The Joint Operations of Teacher-Student and Peer Relationships on Classroom Engagement among Low-Achieving Elementary Students: A Longitudinal Multilevel Study

Abstract

Although both teacher-student relationship (TSR) and peer relationship (PR) have been found important for the development of students’ classroom engagement, little research has been done regarding the joint operations of these two factors. Guided by a developmental systems framework, this study examined longitudinal between-person and within-person associations between TSR/ PR and classroom engagement in a sample of 784 low-achieving students in the first three years of elementary school. A multidimensional approach was used to distinguish positive and negative dimensions of TSR, as well as peer liking and disliking. At the between-person level, results showed that students’ classroom engagement was positively predicted by positive TSR and PR liking and was negatively predicted by negative TSR and PR disliking. Both positive and negative TSR interacted with PR disliking at the between-person level, such that the associations between positive/negative TSR and classroom engagement were stronger for students with lower levels of PR disliking. At the within-person level, changes in classroom engagement were associated with contemporaneous year-to-year changes in positive/negative TSR and PR disliking. No within-person level interaction effects were found. Cross-level interaction showed that the effects of within-person negative TSR on classroom engagement were stronger for students with lower overall levels of PR disliking. Findings highlighted the importance of using a multilevel multidimensional approach to understand the joint operations of TSR and PR in the development of classroom engagement in low-achieving students in early elementary school.

Classroom engagement refers to students’ self-directed academic behaviors and cooperative participation in various learning activities in the classroom settings (Hughes & Kwok, 2006, 2007; Ladd & Dinella, 2009). Extensive research underscores classroom engagement as a critical prerequisite for long-term academic success (Duncan et al., 2007; Hughes et al., 2008; Ladd & Dinella, 2009; Wang et al., 2020). As young children transition to formal schooling, they face a growing number of academic and social requirements and demands that can act as stressors (Carter et al., 2010; Hamre & Pianta, 2001). As such, understanding processes that engage students in classroom learning during this critical transition is essential to identify early risk and protective factors influential to the long-term academic trajectories (Archambault et al., 2022; Welsh et al., 2020). Teacher-student relationships (TSR) and peer relationships (PR) are two proximal social contexts that play influential roles in the development of students’ classroom engagement and motivations (Wentzel & Ramani, 2016; Yang et al., 2018). Positive social interactions with teachers and peers promote students’ engagement, achievement, and academic well-being by way of facilitating the internalization of teachers’ expected learning values and the pursuit of social goals in compliance with peers (Wentzel, 2022). However, existing literature mainly investigated the influences of TSR and PR on academic functioning separately (Skinner et al., 2022), paying little attention to the joint roles of TSR and PR in classroom engagement among early elementary school students. Examining how the interplay between TSR and PR shapes classroom engagement in early elementary school is essential because TSR and PR are integral social relationships that co-exist in the classroom context (Martins et al., 2022; Skinner et al., 2022). Moreover, a dearth of empirical research has examined these effects longitudinally that partitions the within- and between-person level variance. Examining between- and within-person effects separately better elucidate mechanisms that underlie the developmental associations between social relationships and engagement in the classroom settings, with the former revealing inter-individual differences and the latter divulging intra-individual development over time (Curran & Hancock, 2021; Hoffman, 2015). As such, drawing on a sample of low-achieving elementary schoolers, the current study investigated the effects of the multidimensional TSR and PR on students’ classroom engagement at both the within- and between-person levels to better understand how classroom engagement varies as a function of classroom social relationships across the first three years of elementary school.

Classroom Engagement: What Is It and Why Is It Important?

Engagement is a multidimensional construct that is operationalized as students’ emotional, behavioral, and cognitive persistence and involvement during learning activities in multiple settings (Fredricks et al., 2004; Martin et al., 2022; Reschly & Christenson, 2022; Skinner et al., 2009). Some researchers focus on examining general involvement in school-related activities (academic or nonacademic; Wang & Eccles, 2013), whereas others focus more specifically on engaged participation in learning activities in the classroom (Skinner et al., 2009). Given that engagement in the classroom is conceptually more linked to academic development as compared to general school engagement (Martin et al., 2022), the present study focused on examining students’ effortful engagement behaviors within the classroom setting. Classroom engagement is defined as students’ effortful participation, focused attention, persistent involvement, as well as the absence of disruptive behaviors in classroom learning (Hughes et al., 2008; Ladd & Dinella, 2009).

Extensive work, including both cross-sectional and longitudinal studies, has shown that students’ classroom engagement is an important predictor of students’ academic achievement, learning motivations, academic well-being, and school success (Skinner & Raine, 2022). Students who are highly engaged in classroom learning often develop academic skills, mindsets, and coping strategies that support positive academic growth and a successful transition to adulthood (Skinner et al., 2009). In contrast, students who are disengaged from classroom learning miss important opportunities to gain critical academic, social, and coping skills, which often lead to undesired academic trajectories and even early school dropout (Skinner et al., 2009). Given the critical role of classroom engagement as a driving force behind learning (Skinner, 2016), it is important to understand how classroom engagement develops in early years of formal education.

A Relational Conceptualization of Engagement

Students’ classroom engagement has also been conceptualized from an ecological system perspective, which emphasizes the prominent roles of the multiple layers of sociocultural context in the development of classroom engagement (Galindo et al., 2022). Among the multiple functional contexts, classroom is the most proximal and relevant for understanding students’ engagement in classroom learning (Lawson & Lawson, 2013). From this ecological perspective, engagement is not an individual characteristic but a relational characteristic – it emerges from the social interactions within the classroom and reflects the degree to which students are engaged in or disengaged from activities and/or people in the classroom setting (Hofkens & Pianta, 2022). Accordingly, a growing body of literature has highlighted the importance of teacher-student relationship quality and peer relationship quality in shaping the development of classroom engagement (Roorda et al., 2017; Wentzel, 2017).

Two most studied dimensions of TSR in the academic context are positive TSR and negative TSR. Positive TSR refers to supportive, close, and warm interactions between teachers and their students, while negative TSR refers to conflicting relationships characterized by a lack of trust and bond between teachers and their students (Hamre & Pianta, 2001). Students develop bonds and seek emotionally warm and supportive care from their teachers (Pianta & Stuhlman, 2004). Such basic needs are concordant with children’s desire of secured attachment to their caregivers at home (Verschueren & Koomen, 2012). In line with the attachment theory (Bowlby, 1969), positive TSR provides students with a sense of security and confidence to explore and engage in the learning environment (Roorda et al., 2017; Verschueren & Koomen, 2012). To the contrary, negative TSR may prevent students from developing a sense of security, relatedness, and belonging in the classroom, thereby hampering their participation in the learning process (Birch & Ladd, 1997; Hamre & Pianta, 2001; Sabol & Pianta, 2012). A large body of empirical evidence supports such a conceptualization of the associations between TSR and students’ engagement, demonstrating positive correlations between positive TSR and engagement and negative correlations between negative TSR and engagement (Roorda et al., 2017).

Students’ social relationships with their classroom peers also contribute to the development of their classroom engagement (Kindermann & Gest, 2018; Wentzel, 2009). Classroom peer ecology offers students opportunities to participate in learning activities, practice social skills, receive constructive feedback, and share academic values and goals, which all motivate students to be more involved in the classroom learning activities (Wentzel, 2009). Although peer relationships can be conceptualized as dyadic friendships or group memberships, one of the most frequently used operationalization of peer relationships, in particular in childhood, is a student’s overall social standing in the classroom that captures the degree to which the student is liked or disliked by their classmates (Wentzel, 2017). Peer relationship (PR) liking reflects students’ adaptive social functioning in the classroom. Students who are highly liked by their peers benefit from the cooperative learning environment, in which they feel included and safe to explore (Wentzel et al., 2009). Disliked students often lack peer support and are susceptible to bullying and victimization by their classmates, which generates feelings of isolation and internalized stress (Buhs, & Ladd, 2001; Kisfalusi et al., 2022). Therefore, PR disliking creates barriers for students to adapt to the learning environment, which in turn, impedes students’ classroom engagement and academic success (Buhs & Ladd, 2001; Furrer et al., 2014; Ladd et al., 2012).

