89 (.07)***	.93 (.07)***	.86 (.07)***	.93(.07)***	.86 (.09)***	.88 (.09)***	.83 (.08)***	.90 (.11)***
Aggregated. students’ social background	.33 (.14)*	.31 (.13)*	.32 (.13)*	.30 (.13)*	.28 (.14)*	.26 (.13)*	.29 (.13)*	.25 (.13)*
Aggregated student-perceived classroom management		.17 (.11)				.08 (.12)
Aggregated student-perceived cognitive activation			.19 (.10)^(*^)				.12 (.12)
Aggregated student-perceived quality of explanation				.14 (.10)				.09 (.11)
PPTK					.23 (.08)**	.23(.08)**	.20 (.09)*	.23 (.09)**
Explained variance at student-level (R^2within)	59%	59%	60%	59%	58%	58%	57%	58%
Explained variance at class-level (R^2between)	93%	97%	97%	97%	98%	98%	97%	98%

Notes: PPTK: pedagogical-psychological teaching knowledge; Sample: class level N = 28; student level N = 509; random-intercept-model; t1: beginning of the school year; t2: end of the school year; dependent variable = students’ end-of-year mathematics achievement; coefficients are standardized.

⁽*⁾p < .10; *p < .05; **p < .01; ***p < .001.

Discussion

Summary and interpretation of results

To strengthen evidence-based teacher education, we should have a better understanding of which teacher education outcomes are predictive of high instructional quality and student learning. The specific aim of this article was to expand on previous findings relating to the impact of primary school teachers’ PPTK, the three aspects of instructional quality (classroom management, cognitive activation and quality of explanation) and the students’ mathematics achievement.

It should be pointed out in advance that the results presented here must be interpreted carefully due to the small sample size (N = 28) (analogue to Cauet et al., 2015) and the large explained variance at class level (R²_between) as stated in Table 4.

The first research question focuses on the relation between PPTK and student-perceived classroom management, cognitive activation and quality of explanation. The results clearly indicate that PPTK is a significant positive predictor for student-perceived classroom management and quality of explanation. This finding confirms the statement by Rowan et al. (2002) that it is difficult for teachers with low PPTK to prepare mathematical content adequately for the target level. Student-perceived cognitive activation is not a significant predictor. Nevertheless, with a beta coefficient of β = .25, the effect size is only slightly lower than for the other analysed aspects of instructional quality. It can be assumed that the lack of significance is a consequence of the small sample size at class level.

The second research question focuses on the relationship between PPTK and student achievement. PPTK showed a significant positive effect on students’ mathematics achievement. The contextualized measurement of PPTK assesses the teaching of relevant situation-specific skills (analogous to the competence model of Blömeke et al., 2015). The results confirm the assumption that a high level of PPTK is an important prerequisite for supporting successful learning processes.

Although the present study shows that students’ characteristics explain the particularly high variance in school achievement, it also shows that teachers with a well-developed PPTK can influence students’ achievement. This finding is in line with other studies which have concluded that good teachers make a difference to student progress (Fauth et al., 2019; Hattie, 2010).

To sum up, with the contextualized and situation-specific measuring in the present paper, the theoretically assumed importance of situation-specific skills for instructional quality and students’ learning progress can be emphasized. The results indicate that general pedagogical competence, more specifically PPTK, is important for subject-specific learning processes in mathematics.

Strengths and limitations

By looking at teachers’ PPTK, and their direct effects on student-perceived instructional quality and students’ mathematics achievement, this study aimed to empirically examine the theoretically assumed impact of teachers’ situation-specific skills in pedagogical-psychological knowledge and instructional quality on students’ mathematics achievement in primary school (Neuweg, 2014; Terhart, 2012). Although a high proportion of the variance in students’ mathematical achievement is attributable to their previous knowledge and social background, there are still significant effects with PPTK. It should be noted that the results show significant relations between teachers and students, although there was less than one school year between the two measurement points. Additionally, these significant results became evident between the three types of data: (1) standardized, contextualized assessment of one aspect of teachers’ situation-specific skills, (2) students’ questionnaire on the perceived instructional quality and (3) standardized measurement to assess students’ mathematics achievement.

Finally, the results must also be viewed critically. First, it should be noted that the present results are not necessarily transferable to other school levels. However, a study at secondary level reached comparable conclusions (König et al., 2021). Furthermore, teachers’ classroom management, cognitive activation, as well as quality of explanation could be seen as important characteristics of instructional quality. However, there are other important aspects of effective teaching such as MCK, MPCK or the teacher-student-relationship that have not been considered in the present paper. Additionally, the aspects of instructional quality recorded were the students’ perceptions. Although this is a common method (Clausen, 2002), it has disadvantages as well as advantages. For example, it is questionable whether primary school students have adequate language skills and the ability to make a differentiated judgement about what is happening in the classroom. In addition, although instructional quality was recorded in relation to mathematics teachers, it was recorded generally and not in relation to subject-specific content (Blömeke et al., 2020).

