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Elementary Students' Reading Growth Trajectories with and without a Summer Testing Point in the Model

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Title: Elementary Students' Reading Growth Trajectories with and without a Summer Testing Point in the Model
Language: English
Authors: Deborah K. Re (ORCID 0000-0003-0874-1412), Huibin Zhang (ORCID 0000-0002-6066-0356)
Source: Reading Research Quarterly. 2025 60(4).
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 18
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Early Childhood Education
Grade 1
Primary Education
Grade 2
Grade 3
Grade 4
Intermediate Grades
Grade 5
Middle Schools
Descriptors: Elementary School Students, Growth Models, Summer Programs, Reading Programs, Reading Achievement, Testing, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Reading Tests
DOI: 10.1002/rrq.70060
ISSN: 0034-0553
1936-2722
Abstract: Archival data were analyzed with piecewise growth models to determine the seasonal growth of students not reading proficiently who did (treatment students = 144) and did not (control students = 1113) participate in their school district's summer reading program. The rising first- through fifth graders (48% female) were predominately White (74%) and economically disadvantaged (79%). Control students tended to exhibit stable or declining spring-to-fall performance that was significant only in Grade 2, where a measurement artifact may have influenced results. When including a summer testing point in the models for treatment students, performance tended to be stable or declining while the students were receiving summer instruction but then improved during their subsequent summer-to-fall break. Conditional models revealed demographic subgroups had varying patterns of higher or lower growth rates compared to the reference groups, but rarely were these significant. Issues with measurement and implications for planning summer programs are discussed.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1487128
Database: ERIC
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  Value: <anid>AN0188874266;[nrnu]01oct.25;2025Oct28.05:49;v2.2.500</anid> <title id="AN0188874266-1">Elementary Students' Reading Growth Trajectories With and Without a Summer Testing Point in the Model </title> <p>Archival data were analyzed with piecewise growth models to determine the seasonal growth of students not reading proficiently who did (treatment students = 144) and did not (control students = 1113) participate in their school district's summer reading program. The rising first‐ through fifth graders (48% female) were predominately White (74%) and economically disadvantaged (79%). Control students tended to exhibit stable or declining spring‐to‐fall performance that was significant only in Grade 2, where a measurement artifact may have influenced results. When including a summer testing point in the models for treatment students, performance tended to be stable or declining while the students were receiving summer instruction but then improved during their subsequent summer‐to‐fall break. Conditional models revealed demographic subgroups had varying patterns of higher or lower growth rates compared to the reference groups, but rarely were these significant. Issues with measurement and implications for planning summer programs are discussed.</p> <p>Keywords: elementary; growth modeling; reading; summer loss</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/NRNU/01oct25/rrq70060-toc-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="rrq70060-toc-0001.jpg" title="." /> </p> <p></p> <hd id="AN0188874266-3">Introduction</hd> <p>For many decades, extended school breaks—commonly in the summer between academic years—have raised concerns internationally about the potential negative impact on the reading abilities of vulnerable children who lack full and equal access to literacy resources and instructional opportunities during these periods (Cooper et al. [<reflink idref="bib7" id="ref1">7</reflink>]; Davies and Aurini [<reflink idref="bib8" id="ref2">8</reflink>]; Downey et al. [<reflink idref="bib10" id="ref3">10</reflink>]; Heyns [<reflink idref="bib15" id="ref4">15</reflink>]; Tiruchittampalam et al. [<reflink idref="bib40" id="ref5">40</reflink>]; van der Kleij et al. [<reflink idref="bib41" id="ref6">41</reflink>]). Although initial investigations gave the impression that loss was nearly inevitable for elementary‐aged students from marginalized groups and those with reading difficulties, more recent reports have suggested there is a good deal of variation in individual performance (Atteberry and McEachin [<reflink idref="bib2" id="ref7">2</reflink>]) and variation attributable to teachers (Anderson [<reflink idref="bib1" id="ref8">1</reflink>]).</p> <p>Unfortunately, most studies of the summer effect are limited to assessment scores obtained during the school year; therefore, they require inferences about what happened between a testing point in the spring of one school year and the testing point in the fall of the next school year. It often is not known whether available data are from students who did or did not participate specifically in a summer reading program (Gershenson and Hayes [<reflink idref="bib13" id="ref9">13</reflink>]), and students may have been tested months before the end of one school year or after the start of the next (Cooper et al. [<reflink idref="bib7" id="ref10">7</reflink>]; Downey et al. [<reflink idref="bib10" id="ref11">10</reflink>]; Heyns [<reflink idref="bib15" id="ref12">15</reflink>]). This often can mean data are missing at higher than typical rates (Workman et al. [<reflink idref="bib47" id="ref13">47</reflink>]). Thus, researchers must make methodological choices that can bias or produce inconsistent results (Quinn and McIntyre [<reflink idref="bib31" id="ref14">31</reflink>]; von Hippel [<reflink idref="bib43" id="ref15">43</reflink>]). For example, studies have applied linear extrapolation to estimate summer learning, but this has been found to overestimate a perceived loss of abilities (Kuhfeld and Soland [<reflink idref="bib23" id="ref16">23</reflink>]).</p> <p>Although it would be difficult to obtain reading performance data on students when they are not in school, many districts offer summer reading programs, making a summer testing point possible for participating students. The present study gathered archival data on students in Grades 1–5 who were and were not attending a summer reading program to better understand their learning trajectories during the school break.</p> <hd id="AN0188874266-4">Summer Reading Programs</hd> <p>Summer reading programs originally were popularized for two purposes. One was to offer students with fewer home‐ and community‐based resources better access to reading materials and educational opportunities during the break (Harris [<reflink idref="bib14" id="ref17">14</reflink>]), and the other was to extend the instructional supports for students served in special education (Battle v. Commonwealth of Pennsylvania [<reflink idref="bib5" id="ref18">5</reflink>]). Due to funding limitations, the former efforts commonly have been based in community organizations, such as recreation clubs and public libraries, as well as in partnership with schools (McCombs et al. [<reflink idref="bib27" id="ref19">27</reflink>]). In the United States, summer programs for students in special education can be funded through federal entitlements to schools and have to be staffed by qualified personnel.</p> <p>Early in the start of this century, the focus of summer reading programs shifted as legislation was enacted to require U.S. school districts to provide summer reading programs for students not achieving grade level proficiency (Early Learning‐20 Education Code [<reflink idref="bib11" id="ref20">11</reflink>]; Reed et al. [<reflink idref="bib38" id="ref21">38</reflink>]). Yet, a meta‐analysis of intervention studies found inconsistent results, with some positive effects favoring participants over peers not in the summer programs, some null effects, and some negative effects favoring the control groups (Kim and Quinn [<reflink idref="bib21" id="ref22">21</reflink>]). Positive outcomes have been more likely when the programs are designed and supported or delivered by researchers, particularly over multiple years (e.g., Borman and Dowling [<reflink idref="bib6" id="ref23">6</reflink>]).</p> <p>In addition to the aforementioned difficulties with the timing of testing and the handling of missing data, the measures themselves might not be well designed to capture summer learning. For example, assessments may be scaled for within‐ but not between‐school year growth (Kolen and Brennan [<reflink idref="bib22" id="ref24">22</reflink>]). Even when measures appear to be vertically scaled, they can have shifting proficiency ranges for each grade that make performance relative to the benchmark difficult to interpret from spring to fall (Reed et al. [<reflink idref="bib36" id="ref25">36</reflink>]). Measures also may change the format, tested skills, or administration procedures across grade levels (von Hippel [<reflink idref="bib43" id="ref26">43</reflink>]). These issues compound the challenges of determining and properly interpreting summer outcomes or comparing students' school year and summer growth trajectories.</p> <hd id="AN0188874266-5">Seasonal Growth in Reading</hd> <p>Examinations of students' growth in reading skills over time have tended to show the trajectories are not perfectly linear but can demonstrate seasonal variations within and between the school years (Little et al. [<reflink idref="bib25" id="ref27">25</reflink>]; van der Kleij et al. [<reflink idref="bib41" id="ref28">41</reflink>]). A number of studies examining school year and summer growth have used a national database of scores from administering the Measures of Academic Progress (MAP; Northwest Evaluation Association [NWEA] [<reflink idref="bib29" id="ref29">29</reflink>]). This research has shown seasonal variations as well as differences by student ability and by grade (e.g., Atteberry and McEachin [<reflink idref="bib2" id="ref30">2</reflink>]; Johnson and Barker [<reflink idref="bib18" id="ref31">18</reflink>]; Kuhfeld and Soland [<reflink idref="bib23" id="ref32">23</reflink>]; Rambo‐Hernandez et al. [<reflink idref="bib33" id="ref33">33</reflink>]).</p> <p>Nevertheless, there are two primary limitations to these MAP database studies. First, they typically have not contextualized the results by acknowledging the differences in tested skills and administration procedures such as the shift from testing primarily code‐based skills (e.g., letter‐sound knowledge) and providing audio supports in kindergarten and first grade to withdrawing the audio in Grade 2 and increasing the meaning‐based skills assessed (e.g., inferential comprehension). NWEA ([<reflink idref="bib30" id="ref34">30</reflink>]) and some researchers (Little et al. [<reflink idref="bib24" id="ref35">24</reflink>]; Reed et al. [<reflink idref="bib36" id="ref36">36</reflink>]) have noted that these changes cause students' scores to artificially decline at the fall testing point in Grade 2. The second limitation is that the national MAP database does not indicate which students were and were not enrolled in summer reading programs and, relatedly, the studies do not include a summer testing point for anyone in the sample. Hence, it is not possible to know how growth trajectories may differ or be influenced by summer instruction or a lack thereof.</p> <p>The present study addresses the gaps created by the limitations of the national database. Specifically, we examined the MAP scores of cohorts with known instructional and assessment contexts, including a summer testing point for students in a summer program, to contribute new insights into the seasonal growth trajectories of elementary students. This was an extension of an earlier piecewise growth model that found, on average, oral reading performance increased when students were receiving instruction but stagnated or declined while the students were on breaks between the school year and summer instructional periods (Zvoch and Stevens [<reflink idref="bib48" id="ref37">48</reflink>]).</p> <p>However, Zvoch and Stevens' design had several limitations. First, they included only students who participated in a summer reading program, so it was not known whether the performance of non‐participating peers differed. Second, the previous work only measured students' oral reading fluency—not overall reading performance. Third, the study was restricted to students moving from Grade 1 to 2, which are grade levels of rapid growth in oral reading. Finally, Zvoch and Stevens did not explore differences by the key demographics commonly targeted for summer programs, such as special education and free or reduced‐price lunch (FRL) status, a proxy for economic disadvantage. Therefore, we included more grade levels, an equated control group not receiving summer instruction, scores from the computer‐adaptive MAP test of overall reading ability, and an examination of outcomes by demographic subgroups.</p> <hd id="AN0188874266-6">Purpose and Research Questions</hd> <p>Given the lack of clarity on elementary students' summer outcomes and the challenges in measuring and modeling reading performance over time, this exploratory study examined data from students who did and did not participate in a formal summer reading program. Our first research question (RQ1) was: Among students in Grades 1–5 not reading proficiently, how did the growth trajectories of those who participated in a summer reading program (treatment students) differ from the growth of their peers who did not participate in the summer program (control students) across the four testing points? For this exploration, we simultaneously examined the seasonal growth patterns of both treatment and control students from fall to winter, winter to spring, and spring to fall so that we could identify the visual and statistical differences between the two groups. Given findings from previous seasonal growth studies (Little et al. [<reflink idref="bib25" id="ref38">25</reflink>]) as well as reported measurement issues in summer (von Hippel [<reflink idref="bib43" id="ref39">43</reflink>]), we hypothesized that students in both groups would demonstrate strong positive growth from fall to spring and stagnation from spring to fall.</p> <p>Because we had access to a summer reading test score for the treatment students, we also modeled the results of the treatment group separately across the five testing points, asking a second research question: What are the seasonal growth patterns of treatment students from fall to winter, winter to spring, spring to summer, and summer to fall? Given that Zvoch and Stevens' ([<reflink idref="bib48" id="ref40">48</reflink>]) findings of growth from spring to summer when receiving instruction and declines from the end of the summer program to the next fall were based on first and second graders' oral reading fluency performance, we hypothesized we would find a similar pattern in Grades 1 and 2 when students were tested on foundational skills. However, the inconsistent results in summer programs overall (Kim and Quinn [<reflink idref="bib21" id="ref41">21</reflink>]) led us to hypothesize that Grades 3–5 would experience stagnation in overall reading ability during and after the summer program.</p> <p>Finally, to explore differences by student characteristics, we separately modeled growth of the treatment and control groups over the four school‐year time points, addressing the third research question (RQ3): To what extent do the within‐group growth rates of students with different demographic characteristics vary? Summer programs commonly are perceived as more important for students who are economically disadvantaged (van der Kleij et al. [<reflink idref="bib41" id="ref42">41</reflink>]) or served in special education (Battle v. Commonwealth of Pennsylvania [<reflink idref="bib5" id="ref43">5</reflink>]), so we hypothesized these two subgroups would experience greater growth than peers when in a summer program; and more difficulty maintaining their abilities when not receiving instruction.