The Unknowns in the Development of Classroom Engagement

Although there is a strong theoretical foundation for contextualizing the development of students’ engagement in the social relationships within the classroom, there are at least three major gaps in the empirical literature that limit our understanding of the mechanisms underlying engagement development among students of varying characteristics in multiple mutually dependent contexts.

The first gap is the relative lack of research on how the classroom social-relational context may shape the development of classroom engagement in early elementary school years, particularly among students at academic risks (Fredricks, 2022). Previous research mostly investigated the associations between engagement and social relationships in the general student population. However, it is yet unclear whether findings based on the general student population generalize to low-achieving students who struggle in various academic areas and score below average on achievement tests. For example, a previous study found that although provision of choice fostered behavioral engagement among high achieving students, the same classroom environment negatively predicted engagement for low achieving students (Wang & Eccles, 2013). In the same vein, several studies showed that motivational and contextual factors that promoted engagement may differ between average/high achieving students and low-achieving students (Shim et al., 2016; Skilling et al., 2020; Wang & Eccles, 2013). These findings reveal the need to investigate low-achieving students separately to better understand factors that uniquely affect the academic trajectories of these vulnerable students. In addition, although a supportive learning environment and frequent student-teacher interactions may be particularly important for fostering classroom engagement among low-achieving students (Alqurashi, 2022; Roche et al., 2021), these students often experience more relational stressors and less social support than their average and high achieving peers (Hughes & Kwok, 2006; Ladd et al., 1999). Given that low-achieving students are even more susceptible to classroom disengagement as compared to average or high achieving students (Bodovski & Karkas, 2007), there is a critical need to better understand how social-relational factors in the classroom may uniquely shape the development of engagement behaviors among the understudied low-achieving students.

Relatedly, the scarcity of research on classroom engagement in early elementary school is unfortunate. Early elementary school years are a crucial developmental stage when students begin to learn fundamental school knowledge and social emotional skills needed for the increasing academic and social demands during the transition to formal schooling (Hill et al., 2008; Martins et al., 2022). An important line of research within the engagement literature is to investigate the predictive role of disengagement in academic struggles and early school dropout (Archambault et al., 2022). Unfortunately, this literature has similarly focused on understanding disengagement behaviors primarily among at-risk adolescents and college students, with relatively few examined low-achieving young elementary school students (Archambault et al., 2022). Learning and academic development are continuous and cumulative, such that high levels of classroom engagement in early educational stages are likely to set students up for long-term academic success (Ladd & Dinella, 2009; Neuharth-Pritchett & Bub, 2022). As such, it is essential to investigate factors that promote or hinder the development of classroom engagement among low-achieving students early on. This effort will identify early malleable intervention target to build academic resilience among low-achieving students against school failure and early dropout (Welsh et al., 2020; Wentzel, 2020).

Perhaps one of the major obstacles for research on engagement in early elementary school students is the challenge to measure engagement. The most used method to assess classroom engagement among older students is self-report (Fredricks, 2022). This method is not only cost-effective, but also uniquely positioned to capture students’ subjective perception of how they make meaning of their own learning experiences. It is considered particularly valuable to measure emotional and cognitive engagement, as compared to other measures such as observations and reports by others (e.g., teachers), which could be highly inferential (Appleton et al., 2008). However, self-report is not appropriate for measuring engagement for early elementary school students due to their limited literacy skills (Fredricks, 2022). For elementary school students, the existing literature has mainly used teacher reports to assess students’ classroom engagement (Fredricks, 2022). Although there are concerns over teacher rating biases based on student and teacher characteristics (e.g., gender, race/ethnicity, socioeconomic status, ability level, etc; Mason et al., 2014), a point we will return to later, teacher report has been shown to provide a valid assessment of students’ engagement, particularly behavioral engagement for which the indicators are observable learning behaviors in classroom activities (Fredrick, 2022; Furrer & Skinner, 2003; Hughes et al., 2008; Ladd & Dinella, 2009; Rimm-Kaufman et al., 2015). Teacher reported classroom engagement has also been shown to correlate moderately with student self-report and observational measures of classroom engagement in late elementary and early middle school years (Doumen et al., 2012; Skinner et al., 2009), highlighting inter-rater agreement on the assessment of engagement across informants.

The second gap in the literature is the relative scarcity of research that investigates the development of classroom engagement in relation to the interplay between multiple social-relational contexts, with most studies examining the roles of TSR and PR separately (Kindermann, 2011; Wentzel et al., 2012). This approach is problematic because TSR and PR are integral social relationships that co-exist in the classroom context (Martins et al., 2022; Skinner et al., 2022). The effect of one social relation on students’ learning behaviors may be dependent on the effect of the other social relation, and such dependent effect may be synergistic or antagonistic. Therefore, examining the effect of only one type of social relation at a time conceals the mechanism through which these social relations interact or transact to shape the early development of classroom engagement.

According to Skinner et al.’s developmental systems framework (Skinner et al., 2022), multiple social partners (i.e., parents, teachers, and peers) act in concert to contribute to the development of academic functioning. These joint operations on the development of academic functioning can operate in three ways: coactive, contingent, and sequential (Skinner et al., 2022). In a coactive operation, TSR and PR additively influence the development of classroom engagement, with each contributing independently and uniquely. A contingent operation suggests that TSR and PR interactively influence the development of classroom engagement, such that the effect of TSR on classroom engagement depends on PR, and vice versa. Lastly, in a sequential operation, TSR may influence the development of classroom engagement through PR, and PR may also shape the development of classroom engagement through TSR. The primary objective of the present study is to explore whether the first two processes (i.e., coactive and contingent operations) are evident. Future investigations might delve into more complicated methodology that encompasses all three processes.

A few studies examined TSR and PR jointly and found evidence supporting the coactive operation of TSR and PR on the development of classroom engagement (De Laet et al., 2015; Wang & Eccles, 2012). In a sample of fourth to sixth graders, De Laet et al. (2015) found that both TSR and PR were uniquely, but not interactively, associated with students’ behavioral engagement. Similar findings were reported in another sample of seventh to 11^th graders (Wang & Eccles, 2012). In addition, a few studies found evidence of contingent operations in the development of students’ classroom engagement (Furrer & Skinner, 2003; Vollet et al., 2017). Vollet and colleagues (2017) examined a sample of sixth graders and found that peer influence on engagement was stronger for students who experienced lower levels of positive TSR, and the negative effects of a lack of positive TSR on engagement were buffered by highly engaged peers (Vollet et al., 2017). Another study using students from Grades 3 to 6 suggested that positive TSR protected students’ emotional and behavioral engagement from the debilitating effects of negative PR (Furrer & Skinner, 2003). Taken together, these studies demonstrate that the impact of one social partner on classroom engagement may be contingent upon students’ relationships with other social partners (Sabol & Pianta, 2012). However, due to the limited number of studies that investigated multiple social-relational contexts simultaneously, the exact mechanism of such joint operations of multiple social relations awaits further investigation.

An important operationalization issue of TSR and PR is that the positive and negative dimensions of these social relations have been traditionally investigated as two separate dimensions rather than two opposite ends of a continuum (Roorda et al., 2011; 2017; Wentzel et al., 2020). This is in line with the demands-resources model of student engagement, which conceptualizes demands as factors that hinder learning and engagement (e.g., negative TSR and PR disliking) and resources as factors that support learning and engagement (e.g., positive TSR and PR liking; Salmela-Aro et al., 2022). Importantly, the presence of demands is not necessarily indicative of a lack of resources and vice versa, and that the interaction between these resources and demands potentially play important roles in shaping students’ classroom engagement (Salmela-Aro et al., 2022). Numerous studies have empirically highlighted the differences between the positive and negative dimensions of both TSR and PR in relation to students’ classroom engagement. For example, two meta-analyses have revealed stronger associations between engagement and negative TSR than the associations between engagement and positive TSR among elementary schoolers (Roorda et al., 2011; 2017). A recent longitudinal study examining children from kindergarten to second grade showed that only negative TSR, not positive TSR, predicted behavioral engagement (Li et al., 2022). In another study among early elementary schoolers, both negative PR and negative TSR were found to simultaneously predict engagement when included in the same model, whereas only positive PR but not positive TSR predicted engagement when modeled together (Hosan & Hoglund, 2017). These findings suggest that negative TSR may provide an extra burden for early elementary school students as they transition into formal schooling, which may explain why negative TSR has been found to predict classroom engagement more consistently and strongly than positive TSR (Hamre & Pianta, 2005). Together, these findings highlight the importance of using a multidimensional approach to differentiate the effects of the positive and negative dimensions of both TSR and PR when studying their joint operations on students’ engagement.

