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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Educ.</journal-id>
<journal-title>Frontiers in Education</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Educ.</abbrev-journal-title>
<issn pub-type="epub">2504-284X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/feduc.2023.1208854</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Education</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Tiers 1 and 2 of a German MTSS: impact of a multiple baseline study on elementary school students with disruptive behavior</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Nitz</surname>
<given-names>Jannik</given-names>
</name>
<xref rid="c001" ref-type="corresp"><sup>&#x002A;</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/1924364/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hagen</surname>
<given-names>Tobias</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Krull</surname>
<given-names>Johanna</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1124989/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Verbeck</surname>
<given-names>Leonie</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Eiben</surname>
<given-names>Katrin</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hanisch</surname>
<given-names>Charlotte</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hennemann</surname>
<given-names>Thomas</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1119863/overview"/>
</contrib>
</contrib-group>
<aff><institution>Department of Special Education and Rehabilitation, Faculty of Human Sciences, University of Cologne</institution>, <addr-line>Cologne</addr-line>, <country>Germany</country></aff>
<author-notes>
<fn id="fn0001" fn-type="edited-by">
<p>Edited by: Melissa Christine Davis, Edith Cowan University, Australia</p>
</fn>
<fn id="fn0002" fn-type="edited-by">
<p>Reviewed by: Carolyn Gentle-Genitty, Indiana University Bloomington, United States; Sarah Kiefer, University of South Florida, United States</p>
</fn>
<corresp id="c001">&#x002A;Correspondence: Jannik Nitz, <email>jannik.nitz@uni-koeln.de</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>30</day>
<month>06</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>8</volume>
<elocation-id>1208854</elocation-id>
<history>
<date date-type="received">
<day>19</day>
<month>04</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>19</day>
<month>06</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2023 Nitz, Hagen, Krull, Verbeck, Eiben, Hanisch and Hennemann.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Nitz, Hagen, Krull, Verbeck, Eiben, Hanisch and Hennemann</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>Introduction</title>
<p>The prevalence of disruptive behavior is increasing worldwide, affecting the learning process and classroom climate, teacher&#x2013;student relationships, and peer interactions. Disruptive behavior in childhood can have detrimental effects on a child&#x2019;s long-term growth and may predict similar behavior in adolescence and adulthood. Thus, it is not only contemporary education and school research that are concerned with addressing the issues of teacher workload reduction and improvement of students&#x2019; learning environment, but it is also a socially relevant issue. The Multi-tiered Systems of Supports (MTSS) effectively mitigates some of these challenges in the education system and is recognized as a successful framework.</p>
</sec>
<sec>
<title>Methods</title>
<p>Therefore, this single-case study examined the first two tiers of an MTSS developed in Germany (Multimo) to determine the impact of its implementation on 32 students with disruptive behavior. The first hypothesis propose that the implementation of Tier 1 can effectively decrease disruptive behavior among all students and the second one that assigning students to Tier 2 can provide an additional reduction in disruptive behavior. Data analysis included multilevel analyses with piecewise-multilevel models and the overlap index, the Nonoverlap of All Pairs, based on teachers&#x2019; direct behavior rating. All analyses focused exclusively on the outcome variable of disruptive behavior, which was estimated based on teachers&#x2019; daily behavior ratings.</p>
</sec>
<sec>
<title>Results</title>
<p>The results of the study showed a significant reduction of disruptive behavior in elementary school students at Tier 1. Disruptive behavior decreased at Tier 2 as well but did not show a significant change compared with Tier 1.</p>
</sec>
<sec>
<title>Discussion</title>
<p>The study concludes that in the context of an MTSS, the Good Behavior Game and Daily Behavior Report Card can be used together.</p>
</sec>
</abstract>
<kwd-group>
<kwd>MTSS</kwd>
<kwd>single-case study</kwd>
<kwd>multi-level analyses</kwd>
<kwd>disruptive behavior</kwd>
<kwd>elementary school</kwd>
<kwd>SWPBS</kwd>
<kwd>good behavior game</kwd>
<kwd>daily behavior report card</kwd>
</kwd-group>
<contract-num rid="cn1">491454339</contract-num>
<contract-sponsor id="cn1">German Research Foundation<named-content content-type="fundref-id">10.13039/501100001659</named-content></contract-sponsor>
<counts>
<fig-count count="3"/>
<table-count count="4"/>
<equation-count count="0"/>
<ref-count count="93"/>
<page-count count="13"/>
<word-count count="10856"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Educational Psychology</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="sec1" sec-type="intro">
<label>1.</label>
<title>Introduction</title>
<p>One of the main concerns of teachers in different types of schools is low-disruption teaching and the associated development of action knowledge around appropriate interventions to address problem behavior (<xref ref-type="bibr" rid="ref52">Liaupsin and Scott, 2007</xref>; <xref ref-type="bibr" rid="ref73">Ruiz-Olivares et al., 2010</xref>; <xref ref-type="bibr" rid="ref35">Herman et al., 2017</xref>). Additionally, the expression of disruptive behavior in childhood can have negative effects on the child&#x2019;s long-term development and predict disruptive behavior in adolescence and adulthood (<xref ref-type="bibr" rid="ref22">Fergusson et al., 2005</xref>; <xref ref-type="bibr" rid="ref54">Loeber et al., 2009</xref>; <xref ref-type="bibr" rid="ref10">Bradshaw et al., 2010</xref>). Therefore, behavioral problems that significantly disrupt teaching are been topics of pedagogical practice and research for a long time (<xref ref-type="bibr" rid="ref70">Reed et al., 1998</xref>).</p>
<p>Furthermore, disruptive behavior in childhood has negative effects on a society&#x2019;s overall system of functioning (<xref ref-type="bibr" rid="ref16">Cohen, 1998</xref>; <xref ref-type="bibr" rid="ref9">Boldrini et al., 2023</xref>; <xref ref-type="bibr" rid="ref82">Tehrani et al., 2023</xref>). For this reason, the reduction is not only a concern for teachers and parents but also has political and economic dimensions (<xref ref-type="bibr" rid="ref72">Rivenbark et al., 2018</xref>). In this context, teachers are also required to have increased knowledge of dealing with disruptive behavior of students.</p>
<p>Addressing disruptive behavior in schools and designing a systematic environment to reduce such behavior are key areas of school research (<xref ref-type="bibr" rid="ref1">Adamson et al., 2019</xref>; <xref ref-type="bibr" rid="ref93">Zuniga and Cividini-Motta, 2021</xref>; <xref ref-type="bibr" rid="ref75">Serrano et al., 2023</xref>). Part of this field is the investigation of the interplay between school interventions and the effects of implementing systemic school concepts. It receives significant international attention and is backed by robust research results (<xref ref-type="bibr" rid="ref70">Reed et al., 1998</xref>; <xref ref-type="bibr" rid="ref59">O'connor and Hayes, 2020</xref>; <xref ref-type="bibr" rid="ref29">Gagnon et al., 2022</xref>; <xref ref-type="bibr" rid="ref9">Boldrini et al., 2023</xref>). However, a challenge lies in the fact that the research designs of many studies cannot accurately trace the exact developmental trajectories of individual students, which can be better accomplished through single-case studies (<xref ref-type="bibr" rid="ref89">Wilbert et al., 2022</xref>). Tracking specific developmental trajectories offers advantages, particularly for students with disruptive behaviors, as it enables more assessment of the effectiveness and timing of interventions (<xref ref-type="bibr" rid="ref53">Lipien et al., 2023</xref>). Therefore, it is important, from political, social, and societal perspectives, to explore the impact of different school interventions and their application on students in terms of disruptive behavior.</p>
</sec>
<sec id="sec2">
<label>2.</label>
<title>Students&#x2019; disruptive behavior</title>
<p>Disruptive behavior is an umbrella term for different externalizing behaviors. It refers to actions or behaviors that interfere with the normal functioning of a group of students, and can assume multiple forms, including verbal outbursts, physical aggression, or refusal to follow rules or guidelines (<xref ref-type="bibr" rid="ref52">Liaupsin and Scott, 2007</xref>). It is often viewed as a problem in educational settings, where it can impede the learning process for both the individual exhibiting the behavior and their classmates (<xref ref-type="bibr" rid="ref24">Fossum et al., 2008</xref>; <xref ref-type="bibr" rid="ref54">Loeber et al., 2009</xref>). Disruptive behaviors negatively impact the classroom climate (<xref ref-type="bibr" rid="ref69">Reaves et al., 2018</xref>), teachers&#x2019; social relationship with the class (<xref ref-type="bibr" rid="ref17">Cui, 2022</xref>), and peer to peer interactions (<xref ref-type="bibr" rid="ref6">Barth et al., 2004</xref>). Disruptive behavior in elementary schools poses significant challenges as it hinders learning (<xref ref-type="bibr" rid="ref55">Lopez Jimenez et al., 2016</xref>; <xref ref-type="bibr" rid="ref74">Schmerse and Zitzmann, 2021</xref>), creates conflicts among students (<xref ref-type="bibr" rid="ref92">Yamasaki and Nishida, 2009</xref>; <xref ref-type="bibr" rid="ref48">Krause et al., 2021</xref>), and disrupts relationships (<xref ref-type="bibr" rid="ref37">Horn et al., 2021</xref>). It also results in missed instruction and difficulties for teachers in managing behavior and resources, impacting both educators and students. Addressing disruptive behavior early is crucial to prevent long-term social and academic difficulties (<xref ref-type="bibr" rid="ref88">Whitten, 2009</xref>; <xref ref-type="bibr" rid="ref82">Tehrani et al., 2023</xref>).</p>