</p> <hd id="AN0188874266-7">Method</hd> <p></p> <hd id="AN0188874266-8">Transparency and Openness</hd> <p>This study's design and analyses were not pre‐registered but relied upon de‐identified archival data. Members of the research team did not have any contact with the human subjects and did not merge or enhance the dataset provided to them. Thus, the Institutional Review Board declared the research exempt. Under the conditions of the data sharing agreement with the school district, the data cannot be provided to others, but the analytic code is available by emailing the corresponding author. In the sections that follow, we report the determination of the final sample as well as all data exclusions and measures. Analyses were conducted in the R environment (R Core Team [<reflink idref="bib32" id="ref44">32</reflink>]).</p> <hd id="AN0188874266-9">Participants and Setting</hd> <p>This investigation draws upon an archival dataset obtained over a 12‐month period across two school years (i.e., from the fall of one school year to the fall of the following school year). Participants were from a mid‐size district in a Midwestern U.S. state. The treatment group was enrolled in the district's summer reading program, which was designed for students not reading proficiently on the district's winter administration of their universal reading screener. Because some ineligible children may have been admitted to the program if they had a sibling attending or were specifically recommended by a teacher, we limited the analytic sample to only those students who did not meet the proficiency benchmark on the winter administration when the district began recruiting for the summer program (<emph>n</emph> = 144). The control group (<emph>n</emph> = 1113) consisted of students who were eligible for the summer reading program based on their winter reading screener score but did not participate in the program.</p> <p>It is possible that student performance fluctuated above and below the proficiency cut point at each of the three universal screening waves during the school year. For example, 100% of students eligible for the summer program were not reading proficiently at the winter administration, but 22.70% of eligible treatment students and 31.18% of the eligible control students scored above the proficiency cut point on the spring administration. We aligned our analytic sample with how the district determined eligibility for their summer program, applied propensity score weighting to equate the treatment and control groups, and analyzed students' change in performance by each segment (e.g., fall to winter, winter to spring, spring to fall) to better account for changes in performance over time (see Analytic Procedures).</p> <p>Although all students were in kindergarten (K) through fourth grade at the time of recruitment, we refer to them by the grade level they entered the next fall, Grades 1 through 5, because that was the outcome of interest and served to eliminate any students retained in the previous year's grade. The demographic characteristics of each grade's participants can be found in Table 1. As can be seen, the highest numbers of eligible students were in Grades 2 and 3, and the fewest students were in Grade 1. The sample was predominately White and non‐Hispanic, but most students were economically disadvantaged, as indicated by their receiving FRL (treatment = 72.22%; control = 80.05%). There also was a relatively high percentage of students receiving special education services (SPED; treatment = 31.94%; control = 24.71%).</p> <p>1 TABLE Demographic characteristics of treatment and control students by grade level.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left" /><th align="center">Female</th><th align="center">Asian</th><th align="center">Black</th><th align="center">Hispanic</th><th align="center">White</th><th align="center">ML</th><th align="center">FRL</th><th align="center">SPED</th></tr><tr><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th><th align="center"><italic>n</italic></th></tr><tr><th align="center">%</th><th align="center">%</th><th align="center">%</th><th align="center">%</th><th align="center">%</th><th align="center">%</th><th align="center">%</th><th align="center">%</th></tr></thead><tbody valign="top"><tr><td align="left">Grade 1</td></tr><tr><td align="left">Treatment</td><td align="center">5</td><td align="center">0</td><td align="center">0</td><td align="center">1</td><td align="center">10</td><td align="center">0</td><td align="center">6</td><td align="center">1</td></tr><tr><td align="left">(n = 11)</td><td align="center">45.45%</td><td align="center">—</td><td align="center">—</td><td align="center">9.09%</td><td align="center">90.91%</td><td align="center">—</td><td align="center">54.55%</td><td align="center">9.09%</td></tr><tr><td align="left">Control</td><td align="center">68</td><td align="center">3</td><td align="center">8</td><td align="center">23</td><td align="center">97</td><td align="center">22</td><td align="center">85</td><td align="center">22</td></tr><tr><td align="left">(n = 131)</td><td align="center">51.91%</td><td align="center">2.29%</td><td align="center">6.11%</td><td align="center">17.56%</td><td align="center">74.05%</td><td align="center">16.79%</td><td align="center">64.89%</td><td align="center">16.79%</td></tr><tr><td align="left">Grade 2</td></tr><tr><td align="left">Treatment</td><td align="center">21</td><td align="center">2</td><td align="center">1</td><td align="center">3</td><td align="center">30</td><td align="center">3</td><td align="center">26</td><td align="center">12</td></tr><tr><td align="left">(n = 39)</td><td align="center">53.85%</td><td align="center">5.13%</td><td align="center">2.56%</td><td align="center">7.69%</td><td align="center">76.92%</td><td align="center">7.69%</td><td align="center">66.67%</td><td align="center">30.77%</td></tr><tr><td align="left">Control</td><td align="center">99</td><td align="center">1</td><td align="center">8</td><td align="center">37</td><td align="center">165</td><td align="center">32</td><td align="center">191</td><td align="center">44</td></tr><tr><td align="left">(n = 224)</td><td align="center">44.20%</td><td align="center">0.45%</td><td align="center">3.57%</td><td align="center">16.52%</td><td align="center">73.66%</td><td align="center">14.29%</td><td align="center">85.27%</td><td align="center">19.64%</td></tr><tr><td align="left">Grade 3</td></tr><tr><td align="left">Treatment</td><td align="center">23</td><td align="center">1</td><td align="center">1</td><td align="center">3</td><td align="center">30</td><td align="center">2</td><td align="center">27</td><td align="center">15</td></tr><tr><td align="left">(n = 39)</td><td align="center">58.97%</td><td align="center">2.56%</td><td align="center">2.56%</td><td align="center">7.69%</td><td align="center">76.92%</td><td align="center">5.13%</td><td align="center">69.23%</td><td align="center">38.46%</td></tr><tr><td align="left">Control</td><td align="center">138</td><td align="center">3</td><td align="center">17</td><td align="center">30</td><td align="center">231</td><td align="center">32</td><td align="center">240</td><td align="center">78</td></tr><tr><td align="left">(n = 294)</td><td align="center">46.94%</td><td align="center">1.02%</td><td align="center">5.78%</td><td align="center">10.20%</td><td align="center">78.57%</td><td align="center">10.88%</td><td align="center">81.63%</td><td align="center">26.53%</td></tr><tr><td align="left">Grade 4</td></tr><tr><td align="left">Treatment</td><td align="center">18</td><td align="center">0</td><td align="center">2</td><td align="center">3</td><td align="center">21</td><td align="center">2</td><td align="center">21</td><td align="center">9</td></tr><tr><td align="left">(n = 27)</td><td align="center">66.67%</td><td align="center">—</td><td align="center">7.41%</td><td align="center">11.11%</td><td align="center">77.78%</td><td align="center">7.41%</td><td align="center">77.78%</td><td align="center">33.33%</td></tr><tr><td align="left">Control</td><td align="center">113</td><td align="center">2</td><td align="center">16</td><td align="center">45</td><td align="center">171</td><td align="center">34</td><td align="center">207</td><td align="center">67</td></tr><tr><td align="left">(n = 246)</td><td align="center">45.94%</td><td align="center">0.81%</td><td align="center">6.50%</td><td align="center">18.29%</td><td align="center">69.51%</td><td align="center">13.82%</td><td align="center">84.15%</td><td align="center">27.24%</td></tr><tr><td align="left">Grade 5</td></tr><tr><td align="left">Treatment</td><td align="center">11</td><td align="center">0</td><td align="center">0</td><td align="center">3</td><td align="center">24</td><td align="center">1</td><td align="center">24</td><td align="center">9</td></tr><tr><td align="left">(n = 28)</td><td align="center">39.29%</td><td align="center">—</td><td align="center">—</td><td align="center">10.71%</td><td align="center">85.71%</td><td align="center">3.57%</td><td align="center">85.71%</td><td align="center">32.14%</td></tr><tr><td align="left">Control</td><td align="center">111</td><td align="center">1</td><td align="center">13</td><td align="center">38</td><td align="center">153</td><td align="center">19</td><td align="center">168</td><td align="center">64</td></tr><tr><td align="left">(n = 218)</td><td align="center">50.91%</td><td align="center">0.46%</td><td align="center">5.96%</td><td align="center">17.43%</td><td align="center">70.18%</td><td align="center">8.72%</td><td align="center">77.06%</td><td align="center">29.36%</td></tr><tr><td align="left">Total</td></tr><tr><td align="left">Treatment (n = 144)</td><td align="center">78</td><td align="center">3</td><td align="center">4</td><td align="center">13</td><td align="center">115</td><td align="center">8</td><td align="center">104</td><td align="center">46</td></tr><tr><td align="left">Control (n = 1113)</td><td align="center">529</td><td align="center">10</td><td align="center">62</td><td align="center">173</td><td align="center">817</td><td align="center">139</td><td align="center">891</td><td align="center">275</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note:</emph> Treatment group = students who participated in the summer reading program; Control group = students who were eligible for but did not participate in the summer reading program.</p> <p>2 Abbreviations: FRL, free or reduced‐price lunch, a proxy for economic disadvantage; ML, multilingual learners; SPED, students receiving special education services.</p> <hd id="AN0188874266-10">Measure</hd> <p>Students' reading performance was assessed using the MAP (NWEA [<reflink idref="bib29" id="ref45">29</reflink>]) test, which the district administered three times per school year. Students enrolled in the summer program also were tested in July, during the final week of instruction. Thus, the treatment group was tested at five points, whereas the control group was tested at only four points (i.e., Year 1 Fall, Year 1 Winter, Year 1 Spring, and Year 2 Fall). For all students, the fall testing points occurred 2–3 weeks after the start of the school year, the winter testing point was in January, and the spring testing point occurred 2–3 weeks before the end of the school year. Hence, students had minimal exposure to typical school‐year instruction between the spring and fall testing windows.</p> <p>MAP included subtests that varied by grade level and were used to form a composite score that was scaled in Rasch units. Subtests in Grades K‐1 tended to focus more on skills in isolation (e.g., phonological awareness, letter‐sound knowledge, decoding, high‐frequency word knowledge) with some listening comprehension at the literal level. By Grade 2, the subtest emphasis shifted to skills when reading connected text of different genres, with more academic vocabulary and inferential comprehension questions included. The test was computer adaptive and included digital audio support in kindergarten and first grade.</p> <hd id="AN0188874266-11">Summer Program and Comparison to School‐Year Core Instruction</hd> <p>Although the present study was focused on measurement and not intervention, we offer a brief description of the summer program to provide a context for what the summer students experienced. The district‐designed summer program was provided five days per week (except for one holiday) at a centralized location and lasted six weeks, or 29 days total. Reading instruction was delivered for 2 h and 20 min of the morning (cumulative total = 67 h and 40 min), utilizing the district's typical core reading curriculum. The curriculum appears on multiple states' list of high‐quality instructional materials and is considered aligned to scientifically based reading instruction. This was to ensure coherence with (a) the planned scope and sequence as well as (b) how students were taught literacy skills during the school year. However, the specific lessons delivered in the summer were from a unit not taught previously.</p> <p>The reading time was divided into 60 min of whole‐group instruction and 80 min of small‐group differentiated rotations that included one or two 20‐min segments with the teacher, depending on the needs of the students. During the small‐group time, students with the lowest MAP performance received a push‐in intervention delivered by a dedicated reading interventionist. The push‐in intervention replaced 30 min of time students otherwise would have worked independently at computer stations or with other forms of reading practice. In addition, the inclusion of whole‐ and small‐group instruction times during the summer was proportionally similar to the allocation of time in the regular school year, but the intervention time during the school year was offered as a supplement rather than as a small‐group rotation within core instruction. The amount of instructional time per day in the summer exceeded that offered during the regular school year by 50 min, but the duration of the summer program was 151 days less than the regular school year.</p> <hd id="AN0188874266-12">Analytic Procedures</hd> <p></p> <hd id="AN0188874266-13">Data Cleaning</hd> <p>As described earlier, we removed from the dataset any students who did not meet the eligibility criteria for the summer program, and we removed those who lacked pretest scores because missing pretest data has been shown to bias estimates of summer learning (von Hippel [<reflink idref="bib43" id="ref46">43</reflink>]). To address the potential confounding effects of non‐attendance, we reclassified students from the treatment to the control group if they registered for the program but did not attend any sessions (i.e., were "no shows"). This left 1257 students in the analytic sample (treatment <emph>n</emph> = 144; control <emph>n</emph> = 1113). Because the "no show" students did not officially enroll in the summer program, they were not considered part of the attrition. Rather, attrition was defined as the number of eligible students who attended at least one but less than half of the scheduled program sessions. In addition, we considered the students who were absent during the July posttest as part of the summer program attrition. As has been reported elsewhere (Denton et al. [<reflink idref="bib9" id="ref47">9</reflink>]; Kim et al. [<reflink idref="bib20" id="ref48">20</reflink>]; Reed et al. [<reflink idref="bib35" id="ref49">35</reflink>]; White et al. [<reflink idref="bib46" id="ref50">46</reflink>]), summer attrition was high (Grade 1 = 36.84%; Grade 2 = 28.07%; Grade 3 = 22.22%; Grade 4 = 44.44%; Grade 5 = 23.91%).</p> <hd id="AN0188874266-14">Propensity Score Analysis</hd> <p>RQ1 concerned how the growth rates of the treatment and control groups differed longitudinally across the four school‐year testing points. To handle imbalances and make the two groups comparable across demographic characteristics (SPED, multilingual learners [ML], FRL, race, and biological sex), we first applied propensity score analysis (Austin [<reflink idref="bib3" id="ref51">3</reflink>]; Rosenbaum and Rubin [<reflink idref="bib39" id="ref52">39</reflink>]), using the Covariate Balancing Propensity Score (CBPS) estimator (Imai and Ratkovic [<reflink idref="bib16" id="ref53">16</reflink>]). CBPS has outperformed other methods, particularly in studies with smaller sample sizes (Fong et al. [<reflink idref="bib12" id="ref54">12</reflink>]). The propensity score model includes students' baseline MAP scores, biological sex, race, multilingual learner (ML) status, FRL status, and SPED status.