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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Psychol.</journal-id>
<journal-title>Frontiers in Psychology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Psychol.</abbrev-journal-title>
<issn pub-type="epub">1664-1078</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fpsyg.2022.872301</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Psychology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Longitudinal impact of parent-teacher relationship on middle school students&#x2019; academic achievements in China</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Fu</surname> <given-names>Wangqian</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1307515/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Pan</surname> <given-names>Qianqian</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Yuan</surname> <given-names>Ying</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Chen</surname> <given-names>Guanyu</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>Faculty of Education, Beijing Normal University</institution>, <addr-line>Beijing</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>Centre for Research in Pedagogy and Practice, Office of Education Research, National Institute of Education, Nanyang Technological University</institution>, <addr-line>Singapore</addr-line>, <country>Singapore</country></aff>
<aff id="aff3"><sup>3</sup><institution>School of Journalism and Communication, Beijing Normal University</institution>, <addr-line>Beijing</addr-line>, <country>China</country></aff>
<aff id="aff4"><sup>4</sup><institution>Department of Educational and Counselling Psychology and Special Education, Faculty of Education, The University of British Columbia</institution>, <addr-line>Vancouver, BC</addr-line>, <country>Canada</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Carolina Gonz&#x00E1;lvez, University of Alicante, Spain</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Sum Kwing Cheung, The Education University of Hong Kong, Hong Kong SAR, China; Mehmet Y&#x00FC;ksel, Gazi University, Turkey</p></fn>
<corresp id="c001">&#x002A;Correspondence: Qianqian Pan, <email>qianqian.pan@nie.edu.sg</email></corresp>
<fn fn-type="other" id="fn004"><p>This article was submitted to Educational Psychology, a section of the journal Frontiers in Psychology</p></fn>
</author-notes>
<pub-date pub-type="epub">
<day>23</day>
<month>08</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>13</volume>
<elocation-id>872301</elocation-id>
<history>
<date date-type="received">
<day>09</day>
<month>02</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>25</day>
<month>07</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2022 Fu, Pan, Yuan and Chen.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Fu, Pan, Yuan and Chen</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license>
</permissions>
<abstract>
<sec>
<title>Objective</title>
<p>The study aims to discuss the longitudinal impact of the parent-teacher relationship on students&#x2019; academic achievements in China.</p>
</sec>
<sec>
<title>Method</title>
<p>Based on the China Education Panel Survey, covering the data from 438 classes of 112 schools in 28 county-level administrative areas in China, we used the hierarchical linear model to analyze the data.</p>
</sec>
<sec>
<title>Results</title>
<p>We found that the parents&#x2019; active communication with teachers, parents&#x2019; participation in parent meetings, teachers&#x2019; active contact, whether parents are afraid to communicate with teachers, and parents&#x2019; willingness to participate in parent meetings have significant relationships with students&#x2019; academic achievements. At the class level, the extent of teachers&#x2019; stress from parents&#x2019; requests and teachers&#x2019; perception of respect from parents also affected students&#x2019; academic achievements significantly in the Chinese context.</p>
</sec>
<sec>
<title>Conclusion</title>
<p>There was a longitudinal association between the parent-teacher relationship and students&#x2019; academic achievements. The practical implication was discussed in the paper.</p>
</sec>
</abstract>
<kwd-group>
<kwd>parent-teacher relationship</kwd>
<kwd>middle school</kwd>
<kwd>academic achievements</kwd>
<kwd>mainland China</kwd>
<kwd>hierarchical linear model</kwd>
</kwd-group>
<counts>
<fig-count count="0"/>
<table-count count="4"/>
<equation-count count="14"/>
<ref-count count="94"/>
<page-count count="14"/>
<word-count count="10886"/>
</counts>
</article-meta>
</front>
<body>
<sec id="S1" sec-type="intro">
<title>Introduction</title>
<p>Family and school are two important environments closely related to adolescents, and cooperation between the two greatly impacts adolescents&#x2019; development (<xref ref-type="bibr" rid="B48">Lohman et al., 2007</xref>; <xref ref-type="bibr" rid="B27">Guo and Zhang, 2015</xref>). The Chinese government realizes the importance of home-school cooperation and has recently promulgated a series of policy documents to promote home-school cooperation. In 2017, the &#x201C;School Management Standards for Compulsory Education&#x201D; proposed that harmonious relationships among family, school, and community should be built to enhance parents&#x2019; participation in school governance and form a joint effort to educate people (<xref ref-type="bibr" rid="B51">Ministry of Education, 2017</xref>). Although the government is attaching increasing importance to home-school cooperation, there are still many problems with parent-teacher relationships in China. For example, the status of parents and teachers is unequal, showing the characteristics of a one-way communication model, a single form of cooperation under which parents lack the initiative to speak and where the communication channels are not smooth between parents and teachers (<xref ref-type="bibr" rid="B86">Zhang, 2011</xref>; <xref ref-type="bibr" rid="B81">Yang and Liu, 2012</xref>). Since parents and teachers are the two crucial participants in a child&#x2019;s education, their interactions heavily influence child outcomes (<xref ref-type="bibr" rid="B67">Serpell and Mashburn, 2012</xref>). Especially the parent-teacher relationship is critical to the children&#x2019;s social-emotional development (<xref ref-type="bibr" rid="B41">Lang et al., 2020</xref>) and their academic outcome (<xref ref-type="bibr" rid="B40">Kim and Hill, 2015</xref>). Despite existing research having paid attention to the association between parent-teacher relationships and students&#x2019; academic outcomes, little is known about the long-term effects of parent-teacher relationships on students&#x2019; outcomes; especially in China, most classroom teachers teach the same class of students from the enrollment to graduation in middle schools. Therefore, it is essential to investigate whether the impacts of parent-teacher relationships could be carried over. Together, the current study aims to discuss the longitudinal impact of the parent-teacher relationship on students&#x2019; academic achievements in China.</p>
<sec id="S1.SS1">
<title>The influence of parent-teacher relationships on students&#x2019; development</title>
<p>Dozens of studies show that good family school relationships can promote students&#x2019; academic achievements and positively impact students&#x2019; growth (<xref ref-type="bibr" rid="B24">Garcia, 2004</xref>; <xref ref-type="bibr" rid="B61">Pomerantz et al., 2007</xref>; <xref ref-type="bibr" rid="B86">Zhang, 2011</xref>; <xref ref-type="bibr" rid="B40">Kim and Hill, 2015</xref>; <xref ref-type="bibr" rid="B30">Herman and Reinke, 2017</xref>). According to the Ecological systems theory (<xref ref-type="bibr" rid="B5">Bronfenbrenner, 1979</xref>; <xref ref-type="bibr" rid="B6">Bronfenbrenner and Morris, 1998</xref>), adolescent development is influenced directly by the interactions that take place within a single microsystem (such as the family, school, or peer group), as well as the similarities and differences in the pattern of the interactions that occur across these systems. Family and school are the two most important environments closely associated with adolescent development (<xref ref-type="bibr" rid="B48">Lohman et al., 2007</xref>; <xref ref-type="bibr" rid="B64">Santana et al., 2016</xref>).</p>
<p>Research shows that not all family school relationships are good for students (<xref ref-type="bibr" rid="B61">Pomerantz et al., 2007</xref>), and it depends on whether parents and teachers have good relations (<xref ref-type="bibr" rid="B53">Nir and Ami, 2005</xref>; <xref ref-type="bibr" rid="B92">Emerson et al., 2012</xref>; <xref ref-type="bibr" rid="B47">Liang, 2015</xref>). Only a relationship based on mutual trust and honesty can rich and frequent interaction be conducive to the development of students (<xref ref-type="bibr" rid="B14">Constantino, 2003</xref>; <xref ref-type="bibr" rid="B24">Garcia, 2004</xref>). A good relationship between parents and teachers can provide consistent support for students, making students more likely to recognize the benefits of learning (<xref ref-type="bibr" rid="B29">Harris and Goodall, 2009</xref>; <xref ref-type="bibr" rid="B92">Emerson et al., 2012</xref>). <xref ref-type="bibr" rid="B74">Waller (1932)</xref> points out that parents and teachers are natural enemies, not natural collaborators. The complex and crucial connection between families and schools is embodied in the relationships between individual teachers and their students&#x2019; families (<xref ref-type="bibr" rid="B18">Driessen et al., 2005</xref>; <xref ref-type="bibr" rid="B13">Cole, 2013</xref>).</p>
</sec>
<sec id="S1.SS2">
<title>The connotation of the parent-teacher relationship</title>