<p>Approximately 5.7% of children and adolescents worldwide exhibit disruptive behavior (<xref ref-type="bibr" rid="ref65">Polanczyk et al., 2015</xref>) and the estimated prevalence has been increasing (<xref ref-type="bibr" rid="ref4">Barkmann and Schulte-Markwort, 2012</xref>; <xref ref-type="bibr" rid="ref45">Klasen et al., 2017</xref>; <xref ref-type="bibr" rid="ref40">Husky et al., 2018</xref>; <xref ref-type="bibr" rid="ref46">Klipker et al., 2018</xref>; <xref ref-type="bibr" rid="ref68">Ravens-Sieberer et al., 2022</xref>). Additionally, studies in many Western countries have reported significant emotional stress on teachers (<xref ref-type="bibr" rid="ref60">Ozamiz-Etxebarria et al., 2021</xref>; <xref ref-type="bibr" rid="ref2">Agyapong et al., 2022</xref>). The effects of disruptive behavior on teacher health can, therefore, be inferred based on a similar development of prevalence statistics and empirical school research (<xref ref-type="bibr" rid="ref47">Kokkinos et al., 2005</xref>; <xref ref-type="bibr" rid="ref64">Pines and Keinan, 2005</xref>; <xref ref-type="bibr" rid="ref35">Herman et al., 2017</xref>).</p>
</sec>
<sec id="sec3">
<label>3.</label>
<title>Multi-tiered support for students with disruptive behavior</title>
<p>In this context, the leading approach to address disruptive behaviors is the Multi-tiered System of Supports (MTSS) (<xref ref-type="bibr" rid="ref71">Reynolds, 1962</xref>; <xref ref-type="bibr" rid="ref76">Simonsen et al., 2021</xref>; <xref ref-type="bibr" rid="ref2">Agyapong et al., 2022</xref>). A key feature of this framework is the use of multiple interventions to effectively address and reduce the occurrence of the targeted behavior (<xref ref-type="bibr" rid="ref7">Batsche, 2014</xref>). The explicit design of MTSS concepts varies internationally by school and education system (<xref ref-type="bibr" rid="ref78">Steed et al., 2014</xref>; <xref ref-type="bibr" rid="ref57">Nelen et al., 2020</xref>). Tiered prevention was first developed in the 1950s to address public health concerns (<xref ref-type="bibr" rid="ref41">Institute of Medicine Committee on Prevention of Mental Disorders, 1994</xref>). Presently, they are widely adopted because they do not provide merely a one-dimensional answer and seek to link different areas of school support (<xref ref-type="bibr" rid="ref27">Gage et al., 2018</xref>; <xref ref-type="bibr" rid="ref15">Charlton et al., 2021</xref>). They are essentially characterized by an attempt to align a student&#x2019;s problem areas with the interventions of the approach. The MTSS, depending on their origin and design, can target student behaviors or academic achievement, that is, academic learning. Both may be supported depending on the school&#x2019;s format or resources (<xref ref-type="bibr" rid="ref25">Fox et al., 2021</xref>).</p>
<p>The MTSS usually comprises three tiers (<xref ref-type="bibr" rid="ref79">Stoiber and Gettinger, 2016</xref>): Initially, it reaches all students at the first tier. Support is implemented here for the benefit of all students. If students continue to exhibit problem behavior despite universal support, they are moved to the second tier. This tier is characterized by the fact that approximately 10&#x2013;15% of the students in a class receive another appropriate intervention as support in achieving the target behavior (<xref ref-type="bibr" rid="ref38">Huber, 2013</xref>). For this, the target behavior must first be determined, which is accompanied by a diagnostic process. If an identified at-risk student does not exhibit any change in behavior, he or she is moved to the third tier. Here, another 1&#x2013;5% of the students receive an intervention to further reduce the problem behavior. These interventions are often systemic and can also include external support networks (<xref ref-type="bibr" rid="ref20">Eagle et al., 2015</xref>).</p>
<p>However, all applied interventions of the MTSS should be evidence-based in terms of theory (<xref ref-type="bibr" rid="ref79">Stoiber and Gettinger, 2016</xref>; <xref ref-type="bibr" rid="ref76">Simonsen et al., 2021</xref>). In addition, the diagnostic process and teamwork are important components of the MTSS. Many studies and systematic reviews have demonstrated the effectiveness of the MTSS on different target variables, such as self-efficacy (e.g., <xref ref-type="bibr" rid="ref77">Skinner et al., 2014</xref>), stress experience, and behavioral (e.g., <xref ref-type="bibr" rid="ref56">Majeika et al., 2020</xref>) and learning-related effects (e.g., <xref ref-type="bibr" rid="ref28">Gage et al., 2015</xref>) on students. Additionally, positive effects on variables other than disruptive behavior (<xref ref-type="bibr" rid="ref59">O'connor and Hayes, 2020</xref>), such as school or classroom climate (<xref ref-type="bibr" rid="ref15">Charlton et al., 2021</xref>), and internalizing behavior problems (<xref ref-type="bibr" rid="ref87">Weist et al., 2018</xref>) can be derived from different studies.</p>
</sec>
<sec id="sec4">
<label>4.</label>
<title>Good behavior game and daily behavior report card as MTSS interventions related to disruptive behavior</title>
<p>The MTSS with a focus on behavioral issues (MTSS-B) would typically include interventions such as support for positive behavior, social skills training, and individualized behavior plans (<xref ref-type="bibr" rid="ref11">Briesch et al., 2019</xref>). These interventions may emphasize reducing disruptive behavior and promoting positive behavior in the classroom.</p>
<p>One of these potential tier-one interventions is the Good Behavior Game (GBG) (<xref ref-type="bibr" rid="ref5">Barrish et al., 1969</xref>). It is a widely used and well-researched classroom-wide intervention that employs positive reinforcement to promote positive behavior and reduce disruptive behavior (<xref ref-type="bibr" rid="ref42">Joslyn et al., 2019</xref>). The standard arrangement of the GBG involves dividing a class into teams, setting rules, and implementing an interdependent group contingency to encourage students to follow the rules. Points (also called fouls) are given to teams each time a member breaks a rule, and rewards are given to teams with the lowest points (fouls). This approach, along with variations, has been extensively studied. The GBG reduces disruptive behavior and inattention in children with psychiatric disorders, as demonstrated in several single-case studies by <xref ref-type="bibr" rid="ref30">Groves and Austin (2017)</xref>, <xref ref-type="bibr" rid="ref43">Joslyn and Vollmer (2020)</xref>, and <xref ref-type="bibr" rid="ref19">Donaldson et al. (2017)</xref>. Another single-case study by <xref ref-type="bibr" rid="ref63">Pennington and McComas (2017)</xref> demonstrated improvement in on-task behavior in children with attention problems. <xref ref-type="bibr" rid="ref31">Groves and Austin (2019)</xref> also reported reduction in negative peer interactions in students with psychiatric disorders during play.</p>
<p>The positive effect on students (with behavioral problems) has been recently demonstrated in the form of single-case studies in Germany (<xref ref-type="bibr" rid="ref51">Leidig et al., 2022</xref>; <xref ref-type="bibr" rid="ref32">Hagen et al., 2023</xref>). <xref ref-type="bibr" rid="ref51">Leidig et al. (2022)</xref> show significant higher effects of the GBG for students exhibiting disruptive problem behavior. In addition, <xref ref-type="bibr" rid="ref32">Hagen et al. (2023)</xref> indicate that the GBG mitigates students&#x2019; disruptive behavior over the school day and not only after playing the GBG in class. Both studies were conducted in German inclusive primary schools and involved approximately 20&#x2013;30 students. However, research on the GBG with students who have emotional and behavioral disorder (EBD) diagnoses and histories of delinquency is still limited (<xref ref-type="bibr" rid="ref43">Joslyn and Vollmer, 2020</xref>).</p>
<p>Second-tier interventions such as the Daily Behavior Report Card (DBRC) (<xref ref-type="bibr" rid="ref85">Volpe et al., 2013</xref>) are implemented to improve positive behavior or reduce disruptive behavior (<xref ref-type="bibr" rid="ref11">Briesch et al., 2019</xref>). The DBRC is a commonly used intervention to document and provide feedback on student behavior. It includes a clear target behavior, a scale for periodic judgment, a daily monitoring system, and communication between the student&#x2019;s teacher and home. The DBRCs are differentiated from other forms of behavior ratings in terms of their summative rating and emphasis on feedback. Studies have shown that the DBRCs are efficient and effective in improving academic skills and addressing behavioral issues (<xref ref-type="bibr" rid="ref83">Vannest et al., 2010</xref>). To use evidence-based methods, educators seek efficient techniques to address student behaviors, and the DBRCs offer flexibility in implementation with minimal interruption to instructional time. A meta-analysis by <xref ref-type="bibr" rid="ref67">Pyle and Fabiano (2017)</xref> comprising 40 single-case studies demonstrated the efficacy of the DBRC as an intervention for students with Attention Deficit Hyperactivity Disorder (ADHD). The study suggests that the use of higher-quality designs and special education classroom settings can lead to a more rapid and effective behavioral change. Based on these findings, school psychologists, special educators, and clinicians are highly recommended to incorporate the DBRCs in their approach to address on-task and disruptive behavior of children with ADHD.</p>
