Introduction

The quality of day-to-day classroom interactions between teachers and students plays a major role in the competencies and work habits that students develop (Hamre & Pianta, 2001). Studies have shown that teachers’ interactions with individual students in the classroom are influenced by their perceptions and expectations of the students’ competencies (Wang et al., 2018). Depending on whether teachers perceive students as high or low performing, the provided amount and quality of feedback, praise, assistance, and accessibility differs (Rubie-Davies, 2007; Rubie-Davies et al., 2015; Urhahne, 2015; Weinstein, 2002).

The first study concerned with teacher expectancy effects was the famous Pygmalion in the Classroom experiment by Rosenthal and Jacobson (1968), in which they induced falsely high expectations among teachers for randomly selected students. The study showed a link between these incorrect teacher expectations and student outcomes, manifesting in a self-fulfilling prophecy: Students for whom teachers expected high performance due to their supposedly high ability actually demonstrated better performance over the school year compared to students for whom teachers did not hold such high expectations. There is now a vast body of research following from the Pygmalion study (for meta-analyses, see Dusek & Joseph, 1983; Harris & Rosenthal, 1985; for reviews, see Jussim & Harber, 2005; Wang et al., 2018). This research shows that self-fulfilling prophecies can also be observed in everyday classrooms because of teachers’ natural perceptions of students. Most of this research has focussed on the causes and effects of teacher perceptions and expectations regarding student achievement, leaving aside other aspects of students’ classroom behaviour (for a few exceptions, see Gentrup & Rjosk, 2018; Jussim et al., 1996; Madon et al., 1997; Westphal et al., 2016).

In the present study, we argue that in order to gain a comprehensive understanding of how teacher perceptions influence student outcomes, it is important to take into account teachers’ perceptions of student motivation and engagement. When teachers interact with their students, they may not only pay attention to students’ cognitive learning processes; they may also notice whether a student appears motivated and engaged in learning activities for example by paying attention in class or investing a lot of effort in mastering class content. This assumption is supported by prior findings indicating that teachers monitor students’ classroom behaviour (Goldberg et al., 2021; Schnitzler et al., 2020), and consider students’ motivation and engagement in their grading practices (Brookhart et al., 2016; Guskey & Link, 2019) as well as in their reasoning about students’ success and failure (Wang & Hall, 2018). Teachers who perceive a student as motivated and engaged are more likely to offer support, provide better-structured learning opportunities, and foster autonomy (Skinner & Belmont, 1993). In the process, they promote students’ learning and academic achievement. As a result, student outcomes may not solely be influenced by teacher perceptions of student achievement but may also be linked to teacher perceptions of student motivation and engagement.

Teacher perceptions of motivation and engagement and teacher perceptions of achievement are highly intertwined and sometimes hard to distinguish (Brandmiller et al., 2020; Kaiser et al., 2013). Timmermans et al. (2016) showed that teachers’ achievement expectations are influenced by their perceptions of students’ working habits. Similarly, Lavrijsen and Verschueren (2020) reported that teachers’ perceptions of students’ cognitive abilities are shaped by their perceptions of students’ classroom engagement. Hence, while teacher perceptions of student motivation and engagement are closely related to teacher perceptions of student achievement, they should be regarded as a separate construct that is clearly relevant in daily classroom interactions. In the present contribution, we focus on teacher perceptions of students’ motivation and engagement and investigate whether they predict students’ achievement and self-reported motivation and engagement in reading and maths over a 3-year period.

The relevance of teacher perceptions in the classroom

More than half a century of research on teacher perceptions and expectations has yielded a vast body of studies (for reviews, see Brophy, 1983; Jussim & Harber, 2005; Wang et al., 2018). In this section, we will briefly outline the major findings of this work, with a focus on observational studies that investigated how teacher perceptions predict student outcomes in real-world classroom settings, which aligns with the focus of the present study. However, before we can do so, we must clearly distinguish between teacher perceptions and expectations, as these terms are often used interchangeably in the literature (e.g., Blanchard & Muller, 2015; Hinnant et al., 2009; Hughes et al., 2005; Rubie-Davies, 2010; Rubie-Davies et al., 2014). We understand the difference between the two terms as temporal in character: Perceptions refer to the current status quo, whereas expectations are predictions about future developments. We will apply this distinction using the term perceptions whenever teachers were asked about their students’ current status—as in our study—and expectations when teachers were asked about an anticipated future development.Footnote 1

Overall, previous research has found small (Jussim et al., 2009) to moderate associations (Hattie, 2009) between teacher perceptions of student achievement and student outcomes. In the most recent synthesis of previous research, Hattie (2009) reported an effect size for teacher perceptions of d = 0.43 on different performance-related measures. This effect size was derived from eight meta-analyses containing 674 different experimental and observational studies that report information about perception effects in school and other contexts. Moreover, there is also emerging evidence for teacher perception effects on student socio-psychological outcomes such as their self-concept (Timmermans & Rubie-Davies, 2022).