Lastly, despite mounting evidence supporting the associations between TSR/PR and classroom engagement, most of the studies have primarily focused on studying the between-person level effects of TSR and PR on engagement (e.g., Danielsen et al., 2010; De Laet et al., 2015; Vollet et al., 2017), with few studies considering these associations at the within-person level (e.g., Rautanen et al., 2022). This is problematic because between-person and within-person level associations are indicative of different mechanisms that explain why students’ classroom engagement vary as a function of TSR and PR. A between-person level association between TSR/PR and classroom engagement reveals that students who enjoy more positive/fewer negative social relations in the classroom context tend to engage more than other students who experience fewer positive/more negative social relations. However, a between-person level association does not shed light on how social-relational changes within a student over time may bring subsequent changes in this student’s engagement behaviors – a developmental effect that requires a within-person level analysis (Ram & Gerstorf, 2009). As such, there is a lack of understanding of whether the dynamic year-to-year changes in relationships with teachers and peers for a given student foster subsequent changes in their classroom engagement above and beyond associations between these variables at the between-person level.

In addition, a simultaneous investigation of the within- and between-person level effects allows for a cross-level examination of the contingent cooperation, which will shed light on whether the impact of year-to-year changes in one relationship on engagement may be turned on or off by the overall quality of the other relationship. Skinner and colleagues (2022) proposed one specific type of contingent operation of social partners, namely enabling/disabling effects, in which students may obtain “immunity” from negative PR influences if a positive TSR reaches a certain threshold. If this operation holds true, the effects of year-to-year changes of PR on engagement may be disabled or enabled depending on students’ overall levels of TSR. Such a cross-level interaction effect can be tested to investigate the enabling/disabling effects in longitudinal multilevel modeling.

The Current Study

Using a sample of low-achieving students, the current study examined the longitudinal between-person and within-person associations between TSR and PR and students’ classroom engagement in the first three years of elementary school. Considering the three major gaps in the existing literature as reviewed above, the current study aimed to investigate the development of students’ classroom engagement in the context of TSR and PR with three unique design features. First, we investigated the development of classroom engagement in a sample of academically low-achieving elementary school students from Grades 1 to 3. Second, we investigated the joint operations (i.e., coactive and contingent operations) of the multidimensional TSR and PR in relation to the development of classroom engagement. Finally, we utilized longitudinal multilevel modeling to disaggregate the between-person and within-person levels of associations between TSR/PR and classroom engagement and to investigate possible cross-level interaction effects. Specifically, the following research questions were investigated:

1. To what extent is each dimension of TSR and PR associated with classroom engagement at both the within- and between-person levels?

2. To what extent do TSR and PR interact to influence the development of classroom engagement at the within-person, between-person, and cross levels?

Finally, we would like to point out a critical methodological challenge that may have important implications for interpreting the present findings. As reviewed above, teacher report is the most used method (also the method that was used in the present study) to assess engagement and TSR in studies of early elementary school students due to students’ limited literacy skills (Fredrick, 2022; Hofkens & Pianta, 2022). Despite the common usage of teacher reports at this developmental stage (Archambault et al., 2013; Hughes, 2011; Ladd & Dinella, 2009; Saft & Pianta, 2001), there are concerns over teacher rating biases based on student and teacher characteristics (Mason et al., 2014). For example, teachers may hold implicit biases that unconsciously influence their perceptions, expectations, attitudes, and behaviors towards certain groups of students based on students’ gender, race/ethnicity, socioeconomic status (SES), and academic achievement levels (Chin et al., 2020; DeCuir-Gunby & Bindra, 2022; Galindo et al., 2022; Tenenbaum & Ruck, 2007). Previous studies have reported that many teachers hold deficit views of minoritized students, such as those from a racial/ethnic minoritized and low SES background (Brown & Rodriguez, 2017; Cochran-Smith, 2004; Smolkowski et al., 2016). This deficit view may cast a negative bias in teachers’ ratings of minoritized students’ levels of engagement and relationship quality with teachers. In addition, teachers’ perceptions may also be influenced by their own characteristics. For example, teachers tend to give more positive ratings and perceive more positive relationships with students of their own race/ethnicity (Galindo et al., 2022; Saft & Pianta, 2001). Given the current study involved predominantly White teachers paired with racially/ethnically diverse students, relying on teachers’ perceptions to assess students’ engagement and TSR may potentially inflate the observed correlations between the two and produce results that are partly attributable to biases in teachers’ perceptions. To address this methodological concern, we first explored whether there were differences in teacher ratings of classroom engagement and TSR between students of different race/ethnicity, family SES, gender, and between teachers of different race/ethnicity. We also included students’ gender, race/ethnicity, family SES, and achievement levels, as well as teacher race/ethnicity in the multilevel models to control for these potential confounds.

Method

Participants

We used data from the “Impact of Grade Retention: A Development Approach Study,” a secondary dataset obtained from https://dash.nichd.nih.gov/study/14412. Seven hundreds and eighty-four participants (53% male) were recruited in the fall of 2001 or 2002 from 36 schools in three school districts of southeast and central Texas, USA. Only students who scored below the median of their school district literacy test in the Spring of kindergarten or the Fall of Grade 1 were invited to participate in the study (Hughes & Kwok, 2007). Participants were followed annually from Grade 1 to Grade 12 (except Grade 11). For the current analyses, we utilized data in Grade 1 (G1), Grade 2 (G2), and Grade 3 (G3) when all the main constructs were measured.

Among the 784 participants, 37.37% of the students were Hispanic, 34.06% White, 23.21% Black, and 5.36% other races (i.e., Asian, Native American, and Pacific Islander). School records indicated that 61% of the families were eligibility for free or reduced lunch at G1. Approximately 73.90% of the students had parents with an education level of high school or above. Teachers also participated in the study by completing a survey packet in the Spring of each year. At G1, the racial/ethnic composition of teachers was 80.60% White, 13.80% Hispanic, 2.10% African American, and 2.10% Others. At G2, the distribution of teachers’ race/ethnicity was 82.70% White, 13.10% Hispanic, 2.90% African American, and 1.40% Others. At G3, 82.50% of teachers were White, 13.90% Hispanic, 2.20% African American, and 1.40% others.

Assessment Overview

Students’ home room teachers reported students’ classroom engagement and TSR. The classmates of the focal participants provided information on PR via a sociometric interview. A total of 207, 286, and 319 teachers provided reports for 707, 623, and 547 students in G1 to G3, respectively.

Teacher-Reported Classroom Engagement

To assess students’ classroom engagement from G1 to G3, we used the same instruments that were used in the previous studies published from this project (e.g., Hughes& Kwok, 2006; Hughes et al., 2006; Hughes & Zhang, 2007). Teachers rated students’ classroom engagement using eight items from the Conscientious Scale of the Big Five Inventory (BFI; John & Srivastava, 1999) and two items from the Social Competence Scale (SCS; Conduct Problems Prevention Research Group, 2004). Conscientiousness is defined as the level of industriousness, responsibility, and self-control (Roberts et al., 2009). When these characteristics are contextualized in the classroom, they capture students’ behaviors that are central to the definition of classroom engagement. More specifically, classroom engagement is defined as (1) cooperative and compliant behaviors that follow teachers’ instructions (an example item is “reliable in turning in homework assignments”); (2) effortful and goal oriented involvement in class activities (example items include “able to effectively set goals and work toward them” and “makes plans and follows through with them”); (3) sustained attention, resistance against distraction, and inhibited impulsivity (example items include “is easily distracted” and “does things efficiently”); and (4) persistence when facing difficulties in learning (an example item is “perseveres until the task is finished”; Hughes et al., 2008; Ladd & Dinella, 2009; Li-Grinning et al., 2010; Pagani et al., 2012). Each item from the BFI was rated on a 5-point Likert scale from 1 = strongly disagree to 5 = strongly agree. The two items from the SCS were rated on a 6-point Likert scale from 1 = almost never to 6 = almost always. Internal consistency as shown by McDonald’s omega was high for this measure (Table 1). All items are listed in the supplemental materials Table S1.