<p>Good parent-teacher relationships are generally effective at maximizing students&#x2019; potential, based on the mutually rich and frequent interactions built upon trust and honesty (<xref ref-type="bibr" rid="B14">Constantino, 2003</xref>; <xref ref-type="bibr" rid="B24">Garcia, 2004</xref>). According to interpersonal communication theory, the interpersonal relationship measurement can be classified into two variables. The first is the dimension of parent-teacher contact, which considers the individual&#x2019;s judgment of the relationship, such as the frequency of communication, the content, and means of communication, and the efforts the other may make to maintain the relationship. The second is the parent-teacher relationship quality, which mainly refers to the intensity of this judgment and is the perception of the intensity of the former (<xref ref-type="bibr" rid="B17">Dillard et al., 1999</xref>). Generally, an individual&#x2019;s perception of the quality of a relationship comes directly from the state of the communication, such as the frequency of communication and the degree of self-disclosure. Relationships develop over time through a process of self-disclosure (<xref ref-type="bibr" rid="B7">Bylund et al., 2012</xref>). Moreover, a relationship comes from the perception of the individual&#x2019;s influence on others, such as how much influence an individual can have on the decisions or behaviors of others and their evaluation of others as individuals (<xref ref-type="bibr" rid="B84">Zhang, 2016</xref>). Such that, there is a difference between parent-teacher contact and the parent-teacher relationship quality. Parent-teacher contact refers to the frequency of interactions between parents and teachers, whereas the parent-teacher relationship quality refers to the quality of their relationship as well as how well their goals are aligned (<xref ref-type="bibr" rid="B67">Serpell and Mashburn, 2012</xref>; <xref ref-type="bibr" rid="B70">Stormont et al., 2013</xref>; <xref ref-type="bibr" rid="B16">Deng et al., 2018</xref>).</p>
<p>In parent-teacher contact, the frequency of ties and activities between families and schools influences the relationship between parents and teachers (<xref ref-type="bibr" rid="B89">Zhao and Hong, 2012</xref>). The more connections and activities between families and schools are built and held, the better the relationship between teachers and parents will be (<xref ref-type="bibr" rid="B1">Adams and Christenson, 2000</xref>; <xref ref-type="bibr" rid="B52">Minke, 2006</xref>). The more frequent the interaction between parents and teachers, the more likely parents are to pass on their educational expectations to their children, thus promoting students&#x2019; improvement at the cognitive level and success in academic achievement (<xref ref-type="bibr" rid="B25">Goyette and Xie, 1999</xref>; <xref ref-type="bibr" rid="B65">Sebastian and Allensworth, 2012</xref>). Parents&#x2019; participation in parental meetings, voluntary school activities, and initiatives where they learn from teachers about their children&#x2019;s learning or behavior can significantly improve their student&#x2019;s access to school (<xref ref-type="bibr" rid="B59">Perna and Titus, 2005</xref>; <xref ref-type="bibr" rid="B62">Pong et al., 2005</xref>). Regular parental meetings encourage parents to spend more time helping students and supervising school work, which is beneficial to improving students&#x2019; test scores and plays an important role in student attitudes and behaviors (<xref ref-type="bibr" rid="B37">Islam, 2019</xref>). Together, parents&#x2019; participation in parental meetings, school activities, and teacher contact has a significant positive impact on students with low academic achievements. Furthermore, parental behavior can help students understand the importance that their parents attach to school as well as to their learning behavior (<xref ref-type="bibr" rid="B11">Cheng and Li, 2015</xref>; <xref ref-type="bibr" rid="B44">Li, 2017</xref>).</p>
<p>In addition, parent-teacher relationship quality variables means the perception of self-influence on others, such as the extent to which one influences other people&#x2019;s decisions, actions, or evaluations (<xref ref-type="bibr" rid="B84">Zhang, 2016</xref>). The subjective relationship quality in the parent-teacher relationship refers to the parents&#x2019; and teachers&#x2019; emotional perception of the parent-teacher interaction. On the one hand, if parents do not experience a welcoming environment or support from teachers, their participation in constructing the parent-teacher relationship will be reduced. On the other hand, whether teachers receive due respect has a connection to the teachers&#x2019; work enthusiasm and students&#x2019; academic performance (<xref ref-type="bibr" rid="B10">Chen, 2008</xref>). If parents exhibit negative emotions toward the parent-teacher relationship, it will be harder to construct an excellent parent-teacher relationship (<xref ref-type="bibr" rid="B71">Tao, 2016</xref>). So, the emotional experience has an important impact on the parent-teacher relationship and students&#x2019; academic performance.</p>
</sec>
<sec id="S1.SS3">
<title>The parent-teacher relationship in mainland China</title>
<p>Previous studies have shown that contact and communication between teachers and parents are not frequent enough in China (<xref ref-type="bibr" rid="B43">Li, 2013</xref>; <xref ref-type="bibr" rid="B91">Zhu and Gao, 2014</xref>; <xref ref-type="bibr" rid="B85">Zhang, 2018</xref>). It is also possible that schools in China are usually closed, and school-based communication is dominated by schools (<xref ref-type="bibr" rid="B49">Ma, 2010</xref>; <xref ref-type="bibr" rid="B43">Li, 2013</xref>). Therefore, parents&#x2019; participation in school education is limited. At present, the parent-teacher relationship in China is usually manifested by a teacher telling parents about their children&#x2019;s behavior in school, and then the parents participate in their children&#x2019;s school education accordingly (<xref ref-type="bibr" rid="B43">Li, 2013</xref>; <xref ref-type="bibr" rid="B36">Huang, 2016</xref>). From there, most of the links between teachers and parents occur when a student exhibits bad performance, and parents naturally hope that the fewer links there are, the better everyone will be (<xref ref-type="bibr" rid="B87">Zhang, 2003</xref>). On the other hand, teachers report that their relationships with parents are a major source of occupational stress (<xref ref-type="bibr" rid="B26">Grolnick and Seal, 2008</xref>; <xref ref-type="bibr" rid="B57">Pepe and Addimando, 2013</xref>, <xref ref-type="bibr" rid="B58">2014</xref>). Teachers feel more unpleasant experiences are involved in dealing with parent relationships than in other aspects of teaching (<xref ref-type="bibr" rid="B28">Hargreaves and Fullan, 1998</xref>).</p>
<p>Although many research studies have shown that the parent-teacher relationship has an important impact on student&#x2019;s academic achievements (<xref ref-type="bibr" rid="B32">Hill and Tyson, 2009</xref>), the parent-teacher relationship in home-school cooperation has escaped the attention of many Chinese researchers, especially in regard to the lack of quantitative research. There are some limitations on the previous study on the topic. Firstly, the existing studies focus on the status of the parent-teacher relationship and the association between the parent-teacher relationship and students&#x2019; academic outcome at a certain period (<xref ref-type="bibr" rid="B82">Yuan et al., 2019</xref>), that is the use of cross-sectional data. And the long-term effect of the parent-teacher relationship on academic achievement is rare. The unique current social culture and educational environment of mainland China may limit the generalizations of dominant Western research findings on the parent-teacher partnership in China (<xref ref-type="bibr" rid="B16">Deng et al., 2018</xref>). Especially the teachers in a public school in China will widely be in charge of the same classes in the middle school; that is, the same teachers teach students in the 3 years of middle school in China, which may lead to the parent-teacher relationship having a carry-over impact. Since teachers will teach the same class for a long time, the original parent-teacher relationship may give parents and teachers a fixed impression, which will have a long-term impact on their interaction, and then have a long-term impact on students&#x2019; performance (<xref ref-type="bibr" rid="B16">Deng et al., 2018</xref>). Secondly, previous studies take the parent-teacher relationship as a whole variable while didn&#x2019;t discuss the influence of the parent-teacher relationship at a different level. Assessing different aspects of the parent-teacher relationship may provide more detailed evidence to improve the parent-teacher relationship. Therefore, this paper attempts to address the gaps by aiming to examine the longitudinal association between the parent-teacher relationship and students&#x2019; academic achievements in China.</p>
<p>Adolescent development involves various factors, including the social, emotional, and cognitive aspects of the transition from childhood to adulthood (<xref ref-type="bibr" rid="B38">Jaggers et al., 2015</xref>). Compared with the performance at the primary school stage, middle school students&#x2019; academic performance tends to decline because of the great changes in puberty and their environment (<xref ref-type="bibr" rid="B69">Steinberg and Silk, 2002</xref>; <xref ref-type="bibr" rid="B3">Barber and Olsen, 2004</xref>; <xref ref-type="bibr" rid="B39">Keating, 2004</xref>; <xref ref-type="bibr" rid="B42">Lerner and Steinberg, 2004</xref>; <xref ref-type="bibr" rid="B94">Smetana et al., 2004</xref>; <xref ref-type="bibr" rid="B31">Hill and Chao, 2009</xref>). Additionally, the independence of middle school students in all aspects has gradually increased, resulting in a less close parent-teacher relationship than the one that exists in kindergartens and primary schools, and effective cooperation may be reduced (<xref ref-type="bibr" rid="B66">Seginer, 2006</xref>). Therefore, it is worthwhile to use middle school students as research subjects to explore the association between the parent-teacher relationship and middle school students&#x2019; developmental outcomes in the context of mainland China as well as the evidence-based potential practical strategies.</p>
