TEACHER-CHILD RELATIONSHIPS IN UPPER ELEMENTARY SCHOOL:
Towards a Model of Child and Contextual Influences
on Children’s Academic Outcomes
M. Zee (0519421)
Supervisors: Dr. H. M. Y. Koomen
Dr. I. Van der Veen
Thesis 2
Research Master Educational Sciences September 2011
TABLE OF CONTENTS
Abstract ... IV
Introduction ... 5
Predictors of the Teacher-Child Relationship Quality and School Success ... 6
Moderators of the Link between Teacher-Child Relationships and School Success ... 9
Present Study ... 11 Method ... 13 Participants ... 13 Procedures ... 14 Instruments ... 14 Outcome Variables ... 14 Mediator Variables ... 15 Moderator Variables ... 17 Covariates ... 18 Data Analysis ... 18 Results ... 20
Missing Data, Assumptions and Descriptive Statistics ... 20
Measurement Model ... 21 Structural Model ... 23 Direct Effects ... 24 Mediation Effects ... 27 Moderator Effects ... 31 Cross-Validation Sample ... 34
Conclusion and Discussion ... 35
Child and Contextual Features Affecting Teacher-Child Relationships ... 35
Teacher-Child Relationships Affecting Achievement through Children’s Motivational Beliefs ... 37
The Moderating Role of Children’s Background Features on Children’s Academic Adjustment ... 38
Limitations and Future Directions... 40
ABSTRACT
The development of a warm, caring relationship with a teacher is a crucial developmental need of elementary school students. The present study aimed to investigate child (i.e., personality traits and learning problems) and contextual influences (i.e., SES, ethnicity, and parental involvement) on the quality of teacher-child relationships, and the extent to which these relationships can buffer or exacerbate the impact of risk factors on children’s academic adjustment in upper elementary school. Surveys and tests were conducted among a nationally representative sample of 8545 sixth-grade students and their teachers in 395 schools. Theoretically-derived structural equation models were used to test for direct, indirect, and moderation effects. Support was found for a model that identified parental involvement and personality traits as potential predictors of the teacher-child relationship quality, and teacher-children’s motivational beliefs as mediators of the link between relationship quality and reading and math achievement. Moreover, children’s ethnicity, SES, and learning problems were found to partially moderate the relations between teacher-child relationships, and children’s academic adjustment. Implications for theory and practice are discussed.
INTRODUCTION
The affective nature of the teacher-child relationship has nowadays been widely acknowledged to play a crucial role in fostering children’s academic adjustment both during early childhood, and beyond (Hamre & Pianta, 2001; Ladd, Birch, & Buhs, 1999; Roorda, Koomen, Spilt, & Oort, in press). Evidence has indicated that caring teacher-child relationships create a range of opportunities for children’s development, whereas discordant or overly dependent relationships may act as obstacles to academic success (Mantzicopoulos, 2005; Pianta, Steinberg, & Rollins, 1995). When there is a sense of mutual trust and secure relatedness between children and teachers, children are more likely to be motivated to succeed, feel more successful in educational pursuits and, consequently, perform better than children without such supports (Davis, 2003; Hamre & Pianta, 2005; Hughes, Luo, Kwok, & Loyd, 2008; Murray, 2009; Roeser, Midgley, & Urdan, 1996; Thijs & Koomen, 2008). Moreover, beyond its direct links to children’s academic beliefs and outcomes, relational closeness has also been found to buffer the long-term effects of high-risk family environments on the child’s school trajectory (Buyse et al., 2008; Burchinal, Peisener-Feinberg, Pianta, & Howes, 2002; Meehan, Hughes, & Cavell, 2003).
Despite agreement about the importance of the quality of these relationships, however, investigators have been less conclusive about its antecedent conditions, and the mediating and moderating processes through which they might affect children’s performance (e.g., Hughes, Cavell, & Willson, 2001; Mantzicopoulos, 2005; Pianta, Hamre, & Stuhlman, 2003). While teacher-child interactions have long been recognized to be determined by complex child-by-environment transactions, most efforts to identify their underlying sources and consequences seem to have been hindered by the constraints of traditional, single predictor models of development (Coleman & Watson, 2000; Downer, Sabola, & Hamre, 2010; Sutherland, Conroy, Abrams, & Vo, 2010). The present paper attempts to overcome this issue by investigating the processes by which child and contextual variables combine to influence teacher-child relationships in upper elementary school. In addition, this study examines the extent to which these relationships can buffer or exacerbate the impact of risk factors on upper elementary school children’s academic adjustment.
Predictors of the Teacher-Child Relationship Quality and School Success
In examining the role of teacher-child relationships in affecting children’s achievement, ecologically informed studies on relationship quality have currently probed for a number of precursors related to both environmental features, and biological traits (e.g., Downer et al., 2010; Ladd et al., 1999; Moritz Rudasill, 2011; Rimm-Kaufman & Pianta, 2000). Among these, parental involvement has increasingly been targeted as environmental contributor to social relationships and academic success (e.g., Jeynes, 2003). Involved parents may provide an abundance of resources that help children to become acquainted with the behaviors necessary to successfully navigate the classroom (Garg, Kauppi, Lewko, & Urajnik, 2002). A steady stream of research has indicated that children whose parents offer high levels of academic support and opportunities to learn are more likely to develop skills and behaviors that prepare them to be positively engaged in the classroom, and with their teachers (Pianta, 1999; Pianta & Walsh, 1996). Mantzicopoulos (2004), for instance, found that parental involvement significantly contributed to less relational conflict, and more positive classroom experiences. Furthermore, the effects of academically involved parents have been shown to surface in children’s reading performance (Jeynes, 2007; Shaver & Walls, 1998), and in their mathematics achievement (Crane, 1996; Muller, 1998). Thus, parental involvement may set into motion a chain of events that leads to the kinds of beliefs and practices necessary to foster both the teacher-child relationship, and children’s school performance.
The idea that children with particular personality traits are more prone to develop supportive relationships with significant others has also attracted increasing research interest (e.g., Koenig, Barry, & Kochanska, 2010; Shiner & Caspi, 2003). This interest has been fuelled by the belief that personality traits predispose tendencies to think and behave in certain consistent ways, which may reflect habits affecting the quality of teacher-child relationships and hence, academic success (Furnham & Monsen, 2009; Hair & Graziano, 2003; Shiner & Caspi, 2003; Stuhlman & Pianta, 2002). Although some attention has been paid to personality traits and children’s academic adjustment in prior investigations, research on personality has not yet been integrated with research conducted on teacher-child relationships.
Investigative efforts on individual variations in the structure of personality traits have currently coalesced around factors of the Big Five model, including Extraversion, Conscientiousness, Agreeableness, Autonomy, and Neuroticism (e.g., De Raad, 2000; Hendriks, 1997). Extraverted children are generally viewed as effective in social interactions, and display friendly, assertive, and gregarious behavior (Bidjerano & Yun Dai, 2007; Van Bragt, Bakx, Bergen, & Croon, 2011). Evidence has shown that children high in extraversion are more likely to experience positive affect during interactions with their teacher, are ready to seek help when needed, and engage more actively in joint activities (Bidjerano & Yun Dai, 2007; Chamorro-Premuzic & Furnham, 2008; Goldberg, 1990). By spending more time with others, extraverted children may actively create opportunities for warm and cooperative relationships in the course of achieving success in school (Diener, Larsen, & Emmons, 1984; LePine & Van Dyne, 2001). Not surprisingly, teachers have been found to generally favor children who display extraverted and companionable behaviors, relative to more introverted conduct (Brophy & Evertson, 1981; Wentzel, 1991). Extraversion, then, might have a salient position in sustaining warm relationships with teachers, which may ultimately lead to academic success (e.g., De Raad & Schouwenburg, 1996; Laidra, Pullman, & Allik, 2007).