Some studies have indicated that teacher perceptions may be differentially related to outcomes in different domains, such as maths and reading. However, the findings on domain-specific differences are inconsistent: Hinnant et al. (2009) found that teacher perceptions were related to future maths performance but not to future reading performance. In contrast, Sorhagen (2013) and Gentrup et al. (2020) found that teacher expectations were related to student achievement in both domains but reported a stronger link for reading achievement—at least descriptively—when comparing the size of the coefficients. Some studies have found that teacher perceptions are equally related to achievement in maths and reading (Baker et al., 2015; Speybroeck et al., 2012).

Research on long-term effects has found that teacher perceptions (Hinnant et al., 2009) and expectations (de Boer et al., 2010) were related to student outcomes both 1 year later and even 5 years later. Alvidrez and Weinstein (1999) showed a link between the over- or underestimation of kindergarten children’s IQ compared to their actual performance on an IQ test and their grade-point average and achievement 14 years later. Furthermore, de Boer et al. (2010), who monitored students over a 5-year period, reported that teacher expectation effects were strongest in the first year in secondary school when students and teachers met for the first time. The effects diminished somewhat over the course of 2 years but remained stable afterwards. These results are supported by a study focussing on elementary school students by Kuklinski and Weinstein (2001)—they also found the largest effects in Grade 1 rather than in Grades 3 and 5.

One reason for the finding of stronger effects in the first year of elementary or secondary school may be that such situations enable researchers to capture teacher perception effects, because they have control measures of student outcomes from a time point at which students and teachers hardly know each other, and teacher perception effects could not have kicked in. In fact, one of the main criticisms in Jussim and Harber’s (2005) review on teacher perceptions and self-fulfilling prophecies is that the design of most studies does not allow distinguishing whether teacher perception effects occur because of a self-fulfilling prophecy or because teacher perceptions are accurate. Teachers may base their perceptions on factors beyond those captured by the predictors and control variables deployed. If these factors result in a more accurate perception, the links that such studies find between teacher perceptions and the outcome in question might not be regarded as a teacher-perception effect but as an accurate teacher rating about their students’ future development. Given that, teachers spend several hours a week with their students over the course of months or even years and, therefore, have a vast amount of information to base their perceptions on, this criticism from Jussim and Harber (2005) is entirely reasonable. Nonetheless, only a few studies, such as Gentrup et al. (2020) or Muntoni and Retelsdorf (2018), have considered this criticism and measured teacher perceptions at the beginning of a school year. Hence, for a study to truly investigate teacher perception effects, it would have to ensure that teachers have spent little time with their students when they rate them – which is why we consider teacher perceptions at the beginning of Grade 5 when teachers and students have known each other for only a few weeks.

How teacher perceptions influence student outcomes

What we can take from findings on the effects of teacher perceptions of students’ achievement on student outcomes is that teachers apparently communicate and show their positive or negative perceptions of their students, either explicitly or implicitly. In their systematic review of 30 years of literature about the Pygmalion effect, Wang et al. (2018) derived a five-step model that illustrates the link between teacher perceptions and student outcomes. According to this model, teachers begin by perceiving their students (1) and then behave differently towards them based on their perceptions (2). This, in turn, is perceived by their students (3), influencing students’ socio-psychological factors (4), and ultimately affecting their achievement outcomes (5). A link between teacher perceptions and student outcomes that may lead to a self-fulfilling prophecy can only be established if teachers treat their students differently, and students notice this differential treatment.