<p>Both interventions, the GBG and DBRC, are effective in reducing disruptive behavior and promoting positive behavior in the classroom. Their combination within the MTSS has been conceptualized for the German-speaking region but has not yet been evaluated (<xref ref-type="bibr" rid="ref33">Hanisch et al., 2019</xref>).</p>
</sec>
<sec id="sec5">
<label>5.</label>
<title>Research questions and hypotheses</title>
<p>As shown disruptive behavior is an increasingly prevalent issue in the Western school environment. Although there are many educational strategies to address disruptive behavior, the MTSS has been found to be effective in reducing such behavior and involving multiple stakeholders to address school-wide issues. However, further research is required to determine the effectiveness of different interventions within the context of the MTSS. The GBG and DBRC have been identified as potential interventions that may be well-suited for use within the MTSS. The interaction of these different tiers within an MTSS in Germany appears to be novel in the context of research and innovative along the theoretical concept of MTSS in Germany (<xref ref-type="bibr" rid="ref33">Hanisch et al., 2019</xref>). Often, studies remain rather superficial regarding the effectiveness of different interventions or the interaction of the different tiers within an MTSS. Furthermore, a review by <xref ref-type="bibr" rid="ref50">Lee and Gage (2020)</xref> also demonstrated the effectiveness of tiered support in relation to student behavior. This leads to the assumption that it seems to make sense to integrate behavior modification measures into an MTSS and to investigate the outcome regarding disruptive behavior. Therefore, the first question is about testing the effectiveness of the GBG in reducing the disruptive behavior embedded in the MTSS at the first tier.</p>
<disp-quote>
<p><italic>RQ1</italic>: To what extent is the disruptive behavior reduced after the implementation of the Good Behavior Game at Tier 1?</p>
</disp-quote>
<p>Based on RQ1, testing Tier 2 compared to Tier 1 seems reasonable. Presently, there are few comparable studies using single-case studies to test the effects of Tiers 1 and 2 on disruptive behavior. This leads to the second research question.</p>
<disp-quote>
<p><italic>RQ2</italic>: What is the impact of the assignment to Tier 2 on the development of disruptive behavior compared with Tier 1?</p>
</disp-quote>
<p>Based on the formulated questions, the following hypotheses can be derived, which form the basis of this study for the evaluation.</p>
<p>Hypotheses (H):</p>
<disp-quote>
<p><italic>H1</italic>: The Good Behavior Game reduces the disruptive behavior of students exhibiting disruptive behavior.</p>
</disp-quote>
<disp-quote>
<p><italic>H2</italic>: Assigning students to Tier 2 can further reduce students&#x2019; disruptive behavior.</p>
</disp-quote>
</sec>
<sec id="sec6">
<label>6.</label>
<title>The conceptual basis for this study: Multimo Tiers 1 and 2</title>
<p>The conceptual basis for this study is a German MTSS called <italic>Multimo</italic> (<xref ref-type="bibr" rid="ref33">Hanisch et al., 2019</xref>), which was implemented at several elementary schools in the state of North Rhine-Westphalia in 2021 and 2022. It is an approach that makes teachers, parents, students, and school social workers part of the support, and thus, works in a multimodal manner. At the first tier, the GBG (e.g., <xref ref-type="bibr" rid="ref5">Barrish et al., 1969</xref>) was implemented, and at the second tier, the DBRC (e.g., <xref ref-type="bibr" rid="ref85">Volpe et al., 2013</xref>) was implemented in addition to the GBG. The third tier intervention is the SCEP Coaching (Schulbasiertes Coaching bei Kindern mit expansivem Problemverhalten, <xref ref-type="bibr" rid="ref34">Hanisch et al., 2018</xref>), which is not part of this evaluation. The implementation was scientifically accompanied and evaluated based on a single-case study.</p>
<sec id="sec7">
<label>6.1.</label>
<title>Tier 1</title>
<p>The first tier comprises the implementation of the GBG, which reaches all students in the class at the universal level. As the Tier 1 intervention, the GBG is a classroom-based intervention that uses mutual dependence of students to promote appropriate behavior in the class (<xref ref-type="bibr" rid="ref5">Barrish et al., 1969</xref>). This well-researched intervention is considered effective in reducing disruptive behavior and building positive school experiences. <xref ref-type="bibr" rid="ref23">Flower et al. (2014)</xref> identified 22 peer-reviewed articles evaluating the effectiveness of the GBG in reducing disruptive student behavior and enhancing learning. Results from two longitudinal studies showed the GBG&#x2019;s positive impact on health-related dimensions in primary school-aged boys with aggressive behavior. The average intervention effect was <italic>d</italic>&#x2009;=&#x2009;0.50, with a significant and immediate reduction in challenging behavior (&#x2212;20.38%, <italic>p</italic>&#x2009;&#x003C;&#x2009;0.01) after the GBG&#x2019;s introduction. Additionally, it improved social integration and peer acceptance/rejection. A meta-analysis by <xref ref-type="bibr" rid="ref14">Chaffee et al. (2017)</xref> confirmed its effectiveness in supporting student behavior in regular schools. In this study, it was implemented for all students according to the concept at the first tier.</p>
<p>Students in a pre-defined small group receive rewards when they achieve previously defined behavioral goals together. Key features of the intervention include: (1) selection of goals and rules, identification of rule violations, (2) definition of rewards, (3) division of students into two or more teams during a time-defined game phase, (4) use of prompts for rule violations during the game phase, and (5) daily and weekly reward for teams with the fewest rule violations (<xref ref-type="bibr" rid="ref44">Joslyn et al., 2014</xref>; <xref ref-type="bibr" rid="ref49">Lastrapes, 2014</xref>). It, therefore, uses cognitive-behavioral strategies to reduce disruptive behaviors in class and positively reinforce appropriate behaviors. The team aspect also supports mutual support among students in adhering to rules.</p>
<p>The teachers were prepared for the implementation of the GBG in the form of full-day training by the moderators. All open questions regarding the implementation and application were satisfactorily addressed. The university and the facilitators were available for weekly reflection meetings during the implementation, and these were used as required.</p>
</sec>
<sec id="sec8">
<label>6.2.</label>
<title>Tier 2</title>
<p>In the second tier, the teachers also received training from the moderators and social workers. For the teachers, the DBRC was elaborated so that they could subsequently use it for the students who did not sufficiently benefit from the GBG in Tier 1.</p>
<p>Thereafter, the DBRC was implemented according to its original design, which has been proven to be an effective intervention for students in the school setting. The DBRC is a feedback form that uses a rating scale and point system to assess the student&#x2019;s behavior according to specific goals (<xref ref-type="bibr" rid="ref81">Taylor and Hill, 2017</xref>). Its key components include the identification of target behaviors, daily assessment of their occurrence, and regular report-sharing with relevant individuals, such as parents, teachers, and students (<xref ref-type="bibr" rid="ref83">Vannest et al., 2010</xref>). A teacher acts as the implementer and sets a point goal with the student, allowing them to choose a reward if the goal is achieved within a predetermined period (e.g., 30&#x2009;min, a class period, a day, or a week). At the end of this period, the teacher and student review the DBRC, and the latter receives performance feedback and reinforcement if the goal is met. The DBRCs motivate desirable behavior through reinforcement and indirectly reduce disruptive behavior by not providing consequences for it (<xref ref-type="bibr" rid="ref85">Volpe et al., 2013</xref>).</p>
<p>Teachers&#x2019; behavioral goals and agreements with parents and the community were determined on an individual basis and fed back to the university team or facilitators as required. In this manner, the DBRC was implemented in different schools. Additionally, the necessary freedom in the design of the measures and their fit to the students and the environment could be achieved. The DBRC was administered to at-risk children in this sample throughout the period in addition to the GBG. Student behavioral goals were adjusted as required in this process.</p>
</sec>
</sec>
<sec id="sec9" sec-type="method">
<label>7.</label>
<title>Method</title>
<sec id="sec10">
<label>7.1.</label>
<title>Participants and setting</title>
<p>The sample of this single-case study comprised 29 first- and second-grade students of 12 classes at 18 inclusive elementary schools in the federal state of North Rhine-Westphalia (<xref rid="tab1" ref-type="table">Table 1</xref>). The different schools had three to five classes per grade and are located in a rural but urban-adjacent area. The students were selected by teachers based on their disruptive problems. The teachers were asked to identify the three most striking children in the class. The parents and students provided their consent to participate in the study and were informed about the study objectives as well as the interventions involved.</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption>
<p>Descriptive data for all 29 cases.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Case</th>
<th align="center" valign="top">Class</th>
<th align="center" valign="top">Gender</th>
<th align="center" valign="top">Age</th>
<th align="center" valign="top">ITRF<sub>APP</sub></th>
<th align="center" valign="top">ITRF<sub>DOB</sub></th>