<p>This study employs the hierarchical linear model (HLM) to discuss the association between the parent-teacher relationship and middle school students&#x2019; academic achievements by analyzing China Education Panel Survey (CEPS) data, which is a large-scale, nationally representative, longitudinal public database. Two questions were addressed in this study to enhance our understanding of the parent-teacher relationship in mainland China:</p>
<list list-type="simple">
<list-item>
<label>(1)</label>
<p>Does the parent-teacher relationship have a carry-over impact on middle school students&#x2019; academic achievements at the parent-child dyad level<sup><xref ref-type="fn" rid="footnote1">1</xref></sup> ?</p>
</list-item>
<list-item>
<label>(2)</label>
<p>Does the parent-teacher relationship have a carry-over impact on middle school students academic achievements at the class level?</p>
</list-item>
</list>
</sec>
</sec>
<sec id="S2">
<title>Methodology</title>
<sec id="S2.SS1">
<title>Data source</title>
<p>The data used in this study are from a large-scale longitudinal study [2013&#x2013;2014 school year (Wave 1)] and [2014&#x2013;2015 school year (Wave 2)] of the CEPS, a project conducted by the National Survey Research Center (NSRC) at the Renmin University of China. The respondents were middle school students in seventh grade and ninth grade. The sampling method was stratified random sampling based on the average education level and the proportion of migrants in the whole population. In addition, the respondents included parents, teachers, and school administrators. The survey covered 438 classes from 112 schools in 28 county-level administrative areas throughout the country; due to the compulsory education law (<xref ref-type="bibr" rid="B93">Ministry of Education, 2021</xref>) in China, the government administrates compulsory education mainly at the county level. The CEPS survey can represent the overall education situation in China. The questionnaire survey procedure starts with the investigator of NSRC contacting the principals at the selected middle schools and then collecting the students&#x2019; data by questionnaire.</p>
<p>The students&#x2019; ability scores were compiled according to the national students&#x2019; cognitive ability on a 20-item test designed by NSRC, which includes the ability of language, graph, calculation, and logic. The score ranges from 0 to 20. It was completed on the spot in class and was strictly time-controlled. The answers were collected and sealed on the spot. The principals then arranged for the related teachers to fill out the questionnaire to collect the teachers&#x2019; data. After that, the head teachers of the selected classes asked the parents to fill out the questionnaire. Finally, the questionnaire was mailed to NSRC after it was collected by the head teachers. Many studies have analyzed and discussed the problems of education in China based on these data (e.g., <xref ref-type="bibr" rid="B36">Huang, 2016</xref>; <xref ref-type="bibr" rid="B78">Wu, 2016</xref>; <xref ref-type="bibr" rid="B84">Zhang, 2016</xref>; <xref ref-type="bibr" rid="B45">Li and Zheng, 2017</xref>; <xref ref-type="bibr" rid="B56">Pan and Zhang, 2017</xref>; <xref ref-type="bibr" rid="B73">Tong, 2017</xref>; <xref ref-type="bibr" rid="B75">Wei and Ma, 2017</xref>; <xref ref-type="bibr" rid="B88">Zhao et al., 2017</xref>; <xref ref-type="bibr" rid="B21">Fang, 2018</xref>; <xref ref-type="bibr" rid="B46">Liang et al., 2018</xref>). The data are very rich, including basic personal information, students&#x2019; situations in school, parent-child interactions, and home-school interactions, all of which can provide information for us to further study the impacts of the parent-teacher relationship on students&#x2019; academic achievements.</p>
<p>In this study, we used the data of students in Grade 7 to analyze the carry-over impact of the parent-teacher relationship on students&#x2019; achievements for middle school students in China, since the students in seventh grade have the follow-up data 1 year later. After excluding incomplete samples, the sample size of students (parents) was 8,426, and the sample size of classes was 185.</p>
</sec>
<sec id="S2.SS2">
<title>Variables</title>
<p>Data used in the current study were collected from three sources, including a child&#x2019;s responses, responses from one of his/her parents, and responses from his/her classroom teachers. Therefore, we classified variables into two levels, parent-child dyad level and class level.</p>
<sec id="S2.SS2.SSS1">
<title>Student variables</title>
<p>Students&#x2019; academic achievement of 2014&#x2013;2015 (wave-2) was the dependent variable and cognitive ability simultaneously served as a control variable.</p>
<p>Regarding Students&#x2019; academic achievement (SAA), CEPS collected students&#x2019; original mid-term Chinese, math, and English scores in the autumn semester of 2014, which schools provided. Since the full raw scores of each subject were different across schools, we computed students&#x2019; academic scores <italic>via</italic> dividing their gained raw scores by the full raw scores, indicating the percentage of correct of each subject, and then the averaged percentage of correct of three subjects was computed as a measure of students&#x2019; SAA. The students&#x2019; cognitive ability scores were compiled according to the national students&#x2019; cognitive ability on a 20 items test designed by NSRC, which includes the ability of language, graph, calculation, and logic. The score ranges from 0 to 20. Also, Students&#x2019; gender was included as a control variable.</p>
</sec>
<sec id="S2.SS2.SSS2">
<title>Parent-teacher relationship variables</title>
<p>This study measured the parent-teacher relationship on two levels: child-level and class-level. They were all collected in the 2013&#x2013;2014 school year (wave-1). At the parent-child dyad level, parents reported in five following questions:</p>
<list list-type="simple">
<list-item>
<label>(1)</label>
<p>Parents&#x2019; participation. Do this child&#x2019;s parents attend the parent meeting this semester? There were four options, including (a)The school held one, and the parents did attend; (b) The school held one, but the parents didn&#x2019;t attend; (c) Not held yet, but the parents are going to attend once held; and (d)Not held yet, and the parents are not going to attend if held. We recoded (a) and (c) as 1 to represent parents&#x2019; active attitude on it. (See PP in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
</list>
<table-wrap position="float" id="T1">
<label>TABLE 1</label>
<caption><p>Research variables.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left">Levels</td>
<td valign="top" align="center" colspan="2">Variables</td>
<td valign="top" align="left">Codes</td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Level 1: Parent-child dyad level<break/> Responses from Child and Parents</td>
<td valign="top" align="left">Wave 2 student academic achievement</td>
<td valign="top" align="left">W2-SAA</td>
<td valign="top" align="left">Average scores across Chinese, Math, and English</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 2 Cognitive ability</td>
<td valign="top" align="left">W2-CA</td>
<td valign="top" align="left">Standardized total score of the student&#x2019;s cognitive ability test estimated by the three parameter IRT model.</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Student gender</td>
<td valign="top" align="left">SG</td>
<td valign="top" align="left">0 = female, 1 = male</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Parental education level</td>
<td valign="top" align="left">PEL</td>
<td valign="top" align="left">1 = no education, 2 = primary school, 3 = secondary school, 4 = technical secondary school, 5 = vocational high school, 6 = high school, 6 = associate degree, 7 = bachelor, 8 = master and above</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Family economic status</td>
<td valign="top" align="left">FES-C1</td>
<td valign="top" align="left">Difficult reference group</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left"/>
<td valign="top" align="left">FES-C2</td>
<td valign="top" align="left">Medium</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left"/>
<td valign="top" align="left">FES-C3</td>
<td valign="top" align="left">Rich</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 parents&#x2019; participation/willing to participate in parents&#x2019; meeting</td>
<td valign="top" align="left">PP</td>
<td valign="top" align="left">0 = non-participation, 1 = participation</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 frequency of parents contact with teachers actively in this semester</td>
<td valign="top" align="left">PCTA</td>
<td valign="top" align="left">1 = none, 2 = once, 3 = two to four times, 4 = five times and above</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 frequency of teachers contact with parents actively in this semester</td>
<td valign="top" align="left">TCPA</td>