Conscientiousness is generally considered to be the most prominent in school contexts (De Raad & Schouwenburg, 1996). Positive correlations among this trait and motivation (Andersson & Keith, 1997; Furnham, 1995; Ntalianis, 2010) and interest in school (Aluja-Fabregat & Torrubia-Beltri, 1998) have repeatedly been found across all educational levels. Furthermore, conscientiousness has been linked with behavioral tendencies towards orderliness, achievement-orientation, and reliability (Barrick & Mount, 1991; McCrae & John, 1992), which are valued and rewarded in most classrooms. Because highly conscientious students are meticulous and achievement-oriented, they tend to accomplish their goals by being more caring and sociable towards others, adapting implicit and explicit social norms more easily, and investing more in long-term relationships than do their less conscientious counterparts (Asendorpf & Wilpers, 1997; Bartley & Roesch, 2011; Halamandaris & Power, 1999; LePine & Van Dyne, 2001; Noftle & Shaver, 2006). This is likely to result in enhanced self-esteem, motivation, and appreciation by teachers and peers, which may in turn engender
reciprocation in the form of increased achievement (e.g., Bratko et al., 2006; Chamorro-Premuzic & Furnham, 2003; Laidra et al., 2007; Steinmayr & Spinath, 2008).
The salience of Agreeableness as a personality dimension seems also evident in its connection with the quality of the teacher-child relationship. Agreeable students are commonly perceived as friendly, compliant, courteous, and tolerant (Barrick & Mount, 1991). They tend to be more cooperative and generally have higher quality interpersonal interactions, as they minimize interpersonal conflict by being less hostile, or by provoking less aggression from others (Asendorpf & Wilpers, 1997; Barrick, Stewart, & Piotrowski, 2002; Graziano, Jensen-Campbell, & Hair, 1996). In so doing, children may experience more satisfying social environments themselves, which in turn initiates higher levels of motivation to work on school-related tasks, and better prepare them for the academic challenges they face over the course of development (Furrer & Skinner, 2003; Hair & Graziano, 2003). Consequently, agreeableness may also have a prominent position in sustaining close, and less conflictual ties with teachers, and achieving academic success (e.g., De Raad & Schouwenburg, 1996; Laidra et al., 2007).
The factor Autonomy has been associated with tendencies towards seeking novel academic experiences, independence, originality, and with intelligence (McCrae & Costa, 1987; McCrae & John, 1992). This trait has been marked by self-determination theorists as one of the most important psychological needs that are essential for facilitating children’s social and academic adjustment (e.g., Deci & Ryan, 2000, 2008). Empirical work of Verschueren, Buyck, and Marcoen (2001), for instance, has revealed that children are more likely to initiate positive and conflict-free relationships with their teachers when they have dispositions towards curiosity, classroom exploration, and self-determination. Because children higher in autonomy seem to be more open to change, and willing to transfer new skills and behaviors learned in one domain to benefit another, they tend to be more creative in developing solutions when conflict arises (Wayne, Musisca, & Fleeson, 2004). Conflict in the classroom is thereby likely to be reduced, resulting in better relationships and higher achievement scores (e.g., Laidra et al., 2007; Paunonen & Ashton, 2001). Moreover, findings from Roeser and colleagues (2000) also revealed that students’ academic adjustment generally improves when teachers succeed in supporting students’ autonomy needs. In particular, when students feel cared for by, and
related to their teachers, they tend to experience more freedom to navigate the classroom, and also exhibit more autonomous reasons for taking part in school tasks and achieving academically (Ewing & Taylor, 2009). Children’s autonomy may therefore not only contribute to the development of warm relationships with their teachers, but might also initiate the kind of teacher supports that children need to become motivated to succeed.
One personality trait that may have less positive implications for children’s development is neuroticism. Highly neurotic children generally tend to reflect poor emotional adjustment in the form of stress, anxiety, and depression, and are prone to negative affect (Koenig et al., 2010). Neuroticism may act as a catalyst for poor teacher-child relationships by hindering positive interactions, expressing negative attitudes towards the teacher, and limiting teachers’ ability to be sensitive and responsive to the child’s signals (LePine & Van Dyne, 2001; Little & Hudson, 1998). Indeed, research has shown that neurotic students experience others as less available and more threatening which, in turn, may bring about more negative behaviors from teachers (Park & Waters, 1989; Suess, Grossmann, & Sroufe, 1992). Furthermore, in a study of Graziano et al. (2007) it was found that emotionally unstable children are likely to be rated by teachers as difficult to handle, requiring more energy from the teacher to control their behavior, and to assist them with engaging in classroom activities. Children scoring high in neuroticism would therefore have lower quality interactions with teachers in the classroom. Other forms of negative emotionality, such as irritability, anxiety, and mistrust, have also been associated with less warm en more forceful and over-dependent teacher-child relationships (Birch & Ladd, 1998; Howes, 2000; Ladd & Burgess, 1999; Little & Hudson, 1998), and lower achievement scores (e.g., Laidra et al., 2007).
Moderators of the Link between Teacher-Child Relationships and School Success
In addition to a variety of direct and indirect effects, research has more recently advanced potential moderation effects between aspects of the teacher-child relationship and school outcomes. Specifically, the idea that children with particular background characteristics are more susceptible to adverse classroom experiences and poor achievement has attracted growing research attention (e.g., Borman & Overman, 2004; Decker, Dona, & Christenson, 2007; Peguero & Bondy, 2010). Studies
conducted among high-risk populations have suggested, for instance, that the relative strength of the association between the teacher-child relationship quality and academic adjustment may vary according to children’s socioeconomic background (Baker, 1999; Garner & Waajid, 2008; Roorda et al., in press). Specifically, students whose families are less educated, and have less financial and educational resources have been found to be more likely to be negatively influenced by teachers’ expectations and interactions than are other students, leading to lower levels of academic adjustment (Furrer & Skinner, 2003; Pianta & Stuhlman, 2004; Roeser et al., 2000; Trouilloud, Sarrazin, Bressoux, & Bios, 2006). There is also evidence that the quality of the relationships of young lower socioeconomic at-risk children with their teachers becomes progressively more important for their subsequent school adjustment (Roorda et al., in press). Especially for lower-SES children in elementary schools, less close, and more dependent and conflictual relationships with teachers are likely to have a cascading effect on children’s motivation and performance in successive grades (Hamre & Pianta, 2001; Pianta et al., 2005). Consequently, children’s SES is expected to moderate the negative links between unfavorable relationship features and children’s adjustment, such that these links are stronger for low-SES children than for high-SES children.
Likewise, a handful of studies have investigated how ethnicity affects the teacher-child relationships that foster achievement (e.g., Ewing & Taylor, 2009; Murray, Murray, & Waas, 2008; Vedder, Boekaerts, & Seegers, 2005). Prior work, for example, has consistently shown that minority students tend to enjoy more disruptive, and less caring relationships with their teacher than do their non-minority counterparts, and are at increased risk of school failure (e.g., Hamre & Pianta, 2001; Hughes, Gleason, & Zhang, 2005; Hughes & Kwok, 2007; Saft & Pianta, 2001). Some of these studies have furthermore pointed to the specific role of ethnicity as a moderator. Burchinal et al. (2002), and Pallock and Lamborn (2006) established that warm and companionable relationships between teachers and children were more important for the acquisition of minority children’s academic skills, than for non-minority children. Similarly, in their meta-analysis, Roorda and colleagues (in press) found that teacher-child closeness was a stronger predictor of minority students’ achievement, both in primary and secondary school settings. When only primary school studies were considered, the links between closeness and motivation were stronger for non-minority students (ibid.). Not all research, however,
could establish such beneficial links. Ewing and Taylor (2009) found comparable effects of teacher-child closeness, conflict, and dependency on both minority and non-minority teacher-children’s adjustment. Similar results were reported by Hamre and Pianta (2001), and found in the meta-analytic work of Cornelius-White (2007). It has been suggested by some researchers (e.g., Ewing & Taylor, 2009; Murray et al., 2008; Roorda, et al., in press) that these mixed findings are attributable to discrepancies in the ethnic groups being investigated, the outcomes being studied, or the methods being used. Given the yet unclear role of ethnicity as a moderator, no specific hypothesis regarding this background variable was made in the present study.