Table 1.

Measurement Invariance: Model Fit and Model Comparison

	χ2	df	CFI	ΔCFI	RMSEA [90% CI]	ΔRMSEA
Classroom Engagement
Configural	873.68	372	.963	-	.042 [.038, .045]	-
Metric	901.87	390	.962	.001	.041 [.038, .045]	.001
Scalar	924.39	406	.962	< .001	.041 [.037, .044]	< .001
Positive TSR
Configural	1900.19	693	.922	-	.047 [.045, .050]	-
Metric	1925.73	717	.922	< .001	.047 [.044, .049]	< .001
Scalar	1975.68	739	.920	.002	.047 [.044, .049]	< .001
Negative TSR
Configural	568.52	132	.922	-	.065 [.060, .071]	-
Metric	585.23	142	.920	.002	.064 [.058, .069]	.001
Scalar	635.39	150	.913	.007	.065 [.060, .070]	.001

Notes. χ² = chi-square; df = degrees of freedom; CFI = comparative fit index; RMSEA = root mean square error of approximation; TSR = teacher student relationship; The best fitting and most parsimonious models are in bold.

Teacher-Reported Teacher Student Relationships (TSR)

Teachers reported their relationships with students from G1 to G3. Positive and negative dimensions of the TSR from the Teacher Relationship Inventory (TRI; Hughes et al., 2001) were used in the current study. Teachers rated 13 items from TRI to assess positive TSR. Some sample items include: “I enjoy being with this child” and “This child gives me many opportunities to praise him or her.” Teachers rated six items from the TRI to assess negative TSR. Sample items include: “This child and I often argue or get upset with each other” and “I often need to discipline this child”. Previous studies using the same longitudinal sample have demonstrated that these subscales had good psychometric properties, including good construct, convergent, discriminant, and predictive validity (Hughes & Im, 2016; Li et al., 2012; Wu & Hughes, 2014). These scales also demonstrated longitudinal measurement invariance as well as multi-group measurement invariance across gender and race/ethnicity groups (Hughes & Im, 2016; Li et al., 2012; Wu & Hughes, 2014). Table 1 reported high internal consistency reliability for both dimensions. All items are listed in the supplemental materials Table S1.

Peer-Reported Peer Relationships (PR)

To assess students’ peer relationships, a sociometric interview was conducted in the Spring of G1 to G3. Students were interviewed in the classroom individually by the research staff. Students were asked whether they knew each classmate listed on the roster. Students were asked to evaluate only their known classmates. Notably, all students in the classroom were eligible to participate in the sociometric interview, but not all of them were the focal participants of the study. In addition, all students in the classroom were allowed to be rated or nominated. To ensure the validity of the sociometric ratings, students’ peer ratings were only calculated if more than 40% of their classmates participated in the interview (Hughes, 1990; Terry, 2000). It has been shown that sociometric ratings yield valid and reliable assessments of peer relationships (Terry & Coie, 1991; Hughes et al., 2006). The current study utilized two dimensions of PR: PR liking and PR disliking.

PR Liking.

Research staff asked students to name classmates they liked the most with unlimited nominations, and students were encouraged to nominate more if they initially nominated fewer than three classmates. The PR liking score was standardized within each classroom by using the total number of “like most” nominations divided by the total number of raters in the classroom.

PR Disliking.

Researchers asked each student to rate how much they like or dislike playing with each of their known classmates by pointing to one of the five emotional faces from a sad face (1 = do not like at all) to a happy face (5 = like very much). Following the procedure recommended by Asher and Dodge (1986), disliking was standardized within each classroom by the summation of peer ratings of “1” (i.e., do not like at all) divided by the number of raters in the classroom.

Covariates

Child Gender.

Child gender was coded such that 0 = female, 1 = male.

Family SES.

Two variables were used to indicate family SES: (1) economic adversity and (2) parental education. Specifically, school records indicated whether each student was eligible for free or reduced lunch at G1 based on their family income. The economic adversity was coded as 1 = eligible for free or reduced lunch and 0 = not eligible for free or reduced lunch. Parental education was coded such that 0 = high school or below and 1 = above high school.

Race/Ethnicity.

Student race/ethnicity and teacher race/ethnicity were dummy coded such that 0 = Nonwhite and 1 = White.

Academic Achievement.

The Woodcock-Johnson III (WJ-III) Tests of Achievement (Woodcock et al., 2001) was administered to assess reading and math achievement from G1 to G3. For the reading achievement, the Letter-Word Identification, Reading Fluency, and Passage Comprehension subtests were used. The Calculation and Math Fluency subtests were used to assess math achievement. Each student was individually tested by a researcher. An average of the Reading and Math grade equivalence scores was calculated to indicate students’ overall academic achievement at each grade.

Data Analytic Strategies

Data preparation and descriptive analyses were done using SPSS version 28 (IBM Corp, 2021) and R version 1.4.1106 (R Core Team, 2021). Longitudinal measurement invariance and longitudinal multilevel analyses were conducted in Mplus Version 8.9 (Muthén & Muthén, 1998–2017). Maximum likelihood estimators with robust standard errors (MLR) were used for parameter estimation.

Longitudinal measurement invariance tests were conducted for classroom engagement and TSR from G1 to G3. Configural, metric, and scalar invariance models were tested, and the comparisons between the nested models were based on changes in the comparative fit index (CFI) and the root mean square error of approximation (RMSEA). A decrease of less than .01 in CFI and an increase of less than .015 in RMSEA indicate acceptable worsening of the model fit to maintain more restricted invariance structures (Chen, 2007; Cheung & Rensvold, 2002). After establishing longitudinal measurement invariance, latent factor scores were saved and used for subsequent longitudinal multilevel analyses.

Students were nested within the classroom level and teacher level. We calculated the intraclass correlations (ICC) of classroom engagement at the classroom level and teacher level. Results showed that 4.47% and 3.00% of the total variance in classroom engagement were explained by the classroom level and teacher level mean difference, respectively. Because the variance of classroom engagement at the classroom level and teacher level was small (less than 10%; Lee, 2000), and the cluster sizes were also relatively small (i.e., the average cluster size at the teacher level was 9.10; the average cluster size at the classroom level was 9.79), our multilevel model did not include the classroom and teacher levels of analyses. This decision was also justified by prior simulation results showing minimal effects of ignoring clusters on the estimations of within-person level associations (Luo & Kwok, 2012). To test our research questions, we built a series of two-level models (i.e., within-person: Level 1 and between-person: Level 2). Intraclass correlation (ICC) showed that the between-person mean differences explained 65.90% of the total variance in classroom engagement.

The between-person level variables were grand-mean centered. The within-person level TSR and PR predictors were person-mean centered. Centering at both levels was conducted with mean aggregates using the latent factor scores saved in the previous step. Then, a taxonomy of growth curve models was fit to the data (Singer & Willett, 2003). First, we built plausible growth models for the rate of change in classroom engagement over the three time points. Specifically, in Model 1, we tested the overall trajectory for classroom engagement and identified the best fitting growth model. We fit three unconditional growth models: (a) random intercept model, (b) random intercept + fixed linear slope model, (c) random intercept + random linear slope model. Second, we tested our hypotheses by building conditional growth models. We tested the main effects of TSR and PR on classroom engagement at both between- and within-person levels. We then tested the interaction between TSR and PR at the between-person, within-person, and cross-levels. Specifically, in Model 2, we added between-person covariates (i.e., gender, race/ethnicity, economic adversity, parental education, and academic achievement) and the within-person covariate (i.e., teachers’ race/ethnicity across Grades 1 to 3) into the model. In Model 3, we added within-person level parameters, which tested the within-person level main effects of TSR and PR on classroom engagement. In Model 4, we added the between-person level main effects of TSR and PR on classroom engagement. In Model 5, we added the within-person level interactive effects of TSR and PR on classroom engagement. In Model 6, we added the between-person level interactive effects of TSR and PR on classroom engagement. In Model 7, we tested cross-level interactions between TSR and PR. Centered mean calculations with the latent factor scores were used to create the interaction terms.