<td valign="top" align="left">1 = none, 2 = once, 3 = two to four times, 4 = five times and above</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 extent of parents&#x2019; afraid of communicating with teachers</td>
<td valign="top" align="left">PA</td>
<td valign="top" align="left">1 = quite afraid, 2 = a little bit afraid, 3 = not afraid at all</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 parents cooperate with the teacher&#x2019;s requirement</td>
<td valign="top" align="left">PCTR</td>
<td valign="top" align="left">1 = complete, 2 = mostly, 3 = rarely, 4 = not at all</td>
</tr>
<tr>
<td valign="top" align="left">Level 2: class-level<break/> Responses from teachers</td>
<td valign="top" align="left">Wave 1 teachers gender</td>
<td valign="top" align="left">TG</td>
<td valign="top" align="left">0 = female, 1 = male</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 numbers of parents that teachers know</td>
<td valign="top" align="left">NPTK</td>
<td valign="top" align="left">1 = all most none, 2 = a few, 3 = half of a class, 4 = most of a class, 5 = every parent of a class</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 extent if teachers&#x2019; stress from parents&#x2019; request</td>
<td valign="top" align="left">TSPR</td>
<td valign="top" align="left">1 = not at all, 2 = to a small extent, 3 = to a general extent, 4 = to a large extent, 5 = to an extremely large extent</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 teachers&#x2019; perception of respect from parents</td>
<td valign="top" align="left">TPRP</td>
<td valign="top" align="left">1 = none, 2 = just a few, 3 = about a half, 4 = more than half, 5 = all of them</td>
</tr>
<tr>
<td valign="top" align="left"/>
<td valign="top" align="left">Wave 1 teaching experiences</td>
<td valign="top" align="left">TA</td>
<td valign="top" align="left">Mean = 15, SD = 8.97, Median = 14</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn><p>Note. Wave 1 = 2013&#x2013;2014 school year, Wave 2 = 2014&#x2013;2015 school year.</p></fn>
</table-wrap-foot>
</table-wrap>
<list list-type="simple">
<list-item>
<label>(2)</label>
<p>Frequency of parents contact with teachers actively. How many times have this child&#x2019;s parents contacted the teacher at school this semester? Parents responded it on a 4-point scale (1 = Never, 2 = Once, 3 = Two to four times, and 4 = Five times or more). (See PCTA in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
<list-item>
<label>(3)</label>
<p>Frequency of teachers contact with parents actively. How many times has this child&#x2019;s teacher contacted the parents this semester? Parents responded it on a 4-point scale (1 = Never, 2 = Once, 3 = Two to four times, and 4 = Five times or more). (See TCTA in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
<list-item>
<label>(4)</label>
<p>Parents&#x2019; afraid. Are you afraid of communicating with the school teacher? Parents reported it on a 3-point scale (1 = Quite afraid, 2 = A little bit afraid, and 3 = Not afraid at all). (See PA in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
<list-item>
<label>(5)</label>
<p>Parents cooperate with the teacher&#x2019;s requirement. To what extent could you meet the requirement this semester if the teachers require the parents to check their child&#x2019;s homework, such as writing &#x201C;checked,&#x201D; signing names, etc.? Parents responded it on a 4-point scale (1 = Complete, 2 = Mostly, 3 = Rarely, and 4 = Not at all). (See PCTR in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
</list>
<p>At the class level, the classroom teacher responded to three questions to represent the parent-teacher relationship of a particular classroom.</p>
<list list-type="simple">
<list-item>
<label>(1)</label>
<p>Numbers of parents that teachers know. How many parents of your students do you know about? Teachers responded it on a 5-point scale (1 = None, 2 = Just a few, 3 = About a half, 4 = More than half, and 5 = All of them). (See NPTK in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
<list-item>
<label>(2)</label>
<p>Teachers&#x2019; stress from parents&#x2019; request. How much pressure do you have concerning the requirements of students&#x2019; parents. Teachers responded it on a 5-point scale (1 = None, 2 = Low, 3 = Moderate, 4 = High, and 5 = Very high). (See TSRP in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
<list-item>
<label>(3)</label>
<p>Teachers&#x2019; perception of respect from parents. Generally speaking, how many parents of your students pay respect to you? Teachers responded it on a 5-point scale (1 = None, 2 = Just a few, 3 = About a half, 4 = More than half, and 5 = All of them). (See TPRP in <xref ref-type="table" rid="T1">Table 1</xref>).</p>
</list-item>
</list>
<p>In line with existing research, the measures of the parent-teacher relationship also reflected both the parent-teacher contact and parent-teacher relationship quality. More specifically, parents&#x2019; active communication with teachers, teachers&#x2019; active contact with parents, parents&#x2019; participation in parental meetings, the number of parents that the teacher knows, and how parents cooperate with the teacher&#x2019;s requirements represented the parent-teacher contact. Meanwhile, whether parents are afraid to communicate with teachers, teachers&#x2019; stress from parents&#x2019; requests and teachers&#x2019; perception of respect from parents reflect parent-teacher relationship quality.</p>
<p>Besides the aforementioned variables, we also included parental education level, family economic status (FES), teachers&#x2019; gender, and teachers&#x2019; teaching experience (The cumulative time for teachers to engage in teaching work which is measured by year) as control variables. To be noted, we merged the FES into three categories (Difficulty, Medium, and Rich) from a five-category variable (very difficult, some difficult, medium, rich, and very rich) from the original database by merging the first two categories and last two categories due to the small numbers in the first and last categories. (See <xref ref-type="table" rid="T1">Table 1</xref> for details).</p>
</sec>
</sec>
<sec id="S2.SS3">
<title>Analysis method</title>
<p>Due to the data hierarchy, where students were nested in the classroom, the HLM was adopted to account for the dependency among students in the same classroom. Considering that there are only two classes in each grade in each school, it is not suitable to construct a three-level model of student, class, and school. This paper uses a two-level HLM as the analysis model. Level 1 is the parent-child dyad level, and students&#x2019; gender, cognitive abilities, parents reported parent-teacher relationship variables, FES used as the predictors. Considering that categorized variables cannot be directly used in the HLM, a dummy coding method was used to transform the FES into two dummy variables. More specially, the first categorical of FES (FES-C1, difficulty level) was set as the reference level, and then two dummy variables, FES.C2 and FES.C3, represented medium and rich levels, respectively, were created.</p>
<p>Level 2 is the class level, and the teachers reported that parent-teacher variables were used as class-level predictors. In addition, corresponding child-level predictors were aggregated at the class level to separate level-1 and level-2 effects (<xref ref-type="bibr" rid="B33">Hoffman, 2015</xref>, pp. 344).</p>
</sec>
<sec id="S2.SS4">
<title>Model</title>
<p>We followed the step-up model-building approach as suggested by <xref ref-type="bibr" rid="B63">Raudenbush and Bryk (2002)</xref> in the current study.</p>
<p>Step 1: a null model with no predictors were tested to estimate the interclass correlation of the outcome variables.</p>
<p>Model 0:</p>
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<p>In this model, <italic>j</italic> represents different classes; <italic>i</italic> stands for different students; <italic>Y</italic><sub><italic>ij</italic></sub> corresponds to the academic achievement of student <italic>i</italic> in class <italic>j</italic>; &#x03B2;<sub><italic>0j</italic></sub> is the mean of the students&#x2019; academic achievements in class <italic>j</italic>; <italic>r</italic><sub><italic>ij</italic></sub> is the difference between student <italic>i</italic> and the class mean; Var(<italic>r</italic><sub>ij</sub>) reflects the random error at the student/parent level; &#x03B3;<sub><italic>00</italic></sub> is the mean of all students&#x2019; academic achievements; <italic>u</italic><sub><italic>0j</italic></sub> is the difference between the class mean and the all-student mean; andVar(<italic>u</italic><sub>0<italic>j</italic></sub>) reflects the error of the class level.</p>
<p>Step 2: a random intercept model was tested with all level-1 predictors centered at the class mean and corresponding level-2 predictors by aggregating at the class-level to separate level-1 and level-2 effects (<xref ref-type="bibr" rid="B33">Hoffman, 2015</xref>, pp. 344).</p>
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</disp-formula>
<p>Where, <italic>k</italic> represents the <italic>k<sup>th</sup></italic> level-1 predictors, <italic>k</italic> &#x2208; [1,10], meaning no random slopes were specified in this step.</p>
<p>Since SG was a categorical variable and the female as the reference group, the percentage of male students in each classroom was calculated as the level-2 predictor (SGCM). Similarly, the percentage of FES.C2 and FES.C3 at each classroom were computed as the level-2 predictors.</p>
<p>Step 3: a series of random slope models were tested to examine which level-1 coefficients varied significantly across classrooms <italic>via</italic> conducting a likelihood ratio test to compare models with and without the random slopes.</p>