</p> <p>After estimating the propensity scores, we applied inverse probability treatment weighting (IPTW) to balance covariates between the groups (Austin and Stuart [<reflink idref="bib4" id="ref55">4</reflink>]; Lunceford and Davidian [<reflink idref="bib26" id="ref56">26</reflink>]). IPTW assigns weights based on the inverse of each student's propensity score, creating a pseudo‐population with balanced characteristics. This allows for an unbiased comparison of the groups' growth rates. We assessed the effectiveness of the propensity score modeling and IPTW by examining the standardized mean differences (SMD) across all covariates. An SMD less than 0.05 is considered to indicate sufficient balance, suggesting minimal bias in group comparisons (What Works Clearinghouse [<reflink idref="bib45" id="ref57">45</reflink>]). The results in Table 2 show that our approach achieved equilibrium at all grade levels.</p> <p>2 TABLE Covariate balance before and after propensity score weighting.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Grade</th><th align="center">Covariates</th><th align="center">Before propensity score weighting</th><th align="center">After propensity score weighting</th></tr><tr><th align="center">Treated mean</th><th align="center">Control mean</th><th align="center">SMD</th><th align="center">Treated mean</th><th align="center">Control mean</th><th align="center">SMD</th></tr></thead><tbody valign="top"><tr><td align="left">Grade 1</td><td align="center">SPED</td><td align="center">0.083</td><td align="center">0.168</td><td align="center">−0.229</td><td align="center">0.083</td><td align="center">0.083</td><td align="center">< 0.001</td></tr><tr><td align="center">ML</td><td align="center">0.000</td><td align="center">0.168</td><td align="center">−0.464</td><td align="center">0.000</td><td align="center">< 0.001</td><td align="center">< −0.001</td></tr><tr><td align="center">FRL</td><td align="center">0.583</td><td align="center">0.649</td><td align="center">−0.136</td><td align="center">0.583</td><td align="center">0.583</td><td align="center">< 0.001</td></tr><tr><td align="center">Race</td><td align="center">0.917</td><td align="center">0.740</td><td align="center">0.408</td><td align="center">0.917</td><td align="center">0.917</td><td align="center">< −0.001</td></tr><tr><td align="center">Biological sex</td><td align="center">0.417</td><td align="center">0.519</td><td align="center">−0.204</td><td align="center">0.417</td><td align="center">0.417</td><td align="center">< −0.001</td></tr><tr><td align="left">Grade 2</td><td align="center">SPED</td><td align="center">0.293</td><td align="center">0.196</td><td align="center">0.235</td><td align="center">0.293</td><td align="center">0.293</td><td align="center">< −0.001</td></tr><tr><td align="center">ML</td><td align="center">0.073</td><td align="center">0.143</td><td align="center">−0.205</td><td align="center">0.073</td><td align="center">0.073</td><td align="center">< 0.001</td></tr><tr><td align="center">FRL</td><td align="center">0.683</td><td align="center">0.853</td><td align="center">−0.447</td><td align="center">0.683</td><td align="center">0.683</td><td align="center">< 0.001</td></tr><tr><td align="center">Race</td><td align="center">0.756</td><td align="center">0.737</td><td align="center">0.044</td><td align="center">0.756</td><td align="center">0.756</td><td align="center">< −0.001</td></tr><tr><td align="center">Biological sex</td><td align="center">0.537</td><td align="center">0.442</td><td align="center">0.190</td><td align="center">0.537</td><td align="center">0.537</td><td align="center">< 0.001</td></tr><tr><td align="left">Grade 3</td><td align="center">SPED</td><td align="center">0.388</td><td align="center">0.265</td><td align="center">0.271</td><td align="center">0.388</td><td align="center">0.388</td><td align="center">< 0.001</td></tr><tr><td align="center">ML</td><td align="center">0.041</td><td align="center">0.109</td><td align="center">−0.227</td><td align="center">0.041</td><td align="center">0.041</td><td align="center">< −0.001</td></tr><tr><td align="center">FRL</td><td align="center">0.673</td><td align="center">0.816</td><td align="center">−0.354</td><td align="center">0.673</td><td align="center">0.673</td><td align="center">< −0.001</td></tr><tr><td align="center">Race</td><td align="center">0.755</td><td align="center">0.786</td><td align="center">−0.074</td><td align="center">0.755</td><td align="center">0.755</td><td align="center">< 0.001</td></tr><tr><td align="center">Biological sex</td><td align="center">0.510</td><td align="center">0.469</td><td align="center">0.082</td><td align="center">0.510</td><td align="center">0.510</td><td align="center">< 0.001</td></tr><tr><td align="left">Grade 4</td><td align="center">SPED</td><td align="center">0.300</td><td align="center">0.272</td><td align="center">0.062</td><td align="center">0.300</td><td align="center">0.300</td><td align="center">< −0.001</td></tr><tr><td align="center">ML</td><td align="center">0.067</td><td align="center">0.138</td><td align="center">−0.212</td><td align="center">0.067</td><td align="center">0.067</td><td align="center">< −0.001</td></tr><tr><td align="center">FRL</td><td align="center">0.800</td><td align="center">0.841</td><td align="center">−0.112</td><td align="center">0.800</td><td align="center">0.800</td><td align="center">< −0.001</td></tr><tr><td align="center">Race</td><td align="center">0.767</td><td align="center">0.695</td><td align="center">0.156</td><td align="center">0.767</td><td align="center">0.767</td><td align="center">< 0.001</td></tr><tr><td align="center">Biological sex</td><td align="center">0.667</td><td align="center">0.459</td><td align="center">0.414</td><td align="center">0.667</td><td align="center">0.667</td><td align="center">< 0.001</td></tr><tr><td align="left">Grade 5</td><td align="center">SPED</td><td align="center">0.286</td><td align="center">0.294</td><td align="center">−0.017</td><td align="center">0.286</td><td align="center">0.286</td><td align="center">< 0.001</td></tr><tr><td align="center">ML</td><td align="center">0.057</td><td align="center">0.087</td><td align="center">−0.109</td><td align="center">0.057</td><td align="center">0.057</td><td align="center">< 0.001</td></tr><tr><td align="center">FRL</td><td align="center">0.800</td><td align="center">0.771</td><td align="center">0.070</td><td align="center">0.800</td><td align="center">0.800</td><td align="center">< −0.001</td></tr><tr><td align="center">Race</td><td align="center">0.800</td><td align="center">0.702</td><td align="center">0.217</td><td align="center">0.800</td><td align="center">0.800</td><td align="center">< 0.001</td></tr><tr><td align="center">Biological sex</td><td align="center">0.457</td><td align="center">0.509</td><td align="center">−0.104</td><td align="center">0.457</td><td align="center">0.457</td><td align="center">< −0.001</td></tr></tbody></table> </ephtml> </p> <p>3 Abbreviations: FRL, free or reduced‐price lunch, a proxy for economic disadvantage; ML, multilingual learners; SPED, students receiving special education services.</p> <hd id="AN0188874266-15">Conditional Piecewise Growth Modeling With Treatment Indicator (RQ1)</hd> <p>After propensity score weighting, we then proceeded to address RQ1 by fitting conditional piecewise growth models to the data (Moerbeek [<reflink idref="bib28" id="ref58">28</reflink>]; Raudenbush and Bryk [<reflink idref="bib34" id="ref59">34</reflink>]), using the covariates for race, ML, FRL, and SPED. To account for the nesting of the MAP scale scores (Level 1) within students (Level 2) and teachers (Level 3), we used the Year 1 regular academic year teacher. This teacher accounted for the majority of instruction over the year of data included in the analyses, and the control students did not have a teacher in the summer. Piecewise growth modeling (Moerbeek [<reflink idref="bib28" id="ref60">28</reflink>]) was used to estimate two average growth rates, one before the summer program (i.e., Year 1 Fall to Year 1 Spring) and one after the summer program (i.e., Year 1 Spring to Year 2 Fall), for the purposes of determining whether the between‐group differences were significant.</p> <p>The level‐one or student‐level model was1 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0001" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mi mathvariant="italic">ijk</mi></msub><mo linebreak="goodbreak">=</mo><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mi mathvariant="italic">PRE</mi><mi mathvariant="italic">ijk</mi></msub><mo linebreak="goodbreak">+</mo><mo linebreak="goodbreak">+</mo><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mtext mathvariant="italic">POST</mtext><mi mathvariant="italic">ijk</mi></msub><mo linebreak="goodbreak">+</mo><msub><mi>e</mi><mi mathvariant="italic">ijk</mi></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {Y}_{ijk}={\pi}_{0 jk}+{\pi}_{1 jk} WAVE\_{PRE}_{ijk}++{\pi}_{2 jk} WAVE\_{POST}_{ijk}+{e}_{ijk}, $$</annotation></semantics></math> </ephtml> where <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0002" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ {Y}_{ijk} $$</annotation></semantics></math> </ephtml> was the outcome for <emph>i</emph>th measurement point of student <emph>j</emph> in teacher <emph>k</emph>, with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0003" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">$$ i=1,2,\dots, n $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0004" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>J</mi></mrow><annotation encoding="application/x-tex">$$ j=1,2,\dots, J $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0005" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>K</mi></mrow><annotation encoding="application/x-tex">$$ k=1,2,\dots, K $$</annotation></semantics></math> </ephtml> . <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0006" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{0 jk} $$</annotation></semantics></math> </ephtml> was the baseline outcome for student <emph>j</emph> in teacher <emph>k</emph>, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0007" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{1 jk} $$</annotation></semantics></math> </ephtml> was the individual‐specific slope for the period before the summer for student <emph>j</emph> in teacher <emph>k</emph>, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0008" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{2 jk} $$</annotation></semantics></math> </ephtml> was the individual‐specific slope for the period after the summer, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0009" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mi mathvariant="italic">PRE</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ WAVE\_{PRE}_{ijk} $$</annotation></semantics></math> </ephtml> is the time1 indicator taking values (0, 1, 2, 2), <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0010" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mtext mathvariant="italic">POST</mtext><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ WAVE\_{POST}_{ijk} $$</annotation></semantics></math> </ephtml> was the time2 indicator taking values (0, 0, 0, 1), and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0011" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ {e}_{ijk} $$</annotation></semantics></math> </ephtml> was the error term with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0012" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi mathvariant="italic">ijk</mi></msub><mo>~</mo><mi>N</mi><mfenced close=")" open="(" separators=","><mn>0</mn><msubsup><mi>σ</mi><mn>1</mn><mn>2</mn></msubsup></mfenced></mrow><annotation encoding="application/x-tex">$$ {e}_{ijk}\sim N\left(0,{\sigma}_1^2\right) $$</annotation></semantics></math> </ephtml> .</p> <p>The level‐two models were2 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0013" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>β</mi><mrow><mn>01</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Treatment</mtext><mi mathvariant="italic">jk</mi></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{0 jk}={\beta}_{00k}+{\beta}_{01k}{Treatment}_{jk}+{r}_{0 jk}, $$</annotation></semantics></math> </ephtml> 3 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0014" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>β</mi><mrow><mn>11</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Treatment</mtext><mi mathvariant="italic">jk</mi></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{1 jk}={\beta}_{10k}+{\beta}_{11k}{Treatment}_{jk}+{r}_{1 jk}, $$</annotation></semantics></math> </ephtml> 4 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0015" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>β</mi><mrow><mn>21</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Treatment</mtext><mi mathvariant="italic">jk</mi></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{2 jk}={\beta}_{20k}+{\beta}_{21k}{Treatment}_{jk}+{r}_{2 jk}, $$</annotation></semantics></math> </ephtml> with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0016" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{00k} $$</annotation></semantics></math> </ephtml> as the mean score of the control group for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0017" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0018" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{10k} $$</annotation></semantics></math> </ephtml> as the average growth rate of the control group for the period before the summer for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0019" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>,</mo><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ k,{\beta}_{20k} $$</annotation></semantics></math> </ephtml> as the average growth rate of the control group for the period after the summer for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0020" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0021" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>01</mn><mi>k</mi></mrow></msub><mo>,</mo><mspace width="0.5em" /><msub><mi>β</mi><mrow><mn>11</mn><mi>k</mi></mrow></msub><mo>,</mo><mtext>and</mtext><mspace width="0.25em" /><msub><mi>β</mi><mrow><mn>21</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{01k},\kern0.5em {\beta}_{11k},\mathrm{and}\ {\beta}_{21k} $$</annotation></semantics></math> </ephtml> represented differences between the treatment group and control group compared to <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0022" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo>,</mo><mspace width="0.5em" /><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo>,</mo><mtext>and</mtext><mspace width="0.25em" /><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{00k},\kern0.5em {\beta}_{10k},\mathrm{and}\ {\beta}_{20k} $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0023" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{0 jk} $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0024" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{1 jk} $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0025" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{2 jk} $$</annotation></semantics></math> </ephtml> were the related level‐two random effect.</p> <p>The level‐three models were5 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0026" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>γ</mi><mn>000</mn></msub><mo linebreak="goodbreak">+</mo><msub><mi>u</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo>.</mo></mrow><annotation encoding="application/x-tex">$$ {\beta}_{00k}={\gamma}_{000}+{u}_{00k}. $$</annotation></semantics></math> </ephtml></p> <ulist> <item>6 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0027" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>γ</mi><mn>100</mn></msub><mo linebreak="goodbreak">+</mo><msub><mi>u</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo>.</mo></mrow></mrow><annotation encoding="application/x-tex">$$ {\beta}_{10k}={\gamma}_{100}+{u}_{10k}. $$</annotation></semantics></math> </ephtml></item> <item>7 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0028" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>γ</mi><mn>200</mn></msub><mo linebreak="goodbreak">+</mo><msub><mi>u</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub><mo>.