<th align="center" valign="top">ITRF<sub>Total</sub></th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">C1</td>
<td align="center" valign="top">a</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">4</td>
<td align="center" valign="top">17</td>
</tr>
<tr>
<td align="left" valign="top">C2</td>
<td align="center" valign="top">a</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">17</td>
<td align="center" valign="top">4</td>
<td align="center" valign="top">21</td>
</tr>
<tr>
<td align="left" valign="top">C3</td>
<td align="center" valign="top">b</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">18</td>
</tr>
<tr>
<td align="left" valign="top">C4</td>
<td align="center" valign="top">b</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">4</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">9</td>
</tr>
<tr>
<td align="left" valign="top">C5</td>
<td align="center" valign="top">c</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">11</td>
</tr>
<tr>
<td align="left" valign="top">C6</td>
<td align="center" valign="top">c</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">15</td>
</tr>
<tr>
<td align="left" valign="top">C7</td>
<td align="center" valign="top">c</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">14</td>
</tr>
<tr>
<td align="left" valign="top">C8</td>
<td align="center" valign="top">d</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">12</td>
</tr>
<tr>
<td align="left" valign="top">C9</td>
<td align="center" valign="top">e</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">12</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">13</td>
</tr>
<tr>
<td align="left" valign="top">C10</td>
<td align="center" valign="top">e</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">17</td>
<td align="center" valign="top">22</td>
</tr>
<tr>
<td align="left" valign="top">C11</td>
<td align="center" valign="top">f</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">17</td>
<td align="center" valign="top">30</td>
</tr>
<tr>
<td align="left" valign="top">C12</td>
<td align="center" valign="top">f</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">11</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">29</td>
</tr>
<tr>
<td align="left" valign="top">C13</td>
<td align="center" valign="top">f</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">19</td>
<td align="center" valign="top">16</td>
<td align="center" valign="top">35</td>
</tr>
<tr>
<td align="left" valign="top">C14</td>
<td align="center" valign="top">g</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">10</td>
<td align="center" valign="top">18</td>
</tr>
<tr>
<td align="left" valign="top">C15</td>
<td align="center" valign="top">g</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">6</td>
</tr>
<tr>
<td align="left" valign="top">C16</td>
<td align="center" valign="top">g</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">10</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">12</td>
</tr>
<tr>
<td align="left" valign="top">C17</td>
<td align="center" valign="top">h</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">12</td>
</tr>
<tr>
<td align="left" valign="top">C18</td>
<td align="center" valign="top">h</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">13</td>
</tr>
<tr>
<td align="left" valign="top">C19</td>
<td align="center" valign="top">h</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">10</td>
<td align="center" valign="top">13</td>
</tr>
<tr>
<td align="left" valign="top">C20</td>
<td align="center" valign="top">i</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">22</td>
<td align="center" valign="top">21</td>
<td align="center" valign="top">43</td>
</tr>
<tr>
<td align="left" valign="top">C21</td>
<td align="center" valign="top">i</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">13</td>
</tr>
<tr>
<td align="left" valign="top">C22</td>
<td align="center" valign="top">j</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">17</td>
<td align="center" valign="top">35</td>
</tr>
<tr>
<td align="left" valign="top">C23</td>
<td align="center" valign="top">j</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">11</td>
</tr>
<tr>
<td align="left" valign="top">C24</td>
<td align="center" valign="top">j</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">16</td>
<td align="center" valign="top">16</td>
<td align="center" valign="top">32</td>
</tr>
<tr>
<td align="left" valign="top">C25</td>
<td align="center" valign="top">k</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">11</td>
</tr>
<tr>
<td align="left" valign="top">C26</td>
<td align="center" valign="top">k</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">16</td>
</tr>
<tr>
<td align="left" valign="top">C27</td>
<td align="center" valign="top">k</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">14</td>
<td align="center" valign="top">14</td>
<td align="center" valign="top">28</td>
</tr>
<tr>
<td align="left" valign="top">C28</td>
<td align="center" valign="top">l</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">0</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">15</td>
</tr>
<tr>
<td align="left" valign="top">C29</td>
<td align="center" valign="top">l</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">10</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">12</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>ITRF APP, ITRF Academic Productivity/Disorganization sub-scale (cut off&#x2009;&#x2265;&#x2009;9); ITRF DOB, Oppositional/Disruptive sub-scale (cut off&#x2009;&#x2265;&#x2009;4); ITRG Total, ITRF Total Score (cut off&#x2009;&#x2265;&#x2009;11).</p>
</table-wrap-foot>
</table-wrap>
<p>Based on teacher ratings, all 29 nominated students (100%) exhibited disruptive risks on either the total scale or the disruptive behavior scale. The risk assessment was based on the total score of the Integrated Teacher Rating (ITRF, <xref ref-type="bibr" rid="ref13">Casale et al., 2018</xref>) with a cut-off score of &#x2265;11, the <italic>Oppositional/Disruptive</italic> sub-scale with a cut-off score of &#x2265;4, and the <italic>Academic Productivity/Disorganization</italic> sub-scale with a cut-off score of &#x2265;9, following the manual outlined in more detail in Chapter 7.3.1. Most students (93%) in the sample were male (27) and only two students were female (7%). The average age of the students was 7.14&#x2009;years (SD&#x2009;=&#x2009;0.516, median&#x2009;=&#x2009;7) and the age range was 6&#x2013;8&#x2009;years.</p>
</sec>
<sec id="sec11">
<label>7.2.</label>
<title>Implementation</title>
<sec id="sec12">
<label>7.2.1.</label>
<title>The multiplier concept</title>
<p>To implement the MTSS in elementary schools, a multiplier concept was established, which included three stages of professionalization. First, a group of 18 experienced (special education) teachers and school administrators were trained by university staff. These 18 so-called moderators subsequently trained the school staff regarding the implementation of the MTSS and accompanied this process throughout the entire survey period. In full-day training sessions (approximately five full days), the concept of tiered support, individual interventions, and the diagnostic methodology formed the content of the qualification at the schools. The process included weekly exchange meetings with the moderators and the university project team. The implementation of the interventions in the schools was continuously discussed. Similar train-the-trainer concepts have proven to be economical and effective for the dissemination of training content and for monitoring (<xref ref-type="bibr" rid="ref62">Pearce et al., 2012</xref>). They have also been successfully used in school contexts in German-speaking countries (<xref ref-type="bibr" rid="ref8">Behr et al., 2020</xref>).</p>
</sec>
<sec id="sec13">
<label>7.2.2.</label>
<title>Schedule</title>
<p>The time-frame for the implementation of the interventions and the overall concept was approximately 7 months. Tier 1 was implemented in early December 2021; Tier 2 in late January 2022; and Tier 3 in March 2022. Accordingly, the GBG was used for approximately the entire project period (7 months); the DBRC together with the GBG for approximately 5 months; and, in addition, the SCEP Coaching for the last 3 months. The study design impacted the commencement and duration of implementation. This implies that the schools did not commence the interventions simultaneously; the time-gap was as much as 3 weeks (<xref rid="fig1" ref-type="fig">Figure 1</xref>).</p>
<fig position="float" id="fig1">
<label>Figure 1</label>
<caption>
<p>Schedule of the multiple baseline design.</p>
</caption>
<graphic xlink:href="feduc-08-1208854-g001.tif"/>
</fig>
</sec>
</sec>
<sec id="sec14">
<label>7.3.</label>
<title>Design and measures</title>
<sec id="sec15">
<label>7.3.1.</label>
<title>ITRF</title>
<p>To screen children with disruptive behavior pre-selected by teachers, a short version of the German version of the Integrated Teacher Rating Form (ITRF) was used (<xref ref-type="bibr" rid="ref18">Daniels et al., 2014</xref>; <xref ref-type="bibr" rid="ref13">Casale et al., 2018</xref>; <xref ref-type="bibr" rid="ref86">Volpe et al., 2020</xref>). The ITRF is a universal behavior screening tool that focuses on specific behavioral problems in educational settings. Its short version is divided into two sub-scales: <italic>Oppositional/Disruptive,</italic> and <italic>Academic Productivity/Disorganization,</italic> and includes 16 problem-oriented items that assess student behavior in the classroom, such as &#x201C;Does not complete classwork on time,&#x201D; &#x201C;Disrupts others,&#x201D; or &#x201C;Moves around the room.&#x201D; The English ITRF meets common test validity criteria (<xref ref-type="bibr" rid="ref18">Daniels et al., 2014</xref>); it has been translated into German and adapted to the German cultural context (<xref ref-type="bibr" rid="ref13">Casale et al., 2018</xref>).</p>