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<p>Where, <italic>k</italic> represents the <italic>k</italic><sup>th</sup> level-1 predictors, <italic>k</italic> &#x2208; [1,10],&#x03BC;<sub><italic>kj</italic></sub> indicates random slopes were specified in this step. Only the significant random slopes were kept to keep the model as parsimony as possible.</p>
<p>Step 4: class-level predictors were added to models to examine if these class-level predictors could explain the variance of random intercept.</p>
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<p>Step 5: class-level predictors were added to models to examine if these class-level predictors could explain the variance of random slopes.</p>
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<mml:mtext>TPRP</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>014</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TA</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>015</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TG</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>&#x2062;</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="S2.Ex31">
<label>(14)</label>
<mml:math id="M14">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B2;</mml:mi>
<mml:mrow>
<mml:mtext>kj</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x2062;</mml:mo>
<mml:mn>0</mml:mn>
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</mml:msub>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>111</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TSPR</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>112</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>NPTK</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>113</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TPRP</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>114</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TA</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x03B3;</mml:mi>
<mml:mn>115</mml:mn>
</mml:msub>
<mml:mo>&#x2062;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>TG</mml:mtext>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">&#x03BC;</mml:mi>
<mml:mrow>
<mml:mtext>kj</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
<p>Where, &#x03B3;<sub><italic>111</italic></sub> to &#x03B3;<sub><italic>115</italic></sub> represented the class-level coefficients for examining the variance in the random slopes. Only the significant coefficients would be kept in the final model.</p>
</sec>
</sec>
<sec id="S3" sec-type="results">
<title>Results</title>
<p>The following results are shown based on the empirical analysis of the above survey data.</p>
<sec id="S3.SS1">
<title>Descriptive statistics</title>
<p><xref ref-type="table" rid="T2">Table 2</xref> shows the summary of the 8,426 students (parents), including results from both the child and class levels. <xref ref-type="table" rid="T3">Table 3</xref> shows the descriptive statistics of the 185 classes.</p>
<table-wrap position="float" id="T2">
<label>TABLE 2</label>
<caption><p>Description statistics of 8,426 child and parents.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left">Variables</td>
<td valign="top" align="center">Value</td>
<td valign="top" align="center">No. of cases</td>
<td valign="top" align="center">%</td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Parent-child dyad level</td>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left">SG</td>
<td valign="top" align="center">Female</td>
<td valign="top" align="center">4,006</td>
<td valign="top" align="center">47.54</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Male</td>
<td valign="top" align="center">4,420</td>
<td valign="top" align="center">52.46</td>
</tr>
<tr>
<td valign="top" align="left">FES</td>
<td valign="top" align="center">Difficult</td>
<td valign="top" align="center">1,538</td>
<td valign="top" align="center">18.25</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Medium</td>
<td valign="top" align="center">6,314</td>
<td valign="top" align="center">74.93</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Rich</td>
<td valign="top" align="center">543</td>
<td valign="top" align="center">6.44</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Missing</td>
<td valign="top" align="center">31</td>
<td valign="top" align="center">0.37</td>
</tr>
<tr>
<td valign="top" align="left">PP</td>
<td valign="top" align="center">Non-participation in parents&#x2019; meeting</td>
<td valign="top" align="center">770</td>
<td valign="top" align="center">9.14</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Parents&#x2019; participation/willing to participate in parents&#x2019; meeting</td>
<td valign="top" align="center">7,412</td>
<td valign="top" align="center">87.97</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Missing</td>
<td valign="top" align="center">244</td>
<td valign="top" align="center">2.90</td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">Mean</td>
<td valign="top" align="center">SD</td>
</tr>
<tr>
<td valign="top" align="left">W2-SAA</td>
<td valign="top" align="center">Wave 2 student academic achievement</td>
<td valign="top" align="center">65.30</td>
<td valign="top" align="center">19.26</td>
</tr>
<tr>
<td valign="top" align="left">W2-CA</td>
<td valign="top" align="center">Wave 2 cognitive ability</td>
<td valign="top" align="center">0.35</td>
<td valign="top" align="center">0.82</td>
</tr>
<tr>
<td valign="top" align="left">PEL</td>
<td valign="top" align="center">Highest parent&#x2019;s education level</td>
<td valign="top" align="center">4.68</td>
<td valign="top" align="center">2.08</td>
</tr>
<tr>
<td valign="top" align="left">PCTA</td>
<td valign="top" align="center">Wav 1 frequency of parents contact with teachers actively in this semester</td>
<td valign="top" align="center">2.37</td>
<td valign="top" align="center">1.01</td>
</tr>
<tr>
<td valign="top" align="left">TCPA</td>
<td valign="top" align="center">Wave 1 frequency of teachers contact with parents actively in this semester</td>
<td valign="top" align="center">2.11</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">PA</td>
<td valign="top" align="center">Wave 1 extent of parents&#x2019; afraid of communicating with teachers</td>
<td valign="top" align="center">2.79</td>
<td valign="top" align="center">0.43</td>
</tr>
<tr>
<td valign="top" align="left">PCTR</td>
<td valign="top" align="center">Wave 1 parents cooperate with the teacher&#x2019;s requirement</td>
<td valign="top" align="center">1.84</td>
<td valign="top" align="center">0.92</td>
</tr>
<tr>
<td valign="top" align="left">Class level</td>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left">SGCM</td>
<td valign="top" align="center">Wave 1 percentage of male students</td>
<td valign="top" align="center">0.52</td>
<td valign="top" align="center">0.07</td>
</tr>
<tr>
<td valign="top" align="left">FES.c2CM</td>
<td valign="top" align="center">Wave 1 percentage of difficult family</td>
<td valign="top" align="center">19.15</td>
<td valign="top" align="center">17.10</td>
</tr>
<tr>
<td valign="top" align="left">FES.c3CM</td>
<td valign="top" align="center">Wave 1 percentage of medium family</td>
<td valign="top" align="center">75.22</td>
<td valign="top" align="center">15.07</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Wave 1 percentage of rich family</td>
<td valign="top" align="center">7.48</td>
<td valign="top" align="center">5.44</td>
</tr>
<tr>
<td valign="top" align="left">PPCM</td>
<td valign="top" align="center">Wave 1 percentage of Parents&#x2019; participation/willing to participate in parents&#x2019; meeting</td>
<td valign="top" align="center">0.91</td>
<td valign="top" align="center">0.11</td>
</tr>
<tr>
<td valign="top" align="left">W2CACM</td>
<td valign="top" align="center">Class mean of W2CA</td>
<td valign="top" align="center">0.34</td>
<td valign="top" align="center">0.48</td>
</tr>
<tr>
<td valign="top" align="left">PELCM</td>
<td valign="top" align="center">Class mean of PEL</td>
<td valign="top" align="center">4.69</td>
<td valign="top" align="center">1.23</td>
</tr>
<tr>
<td valign="top" align="left">PCTACM</td>
<td valign="top" align="center">Class mean of PCTA</td>
<td valign="top" align="center">2.37</td>
<td valign="top" align="center">0.35</td>
</tr>
<tr>
<td valign="top" align="left">TCPACM</td>
<td valign="top" align="center">Class mean of TCPA</td>
<td valign="top" align="center">2.11</td>
<td valign="top" align="center">0.35</td>
</tr>
<tr>
<td valign="top" align="left">PACM</td>
<td valign="top" align="center">Class mean of PA</td>
<td valign="top" align="center">2.79</td>
<td valign="top" align="center">0.09</td>
</tr>
<tr>
<td valign="top" align="left">PCTRCM</td>
<td valign="top" align="center">Class mean of PCTR</td>
<td valign="top" align="center">1.65</td>
<td valign="top" align="center">0.28</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn><p>Note. Wave 1 = 2013&#x2013;2014 school year, Wave 2 = 2014&#x2013;2015 school year.</p></fn>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="T3">
<label>TABLE 3</label>
<caption><p>Descriptive statistics of 185 classes.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left">Variables</td>
<td valign="top" align="left"/>
<td valign="top" align="center">No. of cases</td>
<td valign="top" align="center">%</td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">TG</td>
<td valign="top" align="left">Female</td>
<td valign="top" align="center">128</td>
<td valign="top" align="center">69.19</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Male</td>
<td valign="top" align="center">57</td>
<td valign="top" align="center">30.81</td>
</tr>
<tr>
<td/>
<td valign="top" align="left"/>
<td valign="top" align="center">Mean</td>
<td valign="top" align="center">SD</td>
</tr>
<tr>
<td valign="top" align="left">TA</td>
<td valign="top" align="left">Wave 1 teacher experiences</td>