Brophy (1983) compiled a list of 17 teacher behaviours through which teachers communicate their negative perceptions of individual students to these students. The list contains behaviours such as differential forms of feedback, reinforcement, interactions, and nonverbal cues given to students perceived as high or low performers. Studies that have analysed differential teacher behaviours since then have echoed these results, concluding that behavioural differences among teachers especially concern the amount and quality of feedback, praise, and assistance they give when students have problems with questions, tasks, and the teachers’ accessibility (Rubie-Davies, 2007; Rubie-Davies et al., 2015; Urhahne, 2015; Weinstein, 2002). Teachers tend to be less supportive towards students whom they perceive as less academically talented or for whom they have lower expectations. They relate less well to these students, which is problematic since these teacher behaviours have been linked to learning outcomes (Rubie-Davies et al., 2006; Rubie-Davies et al., 2015; Zhu et al., 2018). Moreover, there is evidence showing that students are aware of this differential treatment of teachers. In experimental studies that entailed showing only 10-s-long clips of teachers, students were able to detect differences in teachers’ nonverbal behaviour towards low- and high achieving students (Babad, 2005; Babad et al., 2003). In everyday classrooms, students use various cues from their interactions with teachers to infer their teachers’ expectations of their achievement. According to recent qualitative studies, students gauge their teachers’ expectations based on several factors, including the level of confidence teachers communicate toward them, the teaching approaches, the relationship with the teacher, and the learning environment (Johnston et al., 2021, 2023). For instance, when teachers praised students, addressed them as active learners, showed care, and fulfilled their basic needs for autonomy, competence, and relatedness, students believed that their teachers held high expectations for them (Johnston et al., 2023). The way in which teachers communicated their expectations affected students’ socio-psychological and behavioural reactions. If teachers communicated a combination of encouragement, praise, and confidence, students adopted a similar belief in their competence and responded with maintained or increased engagement. Conversely, when teachers unfavourably compared students to their peers without expressing confidence in their potential, students tended to disengage (Johnston et al., 2021). Taken together, these results show that teachers differ in how they behave towards their students depending on their perceptions, and students are aware of this differential treatment.

Teacher perceptions of student motivation and engagement

Students greatly differ with regard to how motivated and engaged they are during classroom learning. Student motivation refers to the multifaceted internal processes that drive and manifest themselves in student engagement (Connell & Wellborn, 1991; Reeve, 2012; Skinner et al., 2008; Skinner et al., 2009), including many different observable behaviours such as effort, persistence, working habits, attendance, and participation in class discussions (Appleton et al., 2006; Fredricks et al., 2004). Therefore, student motivation and engagement are closely related constructs (Wong & Liem, 2022).

Prior studies have shown that student motivation and engagement should be treated as domain-specific constructs (Bong, 2001; Green et al., 2007; Hornstra et al., 2016). Students can be highly motivated and engaged in one subject while being less motivated and engaged in another one. This domain-specificity is particularly pronounced for older students (Green et al., 2007). Additionally, the pattern of association within subjects – that is, how different aspects of student motivation and engagement are related to one another within one school subject – seems to be distinct (Arens et al., 2019; Guay & Bureau, 2018). For example, in German and maths, different motivational facets tend to predict student participation in classroom discussions (Böheim et al., 2020). Hence, studies should take student motivation and engagement as subject-specific constructs into account.

Given that student motivation and engagement are central in everyday classrooms, we argue that teacher perceptions of these constructs, in addition to teachers’ perceptions of student achievement, can shape classroom interactions between students and teachers. Not only do teachers monitor their students’ motivation and engagement (Goldberg et al., 2021; Schnitzler et al., 2020), but they also take it into account in their grading (Brookhart et al., 2016; Guskey & Link, 2019) and reasoning about the causal sources of students’ failure and success (Wang & Hall, 2018). Consequently, interactions between teachers and students may also be affected by teacher perceptions of students’ motivation and engagement. In fact, several studies reported that teachers differ in their interactions with individual students based on their perceptions of students’ motivation and engagement. They provided individual students with more structure and supported their autonomy if they perceived them to be more engaged (Skinner & Belmont, 1993). Moreover, teachers reacted with more sympathy, encouragement, and support if they perceived students’ low ability as the reason for low achievement, whereas they reacted with more anger, criticism, negative feedback, and lower support if they perceived students’ low engagement as the reason for low achievement (Georgiou et al., 2002; Wang & Hall, 2018).

Given these findings, it is likely that teacher perceptions of student motivation and engagement can have an effect on student outcomes. However, while some studies investigated the degree to which teacher perceptions of student motivation and engagement are accurate (e.g., Fiedler et al., 2002; Zhu & Urhahne, 2021), there are very few studies examining the link between teacher perceptions of students’ motivation and engagement (or specific facets of these two constructs) with student outcomes. Jussim (1989) found that teacher perceptions of student effort were associated with maths achievement during Grade 6 but were largely unrelated to students’ motivation. Gentrup and Rjosk (2018) found that during Grade 1, teacher perceptions of student motivation and working habits significantly predicted students’ reading achievement, but not maths achievement. Upadyaya and Eccles (2014, 2015) followed students for 4 years of their primary education starting in Kindergarten, Grade 1, or Grade 3, to investigate how teacher perceptions of students’ effort and personal value influenced students’ interest in maths (Upadyaya & Eccles, 2014) and students’ self-concept in reading and maths (Upadyaya & Eccles, 2015). While longitudinal relations were predominantly non-significant, significant associations were mainly observed between teacher perceptions and students’ interest and self-concept at concurrent time points. As most of these previous studies (Gentrup & Rjosk, 2018; Upadyaya & Eccles, 2014, 2015) focussed on students in their early years of education during Kindergarten and elementary school, it remains unclear whether teacher perceptions of student motivation and engagement are also relevant for secondary school students. Moreover, to gain a comprehensive understanding of such teacher perception effects, it is important not only to investigate how these effects may unfold over longer periods, but also to examine different student outcomes and school subjects. The latter aspect is especially important when it comes to student motivation and engagement, as these are domain-specific constructs.