Furthermore, two issues need to be considered when interpreting the relations with students’ mathematics achievement. On the one hand, it should be noted that although the test for measuring mathematics achievement is adapted to respective levels, its content is very broad. It can be assumed that more curriculum-sensitive tests (for example, referring to the specific learning objectives of a lesson series) would have a more pronounced effect on students’ learning success (e.g. Lange et al., 2015; Seidel & Shavelson, 2007). On the other hand, data from tests with their own metrics, used to record students’ mathematics achievement, should not be disregarded. With the use of z-standardization within class levels (which pinpoints a student relative to other students within the respective class level), the data could be combined into one variable (see Chapter ‘Instruments’). Future research projects should either use the same test for all students (though not viable across a larger age range) or use a test design that allows common scaling via anchor items.

Implications for future research

It is as important as it is challenging to develop contextualized assessments that are reliable and valid (see for an overview, Depaepe et al., 2020). Contextualized, situation-specific assessments can be a solution to go beyond the limited scope of traditional paper-and-pencil assessments. Newer assessments require teachers to apply their knowledge in hypothetical classroom situations (Blömeke et al., 2015; Depaepe et al., 2020; Shavelson, 2010).

The present results emphasize the importance of PPTK for instructional quality and students’ mathematics achievement. However, the results also indicate that more research is needed to gain more evidence-based knowledge about the complex relation between teachers’ competence, instructional quality and students’ learning. There are still many questions to be answered. The mediating role of instructional quality to explain effective learning processes would be highly relevant to gaining deeper insights into the evidence-based development of teacher education. To specify such mediator models, larger sample sizes at class level are needed. Another open question is the impact of the three aspects of professional knowledge (CK, PCK and GPK) on situation-specific skills, on different aspects of instructional quality and on students’ achievement.

Implications for theory and practice

It can be assumed that situation-specific skills are important for instructional quality and students’ achievement (Blömeke et al., 2022; König et al., 2021). This leads to the suggestion that pre-service teachers need learning opportunities to transform their GPK into situation-specific skills and their PPTK, respectively. For teacher education, it is relevant to know how pre-service teachers can acquire the knowledge and skills they need to become effective teachers. For this reason, intervention studies can contribute to a better understanding of the learning process and the kind of learning opportunities that are crucial during initial teacher education and in the professional induction phase.

The result also contributes to the debate about the concept of subject-specific educational content knowledge (SSECK) as a form of specialized content knowledge (SCK) that is essential for teachers (Hudson et al., 2023). However, the present paper cannot give any advice as to the importance of MCK and MPCK for successful learning processes in mathematics. Nevertheless, the present paper also emphasizes the importance of general pedagogical competence (comprising knowledge and situation-specific skills) for subject-specific learning processes, for example, in mathematics.

Conclusion

Despite certain limitations, the present paper contributes to the understanding of the role of teachers’ situation-specific skills in a pedagogical-psychological context for instructional quality and students’ achievement in primary school. The findings emphasize the importance of assessing not only teacher competences but also the various aspects of instructional quality and students’ achievement to expand the insights into teaching and student learning. A more profound understanding of teachers’ professional knowledge, which is relevant for coping successfully with the requirements of complex teaching practice, is essential to comprehend which teacher education outcomes are predictive of high instructional quality and student learning. Such knowledge is seen to be fundamental in strengthening evidence-based and effective teacher education.

Ethics approval statement

Written informed consent was obtained from the parents and the teachers for the data collection. On the day of the survey, the children could decide independently whether they wanted to participate or solve another task in another room or in another class. All subjects gave their informed consent for inclusion before they participated in the study. The consent was approved by the legal office of the St.Gallen University of Teacher Education. There is no ethics committee established at the St.Gallen University of Teacher Education, therefore no approval could be obtained. The St.Gallen University of Teacher Education upholds the regulations of the Swiss Academies; these were followed throughout.

Geolocation information

Switzerland (German-speaking Switzerland)

Acknowledgments

The Open Access publication of this article was funded by the Open Access Publication Fund of the St.Gallen University of Teacher Education (PHSG). Many thanks to Catherine Ferris for proofreading the article.

Disclosure statement

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

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

This work was supported by the Swiss National Science Foundation under [Grant 100019_146172].

Notes

1. In Switzerland, teachers either teach one or two (or more) classes simultaneously (mixed-age groups).

2. For a detailed description of the test and analysis, see Brühwiler et al. (2017).

3. To maximize the understanding of third graders, the test administrators additionally read out statements in the questionnaire. The reliability was acceptable to good (.69 < ICC₂ < .85) within the class levels.

4. The analyses were repeated without the aggregated students’ beginning of-year mathematics achievement due to the high R² at class level. The coefficients of professional knowledge increase, but MPCK remains statistically insignificant. Due to this and the high predictive power of prior knowledge, the authors decided to comprehensively map the influencing variables in the analyses and to consider aggregated students’ beginning of-year mathematics achievement in the analyses.