Teachers' Use of Motivational Messages While Teaching Fractions
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| Title: | Teachers' Use of Motivational Messages While Teaching Fractions |
|---|---|
| Language: | English |
| Authors: | Megan Botello (ORCID |
| Source: | Grantee Submission. 2025 125(4). |
| Peer Reviewed: | Y |
| Page Count: | 25 |
| Publication Date: | 2025 |
| Sponsoring Agency: | National Center for Special Education Research (NCSER) (ED/IES) |
| Contract Number: | R324A200140 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Elementary Education Grade 6 Intermediate Grades Middle Schools Junior High Schools Secondary Education |
| Descriptors: | Grade 6, Fractions, Mathematics Instruction, Teaching Methods, Comparative Analysis, Intervention, Student Motivation, Motivation Techniques, Teacher Student Relationship, Transcripts (Written Records), Audio Equipment, Response to Intervention, Relevance (Education), Middle School Students, Learning Problems |
| DOI: | 10.1086/735431 |
| Abstract: | In this study, our team observed sixth grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy-Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed, comparing teachers taking part in the experimental fractions intervention and teachers teaching business-as-usual. The fraction lessons and motivational messages were coded via teachers' audio recordings over the span of 15 weeks (24 lessons). Findings revealed that teachers in the experimental group used significantly more motivationally-supportive messages than the teachers in the control group, as well as made deeper connections between content and students' lives. These results imply that the use of an intervention including motivational messages can further promote teachers' use of motivational strategies while teaching mathematical content. |
| Abstractor: | As Provided |
| IES Funded: | Yes |
| Entry Date: | 2025 |
| Accession Number: | ED673973 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwH2xCDcAbiShHzYBTpmQEbSAAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDF-PhbHFLXaXDtC_8wIBEICBmxRUxUwkWHuE15HlJNVlRVlclrGCzKIw2x1Yin6H-yPidYm4wMdeEWUH62nPrTs6Y_rWAkIH5t7Hq3gk5Gxzi5srj0gjh-2GoybNORlfWu6I29M_YCwnF1qGsY7sBuCBA4CIO6PCGh0EMkOO1JlmbNhDuNB3PkmZt98uIoDNRIZ8M07nwKYpBZqOqEKyGwErbH2ckVi8ByqB-8TH Text: Availability: 1 Value: <anid>AN0186290813;esj01jun.25;2025Jul02.05:10;v2.2.500</anid> <title id="AN0186290813-1">Teachers' Use of Motivational Messages While Teaching Fractions </title> <p>In this study, our team observed sixth-grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy–Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed, comparing teachers taking part in the experimental fractions intervention and teachers teaching business-as-usual. The fraction lessons and motivational messages were coded via teachers' audio recordings over the span of 15 weeks (24 lessons). Findings revealed that teachers in the experimental group used significantly more motivationally supportive messages than the teachers in the control group, and they made deeper connections between content and students' lives. These results imply that the use of an intervention including motivational messages can further promote teachers' use of motivational strategies while teaching mathematical content.</p> <p>Learning fractions is foundational not only for later mathematics, such as algebra, but also for day-to-day life activities, such as cooking and driving. Unfortunately, fractions are difficult for many students to understand, especially students who experience mathematics learning difficulties (MLD), who may continue to struggle with fractions well into secondary school (Fuchs et al., [<reflink idref="bib24" id="ref1">24</reflink>]). This can have impacts on students' academic and career prospects (Siegler et al., [<reflink idref="bib70" id="ref2">70</reflink>]). Students who have a strong foundation in fraction knowledge are better equipped in courses that lead to careers in science, technology, engineering, and mathematics (STEM) fields (Sadler &amp; Tai, [<reflink idref="bib63" id="ref3">63</reflink>]).