<p><xref ref-type="bibr" rid="ref13">Casale et al. (2018)</xref> indicated high internal consistency for the oppositional and disruptive behavior (OD) scale (&#x03B1;&#x2009;=&#x2009;0.96) and the academic productivity and disorganization (APP) scale (&#x03B1;&#x2009;=&#x2009;0.95). Temporal stability over 2&#x2013;4 weeks was acceptable with values of <italic>r</italic>&#x2009;=&#x2009;0.88 (APP) and <italic>r</italic>&#x2009;=&#x2009;0.78 (OD). The ITRF also demonstrated convergent validity with the Brief Problem Monitor-Teacher and divergent validity from the internalizing problem scales. Receiver operating characteristic curve analyses showed that the ITRF accurately identifies students at risk. This refers to students who, based on their exhibited behavior, should be assigned to either Tier 2 or Tier 3 within the decision-making process of an MTSS. Teachers have highly rated the ITRF for its perceived accuracy, feasibility, acceptability, and usefulness in informing interventions. In conclusion, the ITRF is a reliable and useful tool for teachers to identify and support students with behavioral issues in the classroom.</p>
</sec>
<sec id="sec16">
<label>7.3.2.</label>
<title>Direct behavior rating</title>
<p>Data were collected using the Direct Behavior Rating (DBR) (<xref ref-type="bibr" rid="ref39">Huber and Rietz, 2015</xref>) with a scale on the extent of disruptive behavior (0&#x2013;10). Disruptive behavior was defined as <italic>Behavior that disrupts class or interferes with other children&#x2019;s learning. Examples: shouting in the class, fooling around, inappropriate side talk, or not staying in one&#x2019;s seat.</italic> Along with this definition, teachers filled out the DBR. The definition was visible on the top of the DBR.</p>
<p>The DBR is a combination of systematic observation and rating and is deemed suitable for capturing detailed behavioral processes in the context of single-case studies because of its cost-effectiveness and versatility. It assessed behavior at a specific time during the school day. <xref ref-type="bibr" rid="ref39">Huber and Rietz (2015)</xref> conducted a comprehensive analysis of its performance. They presented acceptable results regarding the reliability, validity, and accuracy of the instrument, although the results may vary depending on the type of behavior being evaluated and who is conducting the assessment. The study focused on the domain of learning and work behaviors, and the DBR produced reliable results, with an &#x025B;2 and &#x0278; score of &#x2265;0.80, after only four measurements (<xref ref-type="bibr" rid="ref84">Volpe et al., 2012</xref>).</p>
<p>For this study, teachers were instructed to complete the DBR no later than 10&#x2009;min after using the intervention (GBG). During the baseline survey, teachers completed the DBR once a day in comparable situations. The number of times the behavior was assessed varied from 83 to 102. In this manner, data were collected by operationalizing a concrete behavior and evaluating it in a specific scenario, always immediately after an explicitly defined time using rating scales. The disruptive behavior was rated using a Likert scale from zero to 10&#x2014;zero representing low disruptive behavior and 10 indicating high disruptive behavior.</p>
</sec>
<sec id="sec17">
<label>7.3.3.</label>
<title>Single-case study</title>
<p>The single-case study was planned and conducted in a multiple baseline design along the presented schedule (<xref ref-type="bibr" rid="ref80">Swoboda et al., 2010</xref>). For this purpose, the different schools were each given different starting times for the interventions. Consequently, the baseline phases differed from one another. The range of data points in the baseline was 15, 20, and 25. The data were entered conventionally using paper and pencil and the DBRs were prepared in advance by the project team and delivered to the teachers. To ensure that the teachers implemented the multiple baseline design along with the research design, DBRs contained explicit instructions that enabled the identification of the start times of the interventions visually and in writing. In addition, ongoing monitoring of the project team occurred. Thus, it was possible to ensure that the research design could be conveniently integrated into everyday school life.</p>
</sec>
<sec id="sec18">
<label>7.3.4.</label>
<title>Data analysis</title>
<p>Data analysis was conducted regarding interference statistics and descriptive statistics for multilevel analyses for single-case data. This includes piecewise-multilevel-models, measures, mean values, standard deviations, and necessary overlap indices. This form of data collection and analysis is recognized as a high-quality approach in the context of recent empirical interventions and school research. A distinctive feature of single-case studies is the students&#x2019; own reference norm created by the baseline. In addition, the regression-based analyses meet the highest scientific standards, and therefore, offer a high degree of validity (<xref ref-type="bibr" rid="ref89">Wilbert et al., 2022</xref>). The three phases comprised 1,498 measurement time points of all cases combined.</p>
<p>First, the cases were considered individually. For this purpose, the mean values in connection with the Nonoverlap of All Pairs (NAP) for Phases B and C were calculated and evaluated. In this process, the values were compared with their respective previous phases (A vs. B; B vs. C). The NAP (<xref ref-type="bibr" rid="ref61">Parker and Vannest, 2009</xref>) is a commonly used index to estimate the overlap between different phases in single-case studies. To calculate the NAP, we first determine the number of data points that overlap between two phases in a single-case study. Next, we divide this value by the total number of pairs (data points) to obtain an index score between 0 and 1. Higher scores indicate greater nonoverlap, whereas lower scores represent more overlap. Additionally, the NAP considers any outliers or extreme values in the dataset that may affect its accuracy. A value in the range of 50&#x2013;65 is considered a small effect; a value in the range 66&#x2013;92 is considered a moderate effect; and a value over 93 is considered a large effect.</p>
<p>Additionally, piecewise-multilevel-regression analyses were calculated across all cases. In this manner, changes across the entire sample can be identified. Based on the piecewise-multilevel-regression analyses, level and slope effects were calculated. The level effect is an intervention effect that leads to an immediate and constant change in behavior at the beginning of the intervention phase. The slope effect is another intervention effect that continuously develops with the start of the intervention (<xref ref-type="bibr" rid="ref90">Wilbert and Lueke, 2022</xref>). Both were set as fixed effects. R Studio (<xref ref-type="bibr" rid="ref66">Posit-Team, 2022</xref>) was used for all analyses and here the scan package (<xref ref-type="bibr" rid="ref90">Wilbert and Lueke, 2022</xref>) was used.</p>
<p>Owing to the complexity of the research questions and the associated significance, the analyses are limited to the first two tiers of the approach. Accordingly, two models were developed: the first facilitates statements about the GBG effect (Tier 1) as an intervention on the first tier, and the second allows statements about the influence of the assignment of a student to the second tier. For the first model, a multilevel regression was calculated across all cases, comparing the baseline phase with Phase B, that is, the intervention period of the GBG. For Model 2, the disruptive behavior of Phase B was compared with that of Phase C, which is the intervention period of Tier 2. No slope effect was calculated for Model 2 because of the focus on the phase difference from B to C. This was calculated in the form of the level effect from Phase B to C.</p>
</sec>
</sec>
</sec>
<sec id="sec19" sec-type="results">
<label>8.</label>
<title>Results</title>
<sec id="sec20">
<label>8.1.</label>
<title>Descriptive statistics</title>
<p><xref rid="tab2" ref-type="table">Table 2</xref> summarizes the descriptive statistics for disruptive behavior, including the NAP as a measure of effect size (<xref ref-type="bibr" rid="ref3">Alresheed et al., 2013</xref>). The non-rescaled NAP (comparing Phases A and B) values revealed that the dependent variable had effects ranging between 5.13 and 100%. More specifically, 13 participants (44.82%) showed small effects; 15 (51.72%) showed medium effects; and one showed strong effects.</p>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption>
<p>Single-case data with NAP for all 29 cases.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Case</th>
<th align="center" valign="top">n<sub>A</sub></th>
<th align="center" valign="top">n<sub>B</sub></th>
<th align="center" valign="top">n<sub>C</sub></th>
<th align="center" valign="top">mis<sub>A</sub></th>
<th align="center" valign="top">mis<sub>B</sub></th>
<th align="center" valign="top">mis<sub>C</sub></th>
<th align="center" valign="top">M<sub>A</sub> (SD)</th>
<th align="center" valign="top">M<sub>B</sub> (SD)</th>
<th align="center" valign="top">M<sub>C</sub> (SD)</th>
<th align="center" valign="top">NAP<sub>A-</sub><sub>B</sub>&#x002A;</th>
<th align="center" valign="top">NAP<sub>B-</sub><sub>C</sub>&#x002A;</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">C1</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">34</td>
<td align="center" valign="top">11</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">14</td>
<td align="char" valign="top" char="(">3.00 (0.50)</td>
<td align="char" valign="top" char="(">2.48 (1.08)</td>
<td align="char" valign="top" char="(">2.70 (0.98)</td>
<td align="char" valign="top" char=".">68.44</td>
<td align="char" valign="top" char=".">43.40</td>
</tr>
<tr>
<td align="left" valign="top">C2</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">34</td>
<td align="center" valign="top">16</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">17</td>
<td align="char" valign="top" char="(">1.75 (0.96)</td>