The hypothesized full multilevel models are described as follows,

• Within-person Level:

  $$\mathit{\text{Classroom}}{\mathit{\text{Engagement}}}_{ij}={\beta }_{0i}+{\beta }_{1i}{(\mathit{\text{Time}})}_{ij}+{\beta }_{2i}\left({\mathit{\text{TSR}}}_{ij}-{\overline{\mathit{\text{TSR}}}}_i\right)+{\beta }_{3i}\left({\mathit{\text{Peer}}}_{ij}-{\overline{\mathit{\text{Peer}}}}_i\right)+{\beta }_{4i}\left({\mathit{\text{TSR}}}_{ij}-{\overline{\mathit{\text{TSR}}}}_i\right)\left({\mathit{\text{Peer}}}_{ij}-\overline{{\mathit{\text{Peer}}}_i}\right)+{\beta }_{5i}(\mathit{\text{Teacher}}{\mathit{\text{Race}}}_{ij}-{\overline{\mathit{\text{Teacher}}\mathit{\text{Race}}}}_i)+{\epsilon }_{ij}$$ (1)¹
• Between-person Level:

  $${\beta }_{0i}={\gamma }_{00}+{\gamma }_{01}{(\mathit{\text{Sex}})}_i+{\gamma }_{02}{(\mathit{\text{Student}}\mathit{\text{Race}})}_i+{\gamma }_{03}{(\mathit{\text{Teacher}}\mathit{\text{Race}})}_i+{\gamma }_{04}{(\mathit{\text{Economic}}\mathit{\text{adversity}})}_i+{\gamma }_{05}{(\mathit{\text{Parental}}\mathit{\text{Education}})}_i+{\gamma }_{06}{(\mathit{\text{Academic}}\mathit{\text{Achievement}})}_i+{\gamma }_{07}{(\overline{\mathit{\text{TSR}}})}_i+{\gamma }_{08}{(\overline{\mathit{\text{PR}}})}_i+{\gamma }_{09}{(\overline{\mathit{\text{TSR}}}*\overline{\mathit{\text{PR}}})}_i+{\delta }_{0i}$$ (2)

  $${\beta }_{1i}={\gamma }_{10}+{\gamma }_{11}{(\mathit{\text{Sex}})}_i+{\gamma }_{12}{(\mathit{\text{Student}}\mathit{\text{Race}})}_i+{\gamma }_{13}{(\mathit{\text{Teacher}}\mathit{\text{Race}})}_i+{\gamma }_{14}(\mathit{\text{Economic}}{\mathit{\text{adversity}})}_i+{\gamma }_{15}{(\mathit{\text{Parental}}\mathit{\text{Education}})}_i+{\gamma }_{16}{(\mathit{\text{Academic}}\mathit{\text{Achievement}})}_i+{\gamma }_{17}{(\overline{\mathit{\text{TSR}}})}_i+{\gamma }_{18}{(\overline{\mathit{\text{PR}}})}_i+{\gamma }_{19}{(\overline{\mathit{\text{TSR}}}*\overline{\mathit{\text{PR}}})}_i+{\delta }_{1i}$$ (3)

  $${\beta }_{2i}={\gamma }_{20}+{\gamma }_{21}{(\overline{\mathit{\text{PR}}})}_i+{\delta }_{2i}$$ (4)

  $${\beta }_{3i}={\gamma }_{30}+{\gamma }_{31}{(\overline{\mathit{\text{TSR}}})}_i+{\delta }_{3i}$$ (5)

  $${\beta }_{4i}={\gamma }_{40}+{\delta }_{4i}$$ (6)

  $${\beta }_{5i}={\gamma }_{50}+{\delta }_{5i}$$ (7)

We evaluated relative model fit using the Satorra-Bentler scaled loglikelihood difference test (Satorra & Bentler, 2010). When comparing two nested models, a significant Satorra-Bentler scaled loglikelihood difference test indicates that the more parsimonious model fits significantly worse than the baseline model.

The percentage of missingness for study variables ranged from 0 to 30%. Little’s missing completely at random (MCAR) test was significant (p < .001), suggesting that the data were not MCAR (Enders, 2010; Little, 1988). Missing pattern analyses showed that child gender, economic adversity, and parental education did not significantly predict missingness. White students had significantly less missingness than non-White students (b = −.52, SE = 2.18, p = .02). Full Information Maximum Likelihood (FIML) was used to address missing data.

Results

Preliminary Analyses

The model fit indices for the longitudinal measurement invariance tests for TSR and classroom engagement are presented in Table 1. For negative TSR, the measurement model showed a poor fit to the data, χ² (699) = 2409.49, p < .001; CFI = .89; RMSEA = .06. A closer inspection of the items suggested two pairs of similarly worded items: (1) “This child gives me (teacher) many opportunities to praise him or her” and “I (teacher) have many opportunities to tell this child he/she is good at things”; (2) “I (teacher) am satisfied with my relationship with this child” and “Overall, I (teacher) am satisfied with my relationship with this child”. Adding correlations between the residuals of each pair of items substantially improved the model fit. All other models showed adequate model fit. The best fitting and most parsimonious models were the scalar invariance model for all three variables. All indicators loaded well (> .50) on their respective latent factors. Latent factor scores were saved and used in the multilevel modeling.

Descriptive statistics for the main study variables are shown in Table 2. Table 3 presents the correlations between the main study variables. At the between-person level, classroom engagement was moderately negatively associated with PR disliking and negative TSR, and moderately positively associated with PR liking and positive TSR. At the within-person level, classroom engagement was weakly positively correlated with positive TSR, and weakly negatively correlated with negative TSR. Classroom engagement was not associated with within-person PR liking or PR disliking.

Table 2.

Descriptive Statistics of the Main Study Variables

Variable names	N	Mean	SD	Median	Min	Max	ω
Classroom engagement
Grade 1	774	.00	.96	.01	−1.98	1.80	.96
Grade 2	774	.14	.90	.17	−1.96	1.80	.95
Grade 3	774	.09	.82	.10	−1.90	1.76	.95
Positive TSR
Grade 1	773	.00	.94	.07	−3.53	1.18	.96
Grade 2	773	−.08	.94	.02	−3.46	1.17	.96
Grade 3	773	−.06	.90	.02	−3.36	1.16	.96
Negative TSR
Grade 1	773	.00	.94	−.28	−.92	2.71	.95
Grade 2	773	−.06	.91	−.36	−.92	2.87	.94
Grade 3	773	−.13	.84	−.45	−.93	2.78	.94
PR liking
Grade 1	602	−.13	.90	−.21	−2.01	2.65
Grade 2	582	−.10	.95	−.20	−2.46	2.68	-
Grade 3	619	−.11	.95	−.20	−2.40	3.20	-
PR disliking
Grade 1	602	.03	.95	−.09	−1.80	3.21
Grade 2	582	.07	1.03	−.20	−1.62	3.75	-
Grade 3	619	.13	.99	−.08	−1.61	3.42	-

Note. ω = Mcdonald’s omega; TSR = teacher-student relationship; PR = peer relationship. Classroom engagement, positive TSR, and negative TSR are latent factor scores.

Table 3.

Bivariate Correlations Between the Main Study Variables

	1	2	3	4	5	6	7	8	9
1. Classroom Engagement	1
2. BP PR disliking	−.40*	1
3. BP PR liking	.36*	−.45*	1
4. BP positive TSR	.59*	−.36*	.29*	1
5. BP negative TSR	−.55*	.41*	−.25*	−.72*	1
6. WP PR disliking	−.03	0	0	0	0	1
7. WP PR liking	.04	0	0	0	0	−.23*	1
8. WP positive TSR	.20*	0	0	0	0	−.06*	.02	1
9. WP negative TSR	−.16*	0	0	0	0	.03	−.02	−.46*	1

Notes.