<td valign="top" align="center">16.92</td>
<td valign="top" align="center">7.16</td>
</tr>
<tr>
<td valign="top" align="left">TSPR</td>
<td valign="top" align="left">Wave 1 extent of teachers&#x2019; stress from parents&#x2019; request</td>
<td valign="top" align="center">15.00</td>
<td valign="top" align="center">8.97</td>
</tr>
<tr>
<td valign="top" align="left">NPTK</td>
<td valign="top" align="left">Wave 1 numbers of parents that teachers know</td>
<td valign="top" align="center">3.58</td>
<td valign="top" align="center">0.87</td>
</tr>
<tr>
<td valign="top" align="left">TPRP</td>
<td valign="top" align="left">Wave 1 teachers&#x2019; perception of respect from parents</td>
<td valign="top" align="center">3.82</td>
<td valign="top" align="center">0.98</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn><p>Note. Wave 1 = 2013&#x2013;2014 school year, Wave 2 = 2014&#x2013;2015 school year.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="S3.SS2">
<title>Multilevel results</title>
<sec id="S3.SS2.SSS1">
<title>Results from step 1 (model 0)</title>
<p>From model 1 in <xref ref-type="table" rid="T4">Table 4</xref>, we can see that the mean of the students&#x2019; class academic achievements is 65.54 (<italic>p</italic> &#x003C; 0.001), the variance of the students (&#x03C3;<sup>2</sup>) is 513.9, and the variance of the classes is 157.9 (<italic>p</italic> &#x003C; 0.001), thus ICC = 0.42, indicating that the application of the HLM to statistical analysis must be considered (<xref ref-type="bibr" rid="B76">Wen, 2009</xref>).</p>
<table-wrap position="float" id="T4">
<label>TABLE 4</label>
<caption><p>Multilevel result.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left"></td>
<td valign="top" align="center">Model 0</td>
<td valign="top" align="center">Model 1</td>
<td valign="top" align="center">Model 1.1</td>
<td valign="top" align="center">Model 2</td>
<td valign="top" align="center">Model 3</td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Fixed effects</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left" colspan="2">Level 1-child level</td>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left">Intercept</td>
<td valign="top" align="center">65.540.94<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">77.4722.68<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">77.6222.63<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">48.7123.39<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">49.5523.39<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">SG</td>
<td/>
<td valign="top" align="center">&#x2013;5.080.31<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;5.050.31<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;5.060.32<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;5.060.32<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">CA</td>
<td/>
<td valign="top" align="center">11.050.24<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">11.020.23<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">11.030.24<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">11.030.24<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">FES.C2</td>
<td/>
<td valign="top" align="center">0.280.48</td>
<td valign="top" align="center">0.210.48</td>
<td valign="top" align="center">0.140.49</td>
<td valign="top" align="center">0.140.48</td>
</tr>
<tr>
<td valign="top" align="left">FES.C3</td>
<td/>
<td valign="top" align="center">&#x2013;0.330.73</td>
<td valign="top" align="center">&#x2013;0.330.73</td>
<td valign="top" align="center">&#x2013;0.460.74</td>
<td valign="top" align="center">&#x2013;0.470.74</td>
</tr>
<tr>
<td valign="top" align="left">PEL</td>
<td/>
<td valign="top" align="center">0.590.09<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">0.570.09<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">0.560.09<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">0.560.09<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">PCTR</td>
<td/>
<td valign="top" align="center">&#x2013;1.750.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.760.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.720.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.730.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">PP</td>
<td/>
<td valign="top" align="center">2.840.66<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">2.820.65<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">2.940.67<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">2.920.67<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">PCTA</td>
<td/>
<td valign="top" align="center">0.480.18<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">0.450.18<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">0.410.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">0.410.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">TCPA</td>
<td/>
<td valign="top" align="center">&#x2013;1.830.19<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.770.22<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.780.23<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.950.91<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">PA</td>
<td/>
<td valign="top" align="center">3.090.37<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">2.920.43<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">2.990.43<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.821.79</td>
</tr>
<tr>
<td valign="top" align="left" colspan="2">Level 2-class level</td>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left">SGCM</td>
<td/>
<td valign="top" align="center">&#x2013;6.018.61</td>
<td valign="top" align="center">&#x2013;6.728.58</td>
<td valign="top" align="center">&#x2013;7.918.42</td>
<td valign="top" align="center">&#x2013;7.798.42</td>
</tr>
<tr>
<td valign="top" align="left">W2CACM</td>
<td/>
<td valign="top" align="center">14.241.8<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">14.331.8<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">13.311.83<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
<td valign="top" align="center">13.331.83<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">FES.c2CM</td>
<td/>
<td valign="top" align="center">0.020.07</td>
<td valign="top" align="center">0.030.07</td>
<td valign="top" align="center">&#x2013;0.020.06</td>
<td valign="top" align="center">&#x2013;0.020.06</td>
</tr>
<tr>
<td valign="top" align="left">FES.c3CM</td>
<td/>
<td valign="top" align="center">0.280.13<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">0.290.13<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">0.230.13</td>
<td valign="top" align="center">0.230.13</td>
</tr>
<tr>
<td valign="top" align="left">PELCM</td>
<td/>
<td valign="top" align="center">0.020.81</td>
<td valign="top" align="center">0.060.8</td>
<td valign="top" align="center">0.620.79</td>
<td valign="top" align="center">0.620.79</td>
</tr>
<tr>
<td valign="top" align="left">PCTRCM</td>
<td/>
<td valign="top" align="center">&#x2013;4.472.61</td>
<td valign="top" align="center">&#x2013;4.162.61</td>
<td valign="top" align="center">&#x2013;3.272.55</td>
<td valign="top" align="center">&#x2013;3.32.55</td>
</tr>
<tr>
<td valign="top" align="left">PPCM</td>
<td/>
<td valign="top" align="center">&#x2013;4.878.97</td>
<td valign="top" align="center">&#x2013;5.088.94</td>
<td valign="top" align="center">&#x2013;1.148.93</td>
<td valign="top" align="center">&#x2013;1.078.93</td>
</tr>
<tr>
<td valign="top" align="left">PCTACM</td>
<td/>
<td valign="top" align="center">1.242.54</td>
<td valign="top" align="center">1.332.53</td>
<td valign="top" align="center">2.182.58</td>
<td valign="top" align="center">2.172.58</td>
</tr>
<tr>
<td valign="top" align="left">TCPACM</td>
<td/>
<td valign="top" align="center">&#x2013;0.042.44</td>
<td valign="top" align="center">0.12.44</td>
<td valign="top" align="center">&#x2013;0.442.49</td>
<td valign="top" align="center">&#x2013;0.412.49</td>
</tr>
<tr>
<td valign="top" align="left">PACM</td>
<td/>
<td valign="top" align="center">&#x2013;3.316.65</td>
<td valign="top" align="center">&#x2013;3.776.64</td>
<td valign="top" align="center">2.426.76</td>
<td valign="top" align="center">2.376.76</td>
</tr>
<tr>
<td valign="top" align="left">TSPR</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x2013;1.660.74<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">&#x2013;1.670.74<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">NPTK</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">0.560.7</td>
<td valign="top" align="center">0.410.7</td>
</tr>
<tr>
<td valign="top" align="left">TPRP</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">2.151.02<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
<td valign="top" align="center">2.131.02<xref ref-type="table-fn" rid="t4fns1">&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">TA</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">0.120.07</td>
<td valign="top" align="center">0.120.07</td>
</tr>
<tr>
<td valign="top" align="left">TG</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x2013;0.131.39</td>
<td valign="top" align="center">&#x2013;0.131.39</td>
</tr>
<tr>
<td valign="top" align="left">TCPA&#x002A;NPTK</td>
<td/>
<td/>
<td/>
<td/>
<td valign="top" align="center">0.040.23</td>
</tr>
<tr>
<td valign="top" align="left">PA&#x002A;NPTK</td>
<td/>
<td/>
<td/>
<td/>
<td valign="top" align="center">1.240.45<xref ref-type="table-fn" rid="t4fns1">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td valign="top" align="left">Random effects</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left">level 2 intercept</td>
<td valign="top" align="center">157.9</td>
<td valign="top" align="center">53.39</td>
<td valign="top" align="center">53.47</td>
<td valign="top" align="center">49.01</td>
<td valign="top" align="center">48.98</td>