<td align="char" valign="top" char="(">1.60 (0.65)</td>
<td align="char" valign="top" char="(">0.47 (0.51)</td>
<td align="char" valign="top" char=".">53.50</td>
<td align="char" valign="top" char=".">88.71</td>
</tr>
<tr>
<td align="left" valign="top">C3</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">1</td>
<td align="char" valign="top" char="(">3.86 (2.88)</td>
<td align="char" valign="top" char="(">4.32 (2.23)</td>
<td align="char" valign="top" char="(">3.31 (1.44)</td>
<td align="char" valign="top" char=".">45.14</td>
<td align="char" valign="top" char=".">69.52</td>
</tr>
<tr>
<td align="left" valign="top">C4</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">2</td>
<td align="char" valign="top" char="(">2.71 (2.58)</td>
<td align="char" valign="top" char="(">2.00 (2.67)</td>
<td align="char" valign="top" char="(">0.29 (0.71)</td>
<td align="char" valign="top" char=".">60.71</td>
<td align="char" valign="top" char=".">69.48</td>
</tr>
<tr>
<td align="left" valign="top">C5</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">13</td>
<td align="char" valign="top" char="(">2.67 (1.97)</td>
<td align="char" valign="top" char="(">2.10 (2.18)</td>
<td align="char" valign="top" char="(">0.18 (0.53)</td>
<td align="char" valign="top" char=".">68.75</td>
<td align="char" valign="top" char=".">89.41</td>
</tr>
<tr>
<td align="left" valign="top">C6</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">12</td>
<td align="center" valign="top">24</td>
<td align="center" valign="top">12</td>
<td align="char" valign="top" char="(">4.67 (2.31)</td>
<td align="char" valign="top" char="(">1.62 (1.26)</td>
<td align="char" valign="top" char="(">1.33 (1.24)</td>
<td align="char" valign="top" char=".">89.58</td>
<td align="char" valign="top" char=".">56.42</td>
</tr>
<tr>
<td align="left" valign="top">C7</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">12</td>
<td align="center" valign="top">21</td>
<td align="center" valign="top">10</td>
<td align="char" valign="top" char="(">5.33 (0.58)</td>
<td align="char" valign="top" char="(">1.26 (1.05)</td>
<td align="char" valign="top" char="(">0.35 (0.49)</td>
<td align="char" valign="top" char=".">100</td>
<td align="char" valign="top" char=".">77.50</td>
</tr>
<tr>
<td align="left" valign="top">C8</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">43</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">32</td>
<td align="center" valign="top">10</td>
<td align="char" valign="top" char="(">6.00 (3.20)</td>
<td align="char" valign="top" char="(">2.38 (2.20)</td>
<td align="char" valign="top" char="(">1.52 (1.89)</td>
<td align="char" valign="top" char=".">81.94</td>
<td align="char" valign="top" char=".">65.91</td>
</tr>
<tr>
<td align="left" valign="top">C9</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">0</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">8</td>
<td align="char" valign="top" char="(">5.04 (1.67)</td>
<td align="char" valign="top" char="(">5.15 (3.36)</td>
<td align="char" valign="top" char="(">4.90 (2.96)</td>
<td align="char" valign="top" char=".">49.63</td>
<td align="char" valign="top" char=".">51.48</td>
</tr>
<tr>
<td align="left" valign="top">C10</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">21</td>
<td align="center" valign="top">15</td>
<td align="char" valign="top" char="(">6.32 (1.39)</td>
<td align="char" valign="top" char="(">4.75 (2.82)</td>
<td align="char" valign="top" char="(">3.00 (3.46)</td>
<td align="char" valign="top" char=".">65.81</td>
<td align="char" valign="top" char=".">73.61</td>
</tr>
<tr>
<td align="left" valign="top">C11</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">22</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">29</td>
<td align="center" valign="top">14</td>
<td align="char" valign="top" char="(">4.17 (1.90)</td>
<td align="char" valign="top" char="(">3.88 (2.06)</td>
<td align="char" valign="top" char="(">4.88 (1.81)</td>
<td align="char" valign="top" char=".">57.03</td>
<td align="char" valign="top" char=".">34.38</td>
</tr>
<tr>
<td align="left" valign="top">C12</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">22</td>
<td align="center" valign="top">10</td>
<td align="center" valign="top">29</td>
<td align="center" valign="top">13</td>
<td align="char" valign="top" char="(">4.87 (2.26)</td>
<td align="char" valign="top" char="(">1.69 (0.87)</td>
<td align="char" valign="top" char="(">2.11 (1.17)</td>
<td align="char" valign="top" char=".">90.21</td>
<td align="char" valign="top" char=".">39.58</td>
</tr>
<tr>
<td align="left" valign="top">C13</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">22</td>
<td align="center" valign="top">11</td>
<td align="center" valign="top">28</td>
<td align="center" valign="top">13</td>
<td align="char" valign="top" char="(">2.14 (0.95)</td>
<td align="char" valign="top" char="(">2.53 (1.46)</td>
<td align="char" valign="top" char="(">3.89 (2.52)</td>
<td align="char" valign="top" char=".">44.75</td>
<td align="char" valign="top" char=".">34.31</td>
</tr>
<tr>
<td align="left" valign="top">C14</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">12</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">5</td>
<td align="char" valign="top" char="(">1.77 (1.59)</td>
<td align="char" valign="top" char="(">6.08 (2.02)</td>
<td align="char" valign="top" char="(">2.28 (2.19)</td>
<td align="char" valign="top" char=".">5.13</td>
<td align="char" valign="top" char=".">88.83</td>
</tr>
<tr>
<td align="left" valign="top">C15</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">19</td>
<td align="center" valign="top">10</td>
<td align="char" valign="top" char="(">2.76 (3.07)</td>
<td align="char" valign="top" char="(">5.64 (0.92)</td>
<td align="char" valign="top" char="(">1.30 (1.13)</td>
<td align="char" valign="top" char=".">24.06</td>
<td align="char" valign="top" char=".">99.77</td>
</tr>
<tr>
<td align="left" valign="top">C16</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">30</td>
<td align="center" valign="top">8</td>
<td align="center" valign="top">18</td>
<td align="center" valign="top">15</td>
<td align="char" valign="top" char="(">3.53 (3.73)</td>
<td align="char" valign="top" char="(">4.50 (3.12)</td>
<td align="char" valign="top" char="(">0.00 (0.00)</td>
<td align="char" valign="top" char=".">42.65</td>
<td align="char" valign="top" char=".">91.67</td>
</tr>
<tr>
<td align="left" valign="top">C17</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">28</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">12</td>
<td align="char" valign="top" char="(">1.50 (0.85)</td>
<td align="char" valign="top" char="(">0.89 (0.70)</td>
<td align="char" valign="top" char="(">1.25 (1.00)</td>
<td align="char" valign="top" char=".">70.50</td>
<td align="char" valign="top" char=".">40.54</td>
</tr>
<tr>
<td align="left" valign="top">C18</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">28</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">13</td>
<td align="char" valign="top" char="(">1.43 (1.28)</td>
<td align="char" valign="top" char="(">0.44 (0.58)</td>
<td align="char" valign="top" char="(">0.00 (0.00)</td>
<td align="char" valign="top" char=".">75.66</td>
<td align="char" valign="top" char=".">70.37</td>
</tr>
<tr>
<td align="left" valign="top">C19</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">40</td>
<td align="center" valign="top">28</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">8</td>
<td align="char" valign="top" char="(">1.29 (1.20)</td>
<td align="char" valign="top" char="(">0.41 (0.75)</td>
<td align="char" valign="top" char="(">0.00 (0.00)</td>
<td align="char" valign="top" char=".">73.54</td>
<td align="char" valign="top" char=".">64.81</td>
</tr>
<tr>
<td align="left" valign="top">C20</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">32</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">3</td>
<td align="char" valign="top" char="(">9.86 (0.35)</td>
<td align="char" valign="top" char="(">7.44 (3.15)</td>
<td align="char" valign="top" char="(">8.72 (1.36)</td>
<td align="char" valign="top" char=".">73.64</td>
<td align="char" valign="top" char=".">45.31</td>
</tr>
<tr>
<td align="left" valign="top">C21</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">32</td>
<td align="center" valign="top">2</td>
<td align="center" valign="top">20</td>
<td align="center" valign="top">3</td>
<td align="char" valign="top" char="(">1.00 (0.52)</td>
<td align="char" valign="top" char="(">0.72 (0.68)</td>
<td align="char" valign="top" char="(">0.69 (0.71)</td>
<td align="char" valign="top" char=".">62.17</td>
<td align="char" valign="top" char=".">51.59</td>
</tr>
<tr>
<td align="left" valign="top">C22</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">26</td>
<td align="center" valign="top">10</td>
<td align="char" valign="top" char="(">7.40 (2.50)</td>
<td align="char" valign="top" char="(">5.32 (2.33)</td>
<td align="char" valign="top" char="(">7.13 (1.96)</td>
<td align="char" valign="top" char=".">75.26</td>
<td align="char" valign="top" char=".">27.37</td>
</tr>
<tr>
<td align="left" valign="top">C23</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">29</td>
<td align="center" valign="top">7</td>
<td align="char" valign="top" char="(">5.74 (3.90)</td>
<td align="char" valign="top" char="(">4.06 (2.93)</td>
<td align="char" valign="top" char="(">3.17 (2.43)</td>
<td align="char" valign="top" char=".">62.17</td>
<td align="char" valign="top" char=".">56.42</td>
</tr>
<tr>
<td align="left" valign="top">C24</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">24</td>
<td align="center" valign="top">11</td>
<td align="char" valign="top" char="(">6.28 (3.10)</td>
<td align="char" valign="top" char="(">6.05 (2.29)</td>
<td align="char" valign="top" char="(">7.36 (2.24)</td>
<td align="char" valign="top" char=".">55.69</td>
<td align="char" valign="top" char=".">33.16</td>
</tr>
<tr>
<td align="left" valign="top">C25</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">13</td>
<td align="center" valign="top">3</td>
<td align="char" valign="top" char="(">2.11 (1.73)</td>