The present study

Previous research has extensively focussed on teacher perceptions of students’ achievement and how they relate to student outcomes. However, based on emerging empirical evidence (Gentrup & Rjosk, 2018; Upadyaya & Eccles, 2014, 2015), we argue that teacher perceptions of student motivation and engagement may also play an important role in student outcomes. Therefore, we aimed to determine whether these perceptions predict student achievement, as well as motivation and engagement in both maths and reading over the course of several school years. Our research questions were as follows:

  • Research Question 1: Are there associations between teacher perceptions of student motivation and engagement at the beginning of secondary school in Grade 5 and student achievement and self-reported motivation and engagement in Grades 6, 7, and 8 in reading?

  • Research Question 2: Are there associations between teacher perceptions of student motivation and engagement at the beginning of secondary school in Grade 5 and student achievement and self-reported motivation and engagement in Grades 6, 7, and 8 in maths?

Following Gentrup and Rjosk (2018), we expected to find an association between teacher perceptions and students’ subsequent achievement. In terms of student motivation and engagement the studies from Upadyaya and Eccles (2014, 2015), which found hardly any longitudinal associations between teacher perceptions and different motivational constructs, made a relation of teacher perceptions with students’ subsequent motivation and engagement unlikely. However, qualitative insights from Johnston et al. (2021, 2023) indicated that students change their motivation and engagement in reaction to teachers’ perceptions, making it plausible to assume teacher perceptions effects. We did not have any expectations regarding different relational patterns in maths and reading because prior evidence has been inconclusive in this regard.

When it comes to teacher perception effects in the context of student motivation, two challenges must be considered. First, students’ motivation cannot be observed directly but must be inferred from their behaviour in classrooms. To address this issue, we focussed not solely on student motivation but also on their engagement as a behavioural proxy of motivation, which can be more easily observed by a third person. Previous research has demonstrated higher correlations between teacher perceptions and student motivation when teachers consider behavioural aspects (Urhahne & Wijnia, 2021).

The second major challenge when investigating the effects of teacher perceptions in real-world classroom settings is ensuring that teachers and students have spent minimal time with each other before teachers are asked to rate their students. This is of crucial importance for understanding the temporal and causal order of teacher perceptions and student outcomes. To address this challenge, we specifically used perception data from teachers who had known their students for just a couple of weeks before rating them. For our study, this was the case at the beginning of Grade 5, when students entered secondary school.

Method

Sample and procedure

Data for the present study were drawn from a larger study (Jonkmann et al., 2013) conducted in secondary schools from two federal states in Germany: Baden-Württemberg and Saxony. The study received approval in terms of ethical standards and data protection guidelines from the Ministry of Education, Youth, and Sports in the state of Baden-Württemberg and the Ministry of Education and Cultural Affairs in the state of Saxony.

Germany employs a tracking system for secondary education, whereby students are sorted into different types of secondary schools after Grade 4 or Grade 6, depending on the state. Students are commonly separated into high, middle, and low tracks depending on their previous achievement. The highest track prepares students for university until Grade 12/13. The middle track provides advanced education until Grade 10 to prepare students for vocational careers, but depending on their achievement, students can pursue further education. The low track offers basic education for students until Grade 9, preparing them for vocational careers and apprenticeships. However, there are also some exceptions. For example, some states offer comprehensive schools or sort students only in two tracks.

Data for the present study were collected between the fall of the 2008/09 school year at schools from the low and middle track when the students were in Grade 5, and the fall of the 2011/12 school year when the students were in Grade 8.Footnote 2 Over that period, there were four measurement points, each at the beginning of the school year.

The study used a two-stage cluster sampling approach. All public schools in the two federal states—except for schools of the highest track, schools for children with special educational needs, and special minority-language schools—were part of the potential sample. From those schools, 107 were randomly selected. In each of the schools, 1–2 classrooms were then chosen at random, resulting in a total of 135 classrooms. From each classroom, approximately 29 students (SD = 6.40) participated in the study after parents and students were informed about the study’s purpose, and parents provided written consent. The total sample of the study comprised 3880 students.