</tr>
<tr>
<td valign="top" align="left" colspan="2">level 2 slope-TCPA</td>
<td/>
<td valign="top" align="center">2.21</td>
<td valign="top" align="center">2.28</td>
<td valign="top" align="center">2.29</td>
</tr>
<tr>
<td valign="top" align="left">level 2 slope-PA</td>
<td/>
<td/>
<td valign="top" align="center">5.89</td>
<td valign="top" align="center">5.98</td>
<td valign="top" align="center">4.65</td>
</tr>
<tr>
<td valign="top" align="left">Level 1 residual</td>
<td valign="top" align="center">213.9</td>
<td valign="top" align="center">130.18</td>
<td valign="top" align="center">127.06</td>
<td valign="top" align="center">128.10</td>
<td valign="top" align="center">128.10</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="t4fns1"><p>Note. SG, student gender; FES, family economic status; PP, Wave 1 parents&#x2019; participation/willing to participate in parents&#x2019; meeting; W2-CA, Wave 2 students&#x2019; cognitive ability; PEL, Highest parent&#x2019;s education level; PCTA, Wave 1 frequency of parents contact with teachers actively in this semester; TCPA, Wave 1 frequency of teachers contact with parents actively in this semester; PA, Wave 1 extent of parents&#x2019; afraid of communicating with teachers; PCTR, Wave 1 parents cooperate with the teacher&#x2019;s requirement; SGCM, Wave 1 percentage of male students; FES.c2CM, Wave 1 percentage of medium family; FES.c3CM, Wave 1 percentage of rich family; PPCM, Wave 1 percentage of Parents&#x2019; participation/willing to participate in parents&#x2019; meeting; W2CACM, Class mean of W2CA; PELCM, Class mean of PEL; PCTACM, Class mean of PCTA; TCPACM, Class mean of TCPA; PACM, Class mean of PA; PCTRCM, Class mean of PCTR; TG, teacher gender; TA, Wave 1 teacher experiences; TSPR, Wave 1 extent of teachers&#x2019; stress from parents&#x2019; request; NPTK, Wave 1 numbers of parents that teachers know; and TPRP, Wave 1 teachers&#x2019; perception of respect from parents. &#x002A;<italic>p</italic> &#x003C; 0.05; &#x002A;&#x002A;<italic>p</italic> &#x003C; 0.01.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="S3.SS2.SSS2">
<title>Results from step 2 (model 1)</title>
<p>The results of model 2 in <xref ref-type="table" rid="T4">Table 4</xref> show that the fixed effects of the control variables on the parent level: the average score of the classes is 0.143 (<italic>p</italic> &#x003C; 0.05) after controlling all the other variables; boys have significantly lower academic achievements than girls (&#x03B3;<sub><italic>01</italic></sub> = &#x2013;5.08, <italic>p</italic> &#x003C; 0.001); as expected, cognitive ability is positively related to students&#x2019; academic achievements (&#x03B3;<sub><italic>02</italic></sub> = 11.05, <italic>p</italic> &#x003C; 0.001); and the parents&#x2019; education level is positively related to students&#x2019; academic achievements (&#x03B3;<sub><italic>03</italic></sub> = 0.59, <italic>p</italic> &#x003C; 0.001). The effect of FES is not significant. Parents&#x2019; willingness to participate in parental meetings to discuss students&#x2019; academic achievements have significantly higher academic achievements than those showing unwillingness (&#x03B3;<sub><italic>06</italic></sub> = 2.84, <italic>p</italic> &#x003C; 0.001). Students who had parents communicating more with teachers have significantly higher academic achievements (&#x03B3;<sub><italic>07</italic></sub> = 0.48, <italic>p</italic> &#x003C; 0.01).</p>
<p>Teachers who actively communicate with parents have significantly lower academic achievements than those who do not actively communicate with parents (&#x03B3;<sub><italic>08</italic></sub> = &#x2013;1.83, <italic>p</italic> &#x003C; 0.001). Parents who were not afraid of communicating with teachers have significantly higher academic achievements than those who are not afraid (&#x03B3;<sub><italic>09</italic></sub> = 3.09, <italic>p</italic> &#x003C; 0.001). students with parents who had less cooperation with the teachers&#x2019; requirements have significantly lower academic achievements (&#x03B3;<sub><italic>010</italic></sub> = &#x2013;1.75, <italic>p</italic> &#x003C; 0.05). At the classroom level, we can find that the class level cognitive ability is significantly positive, indicating that a higher level of class level of cognitive ability is associated with a higher level of academic achievement on average. Even though individual-level FES is not significantly associated with students&#x2019; achievement, the class-level percentage of rich families is significantly positively related to students&#x2019; achievement. Together, these results indicate that, in the same class, student&#x2019;s FES did not impact his/her academic achievement; however, a student in a classroom with a higher percentage of rich families would have a higher academic achievement score.</p>
<p>The results of random effects are as follows: the class&#x2019;s mean academic achievements variance was reduced to 53.39, and the individual residual variance was reduced to 130.18 after including both level-1 and level-2 predictors. Accordingly, level-1 <italic>R</italic><sup>2</sup> = 0.39, and level-2 <italic>R</italic><sup>2</sup> = 0.66, indicating that a total of 39% of the level-1 variance and 66% of level-2 variance have been explained.</p>
</sec>
<sec id="S3.SS2.SSS3">
<title>Results from step 3 (model 1.1)</title>
<p>In this step, we tested a series of models to identify which level-1 coefficients varied across classrooms. As a result, we identified that TCPA and PA effects varied across classrooms. The fixed effects were kept the same as in the last model.</p>
</sec>
<sec id="S3.SS2.SSS4">
<title>Results from step 4 (model 2)</title>
<p>In this step, class-level teacher predictors are included in the model to explain the variance of the class mean of students&#x2019; achievement scores. As shown in <xref ref-type="table" rid="T4">Table 4</xref>, we found that the extent to if teachers&#x2019; stress from parents&#x2019; requests is significantly negatively associated with the class mean of students&#x2019; academic scores, indicating the higher levels of stress teachers perceived, the lower average scores the class had. Also, teachers&#x2019; perception of parents&#x2019; respect significantly impacts class-level academic scores. Regarding the random effects, the variance of the class means academic achievements was reduced to 49.01 from 53.47. Accordingly, level-1 <italic>R</italic><sup>2</sup> = 0.40, and level-2 <italic>R</italic><sup>2</sup> = 0.66, indicating the effects of class-level predictors were very small.</p>
</sec>
<sec id="S3.SS2.SSS5">
<title>Results from step 5 (model 3)</title>
<p>In this step, we tested if class-level predictors could significantly explain the variations of random slopes by including cross-level interactions between parent and teacher predictors. More specifically, if the number of parents that teachers know as class-level predictors could explain the effects of the frequency of teachers contact with parents actively and extent of parents&#x2019; afraid of communicating with teachers as child-level predictors (TCPA&#x002A;NPTK and PA&#x002A;NPTK). The results show that the numbers of parents that teachers knew are significantly positively associated with the slope of the extent of parents&#x2019; afraid of communicating with teachers, indicating that when teachers knew more parents, the impacts of the extent of parents&#x2019; afraid of communicating with teachers become more positive, as a result, parents had lower levels of afraid of communicating with teachers. Accordingly, level-1 <italic>R</italic><sup>2</sup> = 0.40, and level-2 <italic>R</italic><sup>2</sup> = 0.69, as expected, level-2 variances have been further explained by adding these cross-level interactions.</p>
</sec>
</sec>
</sec>
<sec id="S4" sec-type="discussion">
<title>Discussion</title>
<p>In this paper, we focus on the association between the parent-teacher relationship and the student&#x2019;s achievements, aiming to analyze the carry-over impact of the parent-teacher relationship on students&#x2019; achievements for middle school students in China. The HLM was applied to analyze two levels of variables: the parent-child dyad level and class level. Therefore, we organize discussions about the associations of these two levels of variables, including child-level variables and class-level variables, of the parent-teacher relationship with students&#x2019; academic achievements.</p>
<sec id="S4.SS1">
<title>The carry-over impact of the parent-teacher relationship on students&#x2019; academic achievements at the parent-child dyad</title>
<p>For the parent-teacher relationship, the degree and form of parent-teacher contact are strongly associated with students&#x2019; academic achievement. Students with parents who participated in parental meetings and actively communicated with teachers had higher academic achievement, which a large number of studies have proved (e.g., <xref ref-type="bibr" rid="B25">Goyette and Xie, 1999</xref>; <xref ref-type="bibr" rid="B1">Adams and Christenson, 2000</xref>; <xref ref-type="bibr" rid="B65">Sebastian and Allensworth, 2012</xref>). The frequency of parent-teacher interaction could pass on educational expectations to their children, then contribute to their academic achievements.</p>
<p>The cooperation from parents to supervise their children to complete teachers&#x2019; assignments was an important way for parents to engage in their children&#x2019;s schooling (<xref ref-type="bibr" rid="B15">Cook et al., 2018</xref>), which was supported by our findings as well. More specifically, results showed that the less the parents cooperated with teachers&#x2019; requirements, the lower students&#x2019; academic scores were.</p>