Beyond demographic risk factors, children’s learning difficulties have also potential to affect the development of social relationships. Although research on the bond between teachers and children with learning problems is limited, studies have revealed that young children experiencing learning problems not only show poorer school results, but are also less equipped to benefit from warm relationships with their teacher, relative to their typically developing peers (Baker, 2006; Eisenhower, Baker, & Blacher, 2007). Problem behaviors, including intellectual, conduct and learning difficulties, have recurrently been associated with relationships characterized by more conflict and dependency, less self-esteem, and less adaptation in the classroom (Eisenhower et al., 2007; Ladd et al., 1999; McIntyre, Blacher, & Baker, 2006; Pianta & Steinberg, 1992). Of importance, Roorda et al. (in press) have pinpointed the salience of conflictual, rather than warm teacher-child relationships for students at risk of academic failure. In their recent meta-analysis, they found that learning problems moderated the link between negative relationship patterns and children’s academic adjustment, such that the link was stronger for children with learning difficulties. With respect to these empirical results, learning problems are expected to exhibit a negative moderating effect on the association between the quality of the teacher-child relationship and children’s academic adjustment.
Present Study
To summarize, the purpose of the present study was to investigate the role of the teacher-child relationship quality in the associations between children’s background features and academic adjustment in a representative sample including typical and at-risk children in upper elementary
school. Specifically, a bio-ecologically based mediator-moderator model (see Figure 1) was tested positing that (a) children’s personality traits and parental involvement predict the quality of the teacher-child relationship, that (b) the teacher-child relationship quality indirectly affects children’s achievement via the direct effect on children’s motivational beliefs, and that (c) the associations between the teacher-child relationship quality and children’s subsequent school outcomes (i.e., motivational beliefs and achievement) are moderated by students’ background characteristics (i.e., ethnicity, learning problems, and SES).
Figure 1.
Conceptual model Predicting Teacher-Child Relationship Quality and Academic Adjustment
Children’s Personality Parental Involvement Teacher-Child Relationship Quality Motivational Beliefs Academic Achievement SES Ethnicity Learning Problems
METHOD
Participants
The current study was conducted using data from the first wave of the national COOL-cohort study, which started in the academic year of 2007-2008 in the Netherlands. COOL is a prospective longitudinal research project among 550 mainstream primary schools, in which about 38,000 students from Kindergarten, Grade 3, and Grade 6 are tested every three years in language, reading, and mathematics. Extensive information about a number of attitudinal, motivational, and background characteristics is collected as well (Driessen, Mulder, Ledoux, Roeleveld, & Van der Veen, 2007).
Originally, the COOL-cohort consists of a nationally representative part of 420 schools, and a supplementary part of 130 schools with an overrepresentation of minority and non-minority disadvantaged students (Driessen et al., 2007). Given that much less is known about teacher-child relationships in upper elementary grades (Ang et al., 2008; Hamre & Pianta, 2001), the present study made use of a subset of the total sample, in which only sixth-graders from the nationally representative sample were included. This selection left a total of 8545 students from 1001 classes of 395 schools for the analyses. Informed consent was obtained from the parents by providing them with a written account of the study’s purposes, and a permission form in their native language that could be returned to the child’s school.
To evaluate and confirm the hypothesized model, a cross-validation procedure (e.g., Yuan, Marshall, & Weston, 2002) was pursued by randomly generating calibration (N = 4308) and validation (N = 4237) samples. Demographics for the calibration sample indicated that 50.8% of the children were male, having a mean age of 11.6 years (range = 8.0-13.0, SD = .59). Teachers specified an average of 887 students (20.6%) to be at risk of academic problems. Information from the school administrations about ethnicity was available for 97.0% of the children, and revealed that 3351 (77.8%) students had a Dutch, and 826 (19.2%) a non-Dutch origin. Mothers’ educational background, which was on hand for 93.7% of the cases, differed considerably: 9.8% of the mothers had only finished primary school, 23.8% pre-vocational secondary education, 40.8% senior secondary
vocational education, and 19.3% had also finished higher education. The background characteristics for both the calibration, and the validation sample were all comparable to those for the full sample1.
Procedures
Data collection took place in two phases. Between September and December 2007, extensive data about children’s background were obtained from the school administrations, which could be turned in digitally. Between January and April 2008, the math and reading comprehension tests were administered during school hours by teachers themselves. In total, 96.4% of the children were able to take the tests. Non-participation was due to absence or sickness at the time of data collection. After the teachers checked the child’s answers on the tests, they could return them digitally, or by e-mail. In the same period, teachers and children were also asked to fill in the remaining questionnaires regarding personality, parental involvement, the teacher-child relationship quality, and children’s motivational beliefs. The response rate of the child-reported questionnaires was 94.9%, and completed teacher-reported questionnaires were available for 94.3% of the sample.
Instruments
Outcome Variables
Students’ academic achievement was obtained from their performance on individually administered tests for reading comprehension and arithmetic. Both instruments were nationally normed achievement tests developed by the Dutch National Institute for Educational Measurement (CITO). The reading comprehension test evaluated proficiency in the areas of conceptual reasoning and reading. The math test was designed to tap important aspects of the development in children’s mathematical skills, such as geometry, multiplication, and addition (Driessen et al., 2007). To indicate students’ achievement in both subjects, comprehensive total achievement scores were computed for each test separately. The reading comprehension and the arithmetic test prove to have adequate internal consistency (α = .89 -
1 Calibration and validation samples did not significantly differ in gender (t (8543) = .631, p = .528, age (t (8543) = 1.101,
p = .230), SES (t (8543) = .304, p = .761, learning problems (t(8543) = -.035, p = .972, or distribution of ethnicity (t(8273) = 1.044, p = .296).
.95; CITO, 2004), and are associated with other measures of academic ability, such as writing and spelling (ibid.).
Mediator Variables
Personality Traits. Students’ personality traits were measured using a slightly adapted version of the Five Factor Personality Inventory (FFPI; Hendriks et al., 1999, 2008). The FFPI is a 100-item self-report questionnaire developed to evaluate students’ position on the psycho-lexically based facets of Extraversion, Agreeableness, Conscientiousness, Neuroticism, and (Intellectual) Autonomy. Items that made up this measure were rated by students on a five-point Likert-type scale, ranging from 1 (not at all applicable) to 5 (entirely applicable), with higher scores indicating more pronounced values on the five personality dimensions. Example items for each respective dimension are “I like to chat” (Extraversion), “I respect others’ feelings” (Agreeableness), “I do things according to a plan” (Conscientiousness), “I can’t take my mind off my problems” (Neuroticism), and “I can easily link facts together” (Autonomy). The FFPI dimensions have been found to be reliable, with alphas ranging between .76 and .85. Investigators have also provided evidence for the instrument being construct-valid, both nationally and internationally, and across age, gender and culture (e.g., Barelds & Luteijn, 2002; Hendriks et al., 2002, 2003; Perugini & Ercolani, 1998). In the present study, standardized scale scores were used to represent the five personality traits.
Parental Involvement. In order to provide estimates of Parental Involvement, teachers were administered a short, 3-item measure, which assessed the extent to which parents supported the child’s learning, and were actively engaged in the child’s learning process. Items that made up this scale included “In this family, the parents are actively involved with the school”, “In this family, the parents support the child’s learning”, and “In this family, the parents encourage the child’s curiosity”. All items were scored on a 5-point Likert scale, ranging from 1 (definitively not true) to 5 (definitively true). In the present sample, Cronbach's alpha for this measure was .88.