<td align="char" valign="top" char="(">0.75 (0.92)</td>
<td align="char" valign="top" char="(">0.25 (0.45)</td>
<td align="char" valign="top" char=".">73.77</td>
<td align="char" valign="top" char=".">64.06</td>
</tr>
<tr>
<td align="left" valign="top">C26</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">6</td>
<td align="center" valign="top">12</td>
<td align="center" valign="top">7</td>
<td align="char" valign="top" char="(">5.00 (3.27)</td>
<td align="char" valign="top" char="(">2.79 (2.83)</td>
<td align="char" valign="top" char="(">3.50 (2.93)</td>
<td align="char" valign="top" char=".">69.30</td>
<td align="char" valign="top" char=".">40.91</td>
</tr>
<tr>
<td align="left" valign="top">C27</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">14</td>
<td align="center" valign="top">4</td>
<td align="char" valign="top" char="(">2.00 (2.53)</td>
<td align="char" valign="top" char="(">0.03 (0.18)</td>
<td align="char" valign="top" char="(">0.00 (0.00)</td>
<td align="char" valign="top" char=".">74.11</td>
<td align="char" valign="top" char=".">51.61</td>
</tr>
<tr>
<td align="left" valign="top">C28</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">23</td>
<td align="center" valign="top">11</td>
<td align="char" valign="top" char="(">6.50 (1.26)</td>
<td align="char" valign="top" char="(">5.05 (1.84)</td>
<td align="char" valign="top" char="(">6.00 (1.41)</td>
<td align="char" valign="top" char=".">73.35</td>
<td align="char" valign="top" char=".">34.66</td>
</tr>
<tr>
<td align="left" valign="top">C29</td>
<td align="center" valign="top">25</td>
<td align="center" valign="top">45</td>
<td align="center" valign="top">15</td>
<td align="center" valign="top">3</td>
<td align="center" valign="top">28</td>
<td align="center" valign="top">11</td>
<td align="char" valign="top" char="(">2.45 (1.65)</td>
<td align="char" valign="top" char="(">1.12 (1.54)</td>
<td align="char" valign="top" char="(">1.00 (0.82)</td>
<td align="char" valign="top" char=".">73.26</td>
<td align="char" valign="top" char=".">44.85</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>N, number of data points per specified phase; mis, missing data points per specified phase; M, mean of specified phase; SD, standard deviation; NAP, non-rescaled non-overlap of all pairs&#x002A; is given in %.</p>
</table-wrap-foot>
</table-wrap>
<p>The non-rescaled NAP (comparing Phases B and C) values revealed that the dependent variable had effects ranging between 27.4 and 99.8%. More specifically, 19 participants (65.51%) showed small effects; eight (27.58%) showed medium effects; and two showed strong effects (6.89%).</p>
</sec>
<sec id="sec21">
<label>8.2.</label>
<title>Inferential statistics</title>
<sec id="sec22">
<label>8.2.1.</label>
<title>Model 1: comparing baseline and Tier 1 (RQ 1)</title>
<p>In Model 1, the disruptive behavior during three distinct phases is analyzed: Phase A (baseline with no intervention), Phase B (Tier 1), and Phase C (Tier 2), using a multilevel piecewise-regression model. The results show that the intercept of the regression line starts at 3.35. Additionally, the trend effect is significant and positive, with a value of 0.04. This effect includes all data points, even the baseline (Phase A), without any intervention. The level effect of both Phases B and C were significant when compared to the baseline (Phase A) (<xref rid="tab3" ref-type="table">Table 3</xref>).</p>
<table-wrap position="float" id="tab3">
<label>Table 3</label>
<caption>
<p>Fixed effects of the multilevel piecewise-regression model comparing the baseline with Phase B (Tier 1) and C (Tier 2) of the disruptive behavior.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Parameter</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">SE</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="5">
<bold>Fixed effects</bold>
</td>
</tr>
<tr>
<td align="left" valign="top">Intercept</td>
<td align="char" valign="top" char=".">3.35</td>
<td align="char" valign="top" char=".">0.39</td>
<td align="char" valign="top" char=".">8.56</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Trend</td>
<td align="char" valign="top" char=".">0.04</td>
<td align="char" valign="top" char=".">0.01</td>
<td align="char" valign="top" char=".">3.48</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Level Phase B</td>
<td align="char" valign="top" char=".">&#x2212;0.86</td>
<td align="char" valign="top" char=".">0.24</td>
<td align="char" valign="top" char=".">&#x2212;3.58</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Level Phase C</td>
<td align="char" valign="top" char=".">&#x2212;3.13</td>
<td align="char" valign="top" char=".">0.67</td>
<td align="char" valign="top" char=".">&#x2212;4.67</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Slope Phase B</td>
<td align="char" valign="top" char=".">&#x2212;0.06</td>
<td align="char" valign="top" char=".">0.01</td>
<td align="char" valign="top" char=".">&#x2212;4.69</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Slope Phase C</td>
<td align="char" valign="top" char=".">&#x2212;0.08</td>
<td align="char" valign="top" char=".">0.02</td>
<td align="char" valign="top" char=".">&#x2212;4.93</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Specifically, the level effects of Phases B and C were&#x2009;&#x2212;&#x2009;0.86 and&#x2009;&#x2212;&#x2009;3.13, respectively. The level and slope effects of Phase C do not represent an adjusted effect, as they are influenced by Phase B. However, further investigation is required to verify the results of the level effect of Phase C. This is achieved by Model 2, which presents an adjusted value of the level effect of Phase C. The slope effects of both Phases B and C were significant. The slope effect of Phase B was &#x2212;0.06, indicating that disruptive behavior is reduced by &#x2212;0.06 per measurement time point. Similarly, the slope effect of Phase C was &#x2212;0.08, indicating that disruptive behavior is reduced by &#x2212;0.08 per measurement time point. <xref rid="fig2" ref-type="fig">Figure 2</xref> is a schematic representation of Model 1 and its effects.</p>
<fig position="float" id="fig2">
<label>Figure 2</label>
<caption>
<p>Schematic representation of Model 1.</p>
</caption>
<graphic xlink:href="feduc-08-1208854-g002.tif"/>
</fig>
</sec>
<sec id="sec23">
<label>8.2.2.</label>
<title>Model 2: comparing Tiers 1 and 2 (RQ 2)</title>
<p>In Model 2, we examined the disruptive behavior of Phases B and C. Our analysis was focused solely on these two phases. The trend effect was significant at &#x2212;0.02, indicating a decrease in disruptive behavior in both phases together. However, our findings did not reveal a significant level effect between Phases B and C (<xref rid="tab4" ref-type="table">Table 4</xref>). It only shows a decreasing effect in disruptive behavior, which is so small that the levels of the two phases do not significantly differ from each other. Across Phases B and C, disruptive behavior decreases along the significant trend effect (&#x2212;0.02), but no significant level effect is evident to infer a significant change in behavior based on the mean comparison of both phases. <xref rid="fig3" ref-type="fig">Figure 3</xref> is a schematic representation of Model 2 and its effects.</p>
<table-wrap position="float" id="tab4">
<label>Table 4</label>
<caption>
<p>Fixed effects of the multilevel piecewise-regression model comparing Phase B (Tier 1) and C (Tier 2) of disruptive behavior.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Parameter</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">SE</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="5">
<bold>Fixed effects</bold>
</td>
</tr>
<tr>
<td align="left" valign="top">Intercept</td>
<td align="char" valign="top" char=".">3.25</td>
<td align="char" valign="top" char=".">0.41</td>
<td align="char" valign="top" char=".">7.91</td>
<td align="char" valign="top" char=".">&#x003C;0.001</td>
</tr>
<tr>
<td align="left" valign="top">Trend</td>
<td align="char" valign="top" char=".">&#x2212;0.02</td>
<td align="char" valign="top" char=".">0.01</td>
<td align="char" valign="top" char=".">&#x2212;3.16</td>
<td align="char" valign="top" char=".">&#x003C;0.01</td>
</tr>
<tr>
<td align="left" valign="top">Level Phase C</td>
<td align="char" valign="top" char=".">0.03</td>
<td align="char" valign="top" char=".">0.21</td>
<td align="char" valign="top" char=".">0.16</td>
<td align="char" valign="top" char=".">0.87</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig position="float" id="fig3">
<label>Figure 3</label>
<caption>
<p>Schematic representation of Model 2.</p>
</caption>
<graphic xlink:href="feduc-08-1208854-g003.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec id="sec24" sec-type="discussions">
<label>9.</label>
<title>Discussion</title>
<p>The aim of RQ1 was to investigate the effectiveness of Tier 1 (GBG) in reducing disruptive behavior. The results show that through the implementation of the GBG, the disruptive behavior of elementary school students can be significantly reduced. The hypothesis (H1) made in this context can, therefore, be confirmed. The decisive factors here are the key figures of the individual NAP comparisons between the baseline and Phase B, as well as the significant overall effect of &#x2212;0.86 in the comparison of Phases A and B. This is consistent with the results of other studies conducted on German-speaking samples (<xref ref-type="bibr" rid="ref51">Leidig et al., 2022</xref>; <xref ref-type="bibr" rid="ref32">Hagen et al., 2023</xref>). These studies were also single-case studies, but here the GBG was not implemented in the context of the MTSS. Compared to the results of this study, the effects of these two studies were greater. This could be explained by the timing of the research: several schools had just gone through a lockdown period, which complicated various processes within the school. It is difficult to quantify the impact of this factor; however, it should not be overlooked.</p>