</p> <p>When students struggle to learn foundational mathematical concepts such as fractions, they may begin to devalue mathematics altogether, which negatively affects their motivation to learn (Jacobs et al., [<reflink idref="bib41" id="ref4">41</reflink>]). This devaluation is a particular problem in middle school—Hulleman and Barron ([<reflink idref="bib37" id="ref5">37</reflink>]) found that 90% of middle schoolteachers were concerned that students lacked value for mathematics and that decreases in value got worse as students progressed through school. These findings emphasize the need for strategies to increase student motivation within their school activities. Students who perceive their environment to be more motivating have increased engagement in content and a better attitude toward school (Anderman et al., [<reflink idref="bib3" id="ref6">3</reflink>]). Increasing mathematics motivation in middle school is especially important (see Gafoor &amp; Kurukkan, [<reflink idref="bib26" id="ref7">26</reflink>]).</p> <p>Teachers play a large role in improving student motivation, because their instruction directly affects the quality of a student's learning experience (Burić &amp; Kim, [<reflink idref="bib8" id="ref8">8</reflink>]). Although research has shown successful ways of improving students' value for mathematics (e.g., through utility-value interventions; Hulleman &amp; Harackiewicz, [<reflink idref="bib39" id="ref9">39</reflink>]), less is known about how teachers may support student value through mathematics through their language as they engage in math instruction. In the present study, we collected observational data of middle schoolteachers teaching fractions to students with MLD and explored how these teachers use motivational messaging (i.e., utility value, interest, and self-efficacy) while teaching fractions. Two groups of teachers participated: One group taught as they usually would, and the other used a fraction intervention implemented as part of a broader study on teaching fraction sense to students. The intervention included some content presenting the usefulness of fractions in everyday life, but in both groups, teachers had opportunities to include their own motivational messages. We compared the frequency and content of these messages between teachers and across intervention groups to see whether they were associated with implementation of intervention content. Because understanding fractions is foundational for later subjects of mathematics (Resnick et al., [<reflink idref="bib56" id="ref10">56</reflink>]), results from this study may extend to many areas, from arithmetic to algebra to college readiness. In addition, focusing on outcome measures for middle school learners with MLD extends this work to an underresearched population that is especially in need of support (Louick, [<reflink idref="bib45" id="ref11">45</reflink>]).</p> <hd id="AN0186290813-2">Background</hd> <p></p> <hd id="AN0186290813-3">Conceptual Framework</hd> <p>We frame our work within Situated Expectancy–Value Theory (SEVT), established by Eccles and colleagues (Eccles, [<reflink idref="bib23" id="ref12">23</reflink>]; Eccles &amp; Wigfield, [<reflink idref="bib22" id="ref13">22</reflink>]), which posits that academic choice and performance are predicted by expectancies (i.e., the perceived ability to succeed on a task) and value beliefs (i.e., reasons for engaging in a task). Expectancies are theoretically related to other self-belief constructs, such as self-efficacy and self-concept (Bandura, [<reflink idref="bib4" id="ref14">4</reflink>]; Marsh, [<reflink idref="bib50" id="ref15">50</reflink>]). Within SEVT studies, expectancies are often measured using these related constructs (e.g., Eccles &amp; Wigfield, [<reflink idref="bib22" id="ref16">22</reflink>]; Rutherford et al., [<reflink idref="bib62" id="ref17">62</reflink>]). In this study, we focus on self-efficacy as our self-belief construct, because self-efficacy is more keyed toward immediate performance and therefore more likely to be observable as teachers' messages (see Bandura, [<reflink idref="bib4" id="ref18">4</reflink>]; Schunk &amp; Pajares, [<reflink idref="bib65" id="ref19">65</reflink>]). The value part of SEVT consists of the following components: intrinsic value (enjoyment of a task leading to interest), attainment value (importance of a task to one's identity), utility value (usefulness of task for one's goals), and cost (perceived negative consequences of a task). SEVT researchers and theorists suggest that students are motivated to actively participate in academic behaviors based on their understanding of the tasks at hand and their perception of themselves as learners (e.g., Eccles, [<reflink idref="bib20" id="ref20">20</reflink>]; Eccles &amp; Wigfield, [<reflink idref="bib21" id="ref21">21</reflink>]; Rosenzweig et al., [<reflink idref="bib61" id="ref22">61</reflink>]). This theory suggests that the value one holds for a task has implications for learning and engagement of the task.