</mo></mrow><annotation encoding="application/x-tex">$$ {\beta}_{20k}={\gamma}_{200}+{u}_{20k}. $$</annotation></semantics></math> </ephtml> where, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0029" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>γ</mi><mn>000</mn></msub></mrow><annotation encoding="application/x-tex">$$ {\gamma}_{000} $$</annotation></semantics></math> </ephtml> was the grand mean of the control group across all measurement points, students, and teachers; <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0030" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>γ</mi><mn>100</mn></msub></mrow><annotation encoding="application/x-tex">$$ {\gamma}_{100} $$</annotation></semantics></math> </ephtml> was the overall average change of the control group across all measurement points, students, and teachers for the period before the summer; <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0031" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>γ</mi><mn>200</mn></msub></mrow><annotation encoding="application/x-tex">$$ {\gamma}_{200} $$</annotation></semantics></math> </ephtml> was the overall average change of the control group across all measurement points, students, and teachers for the period after the period; and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0032" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo>,</mo><msub><mi>u</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo>,</mo><mtext>and</mtext><mspace width="0.25em" /><msub><mi>u</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {u}_{00k},{u}_{10k},\mathrm{and}\ {u}_{20k} $$</annotation></semantics></math> </ephtml> were related level‐three random effect.</item> </ulist> <hd id="AN0188874266-16">Unconditional Piecewise Growth Model (RQ2)</hd> <p>Because the treatment group was tested five times (including the end of the summer program), we conducted an unconditional piecewise growth model of the treatment group with three segments: before (Year 1 Fall to Year 1 Spring), during (Year 1 Spring to Year 1 Summer), and after the summer program (Year 1 Summer to Year 2 Fall). Similar to the work of Zvoch and Stevens ([<reflink idref="bib48" id="ref61">48</reflink>]), this allowed us to address RQ2 by exploring how the summer data point affected the spring‐to‐fall trajectory of the treatment group.</p> <p>The level‐one or student‐level model was8 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0033" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow>Yijk=π0jk+π1jkWAVE%5fPREijk+π2jkWAVE%5fMIDijk+π3jkWAVE%5fPOSTijk+eijk,</mrow><annotation encoding="application/x-tex">$$ {\displaystyle \begin{array}{c}{Y}_{ijk}={\pi}_{0 jk}+{\pi}_{1 jk} WAVE\_{PRE}_{ijk}+{\pi}_{2 jk} WAVE\_{MID}_{ijk}\hfill \\ {}\kern2em +{\pi}_{3 jk} WAVE\_{POST}_{ijk}+{e}_{ijk},\hfill \end{array}} $$</annotation></semantics></math> </ephtml> where <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0034" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ {Y}_{ijk} $$</annotation></semantics></math> </ephtml> was the outcome for <emph>i</emph>th measurement point of student <emph>j</emph> in teacher <emph>k</emph>, with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0035" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">$$ i=1,2,\dots, n $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0036" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>J</mi></mrow><annotation encoding="application/x-tex">$$ j=1,2,\dots, J $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0037" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>K</mi></mrow><annotation encoding="application/x-tex">$$ k=1,2,\dots, K $$</annotation></semantics></math> </ephtml> . <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0038" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{0 jk} $$</annotation></semantics></math> </ephtml> was the baseline outcome for student <emph>j</emph> in teacher <emph>k</emph>, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0039" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{1 jk} $$</annotation></semantics></math> </ephtml> was the individual‐specific slope for the period before the summer program for student <emph>j</emph> in teacher <emph>k</emph>, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0040" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{2 jk} $$</annotation></semantics></math> </ephtml> was the individual‐specific slope for the period during the summer program, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0041" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\pi}_{3 jk} $$</annotation></semantics></math> </ephtml> was the individual‐specific slope for the period after the summer program, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0042" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mi mathvariant="italic">PRE</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ WAVE\_{PRE}_{ijk} $$</annotation></semantics></math> </ephtml> was the time1 indicator taking values (0, 1, 2, 2, 2), <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0043" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mi mathvariant="italic">MID</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ WAVE\_{MID}_{ijk} $$</annotation></semantics></math> </ephtml> was the time2 indicator taking values (0, 0, 0, 1, 1), <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0044" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">WAVE</mtext><mo>_</mo><msub><mtext mathvariant="italic">POST</mtext><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ WAVE\_{POST}_{ijk} $$</annotation></semantics></math> </ephtml> was the time3 indicator taking values (0, 0, 0, 0, 1), and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0045" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi mathvariant="italic">ijk</mi></msub></mrow><annotation encoding="application/x-tex">$$ {e}_{ijk} $$</annotation></semantics></math> </ephtml> is the error term with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0046" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi mathvariant="italic">ijk</mi></msub><mo>~</mo><mi>N</mi><mfenced close=")" open="(" separators=","><mn>0</mn><msubsup><mi>σ</mi><mn>1</mn><mn>2</mn></msubsup></mfenced></mrow><annotation encoding="application/x-tex">$$ {e}_{ijk}\sim N\left(0,{\sigma}_1^2\right) $$</annotation></semantics></math> </ephtml> .</p> <p>The level‐two models were9 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0047" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{0 jk}={\beta}_{00k}+{r}_{0 jk}, $$</annotation></semantics></math> </ephtml> 10 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0048" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{1 jk}={\beta}_{10k}+{r}_{1 jk}, $$</annotation></semantics></math> </ephtml> 11 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0049" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{2 jk}={\beta}_{20k}+{r}_{2 jk}, $$</annotation></semantics></math> </ephtml> 12 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0050" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo linebreak="goodbreak">=</mo><msub><mi>β</mi><mrow><mn>30</mn><mi>k</mi></mrow></msub><mo linebreak="goodbreak">+</mo><msub><mi>r</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{3 jk}={\beta}_{30k}+{r}_{3 jk}, $$</annotation></semantics></math> </ephtml> with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0051" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{00k} $$</annotation></semantics></math> </ephtml> as the mean score for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0052" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0053" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{10k} $$</annotation></semantics></math> </ephtml> as the average growth rate for the period before the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0054" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0055" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{20k} $$</annotation></semantics></math> </ephtml> as the average growth rate for the period after the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0056" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> . Finally, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0057" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{0 jk} $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0058" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{1 jk} $$</annotation></semantics></math> </ephtml> , ... <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0059" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{3 jk} $$</annotation></semantics></math> </ephtml> were the related level‐two random effects.</p> <p>The level‐three models were the same as equations 5 through 7 and had one additional equation (<reflink idref="bib13" id="ref62">13</reflink>)13 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0063" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>30</mn><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>γ</mi><mn>300</mn></msub><mo>+</mo><msub><mi>u</mi><mrow><mn>30</mn><mi>k</mi></mrow></msub><mo>.</mo></mrow><annotation encoding="application/x-tex">$$ {\beta}_{30k}={\gamma}_{300}+{u}_{30k}. $$</annotation></semantics></math> </ephtml> where, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0067" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>γ</mi><mn>300</mn></msub></mrow><annotation encoding="application/x-tex">$$ {\gamma}_{300} $$</annotation></semantics></math> </ephtml> was the overall average change across all measurement points, students, and teachers for the period after the summer program; and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0068" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo>,</mo><msub><mi>u</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo>,</mo><mo>...</mo><msub><mi>u</mi><mrow><mn>30</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {u}_{00k},{u}_{10k},\dots {u}_{30k} $$</annotation></semantics></math> </ephtml> were related level‐three random effects.</p> <hd id="AN0188874266-17">Conditional Piecewise Growth Models With Other Covariates (RQ3)</hd> <p>For RQ3, we conducted separate conditional piecewise growth models of the treatment and control groups that included covariates for student race, ML status, FRL status, and SPED status. Given that the two groups were considered separately for these analyses, propensity score weighting was not applied. All models took into consideration the random effects introduced by the teacher alongside the fixed effects associated with students' performance in previous testing waves.</p> <hd id="AN0188874266-18">Treatment Group Models</hd> <p>The level‐one or student‐level model was the same as Equation 8.</p> <p>The level‐two models were 14 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0083" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>01</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">ML</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>02</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">FRL</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>03</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">SPED</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>04</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Race</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{0 jk}={\beta}_{00k}+{\beta}_{01k}{ML}_{jk}+{\beta}_{02k}{FRL}_{jk}+{\beta}_{03k}{SPED}_{jk}+{\beta}_{04k}{Race}_{jk}+{r}_{0 jk}, $$</annotation></semantics></math> </ephtml></p> <ulist> <item>15 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0084" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msub><mi>π</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>11</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">ML</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>12</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">FRL</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>13</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">SPED</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>14</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Race</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow></mrow><annotation encoding="application/x-tex">$$ {\pi}_{1 jk}={\beta}_{10k}+{\beta}_{11k}{ML}_{jk}+{\beta}_{12k}{FRL}_{jk}+{\beta}_{13k}{SPED}_{jk}+{\beta}_{14k}{Race}_{jk}+{r}_{1 jk}, $$</annotation></semantics></math> </ephtml></item> <item>16 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0085" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msub><mi>π</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>21</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">ML</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>22</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">FRL</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>23</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">SPED</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>24</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Race</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>r</mi><mrow><mn>2</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow></mrow><annotation encoding="application/x-tex">$$ {\pi}_{2 jk}={\beta}_{20k}+{\beta}_{21k}{ML}_{jk}+{\beta}_{22k}{FRL}_{jk}+{\beta}_{23k}{SPED}_{jk}+{\beta}_{24k}{Race}_{jk}+{r}_{2 jk}, $$</annotation></semantics></math> </ephtml></item> <item>17 <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0086" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>π</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mn>30</mn><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>31</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">ML</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>32</mn><mi>k</mi></mrow></msub><msub><mi mathvariant="italic">FRL</mi><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>33</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">SPED</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mn>34</mn><mi>k</mi></mrow></msub><msub><mtext mathvariant="italic">Race</mtext><mi mathvariant="italic">jk</mi></msub><mo>+</mo><msub><mi>r</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub><mo>,</mo></mrow><annotation encoding="application/x-tex">$$ {\pi}_{3 jk}={\beta}_{30k}+{\beta}_{31k}{ML}_{jk}+{\beta}_{32k}{FRL}_{jk}+{\beta}_{33k}{SPED}_{jk}+{\beta}_{34k}{Race}_{jk}+{r}_{3 jk}, $$</annotation></semantics></math> </ephtml> with <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0087" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>00</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{00k} $$</annotation></semantics></math> </ephtml> as the mean score for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0088" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> after controlling all covariates, <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0089" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>10</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{10k} $$</annotation></semantics></math> </ephtml> as the average growth rate for the period before the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0090" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> after controlling all covariates, and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0091" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>20</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{20k} $$</annotation></semantics></math> </ephtml> as the average growth rate for the period after the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0092" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> after controlling all covariates. <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0093" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>01</mn><mi>k</mi></mrow></msub><mo>,</mo><mo>...</mo><msub><mi>β</mi><mrow><mn>04</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{01k},\dots {\beta}_{04k} $$</annotation></semantics></math> </ephtml> represented how each covariate influenced the mean score for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0094" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0095" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>11</mn><mi>k</mi></mrow></msub><mo>,</mo><mo>...</mo><msub><mi>β</mi><mrow><mn>14</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{11k},\dots {\beta}_{14k} $$</annotation></semantics></math> </ephtml> represented how each covariate influenced the average growth rate for the period before the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0096" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0097" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>21</mn><mi>k</mi></mrow></msub><mo>,</mo><mo>...