<p>In summary, there is an expected positive effect on the expression of disruptive behavior at the first tier of the MTSS across most cases. For more than half of the students (16), at least medium effects (NAP) were identified, and 13 students showed at least small effects. This, in addition to the data from the regression analyses, suggests an effect related to significant parts of the class.</p>
<p>The aim of RQ2 was to investigate the impact of assignment to Tier 2 on the development of disruptive behavior, compared to Tier 1. The results of the study reveal the qualitative impact of the assignment to Tier 2 on disruptive behavior. Through two different multi-level analyses and the resulting models, no significant difference (regarding the mean of disruptive behavior) between Phases B and C can be determined. This implies that no significant difference in students&#x2019; disruptive behavior became measurable through assignment to Tier 2. However, there is a significant difference between the baseline (Phase A) and the assignment to Tier 2 (Phase C). As this is not adjusted in Model 1, Model 2 must be calculated to provide further information about the phase difference from Phase B to C.</p>
<p>All the students accompanied by single-case research in this study have moved on to the second stage of this MTSS. This implies that after implementing the GBG at the universal tier, they also received a DBRC, which supported them in achieving a pre-defined goal regarding behavior. The evaluation of the second tier, which involved continuing the use of the GBG and the additional use of the DBRC for these students, concluded that the two measures can be used together, but there is a slight further reduction of &#x2212;0.02 in disruptive behavior (trend effect of Model 2). The behavior gradually subsides, but this effect cannot be attributed to Tier 2. If a level effect were measurable, it would indicate a special effectiveness of the DBRC in combination with the GBG; however, this cannot be inferred from the results. Follow-up studies should examine this point and apply a methodological design, which is often difficult to implement in practice, to determine the isolated effects of the DBRC. Nevertheless, the overall concept of Tiers 1 and 2 is effective in reducing disruptive behavior.</p>
<p>An additional significant point is the definition of the variable and the resulting observation. Disruptive behavior in the classroom is one of the main factors that can be reduced by the GBG. However, the DBRC is an extremely flexible intervention. The teacher formulates a goal that should serve as a behavioral goal for the student. Thus, behavior goals can focus on other aspects of the behavior that are not captured by the variables and definition used here, resulting in a behavior change that diverts attention from disruptive behavior in the classroom.</p>
<p>In summary, disruptive behavior does not significantly differ between the means of Tiers 1 and 2 (level effect Model 2); however, a further decrease in behavior is evidenced through the trend effect of Model 2. The exact reasons and causes are not clearly identifiable. Nevertheless, a long-term effect of the GBG is conceivable, or a paired effect of both measures together, which, however, does not show a sudden behavioral change.</p>
<p>The overall findings of this study contribute to the existing research landscape on intervention research in the context of disruptive behavior and tiered support. The study extends the current literature by suggesting that the combination of the two tiers investigated can be implemented in school settings and may have varying degrees of effectiveness in reducing disruptive behavior. Methodologically, the study offers valuable insights for future studies aiming to investigate complex interventions and pedagogical systems with similar research inquiries. As demonstrated by previous single case studies in related fields, utilizing students&#x2019; individual developmental trajectories and within-individual reference norms can yield reliable results in assessing the effectiveness of interventions (<xref ref-type="bibr" rid="ref26">Franzen and Kamps, 2008</xref>; <xref ref-type="bibr" rid="ref36">Hill and Flores, 2014</xref>; <xref ref-type="bibr" rid="ref58">Nelson et al., 2018</xref>; <xref ref-type="bibr" rid="ref91">Wu et al., 2019</xref>). Also the data collection method, DBR, employed in this study has proven successful in generating valid outcomes regarding disruptive behavior and teacher evaluations (<xref ref-type="bibr" rid="ref12">Casale et al., 2017</xref>).</p>
<sec id="sec25">
<label>9.1.</label>
<title>Limitations</title>
<p>Although the limitations of the study are mainly related to the research design, they are strongly determined by the pedagogical practice. The comparison of different intervention phases in a multiple baseline design is now a common procedure in intervention research (<xref ref-type="bibr" rid="ref89">Wilbert et al., 2022</xref>). In the best case, however, the different interventions would be mixed in the internal group comparison, so that Group 1, for example, would receive the GBG first, and Group 2 would receive the DBRC first. Accordingly, Group 1 would continue with the DBRC at Tier 2, and Group 2, with the GBG. Thus, comparability would increase in terms of the effectiveness of the intervention between the different groups (<xref ref-type="bibr" rid="ref21">Epstein and Dallery, 2022</xref>). Furthermore, taking away the intervention would be an effective method to test the combination of the two interventions and their interaction. However, from an ethical perspective, it was impossible to implement such a design. Additionally, it was impossible to change the order of the interventions in terms of the framework concept and its content. Thus, it is also impossible to make any definite statement about the sole effect of the DBRC.</p>
<p>Furthermore, the use of the 11-point scale could be viewed as a limitation of the study. The results show that the teachers hardly used values above six. Therefore, a 6-point Likert scale would be a suitable scale, as used in other studies (<xref ref-type="bibr" rid="ref51">Leidig et al., 2022</xref>). Despite the comparatively low rating of the teachers, the students showed externalizing problems and disruptive behavior in the pre-survey by the ITRF.</p>
<p>Ultimately, it is impossible to state when the teachers made the assessment on the DBR sheet. They were initially instructed to do so after using the GBG; however, owing to the challenges of everyday practice, this response behavior may shift to a different time. These are typical problems in single-case studies and are difficult to eliminate.</p>
<p>One final point regarding the study&#x2019;s limitations is that the school routine was reinstated only a few weeks after the COVID-19 pandemic lockdown. While teachers reported no specific effects of the pandemic on the study results from their perspective, it cannot be completely ruled out.</p>
</sec>
<sec id="sec26">
<label>9.2.</label>
<title>Practical implications</title>
<p>The use of the GBG is effective in reducing disruptive behavior in elementary school children. The findings of this study are in line with those of previous studies (<xref ref-type="bibr" rid="ref51">Leidig et al., 2022</xref>; <xref ref-type="bibr" rid="ref32">Hagen et al., 2023</xref>), and emphasize the practical implementation of the GBG in the classroom. Furthermore, the GBG is an effective intervention at the first tier of support in the context of the MTSS.</p>
<p>The second tier requires a stronger focus on problem behavior, which the DBRC can partially achieve. However, the results of the second tier may also be related to the research design. Disruptive behavior continues to decline, but no significant difference is observed between the two tiers. Given the problems with the research design, the results must be interpreted with extreme caution.</p>
<p>Therefore, as a practical implication, the implementation of the GBG at the first tier and the combination of the DBRC and GBG interventions at the second tier can gradually reduce the disruptive behavior of students at inclusive elementary schools. For the practical implementation of an MTSS, it can be inferred from the results that the two interventions GBG and DBRC can be implemented together in both tiers. Additionally, it is relevant to note that the sample comprises children with disruptive behavior. When designing an MTSS with the goal of reducing externalizing or disruptive behavior, the combination of these two tiers seems to be effective and feasible.</p>
</sec>
</sec>
<sec id="sec27" sec-type="data-availability">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="sec28">
<title>Ethics statement</title>
<p>The studies involving human participants were reviewed and approved by Ethikkommission der Humanwissenschaftlichen Fakult&#x00E4;t der Universit&#x00E4;t zu K&#x00F6;ln. Written informed consent to participate in this study was provided by the participants&#x2019; legal guardian/next of kin.</p>
</sec>
<sec id="sec29">
<title>Author contributions</title>
<p>JN: original draft and visualization. JN, ToH, and JK: methodology, software, and formal analysis. JN, ToH, JK, LV, and KE: writing and editing. ThH and CH: supervision and project coordination. JN, ToH, JK, LV, KE, CH, and ThH: conceptualization, review, and editing. All authors contributed to the article and approved the submitted version.</p>
</sec>
<sec id="sec30" sec-type="funding-information">
<title>Funding</title>
<p>University funds were used for this project. There was no external funding but the authors acknowledge support for the Article Processing Charge from the DFG (German Research Foundation, 491454339).</p>
</sec>
<sec id="conf1" 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="sec100" 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>
</body>
<back>
<ack>
<p>For further collegial support the authors thank J&#x00FC;rgen Wilbert, Robert J. Volpe, and Julian B&#x00F6;rger.</p>
</ack>
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