For our analyses, we used data on students who had participated at least once in the study but excluded students who entered the sample in Grade 8. To answer our research questions, we ensured that the teacher who rated a student’s motivation and engagement was also the one who was teaching them in the domain in question in Grade 5. Consequently, we excluded students for whom neither the perceptions of their German nor maths teacher were available, leading to an analytic sample of 2402 students (56% boys) who were on average 10.70 years old (SD = 0.73). For the domain-specific analyses, we had to use a subsample. In Grade 5, there were 58 German teachers (22% male, Mage = 43.82 years, SDage = 12.13) with a teaching experience of 17.89 years (SD = 11.88) teaching n = 1582 (MDES = 0.09) students and 50 maths teachers (28% male, Mage = 45.04 years, SDage = 10.68) with an experience of 21.06 years (SD = 11.48) teaching n = 1289 (MDES = 0.07) students. The two subsamples overlapped and 469 students were included in both subsamples. For the purpose of our study, it is important to note that in Germany, it is common for teachers to teach a class for two consecutive academic years, after which a different teacher continues teaching the class. In our sample, 11% of the students had new German teacher in Grade 6, an additional 38% in Grade 7, and a further 27% in Grade 8. For maths, 12% of the students had another maths teacher in Grade 6, an additional 42% in Grade 7, and a further 25% in Grade 8.

Measures

Teacher perceptions of student motivation and engagement

For each student, teachers were asked to rate student motivation and engagement at the beginning of Grade 5 using five items (“this student participates intensely,” “this student is very motivated in class,” “this student solves tasks quickly,” “this student listens to the teacher,” “this student is punctual and reliable”; α = 0.91). The students were judged on a 5-point Likert scale, ranging from 1 = does not apply at all to 5 = applies completely. The items were specifically designed for this study to assess both student motivation and different behavioural aspects of student engagement that can be observed by a third person.

Student achievement

We measured student achievement at the beginning of each school year using standardised achievement tests for maths and reading comprehension. Most of the test items were taken from comparable large-scale school performance assessments, such as TIMSS (Baumert et al., 1997), ELEMENT (Lehmann & Nikolova, 2005), BIJU (Baumert & Lehmann, 1997), or PISA (Artelt et al., 2001). The tests were designed to reflect the course content for each school year (Jonkmann et al., 2013). To scale the achievement tests, item response theory (IRT) models were used, resulting in estimates of students’ academic achievement in the form of weighted likelihood estimates (WLE; Warm, 1989). WLEs can be considered as individual achievement estimates on a logit scale, with higher values indicating higher competencies. The achievement tests in both maths and reading domains reached acceptable reliability (Maths: Rel(WLE) = 0.70; Reading: Rel(WLE) = 0.71).

Students’ self-reported motivation and engagement

Students’ self-reported domain-specific motivation and engagement were measured with four identical items for maths and German, respectively (“In maths/German, I really make an effort”, “In maths/German I do all of my homework very diligently”, “In maths/German I always give my best”, In maths/German I really am a hard worker”), at the beginning of Grade 5, 6, 7 and 8. The responses were collected on a 4-point Likert scale ranging from 1 = does not apply at all to 4 = applies completely. The scales were adapted from Trautwein et al. (2009) and showed good reliability (α = 0.79-0.87 for maths and α = 0.81-0.86 for German).

Control variables

Because studies have shown associations between teacher perceptions and student characteristics such as SES, migration background, and gender (Brandmiller et al., 2020; Jussim et al., 1996; McKown & Weinstein, 2008; Neuenschwander et al., 2021; Ready & Chu, 2015), we controlled for these characteristics in all our analyses. To measure students’ socio-economic status, we used the International Socio-Economic Index of Occupational Status (ISEI; Ganzeboom et al., 1992), which ranks parental occupations on a scale from 16 (low SES) to 90 (high SES). When data for both parents were available, we used the higher ISEI for the analysis (HISEI). Migration background was dummy coded (0 = both parents born in Germany and 1 = at least one parent not born in Germany). Sex was dummy coded (0 = female, 1 = male). Additionally, we controlled for students’ cognitive abilities at the beginning of Grade 5, which were measured using three sub-tests from the KFT 4–12 + R cognitive ability test (Heller & Perleth, 2000), capturing students’ quantitative, verbal, and non-verbal abilities. The three subtests were IRT-scaled and averaged for the present analyses as a measure of students’ general cognitive abilities. Table 1 presents the descriptive statistics for all variables used in the present study.