</mo><msub><mi>β</mi><mrow><mn>24</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{21k},\dots {\beta}_{24k} $$</annotation></semantics></math> </ephtml> represented how each covariate influenced the average growth rate for the period during the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0098" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> . <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0099" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mrow><mn>31</mn><mi>k</mi></mrow></msub><mo>,</mo><mo>...</mo><msub><mi>β</mi><mrow><mn>34</mn><mi>k</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {\beta}_{31k},\dots {\beta}_{34k} $$</annotation></semantics></math> </ephtml> represented how each covariate influenced the average growth rate for the period after the summer program for the teacher <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0100" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">$$ k $$</annotation></semantics></math> </ephtml> , and <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0101" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>0</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{0 jk} $$</annotation></semantics></math> </ephtml> , <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0102" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>1</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{1 jk} $$</annotation></semantics></math> </ephtml> , ... <ephtml> <math altimg="urn:x-wiley:00340553:media:rrq70060:rrq70060-math-0103" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mrow><mn>3</mn><mi mathvariant="italic">jk</mi></mrow></msub></mrow><annotation encoding="application/x-tex">$$ {r}_{3 jk} $$</annotation></semantics></math> </ephtml> were the related level‐two random effects.</item> </ulist> <p>The level‐three models were the same as equations 5 through 7 and 13.</p> <hd id="AN0188874266-19">Control Group Models</hd> <p>The level‐one or student‐level model was the same as equation 1, and the level‐two models were the same as equations 14 through 16.</p> <p>The level‐three models were the same as equations 5 through 7.</p> <hd id="AN0188874266-20">Results</hd> <p>Table 3 displays the means and standard deviations of the MAP scores for the treatment and control groups in each grade at each testing wave and before propensity score weighting was applied. Recall that the district determined students in both groups were eligible for the summer reading program because they scored below the proficiency benchmark on the winter MAP administration. The distinction between the groups was whether they participated in the summer reading program between Years 1 and 2. We first present the comparison of the two groups' growth trajectories across the four school‐year testing waves. Next, we present the conditional piecewise growth model that included both groups. Lastly, we present the growth trajectories of the treatment group with the summer testing wave included, followed by the results of modeling the treatment and control groups separately. In all analyses, we modeled the grade levels separately, so although we present the results together for parsimony and descriptively identify patterns, we caution against inferring any statistical comparison between grades.</p> <p>3 TABLE Descriptive statistics by measurement wave and grade.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Wave</th><th align="center">Group</th><th align="center">MAP performance by Group</th><th align="center">MAP performance by Wave</th></tr><tr><th align="left" /><th align="center" /><th align="center">Mean</th><th align="center">SD</th><th align="center">Mean</th><th align="center">SD</th></tr></thead><tbody valign="top"><tr><td align="left">Grade 1</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Control</td><td align="center">132.80</td><td align="center">6.10</td><td align="center" valign="middle">132.65</td><td align="center" valign="middle">5.98</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Treatment</td><td align="center">130.91</td><td align="center">3.96</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Control</td><td align="center">138.07</td><td align="center">5.95</td><td align="center" valign="middle">137.95</td><td align="center" valign="middle">6.04</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Treatment</td><td align="center">136.55</td><td align="center">7.13</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Control</td><td align="center">147.50</td><td align="center">9.30</td><td align="center" valign="middle">147.41</td><td align="center" valign="middle">9.05</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Treatment</td><td align="center">146.37</td><td align="center">5.37</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Control</td><td align="center">—</td><td align="center">—</td><td align="center" valign="middle">146.36</td><td align="center" valign="middle">5.10</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Treatment</td><td align="center">146.36</td><td align="center">5.10</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Control</td><td align="center">145.76</td><td align="center">8.01</td><td align="center" valign="middle">146.01</td><td align="center" valign="middle">8.11</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Treatment</td><td align="center">149.09</td><td align="center">9.06</td></tr><tr><td align="left">Grade 2</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Control</td><td align="center">146.57</td><td align="center">8.21</td><td align="center" valign="middle">146.46</td><td align="center" valign="middle">7.97</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Treatment</td><td align="center">145.85</td><td align="center">6.52</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Control</td><td align="center">154.37</td><td align="center">7.33</td><td align="center" valign="middle">154.39</td><td align="center" valign="middle">7.38</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Treatment</td><td align="center">154.54</td><td align="center">7.7</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Control</td><td align="center">162.85</td><td align="center">8.75</td><td align="center" valign="middle">163.03</td><td align="center" valign="middle">8.69</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Treatment</td><td align="center">164.10</td><td align="center">8.40</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Control</td><td align="center">—</td><td align="center">—</td><td align="center" valign="middle">163.03</td><td align="center" valign="middle">12.08</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Treatment</td><td align="center">163.03</td><td align="center">12.08</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Control</td><td align="center">158.19</td><td align="center">11.61</td><td align="center" valign="middle">158.46</td><td align="center" valign="middle">11.73</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Treatment</td><td align="center">160.00</td><td align="center">12.42</td></tr><tr><td align="left">Grade 3</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Control</td><td align="center">157.72</td><td align="center">11.45</td><td align="center" valign="middle">157.20</td><td align="center" valign="middle">11.40</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Treatment</td><td align="center">153.28</td><td align="center">10.33</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Control</td><td align="center">168.49</td><td align="center">11.95</td><td align="center" valign="middle">167.86</td><td align="center" valign="middle">11.94</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Treatment</td><td align="center">163.10</td><td align="center">10.86</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Control</td><td align="center">176.18</td><td align="center">12.14</td><td align="center" valign="middle">175.66</td><td align="center" valign="middle">12.39</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Treatment</td><td align="center">171.74</td><td align="center">13.61</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Control</td><td align="center">—</td><td align="center">—</td><td align="center" valign="middle">172.13</td><td align="center" valign="middle">14.50</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Treatment</td><td align="center">172.13</td><td align="center">14.50</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Control</td><td align="center">175.70</td><td align="center">12.36</td><td align="center" valign="middle">175.56</td><td align="center" valign="middle">12.46</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Treatment</td><td align="center">174.46</td><td align="center">13.32</td></tr><tr><td align="left">Grade 4</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Control</td><td align="center">174.46</td><td align="center">13.20</td><td align="center" valign="middle">174.59</td><td align="center" valign="middle">13.30</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Treatment</td><td align="center">175.92</td><td align="center">14.53</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Control</td><td align="center">182.21</td><td align="center">12.67</td><td align="center" valign="middle">181.99</td><td align="center" valign="middle">12.72</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Treatment</td><td align="center">179.79</td><td align="center">13.25</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Control</td><td align="center">185.99</td><td align="center">13.18</td><td align="center" valign="middle">185.82</td><td align="center" valign="middle">13.23</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Treatment</td><td align="center">184.04</td><td align="center">13.89</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Control</td><td align="center">—</td><td align="center">—</td><td align="center" valign="middle">182.42</td><td align="center" valign="middle">16.75</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Treatment</td><td align="center">182.42</td><td align="center">16.75</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Control</td><td align="center">186.70</td><td align="center">14.14</td><td align="center" valign="middle">186.48</td><td align="center" valign="middle">14.56</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Treatment</td><td align="center">184.25</td><td align="center">18.51</td></tr><tr><td align="left">Grade 5</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Control</td><td align="center">184.91</td><td align="center">14.12</td><td align="center" valign="middle">184.56</td><td align="center" valign="middle">14.14</td></tr><tr><td align="left">Year 1 Fall</td><td align="center">Treatment</td><td align="center">181.82</td><td align="center">14.29</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Control</td><td align="center">191.17</td><td align="center">13.09</td><td align="center" valign="middle">190.88</td><td align="center" valign="middle">12.97</td></tr><tr><td align="left">Year 1 Winter</td><td align="center">Treatment</td><td align="center">188.68</td><td align="center">12.02</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Control</td><td align="center">193.66</td><td align="center">14.34</td><td align="center" valign="middle">193.47</td><td align="center" valign="middle">14.24</td></tr><tr><td align="left">Year 1 Spring</td><td align="center">Treatment</td><td align="center">192.04</td><td align="center">13.57</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Control</td><td align="center">—</td><td align="center">—</td><td align="center" valign="middle">192.18</td><td align="center" valign="middle">16.24</td></tr><tr><td align="left">Year 1 Summer</td><td align="center">Treatment</td><td align="center">192.18</td><td align="center">16.24</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Control</td><td align="center">193.75</td><td align="center">13.26</td><td align="center" valign="middle">193.58</td><td align="center" valign="middle">13.40</td></tr><tr><td align="left">Year 2 Fall</td><td align="center">Treatment</td><td align="center">192.25</td><td align="center">14.64</td></tr></tbody></table> </ephtml> </p> <p>4 <emph>Note:</emph> Treatment group = students who participated in the summer reading program; Control group = students who were eligible for but did not participate in the summer reading program.</p> <hd id="AN0188874266-21">RQ1: Conditional Piecewise Growth Model Comparing the Treatment and Control Groups</hd> <p>Before modeling the data, we first plotted the MAP scale score means to create graphical representations of the treatment and control groups' school‐year growth trajectories (see Figures S1–S5 in the Supporting Information), corresponding to each grade level. These revealed a considerable variation in MAP scores and two intersections of the treatment and control group trajectories. In Grade 2, the treatment group started slightly below the control group's average MAP score in Year 1 Fall, but treatment students overtook the control group by Year 1 Spring. In Grade 4, the opposite was true in that the control group started below the treatment group's average MAP scores in Year 1 Fall but overtook the treatment group by Year 1 Winter. Plotting the data depicts the patterns of performance, but further statistical analysis was necessary to determine whether the trajectories significantly changed from fall to spring or spring to fall.</p> <p>As shown in Table 4, the results of the conditional piecewise growth model including the treatment and control groups simultaneously revealed that both experienced significantly positive growth rates before the summer program (from Year 1 Fall to Year 1 Spring) in all grade levels. This is revealed in the significantly positive values for the control group (second row of Table 4) and the lack of significant differences between the treatment and control groups (third row of Table 4). Although not significant, the latter results also indicate that the treatment groups in Grades 1–3 had slightly higher growth rates than the control groups, whereas the treatment groups in Grades 4 and 5 had slightly lower, non‐significant growth rates than their control counterparts. Nevertheless, the results from within the school year suggest that students in both groups grew at similar rates.</p> <p>4 TABLE RQ1: Conditional piecewise growth rate differences by group.