Teacher-Child Relationship Quality. Teachers’ perceptions of the quality of their relationship with each of their students were estimated using an authorized Dutch translated and slightly adapted version of Student-Teacher Relationship Scale (STRS; Koomen, Verschueren, & Pianta, 2007). Like
its original, the adapted STRS has shown to be represented by three distinct factors that are referred to as the Closeness, Conflict, and Dependency subscales, developed to assess relationship quality for 3 to 12-year-old students (Koomen, Verschueren, Van Schooten, Jak, & Pianta, in press). Closeness measures the extent to which teachers feel their relationship with a child to be characterized by warmth, openness, and proximity, with items such as “I share an affectionate and warm relationship with this child”. The latter two subscales measure negative aspects of teacher-child relationships, which are those where teachers observe the relationship with students to be overly conflictual, or where teachers experience the child to show clingy and demanding behavior. Example items are “This child and I always seem to be struggling”, and “This child reacts strongly to separation from me”.
For the present version of the STRS, 5 items for each subscale have been selected on the basis of the highest factor loadings reported in earlier research (Koomen et al., in press). All items were rated on a 5-point Likert type scale, ranging from 1 (definitely does not apply) to 5 (definitely applies). Investigators using the adapted STRS have reported satisfactory reliability and validity for the STRS, from preschool to upper elementary school, and across gender and age (e.g., Doumen et al., in press; Koomen et al., 2007; Koomen et al., in press). Cronbach’s alphas ranged between .88 and .93 for Closeness, .88 and .91 for Conflict, and .77 and .82 for Dependency. Internal consistency scores in the present study are largely consistent with these findings, .86 for Closeness, .93 for Conflict, and .91 for Dependency, respectively.
Students’ perspective of the teacher-child relationship quality. Considering that teacher-child relationships are dyadic constructs, the quality of teacher-child relationships was also measured from the perspective of the child. Accordingly, students answered 7 questions concerning well-being with respect to the relationship with their teacher, which primarily measure positive aspects of the teacher-child relationship (Peetsma, Wagenaar, & De Kat, 2001). This teacher-child-reported Closeness scale was rated on a 5-point Likert-type scale, ranging from 1 (definitively not true) to 5 (definitively true). Items that made up this scale included statements such as “Usually, my teacher knows how I feel” and “I have a good relationship with my teacher”. Cronbach’s alpha of this scale was satisfactory (α = .78).
Motivational Beliefs. To capture the multifaceted nature of children’s motivational beliefs, both their goals, and expectancies were considered as motivators of academic achievement in the
present research. The Task Motivation Scale (Seegers, Van Putten, & De Brabander, 2002) was used to evaluate children’s motivational goals. This instrument is a self-report instrument composed of 5 items, which measure the extent to which students focus on mastering learning tasks and on learning opportunities in the context of school. All items were rated on 5-point Likert scales that range from 1 (definitively not true) to 5 (definitively true). Examples of items are “I feel satisfied when I have learned something in school that makes sense to me”, and “I feel satisfied when I have learned something new in school”. Support for the psychometric properties of the Task Motivation Scale has been provided by Seegers et al. (2002). Cronbach’s alpha of this measure was .75.
Children rated their expectancies about their capability to perform academic tasks in the classroom using a translated version of the Academic Efficacy subscale from the Patterns of Adaptive Learning Survey (PALS; Midgley et al., 2000). The 6 items of this self-report measure were scored on a 5-point Likert scale, ranging from 1 (definitively not true) to 5 (definitively true). Statements such as “I'm certain I can figure out how to do the most difficult class work” and “I can do almost all the work in class if I don't give up” were included in this scale. The Self-Efficacy Subscale from PALS has been widely applied, demonstrating adequate reliability and validity (Midgley et al., 1998, 2000). The internal consistency of this measure in the present sample was .78.
Moderator Variables
Information about maternal education and ethnicity was collected from the school administrations. Because maternal education has previously been demonstrated to be a good indicator of a number of school-related outcomes (e.g., Magnuson, 2007; Saft & Pianta, 2001), this variable was used as a proxy of children’s socioeconomic status. Maternal education comprised four categories: no more than primary education, secondary prevocational education, senior secondary vocational education, and higher education. Ethnicity was based on the country of birth of the child’s mother. Given the small proportions of ethnic groups other than Dutch in the sample, preliminary analyses of variance were performed to determine whether these minority groups differed with regard to the research variables. The results showed no significant differences (p > .05). Therefore, ethnic minorities were treated as one group, and contrasted with the Dutch majority group. Information about learning
problems was obtained from the teachers. In order to measure learning problems, a dichotomous single-indicator variable was used, requesting the teacher to indicate whether or not the child was admitted to an individualized education program (IEP).
Covariates
The effects of child gender were controlled for in the hypothesized model, given its association with teacher-child relationships and academic adjustment (e.g., Baker, 2006; Hamre & Pianta, 2001; Moritz Rudasill et al., 2006; Saft & Pianta, 2001). Compared with girls, the relationship of boys with their teacher was hypothesized to be characterized by more conflict, and less closeness. Furthermore, girls were expected to report higher levels of task motivation, but lower levels of self-efficacy than their male counterparts. Lastly, given that math is viewed as a stereotypically male activity, boys were expected to outperform girls on the math test, whereas female students were assumed to yield higher scores on the reading comprehension test. Gender was dummy coded, such that girls were assigned a value of 1 and boys a value of 0.
Data Analysis
The data were not independent, as they were nested within classrooms and corresponding teachers. In order to avoid underestimation of standard errors, structural equation modeling (SEM) procedures for complex survey data were warranted in examining the hypothesized theoretical model (Muthén & Muthén, 2007). Unlike traditional linear modeling techniques, this method is quite flexible in that it allows for the simultaneous estimation of direct and indirect influences in hierarchically clustered data, and the adjustment of measurement errors by using latent constructs (Kline, 2011; Preacher, Zyphur, & Zhang, 2010). Model fitting was performed in Mplus, version 5.21, using maximum likelihood estimation with robust standard errors, and a mean-adjusted chi-square statistic test (MLR; Muthén & Muthén, 2007).
At the first stage of analysis, the structure of the measurement model and the overall effects in the hypothesized model (see Figure 1) were evaluated. In these analyses, none of the moderators figured. Next, two alternative models were estimated to test for mediation: a direct effects model, and
a partial mediation model. The existence of moderator effects was subsequently investigated by a series of multi-group analyses. To evaluate the robustness of the moderating effects, unrestricted baseline models were estimated separately for each of the moderator variables. These were then compared to a series of hierarchical structural models assessing invariance in a context of model trimming, where equality constraints were gradually imposed on the measurement weights (construct-level metric invariance), and regression coefficients (invariance of structural model parameters; Kline, 2011). Technically, moderation exists when the difference in Chi-square between the restricted and unrestricted models is statistically significant. In the last stage, the final model was re-tested and, if possible, confirmed using the independent cross-validation sample (Kline, 2011). Multi-group analyses were performed for the full sample of students, in order to specifically test the correspondence between the two subsets. In the literature, this approach is considered the best, and most common method for testing new theoretical models (e.g., Yuan, Marshall, & Weston, 2002).
In all structural models, the latent constructs were group-mean centered by default, and their indicators were treated as continuous variables. For ease of interpretation, reading and math achievement were also centered around their grand mean, and their error variances were allowed to covary. Since both Self-Efficacy, and Task Motivation were assumed to underlie one single construct (i.e., motivational beliefs), and were reported by the same source, their factor covariances were freely estimated as well. Factor covariances among aspects of the teacher-child relationship were, for similar reasons, also included in the model.