Table 1 Descriptive statistics
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Statistical analyses

Missing data

We examined the missing data in our sample before conducting analyses to answer our research questions. For core information about the students (i.e., sex, SES) only very few missing values (around 1%) occurred, because we retrieved this information from the schools themselves. For the key outcome measures—standardised achievement in reading and maths— the response rates were also very high, ranging from 90 to 96% depending on the measurement point, because the tests were conducted during school hours and participation was required by the state. The data collected via student and teacher questionnaires concerning student’s motivation and engagement had notably higher proportions of missing values, ranging from 12 to 24%.

A significant Little’s MCAR test (χ2 = 6748.335, DF = 5677, p < 0.001) indicated that the data were not missing completely at random (MCAR). Therefore, assuming data were missing at random (MAR), we conducted missing data imputation with all the variables, both independent and dependent, from our main analyses (Graham, 2009). Missing data imputation uses all available information, maximising test power and minimising the risk of biased results, as the underlying assumptions in this case are weaker than those of listwise deletion (Collins et al., 2001; Rubin, 1987). To improve the imputation model by reducing between-imputation variance and the risk of bias, we included auxiliary variables in accordance with Collins et al. (2001), namely class-average achievement, class-average socio-economic status, and students’ school grades. We imputed m = 20 datasets with the multivariate imputation by chained equations package in R (MICE; van Buuren & Groothuis-Oudshoorn, 2011) and subsequently estimated all analyses 20 times, combining the results according to Rubin (1987). The fraction of missing information (FMI) of each coefficient, which can be attributed to between-imputation variance and indicates whether the observed data in the imputation model provided good information about the missing values, varied between FMI = 0.06–0.23 with values closer to 0 indicating that the observed data contain much information about the missing values (Madley-Dowd et al., 2019).

Structural equation modelling

To answer our research questions, we employed structural equation modelling, with teacher perceptions of student motivation and engagement and self-reported student motivation and engagement as latent variables. To make sure that student self-reported motivation and engagement was comparable over the different measurement points, we first tested for measurement invariance. Following the procedure described by Byrne (2013), we started by testing for configural invariance and then added more restrictions to the model step by step until we could test our model for strict factorial invariance. All the while, we took note of the recommendations for model fit provided by Chen (2007) as well as Cheung and Rensvold (2002). According to those authors, when testing models with different levels of measurement invariance against each other, the RMSEA should not increase more than 0.015 and the CFI and TLI should not drop more than 0.01. Following these criteria, we assumed strict factorial invariance for our measures of student self-reported motivation and engagement both in reading and maths (see Table 2 for fit indices).

Table 2 Measurement invariance
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To examine our two research questions, we estimated separate models for maths and reading in which we predicted students’ achievement and self-reported motivation and engagement in Grades 6, 7, and 8 based on teacher perceptions of student motivation and engagement in Grade 5 while controlling for students’ achievement, self-reported motivation and engagement, SES, migration background, sex, and cognitive abilities. For each Grade, we included correlations between student self-reported motivation and engagement and achievement. We estimated all model fits using the RMSEA, CFI, TLI, and SRMR fit indices (Hu & Bentler, 1999; Schermelleh-Engel et al., 2003).

All analyses were conducted in Mplus 8.7 (Muthén & Muthén, 2021). We accounted for the multilevel structure of the dataset, students nested in classrooms, by using robust standard errors (TYPE = COMPLEX). We z-standardised all continuous variables and employed MLR as an estimator for all models.

Results

The results of the models we used to answer our research questions are shown in Fig. 1 for reading (research question 1) and in Fig. 2 for maths (research question 2; see also Tables 3 and 4 in the appendix). First, one can see, that the models fitted our data well. Second, we found statistically significant associations between teacher perceptions and our control variables. More specifically, we found that teacher perceptions of student motivation and engagement in Grade 5 held by German teachers were significantly related to students’ migration background, their sex, and their cognitive abilities, indicating that teachers perceived students whose parents were born in Germany, girls, and those with higher cognitive abilities as having higher motivation and engagement. Perceptions of maths teachers were only related to students’ sex. Girls were perceived to have a significantly higher motivation and engagement than boys. Moreover, both student achievement and self-reported motivation and engagement in the respective domain in Grade 5 predicted teacher perceptions of the same constructs indicating that teachers took both constructs into account when they rated students’ motivation and engagement.

Fig. 1
figure 1

Standardised path coefficients for German teacher perceptions.

Note. N = 1582. Solid lines indicate statistically significant associations (p < 0.05). Dotted lines indicate non-significant results (p > 0.05). Only significant coefficients for predictor or outcome variables are shown. Model included correlations between student self-reported motivation and engagement and achievement for each Grade (not shown). RMSEA = 0.03; CFI = 0.97 TLI = 0.96; SRMR = 0.04; χ2(344, N = 1582) = 837.64, p < 0.001

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Fig. 2
figure 2

Standardised path coefficients for maths teacher perceptions.