<p>Our results also showed that parental participation in parent-teacher meetings is also positively related to students&#x2019; academic achievements.</p>
<p>On the one hand, parental participation in parent-teacher meetings reflects the level of parent involvement in children&#x2019;s learning to some extent. The positive relationship between parental involvement in their children&#x2019;s education and students&#x2019; success in school is widely documented in the research literature (<xref ref-type="bibr" rid="B19">Fan and Chen, 2001</xref>; <xref ref-type="bibr" rid="B4">Barnard, 2004</xref>; <xref ref-type="bibr" rid="B72">Todd and Wolpin, 2007</xref>; <xref ref-type="bibr" rid="B34">Houtenville and Conway, 2008</xref>; <xref ref-type="bibr" rid="B12">Cheung and Pomerantz, 2011</xref>). On the other hand, evidence also suggests that some schools failed to fully engage parents and provide them with information about their children&#x2019;s learning and how they are performing in school (<xref ref-type="bibr" rid="B54">Noel et al., 2013</xref>). Therefore, it is critical for parents to actively keep themselves informed about their children&#x2019;s classroom activities, events, and requirements by communicating with teachers actively.</p>
<p>However, we found that parents reported teachers&#x2019; active communication with parents had negative relationships on students&#x2019; academic performance, which might be because, in the face-to-face communication between parents and teachers, teachers always have the clear aim of reflecting on the students&#x2019; misconduct and requesting that parents cooperate with regulations (<xref ref-type="bibr" rid="B79">Xiong, 2007</xref>; <xref ref-type="bibr" rid="B86">Zhang, 2011</xref>). If parents are informed of their children&#x2019;s misconduct in China, they tend to criticize them verbally or even scold them since the children are supposed to obey the rules of parents. So that, telling parents about bad behavior is a punishment in Chinese published schools, which may aggravate students&#x2019; negative emotions, further affecting their academic performance. The relationship between teachers and parents in China is protagonist-supporting as a result of the current education system in China, which is oriented toward a screening function rather than a cultivation function (<xref ref-type="bibr" rid="B2">An, 2005</xref>), leading to strengthening the importance of exams and the status of teachers (<xref ref-type="bibr" rid="B2">An, 2005</xref>; <xref ref-type="bibr" rid="B60">Peterson et al., 2011</xref>). Although policymakers, administrators, and teachers have gradually realized the vital role of parental participation, parents&#x2019; involvement in children&#x2019;s education is still in its initial stage in China (<xref ref-type="bibr" rid="B77">Wu et al., 2017</xref>).</p>
</sec>
<sec id="S4.SS2">
<title>The carry-over impact of the parent-teacher relationship on students&#x2019; academic achievements at the class level</title>
<p>The results of model 3 showed that teachers&#x2019; perception of respect from parents and the extent of teachers&#x2019; stress from parents&#x2019; requests were significantly associated with academic achievement. The higher levels of stress teachers perceived from parents&#x2019; requests, the lower academic achievement; meanwhile, the higher levels of respect teachers perceived from parents, the higher average academic performance. Similar to previous meta-analysis findings, high teachers&#x2019; stress level is linked to poor student outcomes, and the parent-teacher relationship is one of the main sources of teacher stress (<xref ref-type="bibr" rid="B8">Cameron and Andr&#x00E9;, 2005</xref>). Also, having parents&#x2019; respect is a well-known protective factor for teacher retention (<xref ref-type="bibr" rid="B55">Ouyang and Paprock, 2006</xref>; <xref ref-type="bibr" rid="B9">Canter, 2009</xref>).</p>
<p>In addition, results reveal the random effects of the extent of parents&#x2019; afraid of communicating with teachers could be explained by the number of parents that teacher knew; the more parents the teacher knew, the lower level of fear that parents felt about communicating with teachers would become more positive. Together, the results echo that a good parent-teacher relationship link to good academic performance of students. However, the random effects also reveal the non-negligible variation across classrooms. Teachers can teach so many students that they are not familiar with all their children and their parents (<xref ref-type="bibr" rid="B68">Sizer, 1992</xref>; <xref ref-type="bibr" rid="B50">Meier, 2005</xref>), especially when there are many large classes (more than 56 students in a class) in China (<xref ref-type="bibr" rid="B90">Zhou and Xian, 2012</xref>; <xref ref-type="bibr" rid="B83">Zhang, 2013</xref>; <xref ref-type="bibr" rid="B22">Fu and Xu, 2018</xref>). <xref ref-type="bibr" rid="B35">Hu and Luo (2014)</xref> investigated large classes in two cities in Guangxi Province and found that large classes were more abundant in middle and high schools than in primary schools; the number of students in the largest class was 103. Therefore, some classes make it difficult for teachers to be familiar with each student&#x2019;s parents in China. <xref ref-type="bibr" rid="B80">Yang (2006)</xref> found 45.2% of parents contacted teachers when their children fell behind, 19.4% of whom contacted the teacher when their children exhibited problem behavior, while 13.7% took the initiative to communicate with teachers only when the children had special conditions (such as sickness, incomprehension of fees, opinions on teaching methods, and corporal punishment). Thus, the current results also highlight the inequity of education resources, especially the human resources of teachers, in middle schools.</p>
</sec>
</sec>
<sec id="S5">
<title>Practical implication</title>
<p>We found the parent-teacher relationship has a carry-over impact on middle school students&#x2019; academic achievements both at the parent-child dyad level and at the class level. It&#x2019;s important to take measures to promote the parent-teacher relationship for middle school students. First, teachers should develop an equal dialogue with parents and guide parents to take the initiative to participate in school education. It&#x2019;s critical to express welcome and affirmation for parents&#x2019; involvement and avoid parents having fear of communication with teachers. Second, parents should expand the communication channels with teachers, including the participation in school activities, volunteer activities, and so on. Third, the schools should provide a creative, open, inclusive atmosphere to attract parents to participate in the children&#x2019;s education and timely communication with the school about the student&#x2019;s important performance. Promote the healthy interaction between parents and teachers to form a habit and even become a part of the school culture.</p>
</sec>
<sec id="S6">
<title>Limitations and future research directions</title>
<p>Some limitations of this research should be noted. First, the results concerning ethnicity should be interpreted with caution, as all minorities were treated as one group. Second, the data only covered students in seventh grade, and the influence of the parent-teacher relationship may be different for students in other grades (<xref ref-type="bibr" rid="B20">Fan, 2021</xref>). With the increase of grade, children&#x2019;s autonomy gradually improves, and their openness to parents&#x2019; opinions gradually decreases, resulting in a decline in the influence of parental involvement on middle school children (<xref ref-type="bibr" rid="B23">Gao, 2016</xref>).</p>
<p>To address these issues, future research should attempt to compare the differences in the influence of parent-teacher relationships in different grades. Moreover, with the emphasis on students&#x2019; comprehensive quality development in China, students&#x2019; development is not limited to academic success but also career and social development. Thus, future studies are needed to examine the impact of the parent-teacher partnership on other cognitive, behavioral, and social outcomes as well as the linking mechanisms among Chinese students.</p>
</sec>
<sec id="S7" sec-type="data-availability">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="S8">
<title>Ethics statement</title>
<p>Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent from the patients/participants was not required to participate in this study in accordance with the national legislation and the institutional requirements.</p>
</sec>
<sec id="S9">
<title>Author contributions</title>
<p>WF conceived the study, conducted the analysis, took the lead on drafting the manuscript and revised it critically for important intellectual content. QP analyzed the data and revised it critically for important intellectual content. YY contributed to the design of the work and wrote the draft of the manuscript. GC interpreted data for the work and wrote the draft of the manuscript. All authors gave final approval of the version to be published and agree to be accountable of all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.</p>
</sec>
</body>
<back>
<sec id="S10" sec-type="funding-information">
<title>Funding</title>
<p>This research was funded by Grant No. 20YJC880015 from the Department of Social Sciences, Ministry of Education, China.</p>
</sec>
<sec id="S11" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="S12" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<fn-group>
<fn id="footnote1">
<label>1</label>
<p>Parent-child dyad refers to the pairing of a child with his/her parents.</p></fn>
</fn-group>
<ref-list>
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