The overall goodness of fit of the models was evaluated by the mean-adjusted χ2 test, with non-significant chi-squares indicating satisfactory fit. Given the large sample size and statistical power of the test, however, even a trivial discrepancy between the expected and the observed model may lead to rejection of the model (Chen, 2007). Therefore, approximate fit was also assessed with the root mean square of approximation (RMSEA), and the expected cross-validation index (ECVI), along with their associated 90% confidence intervals. These indices were selected due to their widespread use and relative ease of interpretation with regard to the assessment of model fit (Kline, 2011; Raykov & Marcoulides, 2006). The RMSEA is an estimate of the discrepancy between the model and the data, accounting for the number of parameters, with values below .05 reflecting close fit, and below .08
indicating satisfactory fit (Browne & Cudeck, 1993). The ECVI estimates how well the solution attained with one sample will generalize to other samples. Although no clear guidelines for interpretation exist, the ECVI can be used to compare alternative models, with smaller values indicating a better likelihood of generalization (Steiger, 1990). The comparative fit index (CFI) was also obtained, with values ≥ .90 indicating satisfactory fit, and values ≥ .95 indicating close fit (Bentler, 1992).
Component fit was evaluated by inspecting the modification indices, residual correlations, and their associated summary statistic SRMR (standardized root mean square residual). The SRMR is a measure of the overall difference between the observed correlation matrix and the correlation matrix implied by the factor solution (Hu & Bentler, 1998, 1999). While exact model fit is indicated by SRMR values of zero, values below .08 already indicate relatively good fit of the model to the data (Kline, 2011).
Differences in model fit were tested with the Satorra-Bentler scaled chi-square difference test (TRd; Satorra, 2000; Satorra & Bentler, 2010), with non-significant chi-squares indicating equivalent fit, and the CFI-difference, with CFI changes ≥ .02 being indicative of model nonequivalence (Cheung & Rensvold, 2002). Additionally, the RMSEA-based root deterioration per restriction (RDR), and ECVI-differences were calculated using the computer program NIESEM, along with their corresponding 90% confidence intervals. When RDR-values do not exceed .05, they indicate an essentially equivalent fit. ECVI-differences between two hierarchically nested models are considered equal when their 90% confidence interval does not include zero (Dudgeon, 2003, 2004; Oort, 2009).
RESULTS
Missing Data, Assumptions and Descriptive Statistics
Due to the large-scale design of the COOL-cohort study, some amount of missing data in the sample was to be expected. Rather than applying list-wise deletion, missing data on the continuous variables (< 6%) were estimated by means of the EM algorithm, after uncovering no statistically significant deviations from randomness using Little’s MCAR test, p = .901 (Tabachnick & Fidell, 2007).
Afterward, independent samples t-tests demonstrated no statistically significant differences among the means of the research variables in samples with and without imputed data. Tests of skewness and kurtosis were non-significant for all variables included in the study. Evaluation of the assumptions regarding multicollinearity, multivariate normality, and linearity were satisfactory as well, and no outliers were detected.
Table 1 displays the means, standard deviations, and bivariate correlations between the study’s observed and latent variables. Correlational analyses generally revealed modest associations between the variables. As expected, children whose teachers rated them higher on Parental Involvement were more likely to have warmer, and less discordant or dependent relationships. The correlations between the five personality traits and the quality of the teacher-child relationship were also generally in line with hypotheses. Both child-reported and teacher-reported measures of relational Closeness were positively associated with children’s motivational beliefs and academic achievement, whereas relational negativity (i.e., Conflict and Dependency) was predictive of lower motivational beliefs and achievement scores. Lastly, the correlations between children’s background characteristics, aspects of the teacher-child relationship quality, and learning outcomes, though very modest, were also in the expected direction.
Measurement Model
Prior to analyzing the hypothesized model, two underlying measurement models were evaluated using confirmatory factor analysis (CFA). The initial factor model only contained items that were used as indicators of the seven latent constructs (i.e., Parental Involvement, Task Motivation, Self-Efficacy, child-reported Closeness, and the three teacher-reported constructs of the teacher-child relationship quality). After the factor structure for the latent constructs was confirmed, the remaining single indicator variables (i.e., children’s personality traits, their reading and math scores, and gender) were included in the subsequent model. To achieve model identification, the first unstandardized factor loadings of each construct were fixed to equal 1.0, and all latent variable variances and covariances were allowed to be freely estimated. The error variances of the single indicators were set to zero, as perfect measurement of each variable was assumed.
22 | M . Z E E ( 2 0 1 1 ) T ab le 1. M ean s, St andar d D ev iat ion s and C or re lat ion s B et w ee n t he M ea sur ed and L a te n t V ar iab le s In cl ud ed i n t h e S tr uc tur al M od el N o te . E le m en ts a b o v e th e d ia g o n al a re c o rr el at io n s fo r th e v al id at io n s am p le . E le m en ts b el o w t h e d ia g o n al a re c o rr el at io n s fo r th e ca li b ra ti o n s am p le . G en d er : 0 = b o y , 1 = g ir l; L ea rn in g P ro b le m s: 0 = y es , 1 = n o ; E th n ic it y : 0 = n at iv e D u tc h , 1 = n o n -D u tc h . * p > . 0 5 . F o r al l o th er c o rr el at io n s, p < . 0 5 . 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 . E x tr av er si o n - .1 0 .0 2 -. 1 5 -. 0 1 * .0 4 -. 0 5 .0 5 .0 9 .1 4 .0 8 .0 5 .0 4 .0 1 * .0 1 * -. 0 4 .0 4 2 . A g re ea b le n es s .0 9 - .1 2 -. 1 4 .0 2 * .1 2 -. 0 6 -. 2 1 .1 7 .3 0 .1 6 .0 6 .0 8 .0 1 * .0 6 -. 0 5 .0 3 * 3 . C o n sc ie n ti o u sn es s .0 3 * .1 8 - -. 3 4 -. 1 5 .0 5 -. 0 2 * -. 1 0 .0 7 .2 8 .4 5 .3 3 .0 8 .0 7 -. 0 7 .1 9 .0 6 4 . N eu ro ti ci sm -. 