Note. N = 1289. Solid lines indicate statistically significant associations (p < 0.05). Dotted lines indicate non-significant results (p > 0.05). Only significant coefficients for predictor or outcome variables are shown. Model included correlations between student self-reported motivation and engagement and achievement for each Grade (not shown). RMSEA = 0.03; CFI = 0.96; TLI = 0.95; SRMR = 0.05; χ2 (344, N = 1289) = 852.79, p < 0.001

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Turning to the paths in the model that directly addressed research question 1, we found that perceptions of student motivation and engagement held by German teachers at the beginning of Grade 5 predicted student achievement in reading (β = 0.09, SE = 0.03, p = 0.001) but not their self-reported motivation and engagement in reading at the beginning of Grade 6. Hence, students whose teachers perceived them to be more motivated and engaged performed better in a standardised achievement test in reading 1 year later, controlling for earlier achievement, students’ self-reported motivation and engagement, student characteristics, and cognitive ablilities. We did not find any long-term relations between teacher perceptions in Grade 5 and student outcomes in reading in Grade 7 or Grade 8.

As for research question 2, we found that maths teachers’ perceptions of student motivation and engagement in Grade 5 predicted both students’ maths achievement (β = 0.08, SE = 0.04, p = 0.046) and students’ self-reported motivation and engagement (β = 0.10, SE = 0.05, p = 0.039) in maths at the beginning of Grade 6 while controlling for earlier achievement, self-reported motivation and engagement, student characteristics, and cognitive abilities. We also found significant long-term relations between teacher perceptions measured in Grade 5 and student maths achievement in Grade 7 (β = 0.09, SE = 0.04, p = 0.014) and Grade 8 (β = 0.09, SE = 0.03, p = 0.013). This means that students whose maths teachers perceived them to be more motivated and engaged at the beginning of secondary school performed better in a standardised achievement test in maths over the course of the following three school years. However, we did not find any long-term association with students’ self-reported motivation and engagement in maths.

Discussion

Although the link between teacher perceptions of student achievement and students’ achievement development has been well established by numerous scholars and studies (Wang et al., 2018), research on the effects of teacher perceptions of student motivation and engagement on student outcomes remains rather limited (with some exceptions such as Gentrup & Rjosk, 2018, and Upadyaya & Eccles, 2014, 2015). However, considering that teacher perceptions of student motivation and engagement may be equally significant for daily classroom interactions as teacher perceptions of student achievement, we aimed to strengthen the research on teacher perceptions in this regard. Therefore, we investigated the short-term and long-term relations between teacher perceptions of student motivation and engagement and student outcomes, specifically focusing on student achievement and student motivation and engagement in maths and reading, respectively.

We found that teacher perceptions of student motivation and engagement were linked to student outcomes in reading and maths. Teacher perceptions in Grade 5 significantly predicted student achievement in both domains 1 year later. Additionally, we observed long-term effects for maths, with Grade 5 teacher perceptions significantly predicting maths achievement 2 and 3 years later. We also found a significant link from Grade 5 teacher perceptions to student motivation and engagement in maths 1 year later. For the domain of reading, there were no long-term effects on student achievement nor effects on student motivation and engagement.

Teacher perceptions of students’ motivation and engagement: key to student outcomes?

Our findings indicated significant short-term effects of teacher perceptions on student achievement from Grade 5 to Grade 6, which occurred for both domains, reading and maths. These results contrast with the findings from the only other study that investigated this association. Specifically, Gentrup and Rjosk (2018) observed a significant link between elementary teacher perceptions of student motivation and work habits and student achievement 1 year later, but only in the domain of reading, not in maths. In another study (Gentrup et al., 2020) the authors argue that the learning gains in primary education are greater in reading compared to maths, which could explain why teacher perceptions had a smaller effect on maths performance. However, in our study, the descriptive results showed that learning gains from Grade 5 to Grade 6 were comparable and even slightly larger in maths than in reading. This may explain why we observed effects more similar to studies concerned with short-term effects of teacher perceptions and expectations of student achievement, where teacher perceptions were equally important for student achievement in both reading and maths (Baker et al., 2015; Speybroeck et al., 2012).

Our results underscored the relevance of teacher perceptions of student motivation and engagement for student achievement over several years, consistent with longitudinal studies examining teacher perceptions of student achievement (Alvidrez & Weinstein, 1999). We observed consistent effects of teacher perceptions in maths over a 3-year period, whereas in reading, teacher perceptions had a significant effect only on Grade 6 achievement. Therefore, our study demonstrates that the strength and duration of the observed teacher perception effects differed between subjects. This finding aligns with Hinnant et al. (2009), who reported similar differences between reading and maths for teacher perception effects during elementary school, but contradicts other studies that found comparable effects for both domains (Sorhagen, 2013).