^*indicates statistical significance under the type I error rate of .05;

BP = between-person; WP = within-person; TSR = teacher-student relationship; PR = peer relationship; Between-person and within-person variables are orthogonal.

Table S2 – Table S6 in the supplemental materials present teachers’ perceptions of engagement and TSR by students’ gender, race/ethnicity, family SES (i.e., parental education, economic adversity), as well as teachers’ race/ethnicity. Results showed that White students and non-White students were perceived by their teachers to have similar levels of classroom engagement and TSR quality in G1 and G2, but White students were rated to have higher classroom engagement and lower negative TSR than non-White students at G3. Students with higher parental education were rated to have higher positive TSR at G2 and G3, but not at G1. In addition, students with higher parental education were perceived by their teachers to have higher classroom engagement at G3, but not at G1 or G2. Moreover, teachers perceived higher classroom engagement and lower negative TSR for students without economic adversity than for students with economic adversity at G2 and G3, but not at G1. At G2, students without economic adversity were perceived to have more positive TSR than students with economic adversity. Male students were rated to have lower engagement, higher negative TSR, and lower positive TSR consistently across G1 to G3. Lastly, non-White teachers rated students’ engagement higher than White teachers at G1 only.

Longitudinal Multilevel Modeling Results

Model comparison results and fit indices are presented in Tables 4a–4d. The parameter estimates from the four best fitting models for each of the four combinations of the TSR and PR dimensions in predicting classroom engagement are presented in Table 5. For clarity and simplicity of presentation, effects of the covariates are presented in the supplemental materials Table S6.

Table 4a.

Model Comparison for the Effects of Positive TSR and PR Liking on Classroom Engagement

		Compared With	Ho value	Ho Scaling Correction Factor	# Free Parameters	Δdf	LLCD	(ΔSatorra-Bentler Scaled χ2) - TRd - using LL	p
M1	Random Linear	-	−2506.89	1.01	6	-	-	-	-
M2	M1 + covariates	M1	−1718.62	0.97	19	13	0.95	1651.96	0.00
M3	M2 + WP TSR and WP Peer	M2	−1382.81	1.01	22	3	1.26	535.09	0.00
M4	M3 + BP TSR and BP Peer	M3	−1204.85	1.03	26	4	1.15	309.02	0.00
M5	M4 + WP interaction	M4	−1204.38	1.03	27	1	0.92	1.03	0.31
M6	M4 + BP interaction	M4	−1204.31	1.03	28	2	1.03	1.06	0.59
M7	M4 + Cross Level interactions	M4	−1203.75	1.03	28	2	0.96	1.16	0.56

Notes. Model 1 is the growth model with random intercept and random linear slope. TSR = teacher student relationship. PR = peer relationship. WP = within-person; BP = between person; −2LL = −2 log-likelihood; df = degrees of freedom. The best fitting and most parsimonious model is in bold face.

Table 4d.

Model Comparison for the Effects of Negative TSR and PR Disliking on Classroom Engagement

		Compared With	Ho value	Ho Scaling Correction Factor	# Free Parameters	Δdf	LLCD	(ΔSatorra-Bentler Scaled χ2) - TRd - using LL	p
M1	Random Linear	-	−2506.89	1.01	6	-	-	-	-
M2	M1 + covariates	M1	−1718.62	0.97	19	13	0.95	1651.96	0.00
M3	M2 + WP TSR and WP Peer	M2	−1409.12	0.99	22	3	1.11	559.17	0.00
M4	M3 + BP TSR and BP Peer	M3	−1276.65	0.99	26	4	0.99	268.35	0.00
M5	M4 + WP interaction	M4	−1276.65	0.99	27	1	0.99	0.01	0.92
M6	M4 + BP interaction	M4	−1268.34	1.00	28	2	1.10	15.17	0.00
M7	M6 + Cross Level interactions	M6	−1265.22	1.00	30	2	0.98	6.35	0.04

Notes. Model 1 is a growth model with random intercept and random linear slope. TSR = teacher student relationship. PR = peer relationship. WP = within-person; BP = between person; −2LL = −2 log-likelihood; df = degrees of freedom. The best fitting and most parsimonious model is in bold face.

Table 5.

Parameter Estimates and Standard Errors from the Best Fitting Models for the Effects of TSR and PR on Classroom Engagement

	Positive TSR & PR Liking	Negative TSR & PR Liking	Positive TSR & PR Disliking	Negative TSR & PR Disliking
Fixed Effect
Intercept	.18(.09)	.16(.10)	.13(.10)	.10(.10)
Linear slope	.10(.07)	.03(.07)	.11(.06)	.06(.07)
WP TSR	.30(.03) *	−.33(.04) *	.30(.03) *	−.35(.04) *
WP PR	.04(.03)	.04(.03)	−.06(.02) *	−.07(.02) *
BP TSR	.57(.05) *	−.44(.05) *	.60(.05) *	−.24(.04) *
BP PR	.27(.04) *	.29(.05) *	−.24(.04) *	−.48(.05) *
BP TSR × BP PR	-	-	−.14(.05) *	.15(.05) *
BP TSR × Time	−.02(.03)	−.01(.03)	−.03(.03)	.01(.03)
BP PR × Time	.02(.03)	.04(.03)	−.04(.03)	−.04(.03)
BP TSR × BP PR × Time	-	-	.02(.03)	−.01(.03)
WP TSR × BP PR	-	-	-	.12(.06) *
BP TSR × WP PR	-	-	-	−.02(.03)
Random Effects
Intercept	.15(.02) *	.17(.02) *	.15(.02)*	.19(.02) *
Linear slope	.003(.01)	.003(.01)	.002(.01)	.003(.01)
WP TSR	.03(.02) *	.04(.03)	.04(.02) *	.03(.03)
WP PR	.01(.02)	.02(.02)	.01(.02)	.01(.02)
Residual	.25(.02) *	.27(.02) *	.24(.02) *	.27(.02) *
Fit indices
−2LL	2409.70	2524.43	2403.50	2530.44
AIC	2461.71	2576.43	2459.50	2590.44
Sample-Size Adjusted BIC	2513.26	2627.98	2515.02	2649.92
df	26	26	28	30

Notes. Covariates (gender, economic adversity, parental education, student race, teacher race, and academic achievement achievement) were controlled for. Their effects are presented in the supplemental materials Table S6. WP = within-person; BP = between-person; TSR = teacher-student relationship; PR = peer relationship; −2LL = −2 Log Likelihood; AIC = Akaike information criterion; BIC = Bayesian information criterion; df = Degrees of Freedom.

^*indicates statistical significance under the type I error rate of .05.

Significant parameters are bolded.

Results suggested that the unconditional growth model for classroom engagement was best captured by a random intercept with a random linear slope (−2LL = 5013.78; AIC = 5025.78; sample-size adjusted BIC = 5041.22). On average, students’ classroom engagement increased over the first three years of elementary school (b = .05, SE = .01, p = .001). Next, the model with the covariates (i.e., gender, economic adversity, parental education, student race, overall achievement, and teacher race) fit significantly better than the unconditional model (ΔLR = 1651.96, Δdf = 13, p < .001). Overall, male students were less engaged in the classroom than female students (b = −.42, SE = .07, p < .001). Students with higher overall academic achievement had higher classroom engagement (b = .51, SE = .04, p < .001). In terms of the effects of covariates on the linear slope of classroom engagement, White students showed more increases in classroom engagement than non-White students (b = .10, SE = .05, p = .04). Students with higher academic achievement had slower increases of classroom engagement (b = −.06, SE = .02, p = .02). No other covariates significantly predicted the intercept or linear slope of classroom engagement.

The Main Effects of TSR and PR on Classroom Engagement at the Within- and Between-Person Levels

As shown in Table 5, both dimensions of TSR and PR significantly predicted students’ classroom engagement at the between-person level. Specifically, students who had higher overall positive TSR were more engaged in the classroom compared with students who had lower overall levels of positive TSR. On the other hand, students who had higher overall levels of negative TSR were less engaged in the classroom than students who had lower overall levels of negative TSR. Similarly, students who had higher levels of PR liking showed higher levels of classroom engagement compared with students who had lower levels of PR liking. Moreover, students who had higher levels of PR disliking showed lower levels of classroom engagement compared with students who had lower PR disliking scores.