1 9 -. 1 4 -. 3 4 - .1 4 -. 0 4 .1 4 .1 0 -. 0 2 * -. 2 0 .-.1 8 -. 1 8 -. 0 4 -. 0 7 -. 0 1 .0 4 .0 5 5 . A u to n o m y .0 1 * .0 4 -. 1 6 .1 2 - .0 5 -. 0 3 -. 1 3 .0 0 1 * -. 0 1 * -. 0 5 -. 0 1 * .0 1 * .0 3 * .1 0 .0 0 * .0 3 * 6 . P ar . In v o lv em en t .0 5 .1 4 .0 4 -. 0 7 .0 6 - -. 2 3 -. 2 7 .2 8 .1 1 .0 5 .0 4 .3 8 .3 1 .2 7 -. 2 2 .0 7 7 . D ep en d en cy -. 0 2 * -. 0 9 -. 0 3 * .1 4 -. 0 6 -. 2 3 - .4 9 -. 0 6 -. 0 1 * .0 2 * -. 1 4 -. 1 4 -. 1 3 -. 0 9 .0 6 -. 1 4 8 . C o n fl ic t .0 5 -. 2 3 -. 1 2 .1 0 -. 1 3 -. 3 2 .5 4 - -. 4 2 -. 2 7 -. 0 7 -. 0 3 * -. 1 2 -. 0 6 -. 1 0 .0 6 -. 1 1 9 . C lo se n es sTE A C H E R .1 1 .1 7 .0 7 -. 0 2 * -. 0 1 * .3 1 -. 0 6 -. 4 6 - .3 6 .1 5 .0 5 .1 2 .0 6 .0 5 -. 0 7 .0 1 * 1 0 . C lo se n es sCH IL D .1 6 .3 1 .2 9 -. 2 0 -. 0 2 * .1 7 -. 0 6 -. 3 1 .3 8 - .4 8 .3 3 .1 0 .0 8 .0 4 -. 0 1 * .0 4 1 1 . T as k M o ti v at io n .0 8 .1 8 .4 7 -. 1 9 -. 0 6 .0 6 -. 0 4 -. 1 1 .1 5 .4 6 - .5 3 .0 8 .0 5 .0 4 .1 4 .0 6 1 2 . S el f-E ff ic ac y .0 5 .0 9 .3 3 -. 1 8 -. 0 2 * .0 6 -. 1 7 -. 0 8 .0 8 .3 2 .5 3 - .2 8 .3 5 .0 4 .0 9 .1 3 1 3 . M at h .0 4 .1 0 .0 8 -. 0 5 .0 2 * .4 3 -. 1 4 -. 1 6 .1 6 .1 4 .1 1 .2 6 - .6 1 .2 6 -. 1 4 .1 9 1 4 . R ea d in g .0 2 * .0 2 * .0 7 -. 0 8 .0 3 * .3 4 -. 1 3 -. 1 0 .1 0 .1 1 .0 8 .3 4 .6 1 - .2 1 -. 1 1 .2 4 1 5 . S E S .0 1 * .0 6 -. 0 8 -. 0 2 * .1 0 .3 3 -. 1 1 -. 1 0 .0 5 .0 4 .0 4 -. 0 7 .2 8 .2 4 - -. 0 6 .0 8 1 6 . E th n ic it y -. 0 5 -. 0 6 .1 9 .0 2 * -. 0 4 -. 2 1 .0 5 .0 1 * -. 0 5 .0 1 * .1 7 .1 5 -. 1 4 -. 1 1 -. 1 1 - .0 5 1 7 . L ea rn in g P ro b l. .0 4 .0 5 .0 4 .0 5 .0 4 .1 1 -. 1 5 -. 1 1 .0 3 * .0 4 .1 1 .0 7 .2 0 .2 4 .0 8 .0 4 - 1 8 . G en d er .1 0 .3 2 .0 5 .1 4 -. 0 7 .0 4 .0 0 * -. 1 8 .1 7 .0 9 .0 8 -. 1 0 .1 0 -. 1 3 -. 0 1 * .0 0 * .0 5 MS I .8 2 1 .8 9 .4 6 1 .0 6 .5 2 3 .6 3 2 .0 3 1 .7 5 3 .4 8 3 .6 5 3 .9 1 3 .6 5 1 1 6 .6 0 5 5 .8 7 2 .7 7 - - S DS1 M S2 S DS2 .7 5 .8 3 .7 5 .9 4 1 .8 9 .9 5 .9 1 .4 5 .9 2 .8 5 1 .0 7 .8 5 .7 5 .5 2 .7 5 .8 8 3 .6 4 .8 8 .7 7 2 .0 4 .7 7 .8 0 1 .7 5 .7 9 .6 6 3 .4 9 .6 5 .6 4 3 .6 6 .6 4 .5 8 3 .9 0 .5 8 .6 0 3 .6 4 .6 1 8 .9 3 1 1 6 .6 7 8 .8 7 1 5 .4 8 5 6 .0 3 1 5 .5 3 .8 8 2 .7 5 .8 8 - - - - - -
The first measurement model demonstrated a satisfactory fit to the data, χ2 (573) = 5488.99, p < .001, RMSEA = .045 (90% CI [.044, .046]), CFI = .92, SRMR = .041, ECVI = 1.31 (90% CI [1.26, 1.37]). In order to diagnose potential sources of misfit, the model’s correlation residuals and modification indices were inspected. Three residuals appeared to be over-predicted by the model. Stepwise addition of these correlation residuals resulted in a more satisfactory model: χ2 (570) = 3340.87, p < .001, RMSEA = .034 (90% CI [.032, .035]), CFI = .96, SRMR = .037, ECVI = .82 (90% CI [.78, .86]). The model with single indicators included also yielded a good fit to the data, χ2 (802) = 4522.28, p < .001, RMSEA = .033 (90% CI [.032, .034]), CFI = .95, SRMR = 0.035, ECVI = 1.14 (90% CI [1.09, 1.19]). In this model, no systematic patterns of misfit were identified, and the factor loadings, standard errors (see Table 2), and inter-factor correlations were of the appropriate sign and/or magnitude. These results provide evidence that the factors correspond to the hypothesized structure, and confirm the internal validity and a common factor structure of the measures.
Structural Model
The initial structural model tested was the hypothesized model with main effects only, in which all variables were controlled for the influences of gender, and in which the moderators did not figure. The overall fit of the observed variance-covariance matrix to this model was acceptable: χ2 (833) = 6466.20, p < .001, RMSEA = .040 (90% CI [.039-.041]), SRMR = .055, CFI = .92, ECVI = 1.58 (90% CI [1.52-1.64]). However, inspection of modification indices indicated that the model did not fully explain the observed association between parental involvement and children’s reading and math achievement, and between conscientiousness and both measures of children’s motivational beliefs. Since stepwise addition of these pathways was theoretically defensible and resulted in improved model fit (TRd (4) = 1704.50, p < .001, ∆CFI = .02, RDR = .31 (90% CI [.30, .33]), ∆ECVI = .39 (90% CI [.36, .43]), they were maintained in the modified model. With the additional parameters incorporated, the test results demonstrated a satisfactory fit of the final model to the data: χ2 (829) = 5314.43, p < .001, RMSEA = .035 (90% CI [.035-.036]), SRMR = .042, CFI = .94, ECVI = 1.31 (90% CI [1.26-1.36]), and thus provided support for the hypothesized model.
Table 2.
Maximum Likelihood Estimates with Robust Standard Errors for the Measurement Model
Factor Loadings Unstandardized SE Standardized R2
Dependency Dep1 Dep2 Dep3 Dep4 Dep5 1.00 .96 .85 .87 .92 - .02 .03 .02 .02 .80 .86 .81 .86 .79 .64 .73 .65 .74 .63 Conflict Confl1 Confl2 Confl3 Confl4 Confl5 1.00 1.01 1.05 .99 1.15 - .02 .03 .03 .02 .90 .86 .83 .84 .86 .80 .74 .69 .70 .73 Closenessteacher Closet1 Closet2 Closet3 Closet4 Closet5 1.00 .99 1.11 .87 1.01 - .02 .04 .04 .04 .62 .66 .89 .81 .81 .39 .44 .79 .66 .65 Closenesschild Closec1 Closec2 Closec3 Closec4 Closec5 Closec6 Closec7 1.00 1.17 1.19 1.35 1.18 1.18 1.21 - .03 .04 .05 .03 .05 .06 .65 .62 .58 .75 .72 .67 .53 .42 .39 .34 .56 .52 .45 .28 Task Motivation Motiv1 Motiv2 Motiv3 Motiv4 Motiv5 1.00 1.12 1.15 1.01 1.35 - .05 .03 .04 .04 .66 .53 .71 .58 .77 .43 .28 .51 .33 .60 Self-efficacy Effic1 Effic2 Effic3 Effic4 Effic5 Effic6 1.00 1.38 .77 1.12 1.14 1.47 - .05 .04 .04 .04 .04 .57 .74 .46 .65 .69 .80 .32 .55 .21 .43 .48 .64 Par. Involvement Inv1 Inv2 Inv3 1.00 1.13 1.15 - .03 .02 .70 .94 .93 .49 .88 .86 Note. p < .001for all standardized factor loadings. Factor (co)variances and error covariances are not presented in the table.
Direct Effects
The final structural model, and standardized regression coefficients are shown in Table 3 and in Figure 2. Dashed lines represent the paths added post hoc. The patterns of association between the teacher-child relationship qualities and teacher-children’s personal resources largely reflected the hypothesized effects.
As expected, children whose parents were more involved in their learning process were likely to form closer (β = .29 for teacher-reported Closeness, and β = .12 for child-reported Closeness, p < .001), less discordant (β = -.29, p < .001), and less dependent (β = -.21, p < .001) relationships with their teacher. In addition, Parental Involvement had significant positive effects on reading (β = .33, p < .001) and math achievement (β = .41, p < .001).