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Parameter</th><th align="center">Estimate</th><th align="center">Standard error</th><th align="center"><italic>t</italic></th><th align="center"><italic>p</italic></th></tr></thead><tbody valign="top"><tr><td align="left">Grade 1</td></tr><tr><td align="left">Intercept</td><td align="center">132.369</td><td align="center">0.693</td><td align="center">190.923</td><td align="center">< 0.001</td></tr><tr><td align="left">Control Group: Year 1 Fall‐to‐Spring</td><td align="center">7.181</td><td align="center">0.545</td><td align="center">13.165</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Fall‐to‐Spring</td><td align="center">1.046</td><td align="center">0.957</td><td align="center">1.093</td><td align="center">0.281</td></tr><tr><td align="left">Control Group: Year 1 Spring to Year 2 Fall</td><td align="center">−0.905</td><td align="center">1.152</td><td align="center">−0.785</td><td align="center">0.437</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Spring to Year 2 Fall</td><td align="center">3.740</td><td align="center">2.023</td><td align="center">1.849</td><td align="center">0.070</td></tr><tr><td align="left">Grade 2</td></tr><tr><td align="left">Intercept</td><td align="center">146.649</td><td align="center">0.574</td><td align="center">255.570</td><td align="center">< 0.001</td></tr><tr><td align="left">Control Group: Year 1 Fall‐to‐Spring</td><td align="center">8.091</td><td align="center">0.390</td><td align="center">20.734</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Fall‐to‐Spring</td><td align="center">1.141</td><td align="center">0.618</td><td align="center">1.847</td><td align="center">0.067</td></tr><tr><td align="left">Control Group: Year 1 Spring to Year 2 Fall</td><td align="center">−4.559</td><td align="center">0.779</td><td align="center">−5.853</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Spring to Year 2 Fall</td><td align="center">0.600</td><td align="center">1.471</td><td align="center">0.408</td><td align="center">0.684</td></tr><tr><td align="left">Grade 3</td></tr><tr><td align="left">Intercept</td><td align="center">158.279</td><td align="center">0.842</td><td align="center">188.068</td><td align="center">< 0.001</td></tr><tr><td align="left">Control Group: Year 1 Fall‐to‐Spring</td><td align="center">9.190</td><td align="center">0.410</td><td align="center">22.430</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Fall‐to‐Spring</td><td align="center">0.143</td><td align="center">0.778</td><td align="center">0.184</td><td align="center">0.854</td></tr><tr><td align="left">Control Group: Year 1 Spring to Year 2 Fall</td><td align="center">−0.905</td><td align="center">0.768</td><td align="center">−1.178</td><td align="center">0.245</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Spring to Year 2 Fall</td><td align="center">3.044</td><td align="center">1.251</td><td align="center">2.433</td><td align="center">0.016</td></tr><tr><td align="left">Grade 4</td></tr><tr><td align="left">Intercept</td><td align="center">175.264</td><td align="center">0.899</td><td align="center">194.878</td><td align="center">< 0.001</td></tr><tr><td align="left">Control Group: Year 1 Fall‐to‐Spring</td><td align="center">5.762</td><td align="center">0.420</td><td align="center">13.734</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Fall‐to‐Spring</td><td align="center">−1.308</td><td align="center">0.700</td><td align="center">−1.867</td><td align="center">0.064</td></tr><tr><td align="left">Control Group: Year 1 Spring to Year 2 Fall</td><td align="center">−0.347</td><td align="center">0.882</td><td align="center">−0.393</td><td align="center">0.697</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Spring to Year 2 Fall</td><td align="center">0.964</td><td align="center">1.460</td><td align="center">0.660</td><td align="center">0.510</td></tr><tr><td align="left">Grade 5</td></tr><tr><td align="left">Intercept</td><td align="center">177.707</td><td align="center">1.873</td><td align="center">94.871</td><td align="center">< 0.001</td></tr><tr><td align="left">Control Group: Year 1 Fall‐to‐Spring</td><td align="center">6.958</td><td align="center">0.811</td><td align="center">8.579</td><td align="center">< 0.001</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Fall‐to‐Spring</td><td align="center">−0.207</td><td align="center">1.196</td><td align="center">−0.173</td><td align="center">0.863</td></tr><tr><td align="left">Control Group: Year 1 Spring to Year 2 Fall</td><td align="center">1.236</td><td align="center">0.471</td><td align="center">2.623</td><td align="center">0.012</td></tr><tr><td align="left">Difference Between Treatment and Control Groups: Year 1 Spring to Year 2 Fall</td><td align="center">0.843</td><td align="center">0.664</td><td align="center">1.269</td><td align="center">0.206</td></tr></tbody></table> </ephtml> </p> <p>5 <emph>Note:</emph> Intercept represents the average MAP scores at Year 1 Fall for the control group. Bold values indicate significant results.</p> <p>After the summer (from Year 1 Spring to Year 2 Fall), the results in Table 4 indicate that the treatment groups in all grades demonstrated a pattern of higher growth rates compared to peers in the control groups, but this was a significant between‐group difference only in Grade 3 (fifth row of Table 4). Specifically, the third‐grade control group experienced slightly negative growth, whereas the treatment group demonstrated positive and significantly higher growth than their peers who did not participate in the summer program.</p> <hd id="AN0188874266-22">RQ2: Unconditional Piecewise Growth Model of the Treatment Group Only and Including the Summe...</hd> <p>To create a more nuanced picture of how students' reading performance changed during the summer, we examined the growth trajectories of the treatment group with the July testing wave included. Before modeling the data, we first plotted the MAP scale score means to create graphical representations of the treatment group's growth from Fall Year 1 to Fall Year 2. Figures S6–S10 in the Supporting Information show a trend of stagnating or declining performance while students were in the summer program, with some rebounding of performance in Grades 1, 3, and 4 after summer instruction ended. Students in Grades 2 and 4 exhibited a decline in their reading scores from Spring to Summer. However, statistical analysis was necessary to determine whether the change in trajectories at these time points were statistically significant.</p> <p>The intercept in the results of the unconditional piecewise growth model shown in Table 5 signifies the treatment students' average MAP scores at Year 1 Fall. All grades exhibited significantly positive growth across the school year (Year 1 Fall to Year 1 Spring), with Grades 1–3 showing higher growth rates compared to Grades 4–5. Notably, none of the spring‐to‐summer or summer‐to‐fall results were statistically significant at any grade level. There was no indication that participating in the summer program significantly changed performance, nor was there a consistent pattern in the data of scores trending upwards from Year 1 Spring to Year 1 Summer. Yet, there was a consistent pattern of non‐significant positive growth at most grade levels from Summer to Year 2 Fall when treatment students were no longer receiving instruction. Only Grade 2 exhibited declines from Year 1 Summer to Year 2 Fall, but this was not significant and might reflect the change in subtest composition and the withdrawal of digital audio supports for the first time that fall (NWEA [<reflink idref="bib30" id="ref63">30</reflink>]).</p> <p>5 TABLE RQ2: Unconditional piecewise growth model of the treatment group only.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Parameter</th><th align="center">Estimate</th><th align="center">Standard error</th><th align="center"><italic>t</italic></th><th align="center"><italic>p</italic></th></tr></thead><tbody valign="top"><tr><td align="left">Grade 1</td></tr><tr><td align="left">Intercept</td><td align="center">129.814</td><td align="center">1.606</td><td align="center">80.822</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Fall to Year 1 Spring</td><td align="center">7.706</td><td align="center">0.977</td><td align="center">7.886</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Spring to Year 1 Summer</td><td align="center">1.047</td><td align="center">2.049</td><td align="center">0.511</td><td align="center">0.618</td></tr><tr><td align="left">Year 1 Summer to Year 2 Fall</td><td align="center">3.207</td><td align="center">3.081</td><td align="center">1.041</td><td align="center">0.326</td></tr><tr><td align="left">Grade 2</td></tr><tr><td align="left">Intercept</td><td align="center">145.733</td><td align="center">1.060</td><td align="center">137.434</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Fall to Year 1 Spring</td><td align="center">9.122</td><td align="center">0.617</td><td align="center">14.790</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Spring to Year 1 Summer</td><td align="center">−0.797</td><td align="center">1.630</td><td align="center">−0.489</td><td align="center">0.629</td></tr><tr><td align="left">Year 1 Summer to Year 2 Fall</td><td align="center">−3.189</td><td align="center">1.947</td><td align="center">−1.638</td><td align="center">0.117</td></tr><tr><td align="left">Grade 3</td></tr><tr><td align="left">Intercept</td><td align="center">152.819</td><td align="center">1.757</td><td align="center">86.981</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Fall to Year 1 Spring</td><td align="center">9.037</td><td align="center">0.865</td><td align="center">10.448</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Spring to Year 1 Summer</td><td align="center">0.369</td><td align="center">1.534</td><td align="center">0.241</td><td align="center">0.811</td></tr><tr><td align="left">Year 1 Summer to Year 2 Fall</td><td align="center">2.259</td><td align="center">1.603</td><td align="center">1.409</td><td align="center">0.167</td></tr><tr><td align="left">Grade 4</td></tr><tr><td align="left">Intercept</td><td align="center">175.821</td><td align="center">2.940</td><td align="center">59.805</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Fall to Year 1 Spring</td><td align="center">4.079</td><td align="center">1.118</td><td align="center">3.649</td><td align="center">0.002</td></tr><tr><td align="left">Year 1 Spring to Year 1 Summer</td><td align="center">−1.727</td><td align="center">1.772</td><td align="center">−0.974</td><td align="center">0.344</td></tr><tr><td align="left">Year 1 Summer to Year 2 Fall</td><td align="center">1.880</td><td align="center">2.291</td><td align="center">0.820</td><td align="center">0.421</td></tr><tr><td align="left">Grade 5</td></tr><tr><td align="left">Intercept</td><td align="center">182.765</td><td align="center">3.011</td><td align="center">60.705</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Fall to Year 1 Spring</td><td align="center">5.100</td><td align="center">0.884</td><td align="center">5.769</td><td align="center">< 0.001</td></tr><tr><td align="left">Year 1 Spring to Year 1 Summer</td><td align="center">−0.383</td><td align="center">1.937</td><td align="center">−0.198</td><td align="center">0.845</td></tr><tr><td align="left">Year 1 Summer to Year 2 Fall</td><td align="center">0.285</td><td align="center">1.847</td><td align="center">0.154</td><td align="center">0.879</td></tr></tbody></table> </ephtml> </p> <p>6 <emph>Note:</emph> Intercept represents the average MAP scores at Year 1 Fall for treatment group students. Bold values indicate significant results.</p> <hd id="AN0188874266-23">Subgroup Analyses</hd> <p></p> <hd id="AN0188874266-24">RQ3: Conditional Piecewise Growth Model of the Treatment Group Only</hd> <p>Table 6 presents the outcomes of the conditional piecewise growth model applied to the treatment group. These models considered students' demographic characteristics (i.e., race, ML, FRL, and SPED), but because there were no students identified as ML in the first‐grade summer program, no results are available for this subgroup. The intercept in the model signifies the average MAP scale scores at Year 1 Fall for the reference group of non‐Hispanic, White, non‐ML, non‐FRL, and non‐SPED treatment students. In all grades, that reference group exhibited a pattern of positive growth rates before participating in the summer program (from Year 1 Fall to Year 1 Spring), and this was statistically significant in Grades 1–3. The reference group in all grades had consistent indications of non‐significant positive growth while in the summer program and inconsistent patterns of non‐significant change after the summer program. Collectively, the results suggest neither the period with nor without instruction in the summer made a meaningful difference in reference group performance. Only in Grade 2 did the reference group demonstrate a significant summer‐to‐fall decline.</p> <p>6 TABLE RQ3: Conditional piecewise growth model of the treatment group only.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Parameter</th><th align="center">Grade 1</th><th align="center">Grade 2</th><th align="center">Grade 3</th><th align="center">Grade 4</th><th align="center">Grade 5</th></tr><tr><th align="center">Est.</th><th align="center"><italic>p</italic></th><th align="center">Est.</th><th align="center"><italic>p</italic></th><th align="center">Est.</th><th align="center"><italic>p</italic></th><th align="center">Est.</th><th align="center"><italic>p</italic></th><th align="center">Est.</th><th align="center"><italic>p</italic></th></tr><tr><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th></tr></thead><tbody valign="top"><tr><td align="left">Intercept</td><td align="center">129.2883.042</td><td align="center">< 0.00142.505</td><td align="center">148.2181.724</td><td align="center">< 0.00185.973</td><td align="center">155.2743.318</td><td align="center">< 0.00146.789</td><td align="center">191.6134.344</td><td align="center">< 0.00144.106</td><td align="center">185.0916.724</td><td align="center">< 0.00127.527</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr</td><td align="center">7.8031.961</td><td align="center">0.0013.979</td><td align="center">9.0471.185</td><td align="center">< 0.0017.636</td><td align="center">10.1491.602</td><td align="center">< 0.0016.337</td><td align="center">2.3392.224</td><td align="center">0.3021.052</td><td align="center">3.8192.369</td><td align="center">0.1211.612</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: Other Race</td><td align="center">1.3893.906</td><td align="center">0.7270.356</td><td align="center">−0.8721.816</td><td align="center">0.634−0.480</td><td align="center">0.0311.901</td><td align="center">0.9870.016</td><td align="center">1.5223.268</td><td align="center">0.6450.466</td><td align="center">4.1802.836</td><td align="center">0.1501.474</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: ML</td><td align="center">—</td><td align="center">—</td><td align="center">−0.5432.916</td><td align="center">0.853−0.186</td><td align="center">3.4483.729</td><td align="center">0.3580.925</td><td align="center">−1.1136.329</td><td align="center">0.862−0.176</td><td align="center">−3.9905.154</td><td align="center">0.443−0.774</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: FRL</td><td align="center">−0.7412.394</td><td align="center">0.761−0.309</td><td align="center">0.5531.488</td><td align="center">0.7120.372</td><td align="center">−1.5281.565</td><td align="center">0.332−0.976</td><td align="center">1.2522.746</td><td align="center">0.6520.456</td><td align="center">1.0822.693</td><td align="center">0.6920.402</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: SPED</td><td align="center">1.6973.932</td><td align="center">0.6720.432</td><td align="center">−0.1771.499</td><td align="center">0.906−0.118</td><td align="center">−1.0011.594</td><td align="center">0.532−0.628</td><td align="center">1.3842.398</td><td align="center">0.5680.577</td><td align="center">−0.0401.933</td><td align="center">0.984−0.021</td></tr><tr><td align="left">Yr 1 Spr to Yr 1 Summ</td><td align="center">4.3463.898</td><td align="center">0.2811.115</td><td align="center">0.2902.629</td><td align="center">0.9130.110</td><td align="center">2.1002.883</td><td align="center">0.4700.728</td><td align="center">0.1323.581</td><td align="center">0.9710.037</td><td align="center">6.0885.154</td><td align="center">0.2501.186</td></tr><tr><td align="left">Yr 1 Spr to Yr 1 Summ: Other Race</td><td align="center">−13.2007.508</td><td align="center">0.094−1.758</td><td align="center">4.4083.724</td><td align="center">0.2431.184</td><td align="center">−7.5113.751</td><td align="center">0.051−2.002</td><td align="center">0.2765.140</td><td align="center">0.9580.054</td><td align="center">−0.9846.006</td><td align="center">0.871−0.164</td></tr><tr><td align="left">Yr 1 Spr to Yr 1 Summ: ML</td><td align="center">—</td><td align="center">—</td><td align="center">−8.4106.724</td><td align="center">0.221−1.251</td><td align="center">−0.4327.216</td><td align="center">0.953−0.06</td><td align="center">2.9329.510</td><td align="center">0.7610.308</td><td align="center">−4.07510.813</td><td align="center">0.709−0.377</td></tr><tr><td align="left">Yr 1 Spr to Yr 1 Summ: FRL</td><td align="center">−2.5674.637</td><td align="center">0.586−0.553</td><td align="center">−0.5583.046</td><td align="center">0.856−0.183</td><td align="center">0.6572.991</td><td align="center">0.8270.220</td><td align="center">0.3274.494</td><td align="center">0.9430.073</td><td align="center">−6.2725.831</td><td align="center">0.295−1.076</td></tr><tr><td align="left">Yr 1 Spr to Yr 1 Summ: SPED</td><td align="center">−12.5137.971</td><td align="center">0.140−1.570</td><td align="center">−3.6073.032</td><td align="center">0.241−1.190</td><td align="center">−1.0333.022</td><td align="center">0.734−0.342</td><td align="center">−6.5093.843</td><td align="center">0.104−1.694</td><td align="center">−3.0904.096</td><td align="center">0.457−0.754</td></tr><tr><td align="left">Yr 1 Summ to Yr 2 Fall</td><td align="center">9.2205.699</td><td align="center">0.1341.618</td><td align="center">−6.6553.254</td><td align="center">0.049−2.045</td><td align="center">−3.8213.122</td><td align="center">0.230−1.224</td><td align="center">3.7565.165</td><td align="center">0.4760.727</td><td align="center">−8.6714.617</td><td align="center">0.074−1.878</td></tr><tr><td align="left">Yr 1 Summ to Yr 2 Fall: Other Race</td><td align="center">4.2709.977</td><td align="center">0.6760.428</td><td align="center">−3.3865.002</td><td align="center">0.503−0.677</td><td align="center">8.7864.106</td><td align="center">0.0402.140</td><td align="center">2.3277.348</td><td align="center">0.7550.317</td><td align="center">2.7045.727</td><td align="center">0.6400.472</td></tr><tr><td align="left">Yr 1 Summ to Yr 2 Fall: ML</td><td align="center">—</td><td align="center">—</td><td align="center">11.9797.995</td><td align="center">0.1431.498</td><td align="center">0.6407.879</td><td align="center">0.9360.081</td><td align="center">−0.18113.497</td><td align="center">0.989−0.013</td><td align="center">−8.34910.446</td><td align="center">0.430−0.799</td></tr><tr><td align="left">Yr 1 Summ to Yr 2 Fall: FRL</td><td align="center">−9.6946.302</td><td align="center">0.146−1.538</td><td align="center">1.9734.099</td><td align="center">0.6330.481</td><td align="center">6.4243.264</td><td align="center">0.0571.968</td><td align="center">−5.9026.491</td><td align="center">0.374−0.909</td><td align="center">9.3595.265</td><td align="center">0.0891.778</td></tr><tr><td align="left">Yr 1 Summ to Yr 2 Fall: SPED</td><td align="center">−4.22012.158</td><td align="center">0.738−0.347</td><td align="center">7.0814.133</td><td align="center">0.0961.713</td><td align="center">−0.8473.297</td><td align="center">0.799−0.257</td><td align="center">7.1915.508</td><td align="center">0.2071.306</td><td align="center">2.8163.856</td><td align="center">0.4700.730</td></tr></tbody></table> </ephtml> </p> <ulist> <item>7 <emph>Note:</emph> Intercept represents the average MAP scores at Year 1 Fall for White, non‐Hispanic, non‐ML, non‐FRL, and non‐SPED students. Bold values indicate significant results.