At the within-person level, both positive and negative TSR significantly predicted classroom engagement. Within-person increases in positive TSR were associated with contemporaneous increases in classroom engagement. That is, when a student had higher positive TSR than their typical level, they also exhibited higher classroom engagement than their all-time average level of classroom engagement. Moreover, when a student had higher negative TSR than their typical level, they also exhibited lower classroom engagement than their all-time average level of classroom engagement.

At the within-person level, PR disliking significantly predicted classroom engagement, whereas PR liking did not significantly predict classroom engagement. When a student received a higher PR disliking rating than their typical level, they had lower classroom engagement than their all-time average level of classroom engagement.

The Interactive Effects of TSR and PR on Classroom Engagement at the Between-Person, Within-Person, and Cross Levels²

According to the best fitting models, there was no significant interaction effect of TSR and PR on classroom engagement at the within-person level. At the between-person level, both positive and negative TSR interacted with PR disliking in predicting engagement, whereas PR liking did not interact with either dimension of TSR. We further conducted post-hoc simple slope analyses to interpret the interaction effects. Overall, the effects of TSR on classroom engagement were stronger for students with lower levels of PR disliking (positive TSR: b = .71, SE = .07, p < .001; negative TSR: b = −.59, SE = .08, p < .001 at 1 SD below the mean of between-person PR disliking) than for students with higher levels of PR disliking (positive TSR: b = .49, SE = .05, p < .001; negative TSR: b = −.36, SE = .05, p < .001 at 1 SD above the mean of between-person PR disliking).

One model (negative TSR and PR disliking) exhibited a cross-level interaction effect, such that the interaction between within-person negative TSR and between-person PR disliking significantly predicted classroom engagement. Simple slope analyses showed that the effect of within-person negative TSR on classroom engagement was stronger for students who had lower overall levels of PR disliking (at 1 SD below the between-person mean of PR disliking: b = −.45, SE = .06, p < .001) than for students with higher overall levels of PR disliking (at 1 SD above the between-person mean of PR disliking: b = −.26, SE = .06, p < .001).

Discussion

Classroom engagement critically contributes to students’ academic success in the long run (Fradricks et al., 2004; Furrer et al., 2014). Guided by the developmental systems framework (Skinner et al., 2022), the present study examined the roles of students’ relationships with teachers and peers in the development of classroom engagement in a sample of low-achieving students from G1 to G3. To our knowledge, the current study is the first to examine the effects of multidimensional TSR and PR on students’ classroom engagement at both the between-person and within-person levels in early elementary school years, which contributes important insights into the dynamic associations between social-relational ecology in the classroom and early engagement development among low-achieving students. We identified three major gaps in the literature on the associations between TSR/PR and students’ classroom engagement, namely the scarcity of research that investigated (1) low-achieving students in early elementary school years, (2) effects of the interplay between the multidimensional TSR and PR, and (3) both between-person and within-person levels of associations. We focused on highlighting how the present study contributed to addressing these critical gaps when reviewing the current findings in the following section.

To answer our first research question “To what extent is each dimension of TSR and PR associated with classroom engagement at both the within- and between-person levels”, we found that between-person level of positive/negative TSR and PR liking/disliking predicted students’ initial classroom engagement but not the rate of change in classroom engagement over time. These between-person level findings suggest that the associations between classroom engagement and TSR/PR are partially explained by the covariation between stable trait-like individual differences among students in social relationships and academic adjustment. These findings are consistent with previous studies that showed additive effects of TSR and PR on engagement in other school stages (e.g., De Laet et al., 2015; Vollet et al., 2017; Wang & Eccles, 2012).

At the within-person level, year-to-year fluctuations of positive and negative TSR for a given student were both associated with fluctuations in the student’s classroom engagement in the same year. In addition, although PR disliking negatively predicted classroom engagement at the within-person level, PR liking did not exhibit a within-person level effect. Together, these within-person level findings advance our understanding of the social-relational context for early engagement development in several ways. First, compared to between-person level associations, these within-person level associations provide much stronger developmental evidence supporting the influences of TSR/PR on students’ engagement growth. This is because within-person level effects capture inter-related developmental processes within a single person, thus excluding the confounding of individual difference factors between people. Second, although both dimensions of TSR predicted classroom engagement at the within-person level, only the negative dimension of PR demonstrated a within-person level effect. These findings suggest that the contributions of PR to the development of classroom engagement may be less consistent than the contributions of TSR in early elementary school years. Such findings extend the existing literature (Roorda et al., 2011) by providing strong support for the influential role of teachers in enhancing or undermining students’ classroom engagement in early school years. These findings are also consistent with the notion that peer influences on learning behaviors and academic outcomes may be more salient for upper elementary school than early elementary school students (Gifford-Smith & Brownell, 2003; Lynch & Cicchetti, 1997). Finally, these findings underscore the need to distinguish between PR liking and disliking in understanding students’ learning behaviors in the classroom, such that high PR liking does not amount to low PR disliking and vice versa (Hendrickx et al., 2016; Hughes & Im, 2016). The differential effects of the different dimensions of PR suggest that low-achieving early elementary students may be particularly vulnerable to unfavorable evaluations by their peers.

To answer our second research question “To what extent do TSR and PR interact to influence the development of classroom engagement at multiple levels of analysis”, we found that between-person PR disliking moderated both the between- and within-person effects of negative TSR on classroom engagement. Specifically, students who were less disliked by their peers were more vulnerable to the effects of negative TSR on classroom engagement. Although this finding supports the conceptualization of contingent operation of TSR and PR on classroom engagement (Skinner et al., 2022), the specific interaction pattern is inconsistent with the two existing studies that also found interactive effect between TSR and PR on engagement (Furrer & Skinner, 2003; Vollet et al., 2017). In those two studies, positive TSR was found to buffer the negative effect of negative PR (or lack of positive PR) on students’ classroom engagement (Furrer & Skinner, 2003; Vollet et al., 2017). Several critical differences in study design may account for the discrepant findings among studies. First, the operationalization of TSR and PR was inconsistent across studies. One study operationalized TSR and PR using students’ perception of relatedness to their teachers and peers (Furrer & Skinner, 2003), and the other operationalized TSR by teacher involvement (Vollet et al., 2017). As a result, different studies may capture slightly different processes that are specific to the measured constructs. Second, the present study partitioned the associations between TSR/PR and classroom engagement to between- and within-person levels, whereas the two previous studies focused on only the between-person level associations (Furrer & Skinner, 2003; Vollet et al., 2017). Because between-person and within-person level associations are indicative of different developmental mechanisms, it is possible that the present findings captured more dynamic cross-level associations that were not detectable when only between-person level associations were investigated. Alternatively, differences in sample characteristics across studies may contribute to explaining the discrepant findings. The two previous studies examined upper elementary school and middle school students (Furrer & Skinner, 2003; Vollet et al., 2017), whereas the present study used a sample of low-achieving early elementary school students. It is possible that low-achieving students experience a great deal of struggles to meet the increasing social and academic requirements especially as they transition into formal schooling. Consequently, they may be particularly vulnerable to the presence of any demand that hinders their learning and engagement, such that when one demand subsides other demands become more salient. This may explain why the negative effect of social strain in TSR on engagement was counterintuitively stronger for students who were less disliked by their peers.