The anticipated effects of children’s personality traits on the teacher-child relationship qualities were only partially supported by the model. First, small though significant associations were found among teacher-child Dependency and Agreeableness (β = -.05, p < .05), Neuroticism (β = .15, p < .001), and Autonomy (β = -.06, p < .001). The hypothesized relationships between Dependency, Extraversion, and Conscientiousness, however, could not be confirmed. In addition, after controlling for the effects of gender, the paths from Extraversion (β = .11, p < .001), Agreeableness (β = -.14, p < .001), Conscientiousness (β = -.05, p < .01), Neuroticism (β = .07, p < .001), and Autonomy (β = -.06, p < .001) to conflict were all statistically significant. Teacher-reported Closeness was affected by Extraversion (β = .10, p < .001), Agreeableness (β = .12, p < .001), and Conscientiousness (β = .05, p < .01), and student-reports of Closeness were related to all respective personality traits, but Autonomy (Extraversion: β = .11, p < .001; Agreeableness: β = .24, p < .001; Conscientiousness: β = .22, p < .001; Neuroticism: β = -.07, p < .001). Overall, the final model accounted for 7.4% of the variance in Dependency, 16.9% of the variance in Conflict, 13.9% of the variance in teacher-reported Closeness, and 18.8% of the variance in child-reported Closeness.
Features of the solution related to the quality of teacher-child relationships and children’s motivational beliefs warranted the need of a more advanced clarification of the model. First, as expected, there were positive effects of student-reported Closeness on Task Motivation (β = .37, p < .001), and on Self-Efficacy (β = .27, p < .001). However, with other aspects of the teacher-child relationship in the model, the significant correlations found between teacher-reported Closeness and the two motivational measures could not be confirmed by the model. Moreover, the impact of Dependency was found to be negative for Self-Efficacy (β = -.21, p < .001), but non-significant for Task Motivation. The direct effect of Conscientiousness on the two motivational constructs was positive (Self-Efficacy: β = .27, p < .001; Task Motivation: β = .37, p < .001).
Most unexpectedly, Conflict was positively correlated to both children’s Task Motivation (β = .07, p < .01), and Self-Efficacy (β = .14, p < .001). It is likely that Conflict might have functioned as a suppressor variable for the relationship between other aspects of the relationship quality and children’s motivational beliefs. First, in line with the suppressor phenomenon (Maassen & Bakker, 2001), Conflict correlated substantially to Dependency (r = .54), and had modest correlations with Self-Efficacy (r = -.08), and Task Motivation (r = -.11). The effects of Conflict on children’s motivational beliefs, however, were opposite in sign, and the paths between Dependency and the two motivators took on values which are higher than originally found in Table 1. In addition, when fixing the path of Conflict on the two motivators to zero, the effects of Dependency on Self-Efficacy (β = -.14, p < .001) and on Task Motivation (β = -.01, p < .001) were decreased. Thus, the association between Dependency and children’s motivational beliefs is larger when Conflict is incorporated in the equation, and the path coefficients for Conflict seem to be not substantial enough to yield the expected positive association (Maassen & Bakker, 2001). Yet, this should not be interpreted to imply that teacher-child Conflict is positively related to Task Motivation and Self-Efficacy. Rather, Conflict acts, to some extent, as a correction factor in the model for predicting the association between Dependency and motivational beliefs.
Children’s Self-Efficacy appeared to be a significant predictor of their reading (β = .39, p < .001), and math achievement (β = .29, p < .001). Contrary to what was anticipated, Task Motivation had a significant negative contribution to children’s reading and math achievement (β = -.14; β = -.08, p < .001), after controlling for the effects of gender. Comparison of the results of the final model and the correlations in Table 1 again suggests that these unexpected findings were likely to be due to the presence of a negative suppressor. Specifically, when entered alone, both Self-Efficacy, and Task Motivation did significantly and positively relate to reading (β = .30; β = .07, p < .001) and math achievement (β = .24; β = .08, p < .001). With both motivators in the model, however, the effect of Self-Efficacy on reading and math increased, and the effect of Task Motivation on achievement became stronger, and negative in sign. This may indicate that Task Motivation has much more in common with Self-Efficacy, than with the variance of reading and math achievement, and therefore is irrelevant for the two academic outcome variables. Indeed, the substantial correlation
between Self-Efficacy and Task Motivation (r = .53) suggests the negative suppressor phenomenon to be at work. Given that children’s performance was better explained by a linear conjunction of both motivators than by Self-Efficacy alone, the effects of Task Motivation and Self-Efficacy were as well interpreted in combination with each other (Maassen & Bakker, 2001).
As Table 1 already demonstrated, gender was significantly associated with several study variables, but did not seem to have any confounding influences on the hypothesized relationships. As expected, teachers generally experienced less Conflict (β = -.14, p < .001), and more Closeness (β = .11, p < .001) in the relationship with female students. Moreover, girls appeared to be more task motivated (β = .05, p < .01), but less self-efficacious (β = -.12, p < .001). Interestingly, with regard to their academic achievement, girls appeared to score higher on the math test (β = .10, p < .001), whereas boys performed better on the reading test (β = -.09, p < .001). Jointly, the variables accounted for 33.8% of the variance in Task Motivation, 21.4% of the variance in Self-Efficacy, 25.2% of the variance in math achievement, and 24.3% of the variance in reading comprehension.
Mediation Effects
In order to establish whether children’s motivational beliefs significantly mediated the association between the teacher-child relationship qualities and academic achievement, a set of alternative models was estimated following Baron and Kenny’s (1986) key principles of mediation analysis. For mediation to be supported, four conditions must hold: (1) the predictors (teacher-child relationship qualities) must be related to the mediators (Self-Efficacy and Task Motivation); (2) the mediators must be related to the outcome variables (math and reading achievement); (3) it is preferred, but not strictly necessary that the predictors are related to the outcome variables when the effects of the mediators are fixed to zero; and (4) the direct effects between the predictors and the outcome variables must be considerably reduced when the mediators are included back into the model.
As demonstrated by the results outlined in Table 3, the final model provides partial support for the first condition, and full support for the second condition. To establish the third condition, the direct effects of the teacher-child relationship qualities on math and reading achievement were freely estimated, and the effects of the mediators were constrained to equal zero. The resulting direct effects
model fitted the data significantly worse than the final model (TRd (4) = 782.12, p < .001), and accounted for less variance in math (23.1%) and reading comprehension (18.4%).
When eliminating Self-Efficacy and Task Motivation from the model, Dependency appeared to have a negative influence on math (β = -.17, p < .001), and reading achievement (β = -.19, p < .001), whereas direct links between Conflict and the two measures of achievement were not supported by the model. Above and beyond the effects of Parental Involvement and gender, small though significant effects of child-reported Closeness on math (β = .07, p < .001), and reading achievement (β = .07, p < .001) were found. Unexpectedly, there were small negative associations between teacher- reported Closeness and math (β = -.06, p < .01), and reading (β = -.05, p < .05), suggesting that teacher-reported Closeness merely had the role of correction factor in the model for predicting the relationships between other aspects of the teacher-child relationship, and children’s achievement.
To test for full mediation, a partially mediated model was fitted, in which Task Motivation and Self-Efficacy were inserted back into the model. This process caused the direct effects of Dependency on math (β = -.13, p < .001), and reading (β = -.13, p < .001) to be considerably reduced. The presence of Task Motivation and Self-Efficacy in the model also decreased the direct effects of child-reported Closeness on math (β = .01, p > .05) and reading (β = .00, p > .05) to a degree where they were no longer statistically significant. These results suggest that Self-Efficacy, in conjunction with Task Motivation, appeared to fully mediate the effects of child-reported Closeness on children’s reading and math achievement, and to partially mediate the effects of relational Dependency on children’s performance. The direct effects of teacher-reported Closeness on both measures of achievement, however, remained present in the partially mediated model. This suggests that the negative effects of teacher-reported Closeness on children’s achievement were not mediated by their motivational beliefs. Yet, the occurrence of suppressors, which suggest a more complex set of associations among the teacher-child relationship variables, preclude a precise interpretation of these findings.