Our results showed almost no significant association between teacher perceptions and student motivation and engagement. This finding is consistent with the observations made by Upadyaya and Eccles (2014, 2015), who reported only a minor role of teacher perceptions of student motivation in predicting students’ subsequent interest and self-concept among Kindergarten and elementary school children. Our study extends this understanding to secondary school settings, demonstrating similar weak associations for the domains of reading and maths when adopting a more behaviourally-related conceptualization of student motivation. One possible explanation for these weak associations could be the decline in student motivation and engagement from Grade 5 to Grade 8, as observed descriptively in our study, which may lessen the likelihood of teacher perceptions exerting a strong and significant effect.

Limitations

Several limitations must be considered when interpreting our results. First, our study design was correlational and not experimental; hence, we cannot establish causality or rule out the influence of confounding variables. However, our longitudinal approach, combined with the inclusion of strong control variables, enables us to draw meaningful conclusions from our observational study.

Second, it is debatable whether we sufficiently controlled for student motivation and engagement as reported by students themselves. The measurement we used may not have fully captured the same aspects that teachers had in mind when rating their students. Although both teachers’ and students’ questionnaires addressed engagement, the wording of the items for students differed slightly from those items for teachers. As an example, students reported on their effort invested in their homework in one item, which was not part of the teachers’ questionnaire.

Third, we solely focussed on the effects of teacher perceptions of student motivation and engagement and did not take teacher perceptions of student achievement into account. Prior studies have indicated that although these are distinct constructs, they are also correlated (Brandmiller et al., 2020; Gentrup & Rjosk, 2018; Kaiser et al., 2013). Therefore, we cannot rule out the possibility that the significant links we found between teacher perceptions of student motivation and engagement and student outcomes were confounded with teacher perceptions of student achievement, despite including controls for student achievement in all analyses.

Fourth, as we described earlier, in our sample, many students had a new teacher after Grade 7. It seems plausible that the effects of teacher perceptions fade out when students have a new teacher. A new teacher may have different perceptions, introducing other dynamics in the classroom, which could potentially influence student outcomes differently.

Fifth, the reliability of our standardised achievement tests were not ideal, with values of 0.70 for maths and 0.71 for reading. These values can be interpreted as borderline according to often used thresholds and indicate that measurement errors come into play here (Clifton, 2020).

Implications for practice and future research

Our findings have important implications for teachers and teacher education. Our findings showed that the way teachers perceive their students’ motivation and engagement can have important consequences for students’ academic development. Hence, it is vital to address teacher perception effects in teacher education and professional development programs, so teachers are aware of the impact their implicit perceptions of students can have. Moreover, teachers need to know that their perceptions can be systematically biased, particularly by student sociodemographic characteristics (Wang et al., 2018). In our study, being a boy and having a migration background affected teachers’ perceptions of students’ motivation and engagement negatively. Furthermore, it is essential for teachers to understand the complex processes through which their perceptions can potentially become self-fulfilling prophecies (Wang et al., 2018) and to highlight the critical role of (subtle) differential teaching behaviour particularly for the development of students’ achievement. Teachers equipped with this knowledge might be more likely to reflect actively on their own teaching practice and the question of whether they interact differently with students for whom they hold different perceptions. Given that differential teaching behaviour might occur unintentionally and through subtle interactions, teachers could also seek feedback from their students and colleagues or videotape their instruction to uncover such processes.

Our findings also have important implications for future research on teacher perceptions and their effects on student outcomes. In order to gain a comprehensive understanding of teacher perception effects, it is important to consider teacher perceptions of motivation and engagement and teacher perceptions of achievement simultaneously. It remains unclear whether teacher perceptions of student motivation and engagement lead to different teacher behaviours towards and interactions with students than in the case of teacher perceptions of student achievement. While findings from research on teacher perceptions of achievement might be applicable, teacher perceptions of student motivation and engagement could be associated with distinct teacher behaviours. For instance, teachers who perceive a student as especially motivated may foster and support their engagement and interest, while they might challenge a high-performing student with more challenging learning tasks. Moreover, it remains uncertain which specific teacher behaviours might lead to higher student achievement while having a lesser impact on student motivation and engagement, as overserved in our study and others (Upadyaya & Eccles, 2014, 2015).

Taken together, there are many studies concerned with whether there is a relation between teacher perceptions and student outcomes and only few studies that focus on how these perceptions may influence student outcomes. In our view, this should be a way forward for future research to address remaining questions and challenges. Students’ academic development includes not only their achievement but also their motivation and engagement. Therefore, teacher perception research should also consider this fact.