Limitations

Despite the numerous strengths of this study including the use of multilevel modeling to partition the longitudinal within- and between-person level associations, a large sample size, and strong theoretical backgrounds, we acknowledge the following limitations. First, both TSR and classroom engagement were assessed using only teacher reports. Teacher ratings may be subject to their implicit or explicit biases based on students’ demographic (e.g., race/ethnicity, gender, family SES), behavioral (e.g., achievement), and relational (e.g., peer) characteristics. For example, our findings showed that there were developmentally increasing disparities in teachers’ perceptions of classroom engagement and TSR between White and non-White students as well as between students of high and low SES. This developmental trend is consistent with the Social Equity Theory which highlights the increasing effects of signal influences on academic outcomes beginning at around third grade (McKown, 2013). Such perceptual bias of teachers may potentially inflate the observed associations between TSR and classroom engagement and introduce biases in the results for certain groups of students. This reliance on teacher ratings may also introduce alternative explanations to the present findings such that the observed associations may capture the degree to which students’ engagement behaviors and peer relationships influence teacher perceptions of TSR. Therefore, future studies should obtain information from multiple sources such as employing observational measures to better understand the dynamic association between TSR and engagement in young elementary school students. In addition, some of the items to assess classroom engagement were taken from a personality scale. Engagement can be dynamic that changes from moment to moment and class to class. As such, a trait-like personality measure may not fully capture this state-like attribute of engagement. Future studies should use alternative engagement measures to investigate the replicability of the present findings. Relatedly, our study constructs were measured annually, which may not capture the temporal changes of social relationships and classroom engagement as they emerge across more micro-level time scales (e.g., days, months). Future studies would benefit from implementing intensive longitudinal design to sample within-person variability more frequently to uncover the dynamic associations between social relationships and classroom engagement development across different time scales. Finally, the present study included only low-achieving students. Due to the scarcity of existing research on low-achieving students as well as lack of a comparison group of average/high achieving students in our design, we were not able to definitively attribute the unique findings to the use of a low-achieving sample. As such, future studies should investigate its replicability in other low-achieving samples as well as its generalizability to average/high achieving students.

Implications

As scholars have highlighted the importance of contextual factors on the long-term development of student academic wellbeing (Skinner et al., 2022; Wentzel, 2022), the current study corroborated the idea that early development of classroom engagement is open to the influences of social relationships with both teachers and peers (Roorda et al., 2017; Rubin et al., 2015). Our findings support both the coactive and contingent operations in the associations between TSR/PR and classroom engagement. Our findings of the contingent operation at both the between-person and cross levels highlight the salience of any social strain on lowering engagement among low-achieving early elementary school students even in the absence of other relationship problems. These findings call for additional work that focuses on low-achieving students in the transitioning into formal schooling, which will ultimately advance our theoretical understanding of the unique ways in which these vulnerable students interact with their social-relational contexts in early academic development.

To promote classroom engagement among low-achieving early elementary school students, our findings suggest that improving TSR quality may be particularly beneficial given its consistent associations with students’ engagement behaviors at both the between- and within-person levels. Intervention efforts that incorporate teacher training and practices to promote their social emotional skills, knowledge of effective and ineffective interactions, as well as culturally competent practices would help teachers build positive classroom ecology. For example, socioemotional learning interventions have been shown to promote teachers’ social, emotional, and psychological well-being (Oliveira et al., 2021), which in turn better equip teachers to manage students’ conflicts, create supportive learning environment, maintain healthy relationships with students, and cultivate classroom engagement (Jenning & Greenberg, 2009; Schonert-Reichl, 2017). Interventions that target at promoting teachers’ knowledge of effective interactions and awareness of their own behaviors in the classroom have been shown to foster growth in positive teacher-student interactions, improve students’ engagement, and result in subsequent academic gains (Allen et al., 2011; Gregory et al., 2014; Pianta et al., 2008). In addition, it is critical to highlight the importance of cultural competence training for teachers. For example, in our racial/ethnically and socioeconomically diverse sample of students, most teachers are White. Our findings, in line with the literature on potential teacher bias and unfair treatment of marginalized youth, suggested that teachers perceived racial/ethnic minority and low SES students as less engaged and having more relational problems. As such, building the cultural competencies in the current teaching force may help foster culturally responsive and sustaining teaching practices to promote engagement among marginalized student populations (Brown & Rodriguez, 2017; Souto-Manning & Emdin, 2020).

Finally, as social relations often develop in a transactional manner, classroom-based interventions on improving students’ social skills may complement teacher training program in improving engagement among low-achieving early elementary school students by way of improving TSR and PR (Bacete et al., 2019; January et al., 2011). Example prevention and intervention programs, such as peer-mediated learning practices (PML; Ginsburg-Block et al., 2006) and socioemotional learning (Wigelsworth et al., 2022) have shown benefits in enhancing students’ social relationships with teachers and peers as well as positive learning outcomes (Jennings & Greenberg, 2009; Ladd et al., 2012; Poling et al., 2022).

Conclusion

By disaggregating the between-person and within-person components, the current study furthers our understanding of how social relationships with teachers and peers are associated with classroom engagement among low-achieving students in early elementary school. Overall, our findings suggested that students who were highly competent in social domains also exhibited behavioral and regulatory competencies in the classroom (Wentzel, 2009). In addition, for a given student, a year-to-year improvement in classroom engagement was observed along a simultaneous improvement in positive relationships with teachers, as well as a decline in negative relationships with teachers and peers. Our study calls for additional work on the development of classroom engagement among academically low-achieving students during the transition to formal schooling, which will provide the much-needed theoretical insights into the unique social-relational mechanisms underlying the early academic development among these vulnerable students. Our findings also inform school-based programs to simultaneously implement interventions that target improving both teacher-student and peer relationship quality within the classroom to enhance positive academic learning.

Table 4b.

Model Comparison for the Effects of Negative TSR and PR Liking on Classroom Engagement

		Compared With	Ho value	Ho Scaling Correction Factor	# Free Parameters	Δdf	LLCD	(ΔSatorra-Bentler Scaled χ2) - TRd - using LL	p
M1	Random Linear	-	−2506.89	1.01	6	-	-	-	-
M2	M1 + covariates	M1	−1718.62	0.97	19	13	0.95	1651.96	0.00
M3	M2 + WP TSR and WP Peer	M2	−1411.21	1.01	22	3	1.23	501.26	0.00
M4	M3 + BP TSR and BP Peer	M3	−1262.21	1.00	26	4	0.99	301.63	0.00
M5	M4 + WP interaction	M4	−1261.99	1.00	27	1	0.97	0.46	0.46
M6	M4 + BP interaction	M4	−1262.20	1.00	28	2	0.94	0.03	0.95
M7	M4 + Cross Level interactions	M4	−1262.06	1.00	28	2	0.90	0.35	0.83

Notes. Model 1 is the growth model with random intercept and random linear slope. TSR = teacher student relationship. PR = peer relationship. WP = within-person; BP = between person; −2LL = −2 log-likelihood; df = degrees of freedom. The best fitting and most parsimonious model is in bold face.

Table 4c.

Model Comparison for the Effects of Positive TSR and PR Disliking on Classroom Engagement

		Compared With	Ho value	Ho Scaling Correction Factor	# Free Parameters	Δdf	LLCD	(ΔSatorra-Bentler Scaled χ2) - TRd - using LL	p
M1	Random Linear	-	−2506.89	1.01	6	-	-	-	-
M2	M1 + covariates	M1	−1718.62	0.97	19	13	0.95	1651.96	0.00
M3	M2 + WP TSR and WP Peer	M2	−1381.73	1.00	22	3	1.20	561.76	0.00
M4	M3 + BP TSR and BP Peer	M3	−1207.79	1.01	26	4	1.08	321.58	0.00
M5	M4 + WP interaction	M4	−1207.05	1.03	27	1	1.34	1.10	0.29
M6	M4 + BP interaction	M4	−1201.75	1.00	28	2	0.88	13.72	0.00
M7	M6 + Cross Level interactions	M6	−1199.73	1.00	30	2	0.94	4.32	0.12

Notes. Model 1 is the growth model with random intercept and random linear slope. TSR = teacher student relationship. PR = peer relationship. WP = within-person; BP = between person; −2LL = −2 log-likelihood; df = degrees of freedom. The best fitting and most parsimonious model is in bold face.

Highlights:

• The effects of teacher-student relationships (TSR) and peer relationships (PR) on the classroom engagement (CE) of low-achieving students were examined.

• Positive and negative TSR predicted CE at both between- and within-person levels

• PR disliking negatively predicted CE at both between- and within-person levels

• PR liking positively predicted CE only at the between-person level

• The associations between TSR and CE were stronger for students with lower levels of PR disliking

Data availability statement:

The current study used a secondary data set that is publicly available to interested researchers through NICHD Dash (https://dash.nichd.nih.gov/).