</item> <item>8 Abbreviations: Est, estimate; FRL, free or reduced‐price lunch, a proxy for economic disadvantage; ML, multilingual learners (none were present in grade 1); Other Race, race or ethnicity other than White non‐Hispanic; SPED, students receiving special education services; Spr, spring; Std Err, standard error; Summ, summer; Yr, year.</item> </ulist> <p>Among the subgroups of treatment students, there were varying patterns of positive and negative growth relative to the reference group. None were statistically significant during the school year or the summer program; but after the summer program, Grade 3 treatment students identified as a race other than White (i.e., Asian, Black, or Hispanic) had significantly greater growth than the reference group when not receiving any instruction.</p> <hd id="AN0188874266-25">RQ3: Conditional Piecewise Growth Model of the Control Group Only</hd> <p>Table 7 presents the results of the conditional piecewise growth model applied to the control group. Similar to Table 6, the intercept in this analysis represents the average scores at Year 1 Fall for the reference group composed of non‐Hispanic, white, non‐ML, non‐FRL, and non‐SPED control group students. Across all grades, the reference group exhibited significantly positive growth before the summer (from Year 1 Fall to Year 1 Spring), with Grade 4 showing the lowest positive growth rate. After the summer break (Year 1 Spring to Year 2 Fall), Grades 1–3 control students in the reference group demonstrated a pattern of negative growth, but only for second graders was there a statistically significant decline. Conversely, the pattern of data among the Grades 4 and 5 reference group showed indications of positive but non‐significant growth.</p> <p>7 TABLE RQ3: Conditional piecewise growth model of the control group only.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Parameter</th><th align="center">Grade 1</th><th align="center">Grade 2</th><th align="center">Grade 3</th><th align="center">Grade 4</th><th align="center">Grade 5</th></tr><tr><th align="center">Est.</th><th align="center"><italic>p</italic> value</th><th align="center">Est.</th><th align="center"><italic>p</italic> value</th><th align="center">Est.</th><th align="center"><italic>p</italic> value</th><th align="center">Est.</th><th align="center"><italic>p</italic> value</th><th align="center">Est.</th><th align="center"><italic>p</italic> value</th></tr><tr><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th><th align="center">Std Err</th><th align="center"><italic>t</italic></th></tr></thead><tbody valign="top"><tr><td align="left">Intercept</td><td align="center">130.7850.914</td><td align="center">< 0.001143.116</td><td align="center">148.0751.366</td><td align="center">< 0.001108.383</td><td align="center">160.5321.535</td><td align="center">< 0.001104.578</td><td align="center">182.6431.782</td><td align="center">< 0.001102.476</td><td align="center">177.6353.022</td><td align="center">< 0.00158.788</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr</td><td align="center">8.1900.816</td><td align="center">< 0.00110.034</td><td align="center">8.7110.828</td><td align="center">< 0.00110.518</td><td align="center">9.5920.797</td><td align="center">< 0.00112.041</td><td align="center">5.2990.775</td><td align="center">< 0.0016.839</td><td align="center">9.1261.395</td><td align="center">< 0.0016.541</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: Other Race</td><td align="center">1.4871.078</td><td align="center">0.1701.379</td><td align="center">−1.5640.742</td><td align="center">0.036−2.106</td><td align="center">−0.1650.863</td><td align="center">0.849−0.191</td><td align="center">−0.1920.679</td><td align="center">0.777−0.283</td><td align="center">−1.0321.348</td><td align="center">0.445−0.765</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: ML</td><td align="center">0.3701.217</td><td align="center">0.7610.304</td><td align="center">2.4340.969</td><td align="center">0.0132.510</td><td align="center">−0.8631.144</td><td align="center">0.452−0.754</td><td align="center">2.1460.903</td><td align="center">0.0182.378</td><td align="center">0.7442.192</td><td align="center">0.7350.339</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: FRL</td><td align="center">−1.8640.875</td><td align="center">0.035−2.131</td><td align="center">−0.3860.841</td><td align="center">0.647−0.458</td><td align="center">0.0640.838</td><td align="center">0.9390.076</td><td align="center">0.1890.807</td><td align="center">0.8150.234</td><td align="center">−2.6441.369</td><td align="center">0.054−1.931</td></tr><tr><td align="left">Yr 1 Fall to Yr 1 Spr: SPED</td><td align="center">−0.0961.125</td><td align="center">0.932−0.086</td><td align="center">−0.0400.745</td><td align="center">0.958−0.053</td><td align="center">−1.1080.742</td><td align="center">0.136−1.494</td><td align="center">0.5690.661</td><td align="center">0.3900.861</td><td align="center">−0.1471.236</td><td align="center">0.905−0.119</td></tr><tr><td align="left">Yr 1 Spring to Yr 2 Fall</td><td align="center">−1.5161.323</td><td align="center">0.255−1.146</td><td align="center">−7.3571.706</td><td align="center">< 0.001−4.313</td><td align="center">−0.8341.299</td><td align="center">0.522−0.642</td><td align="center">1.5041.479</td><td align="center">0.3101.017</td><td align="center">0.1600.743</td><td align="center">0.8300.215</td></tr><tr><td align="left">Yr 1 Spring to Yr 2 Fall: Other Race</td><td align="center">−2.4421.888</td><td align="center">0.198−1.293</td><td align="center">2.0701.628</td><td align="center">0.2051.272</td><td align="center">−0.6291.385</td><td align="center">0.650−0.454</td><td align="center">−1.4291.280</td><td align="center">0.265−1.116</td><td align="center">0.8620.710</td><td align="center">0.2261.214</td></tr><tr><td align="left">Yr 1 Spring to Yr 2 Fall: ML</td><td align="center">−0.0692.158</td><td align="center">0.974−0.032</td><td align="center">1.4332.100</td><td align="center">0.4960.682</td><td align="center">−0.5431.839</td><td align="center">0.768−0.295</td><td align="center">−0.7001.701</td><td align="center">0.681−0.412</td><td align="center">2.0871.158</td><td align="center">0.0721.802</td></tr><tr><td align="left">Yr 1 Spring to Yr 2 Fall: FRL</td><td align="center">1.5691.519</td><td align="center">0.3031.033</td><td align="center">1.3391.800</td><td align="center">0.4580.744</td><td align="center">0.3711.348</td><td align="center">0.7830.275</td><td align="center">−0.2701.521</td><td align="center">0.859−0.177</td><td align="center">0.5120.724</td><td align="center">0.4800.707</td></tr><tr><td align="left">Yr 1 Spring to Yr 2 Fall: SPED</td><td align="center">0.1181.927</td><td align="center">0.9510.061</td><td align="center">4.4971.621</td><td align="center">0.0062.774</td><td align="center">−0.9491.193</td><td align="center">0.427−0.795</td><td align="center">−3.1571.247</td><td align="center">0.012−2.533</td><td align="center">1.0210.651</td><td align="center">0.1181.567</td></tr></tbody></table> </ephtml> </p> <ulist> <item>9 <emph>Note:</emph> Intercept represents the average MAP scores at Year 1 Fall for White, non‐Hispanic non‐ML, non‐FRL, and non‐SPED students. Bold values indicate significant results.</item> <item>10 Abbreviations: Est, estimate; FRL, free or reduced‐price lunch, a proxy for economic disadvantage; ML, multilingual learners (none were present in grade 1); Other Race, race or ethnicity other than White non‐Hispanic; SPED, students receiving special education services; Spr, spring; Std Err, standard error; Yr, year.</item> </ulist> <p>Both before and after the summer break, growth rates for the demographic subgroups of control students showed varying patterns of positive and negative growth relative to the reference group. Four were statistically significant before summer. These included significantly negative growth relative to the reference group for Grade 1 control students receiving FRL and Grade 2 control students identified as a race other than White. The two significantly positive growth rates before summer were found for second and fourth graders identified as ML. After the summer break, the only two significant growth rates were for control students in SPED. In Grade 2, the SPED students had significantly positive growth compared to the reference group, whereas the Grade 4 SPED students had significantly negative growth.</p> <hd id="AN0188874266-26">Discussion</hd> <p>Overall, our longitudinal analyses were consistent with previous findings that indicate there are variations in student growth within and across school years, as well as by certain demographic characteristics, but there were no systematic patterns of loss in abilities due to a lack of summer instruction (Atteberry and McEachin [<reflink idref="bib2" id="ref64">2</reflink>]; Reed et al. [<reflink idref="bib36" id="ref65">36</reflink>]). It should be noted that our sample consisted of students eligible for the school district's summer program due to not meeting MAP benchmarks. There were higher‐than‐typical percentages of students receiving SPED services and those from economically disadvantaged backgrounds—two classifications that historically have been targeted for summer reading programs (Battle v. Commonwealth of Pennsylvania [<reflink idref="bib5" id="ref66">5</reflink>]; Harris [<reflink idref="bib14" id="ref67">14</reflink>]). We discuss the results by research question.</p> <hd id="AN0188874266-27">RQ1: Comparing Treatment and Control Growth Trajectories Without a Summer Testing Point</hd> <p>As reported elsewhere (Kuhfeld and Soland [<reflink idref="bib23" id="ref68">23</reflink>]), curvilinear growth trajectories generally were observed among the present sample of students in Grades 1–5, with data trends that varied by testing wave and by grade for both groups (see Figures S1–S5 in the Supporting Information). Although neither the treatment nor control group was scoring proficiently at the Year 1 Winter MAP administration, the treatment group tended to score slightly lower on average at all testing points before propensity score weighting, and their rate of change was only negligibly higher than the control group. This suggests that elementary students performing below proficiency cut points still exhibit a range of abilities (James et al. [<reflink idref="bib17" id="ref69">17</reflink>]; Vargas et al. [<reflink idref="bib42" id="ref70">42</reflink>]), and even if those lower in the "not proficient" distribution experience similar benefit from the school‐year instruction (i.e., similar rates of positive growth), usually that will not be enough to help them catch up with their "not proficient" peers performing higher in the distribution.</p> <p>After propensity score weighting, all students included in the conditional piecewise growth model—regardless of group membership—demonstrated statistically significantly positive growth during the school year. Unfortunately, participating in a summer reading program did not guarantee an acceleration in students' learning. Although the significant Grade 2 declines observed from Year 1 Spring to Year 2 Fall probably were an artifact of the change in test format, skill difficulty, and administration procedures (Little et al. [<reflink idref="bib24" id="ref71">24</reflink>]; NWEA [<reflink idref="bib30" id="ref72">30</reflink>]; Reed et al. [<reflink idref="bib36" id="ref73">36</reflink>]), treatment students exhibited only slightly less decline than the control students. This suggests treatment students were no better prepared than their propensity score weighted peers for having the audio supports withdrawn or transitioning to more items with connected text reading and a greater emphasis on comprehension and vocabulary. In addition, Grade 5 students' performance was statistically significantly better without having participated in the summer program and not significantly improved with the provision of summer reading instruction. Overall, our hypothesis of positive school‐year growth but stagnant summer performance was confirmed for treatment and control students.</p> <p>Such findings would seem to make it difficult for schools to justify the high costs of holding summer reading programs (Reed et al. [<reflink idref="bib37" id="ref74">37</reflink>]), but there were two exceptions in the results. Figures S1 and S3 in the Supporting Information reveal that treatment students in Grade 1 surpassed the control group by Year 2 Fall, and treatment students in Grade 3 nearly closed the gap with control group students by Year 2 Fall. However, our piecewise growth model found that the Year 1 Spring to Year 2 Fall growth was statistically significant only in Grade 3, which may have been due to the small sample size in Grade 1. It also is worth noting that treatment students in these grades had been experiencing a higher rate of growth than their control group peers prior to summer, which may have meant the summer instruction was well timed for furthering that trajectory. Thus, findings from the group comparisons demonstrate that it could be insightful to model all time points from the school‐year administrations rather than just spring and fall, as is typical in studies of the summer effect (e.g., Atteberry and McEachin [<reflink idref="bib2" id="ref75">2</reflink>]; Rambo‐Hernandez et al. [<reflink idref="bib33" id="ref76">33</reflink>]).</p> <p>It is curious why the summer reading program would have benefited Grade 3 students when it did not improve the performance of students in Grades 4 and 5, given that all three of these grade levels have similar MAP test formats. Yet, there are increasing expectations for inferential comprehension and academic vocabulary knowledge across the grades (NWEA [<reflink idref="bib29" id="ref77">29</reflink>]), so it is possible the short instructional time period of summer (6 weeks) was not sufficient for improving more complex comprehension and vocabulary skills that might take more time and support to develop. Indeed, reported effects on reading achievement have been stronger when participation in a summer program spans multiple years (Borman and Dowling [<reflink idref="bib6" id="ref78">6</reflink>]). Because the spring‐to‐fall growth trajectories in the RQ1 analyses did not include a summer testing point, it also is possible that information on students' performance could be missed or misunderstood—a potential we explored by analyzing the treatment and control groups separately.