T E A C H E R -C H I L D R E L A T I O N S H I P S I N U P P E R E L E M E N T A R Y S C H O O L | 29 T ab le 3. M a xi m um L ik el ihood E st im at es f or t h e F ina l S tr u ct u ra l M o de l o f A n te ce de nt s and C on se qu enc es o f th e T eac h er -C h il d R el a ti on sh ip Q ua li ty N o te . S ta n d ar d iz ed r eg re ss io n c o ef fi ci en ts ( β ) ar e re p o rt ed . D ir ec t ef fe ct s o f th e al te rn at iv e m ed ia ti o n m o d el s ar e n o t p re se n te d i n t h e ta b le . G en d er w as c o d ed a s a b in ar y v ar ia b le ( 0 = b o y s an d 1 = g ir ls ). D ir = d ir ec t ef fe ct s; I n d . = t o ta l in d ir ec t ef fe ct s; T o ta l = t o ta l ef fe ct s. a p > . 0 5 . D ep en d en cy C o n fl ic t C lo se n es steac h er C lo se n es schi ld M o ti v at io n S el f-ef fi ca cy R ea d in g M at h d ir . in d to ta l d ir . in d . to ta l d ir . in d to ta l d ir . in d to ta l d ir . in d . to ta l d ir . in d . to ta l d ir . in d to ta l d ir . in d . E x tr av . .0 3 a - .0 3 a .1 1 - .1 1 .1 0 - .1 0 .1 1 - .1 1 - .0 5 .0 5 - .0 4 .0 4 - .0 1 a .0 1 a - .0 1 a A g re e. -. 0 5 - -. 0 5 -. 1 4 - -. 1 4 .1 2 - .1 2 .2 4 - .2 4 - .0 8 .0 8 - .0 6 .0 6 - .0 1 a .0 1 a - .0 1 a C o n sc . .0 2 a - .0 2 a -. 0 5 - -. 0 5 .0 5 - .0 5 .2 2 - .2 2 .3 7 .0 7 .4 4 .2 7 .0 5 .3 2 - .0 1 a .0 1 a - .0 1 a N eu r. .1 5 - .1 5 .0 7 - .0 7 -. 0 3 a - -. 0 3 a -. 0 7 - -. 0 7 - -. 0 2 -. 0 2 - -. 0 4 -. 0 4 - .0 1 a .0 1 a - .0 1 a A u to n . -. 0 6 - -. 0 6 -. 0 6 - -. 0 6 -. 0 2 a - -. 0 2 a .0 1 a - .0 1 a - .0 1 a .0 1 a - .0 2 .0 2 - .0 1 a .0 1 a - .0 1 a P ar . In v . -. 2 1 - -. 2 1 -. 2 9 - -. 2 9 .2 9 - .2 9 .1 2 - .1 2 - .0 3 .0 3 - .0 4 .0 4 .3 3 .0 1 a .3 4 .4 1 .0 1 a D ep en d . - - - - - - - - - - - - -. 0 3 a - -. 0 3 a -. 2 1 - -. 2 1 - -. 0 8 -. 0 8 - -. 0 6 C o n fl ic t - - - - - - - - - - - - .0 7 - .0 7 .1 4 - .1 4 - .0 5 .0 5 - .0 4 C lo set. - - - - - - - - - - - - .0 0 a - .0 0 a .0 3 a - .0 3 a - .0 1 a .0 1 a - .0 1 a C lo sec. - - - - - - - - - - - - .3 7 - .3 7 .2 7 - .2 7 - .0 6 .0 6 - .0 5 M o ti v . - - - - - - - - - - - - - - - - - - -. 1 4 - -. 1 4 -. 0 8 - E ff ic . - - - - - - - - - - - - - - - - - - .3 9 - .3 9 .2 9 - R ea d . - - - - - - - - - - - - - - - - - - - - - - - M at h - - - - - - - - - - - - - - - - - - - - - - - G en d er -. 0 1 a - -. 0 1 a -. 1 4 - -. 1 4 .1 1 - .1 1 -. 0 1 a - -. 0 1 a .0 5 - .0 5 -. 1 2 - -. 1 2 .1 0 - .1 0 .0 9 -
30 | M . Z E E ( 2 0 1 1 ) F ig ur e 2. F inal St ruc tur a l M ode l N o te . D as h ed l in es r ep re se n t p at h s ad d ed p o st h o c. F o r re as o n s o f p ar si m o n y , th e fr ee ly e st im at ed f ac to r co v ar ia n ce s ar e n o t d is p la y ed . E x tr av . = E x tr av er si o n ; A g re e. = A g re ea b le n es s; N eu ro N eu ro ti ci sm ; A u to n . = A u to n o m y ; P ar . In v . = P ar en ta l In v o lv em en t; C lo se n . = T ea ch er -r ep o rt ed C lo se n es s; C o n fl . = C o n fl ic t; D ep en d . = D ep en d en cy ; C lo se 2 = C h il d -r ep o rt ed C lo se n es s; M T as k M o ti v at io n ; E ff ic . = S el f-E ff ic ac y ; M at h = M at h t es t; R ea d = R ea d in g c o m p re h en si o n t es t. E x tr a v . C o n s c. A u to n . N e u ro t. A g re e. D D D D D P ar . In v . P 1 P 2 P 3 ε ε ε D e p e n d . D 2 D 3 D 4 ε ε ε D 5 D 1 ε ε C lo se 2 C 3 C 4 C 5 ε ε C 6 C 2 ε ε C 1 C 7 ε ε ε C o n fl . C 2 C 3 C 4 ε ε ε C 5 C 1 ε ε C lo se n . C 2 C 3 C 4 ε ε ε C 5 C 1 ε ε M o ti v . M 2 M 3 M 4 ε ε ε M 5 M 1 ε ε E ff ic . E 4 E 3 E 1 ε ε ε E 2 E 5 ε ε E 6 ε M a th R e ad D D
Moderator Effects
To evaluate potential moderation effects of children’s ethnicity, SES, and learning problems, a multi-group approach was adopted (see Method). For each of the respective moderators, therefore, the full calibration sample was divided into two contrasting subsamples. Since SES originally consisted of four categories, this variable was recoded, such that the two lowest categories formed the low-SES group, and the two highest categories formed the high-SES group. The subgroups of ethnicity and learning problems comprised Dutch and non-Dutch children, and children with and without learning difficulties, respectively.
Ethnicity. The overall fit of the baseline model without ethnicity-invariance constraints was satisfactory: χ2 (1687) = 6538.11, p < .001, RMSEA = .037 (90% CI [.036, .038]), CFI = .93, SRMR = .045, ECVI = 1.71 (90% CI [1.65, 1.77]). To test whether the latent constructs were manifested the same way in native Dutch and minority students, cross-group equality constraints were imposed on the model’s measurement weights. Although this procedure caused a statistically significant drop in overall model fit (TRd (29) = 64.39, p < .05), the approximate fit indices indicated construct-level metric invariance to hold across ethnicity (∆CFI = .00, RDR = .024 (90% CI [.016, .032]), ∆ECVI = -.001 (90% CI [-.0038, .0076]). Analyses therefore proceeded to test whether the magnitudes or directions of direct effects in the model significantly differed across ethnicity. Results of the moderation analysis are given in Table 4.
First, ethnicity showed to be a moderator of the positive relationship between child-reported Closeness and Task Motivation, such that the link was significantly stronger for Dutch students. The direction and magnitude of effects of other aspects of the teacher-child relationship on Task Motivation did not differ across ethnicity. Minority status also exhibited a moderating effect on the links between teacher-child relationship qualities and Self-Efficacy. Specifically, the negative effect of Conflict on Self-Efficacy was significantly stronger for minority students, while Dependency and child-reported Closeness both had a stronger influence on Dutch students’ efficacy beliefs. Interestingly, albeit prior main effects could not be established, the association between teacher-reported Closeness and Self-Efficacy appeared to be significantly more important for minorities than for majorities. Lastly, the positive links between Self-Efficacy and each of the achievement measures