</p> <p>SEVT can be applied in classroom settings to improve motivation in various ways, such as by including hands-on experiences and engaging course material to promote students' interest in the content area (Bergin, [<reflink idref="bib6" id="ref23">6</reflink>]; Holstermann et al., [<reflink idref="bib36" id="ref24">36</reflink>]). Along with self-efficacy, the aspects of SEVT theory that are most relevant to the present study include "utility value" and "intrinsic value," referred to herein as "interest." Considering utility value provides connections between students' lives and content, and these connections improve STEM motivation by eliciting greater interest (Gaspard et al., [<reflink idref="bib27" id="ref25">27</reflink>]). Humor and teacher enthusiasm also enhance situational interest (Lu'mu et al., [<reflink idref="bib47" id="ref26">47</reflink>]; Machlev &amp; Karlin, [<reflink idref="bib48" id="ref27">48</reflink>]). We explore self-efficacy in this study through teachers' use of praise and encouragement while teaching. Research has shown that praise and encouragement influence students' self-efficacy (Denton, [<reflink idref="bib15" id="ref28">15</reflink>]; Main, [<reflink idref="bib49" id="ref29">49</reflink>]; Wang et al., [<reflink idref="bib73" id="ref30">73</reflink>]). One study by Wang and colleagues ([<reflink idref="bib73" id="ref31">73</reflink>]) suggests a positive relationship between self-efficacy and praise: The more praise teachers provided, the better self-efficacy was among students.</p> <hd id="AN0186290813-4">Interventions Grounded in SEVT</hd> <p>The growing literature on SEVT and self-efficacy interventions across contexts consistently demonstrates the effectiveness of these interventions in enhancing student motivation. Utility value, a central construct within SEVT, is particularly responsive to interventions, making it a crucial focus for improving student motivation (Eccles &amp; Wigfield, [<reflink idref="bib21" id="ref32">21</reflink>]). Research shows that emphasizing the relevance of content to students' lives can significantly boost their motivation and engagement. For example, utility-value interventions have been associated with increased student interest, perceived relevance, and academic performance (Gaspard et al., [<reflink idref="bib27" id="ref33">27</reflink>]; Harackiewicz et al., [<reflink idref="bib32" id="ref34">32</reflink>]; Hulleman &amp; Harackiewicz, [<reflink idref="bib39" id="ref35">39</reflink>]).</p> <p>Teachers play a critical role in this process, because their communication of content relevance greatly influences students' perceptions of its value. Studies indicate that when teachers frequently make relevance statements, students are more likely to view the material as valuable (Hulleman, Schrager, et al., [<reflink idref="bib40" id="ref36">40</reflink>]; Schmidt et al., [<reflink idref="bib64" id="ref37">64</reflink>]). In addition, SEVT interventions that focus on enhancing self-efficacy, particularly in mastery-oriented classrooms, have been shown to improve students' confidence in their abilities and their overall value beliefs (e.g., Eccles &amp; Wigfield, [<reflink idref="bib22" id="ref38">22</reflink>]). For instance, Newton et al. ([<reflink idref="bib51" id="ref39">51</reflink>]) found that students' self-efficacy beliefs improved during a fractions unit in a classroom that emphasized understanding over performance.