</p> <hd id="AN0188874266-28">RQ2: Treatment Group Seasonal Growth With a Summer Testing Point</hd> <p>Our hypotheses of significant growth in Grades 1–2 and stagnation in Grades 3–5 during the summer program were rejected, as were our hypotheses of decline in Grades 1–2 and continued stagnation in Grades 3–5 after the summer program. In fact, the unconditional models revealed that treatment students had non‐significant trends toward stable or declining performance while receiving summer instruction (Year 1 Spring through Year 1 Summer) Then—with the exception of Grade 2—treatment students demonstrated non‐significant positive growth in the summer‐to‐fall break from instruction. To our knowledge, the present study is the first to report scores trending upward between the end of a summer program and the start of the next school year.</p> <p>Although the growth rates during and after the summer program were not significant, our findings are in contrast with those of Zvoch and Stevens ([<reflink idref="bib48" id="ref79">48</reflink>]) whose piecewise growth models found that students increased in performance during their summer instruction and had declining growth rates between the end of the program and the start of fall. There are two important differences in the studies. First, the summer program in the Zvoch and Stevens ([<reflink idref="bib48" id="ref80">48</reflink>]) study occurred with a relatively equal break between the spring and fall instruction, whereas the present study's summer program began immediately after the spring instruction ended. This left a longer break between summer and fall instruction that, if the Zvoch and Stevens results had held, should have resulted in greater declines but did not.</p> <p>The fact that students tended to increase during the longer break could be related to the second difference from the Zvoch and Stevens study. That is, the previous work modeled students' words read correctly per minute on an oral reading fluency measure, whereas the present study used data from a computer‐adaptive assessment of overall reading ability with composite scores scaled in Rasch units. It is possible that students' fluency could become rusty when not rehearsed (Reed et al. [<reflink idref="bib36" id="ref81">36</reflink>]), and because the passages on such measures increase in difficulty between grade levels, the cut score for proficiency typically is lower in fall than in spring. Hence, oral reading fluency scores may only appear to decline in fall, when students' performance relative to the cut point for proficiency actually might be increasing (Reed et al. [<reflink idref="bib36" id="ref82">36</reflink>]).</p> <p>Given the improved summer‐to‐fall performance found on the computer‐adaptive measure, it is possible the summer program better prepared students for starting strong in most grades and requiring less catch up in Grade 4. There is evidence to suggest that reading development might benefit from sequential school‐year and summer interventions that distribute the instructional and practice time and allow for greater consolidation of learning (Katzir et al. [<reflink idref="bib19" id="ref83">19</reflink>]). However, our results also might suggest that, similar to measures of oral reading fluency, MAP is scaled to be more suitable for tracking within‐ than between‐school year growth (Kolen and Brennan [<reflink idref="bib22" id="ref84">22</reflink>]). After all, the summer test was an extra administration at the Year 1 grade level without an established benchmark for proficiency. Whether upwardly or downwardly biased, questions remain about the appropriateness of using tests designed to track school‐year growth for measuring outcomes of summer learning.</p> <hd id="AN0188874266-29">RQ3: Subgroup Performance in Separate Treatment and Control Group Models</hd> <p></p> <hd id="AN0188874266-30">Treatment Group With a Summer Testing Point</hd> <p>Results of the conditional piecewise growth models that included the summer testing point for treatment students revealed that the reference group tended to have non‐significant trends of stable or increasing performance while receiving summer instruction (Year 1 Spring through Year 1 Summer); whereas subgroup performance often trended downward during this time. After the summer instruction ended, the Grades 1 and 4 reference groups exhibited a non‐significant trend of increasing performance that exceeded their growth during the summer program. This change in trajectory was particularly noteworthy for Grade 4 because, when the summer testing point was not included in the model (see Figure S4 in the Supporting Information), it appeared treatment students only declined from spring to fall. The fact that growth did not occur consistently for vulnerable subgroups of students receiving instruction runs contrary to the typical rationale for summer programs, which postulates students decline when they do not have full and equal access to literacy resources and instruction (Cooper et al. [<reflink idref="bib7" id="ref85">7</reflink>]; Davies and Aurini [<reflink idref="bib8" id="ref86">8</reflink>]; Downey et al. [<reflink idref="bib10" id="ref87">10</reflink>]; Heyns [<reflink idref="bib15" id="ref88">15</reflink>]; Tiruchittampalam et al. [<reflink idref="bib40" id="ref89">40</reflink>]; van der Kleij et al. [<reflink idref="bib41" id="ref90">41</reflink>]). Hence, our hypothesis was rejected.</p> <hd id="AN0188874266-31">Control Group Without a Summer Testing Point</hd> <p>As with the between‐group comparisons, the model for the control group alone relied on the school‐year MAP data because control students did not participate in the summer program or summer testing. There were variations in the rates of growth but few significant differences by demographic characteristics. Spring‐to‐fall growth among control students in Grades 1 and 2 showed a declining trend, whereas the trend was to have relatively stable performance in Grades 3 to 5. The former could be indicative of forgetting or becoming unrehearsed in the word‐level skills tested (Reed et al. [<reflink idref="bib36" id="ref91">36</reflink>]). The latter is consistent with previous research that has found stagnation may be more likely than loss over the summer (von Hippel et al. [<reflink idref="bib44" id="ref92">44</reflink>]). In only two cases was student growth significantly slower while not receiving instruction: the Grade 2 reference group and the Grade 4 SPED subgroup.</p> <hd id="AN0188874266-32">Limitations and Directions for Future Research</hd> <p>Our sample focused on students not reading proficiently who have been the focus of U.S. state policies on summer reading programs since the early 2000s (Early Learning‐20 Education Code [<reflink idref="bib11" id="ref93">11</reflink>]; Reed et al. [<reflink idref="bib38" id="ref94">38</reflink>]), and it included high percentages of the students who historically have been targeted for summer reading programs (Cooper et al. [<reflink idref="bib7" id="ref95">7</reflink>]; Davies and Aurini [<reflink idref="bib8" id="ref96">8</reflink>]; Downey et al. [<reflink idref="bib10" id="ref97">10</reflink>]; Heyns [<reflink idref="bib15" id="ref98">15</reflink>]; Tiruchittampalam et al. [<reflink idref="bib40" id="ref99">40</reflink>]; van der Kleij et al. [<reflink idref="bib41" id="ref100">41</reflink>]). However, the sample was predominately White, non‐Hispanic, monolingual English speakers. Therefore, our results may not generalize to students with greater racial, ethnic, and language diversity. In addition, our samples of treatment students were relatively small, so it is possible growth would differ if modeled with larger groups. Thus, future research should seek to model the growth trajectories of treatment and control students with a more diverse group and a larger number of students in a summer reading program.</p> <p>The low enrollment and high attrition rates in the district's summer program were similar to what has been reported elsewhere (Denton et al. [<reflink idref="bib9" id="ref101">9</reflink>]; Kim et al. [<reflink idref="bib20" id="ref102">20</reflink>]; Reed et al. [<reflink idref="bib35" id="ref103">35</reflink>]; White et al. [<reflink idref="bib46" id="ref104">46</reflink>]) but might suggest there was something distinguishing the treatment and control groups that we did not know and for which we have not accounted. The fact that the control groups generally performed at the higher end of the "not proficient" distribution relative to the treatment group, it could be that families are only committed to having their children participate if the children were more obviously struggling with reading. Mixed methods research might be useful in elucidating why families do and do not ensure their children enroll and fully attend summer programs.</p> <hd id="AN0188874266-33">Implications</hd> <p>Based on the positive spring‐to‐fall outcomes for Grades 1 and 3 treatment students who either surpassed or closed the gap with the control groups, it may be that summer programs could be more consistently successful if they focused on discrete skills and lower‐level comprehension. This could be important information for schools planning their summer offerings, which are held for short durations. It is possible schools—or perhaps the state policies driving the current summer programming (Reed et al. [<reflink idref="bib38" id="ref105">38</reflink>])—set unrealistic expectations for what and how much participating students should learn.</p> <p>Nevertheless, summer outcomes will remain difficult to determine until measures are developed that are valid and reliable for assessing summer growth. As has been noted (Little et al. [<reflink idref="bib24" id="ref106">24</reflink>]; NWEA [<reflink idref="bib30" id="ref107">30</reflink>]; Reed et al. [<reflink idref="bib36" id="ref108">36</reflink>]), our findings again demonstrate a measurement artifact of the MAP test at the start of Grade 2 when the audio supports are withdrawn and the composition of the test changes. Yet, the findings also contribute new information about a potential issue with measuring students' reading performance between grades. Because we had a summer testing point on treatment students, we were able to model their spring‐to‐summer and summer‐to‐fall growth trajectories. As previously described, these revealed that students might experience flat or declining performance while in the summer program and still be tested at their Year 1 grade levels but then inexplicably increase between the cessation of their summer instruction and the start of the new school year when tested at the Year 2 grade levels. The control students could not be tested in the summer, so it is not known whether their growth trajectories exhibit similar patterns.</p> <p>We also do not know the extent to which our findings might differ if students had been administered a different assessment. All instruments provide only an estimate of students' true reading abilities, so future research is needed with data gathered from other measures. Given the amount of research that has been devoted to the summer effect, it is critical that the measurement of students' growth between school years be investigated so that findings can properly inform educational policies and districts' allocation of resources.</p> <hd id="AN0188874266-34">Conclusions</hd> <p>What can be concluded from available data is that loss is not inevitable for all students from marginalized groups who are not in summer reading programs. Unfortunately, gain also is not guaranteed for students who do participate in summer reading programs. To the extent that improved reading performance is possible for even some vulnerable students not meeting proficiency benchmarks, it behooves researchers to continue investigating what is most successful at contributing to positive outcomes and the technically adequate ways of measuring summer learning.</p> <hd id="AN0188874266-35">Ethics Statement</hd> <p>Members of the research team did not have any contact with the human subjects and did not merge or enhance the dataset provided to them. Thus, the Institutional Review Board declared the research exempt.</p> <hd id="AN0188874266-36">Conflicts of Interest</hd> <p>The authors declare no conflicts of interest.</p> <hd id="AN0188874266-37">Data Availability Statement</hd> <p>Under the conditions of the data sharing agreement with the school district, the data cannot be provided to others; but the analytic code is available by emailing the corresponding author.</p> <p>GRAPH: Data S1: Supplementary Figures.</p> <ref id="AN0188874266-38"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref8" type="bt">1</bibl> <bibtext> Funding: This research was supported by the Iowa Department of Education (Contract #001622). The content is solely the responsibility of the authors and does not necessarily represent the official views of the funder.</bibtext> </blist> </ref> <ref id="AN0188874266-39"> <title> References </title> <blist> <bibtext> Anderson, D. 2019. 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  Data: <searchLink fieldCode="SO" term="%22Reading+Research+Quarterly%22"><i>Reading Research Quarterly</i></searchLink>. 2025 60(4).
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 18
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+1%22">Grade 1</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+3%22">Grade 3</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Growth+Models%22">Growth Models</searchLink><br /><searchLink fieldCode="DE" term="%22Summer+Programs%22">Summer Programs</searchLink><br /><searchLink fieldCode="DE" term="%22Reading+Programs%22">Reading Programs</searchLink><br /><searchLink fieldCode="DE" term="%22Reading+Achievement%22">Reading Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Testing%22">Testing</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+1%22">Grade 1</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+3%22">Grade 3</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="DE" term="%22Reading+Tests%22">Reading Tests</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1002/rrq.70060
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0034-0553<br />1936-2722
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Archival data were analyzed with piecewise growth models to determine the seasonal growth of students not reading proficiently who did (treatment students = 144) and did not (control students = 1113) participate in their school district's summer reading program. The rising first- through fifth graders (48% female) were predominately White (74%) and economically disadvantaged (79%). Control students tended to exhibit stable or declining spring-to-fall performance that was significant only in Grade 2, where a measurement artifact may have influenced results. When including a summer testing point in the models for treatment students, performance tended to be stable or declining while the students were receiving summer instruction but then improved during their subsequent summer-to-fall break. Conditional models revealed demographic subgroups had varying patterns of higher or lower growth rates compared to the reference groups, but rarely were these significant. Issues with measurement and implications for planning summer programs are discussed.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1487128
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1487128
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/rrq.70060
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
    Subjects:
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Growth Models
        Type: general
      – SubjectFull: Summer Programs
        Type: general
      – SubjectFull: Reading Programs
        Type: general
      – SubjectFull: Reading Achievement
        Type: general
      – SubjectFull: Testing
        Type: general
      – SubjectFull: Grade 1
        Type: general
      – SubjectFull: Grade 2
        Type: general
      – SubjectFull: Grade 3
        Type: general
      – SubjectFull: Grade 4
        Type: general
      – SubjectFull: Grade 5
        Type: general
      – SubjectFull: Reading Tests
        Type: general
    Titles:
      – TitleFull: Elementary Students' Reading Growth Trajectories with and without a Summer Testing Point in the Model
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Deborah K. Re
      – PersonEntity:
          Name:
            NameFull: Huibin Zhang
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 10
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 0034-0553
            – Type: issn-electronic
              Value: 1936-2722
          Numbering:
            – Type: volume
              Value: 60
            – Type: issue
              Value: 4
          Titles:
            – TitleFull: Reading Research Quarterly
              Type: main
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