</p> <p>Although these interventions show promise, it is essential to understand their effectiveness across various contexts and how they can support teachers in fostering student motivation. The effectiveness of SEVT-based interventions may vary depending on factors such as student achievement levels, subject matter, and classroom environment, with existing research indicating moderate effect sizes (<emph>d</emph> = 0.12–0.39; Hulleman &amp; Harackiewicz, [<reflink idref="bib39" id="ref40">39</reflink>]). The current study extends this literature by examining how an intervention designed for fraction learning affects teachers' use of SEVT-based motivational language—specifically, language promoting utility value, interest, and self-efficacy. This study focuses on the differences in teacher language between intervention and control conditions rather than directly measuring student outcomes, with the aim of understanding how such interventions can ultimately support teachers in benefiting their students.</p> <hd id="AN0186290813-5">Motivation and Mathematics Learning Difficulties</hd> <p>SEVT-based interventions have not been reported in the literature with this population, but there is reported research using other motivational constructs that may be helpful. For example, self-determination theory (Deci &amp; Ryan, [<reflink idref="bib12" id="ref41">12</reflink>]) and goal orientation theory (Ames, [<reflink idref="bib2" id="ref42">2</reflink>]) have been used to investigate the motivation beliefs of students with learning difficulties (Konrad et al., [<reflink idref="bib44" id="ref43">44</reflink>]; Sideridis, [<reflink idref="bib67" id="ref44">67</reflink>]). Researchers (Ames, [<reflink idref="bib2" id="ref45">2</reflink>]; Dweck &amp; Leggett, [<reflink idref="bib18" id="ref46">18</reflink>]) have found that the type of goal (e.g., mastery or performance-avoidance) a student with learning difficulties sets is associated with aspects of their academic well-being. Each theoretical frame employed to study motivation among this population provides new insights for researchers and teachers working to improve students' educational experiences (Louick, [<reflink idref="bib45" id="ref47">45</reflink>]).</p> <p>SEVT has garnered growing interest as a valuable tool in understanding the motivations of students with learning difficulties (e.g., Louick, [<reflink idref="bib45" id="ref48">45</reflink>]; Newton et al., [<reflink idref="bib51" id="ref49">51</reflink>]). This is because SEVT highlights various factors, such as cultural influences and the beliefs of those who have an impact on the student (socializers), that accumulate over time and shape a student's current motivation toward academic tasks (Eccles &amp; Wigfield, [<reflink idref="bib22" id="ref50">22</reflink>]; Lovett et al., [<reflink idref="bib46" id="ref51">46</reflink>]). In addition, some view SEVT as a promising approach for educators to improve their lesson planning and learning environment design for students with learning difficulties (De La Paz &amp; Butler, [<reflink idref="bib14" id="ref52">14</reflink>]). Furthermore, Louick ([<reflink idref="bib45" id="ref53">45</reflink>]) found that middle schoolteachers believe students with learning difficulties develop their motivation and engagement based on expectancy and value for success, which are shaped by societal constructions, socializers' beliefs, individual characteristics, and past experiences. These findings highlight the need for a comprehensive approach to understanding motivation in these students.</p> <p>In addition, Newton and colleagues ([<reflink idref="bib51" id="ref54">51</reflink>]) studied the population of students with learning disabilities, measuring their motivation using surveys and interviews. Their results showed improved self-efficacy beliefs and value for fractions during the fractions unit due to a mastery-oriented classroom, which emphasized understanding over performance. The current study will build on this prior work by examining the specific language that teachers use to promote student motivation for students with learning difficulties while learning fractions, with and without the use of a fraction-learning intervention.</p> <hd id="AN0186290813-6">Teaching Moves That Benefit Fraction Instruction</hd> <p>It is important that teachers recognize the challenges inherent in fraction learning and teach underlying fraction concepts so that students can develop deep understanding (Dyson et al., [<reflink idref="bib16" id="ref55">16</reflink>]; Jordan et al., [<reflink idref="bib42" id="ref56">42</reflink>], [<reflink idref="bib43" id="ref57">43</reflink>]). There are many ways teachers can help develop fraction sense. Such methods include the use of anchored instruction (the use of a real-life context to ground instruction; Bottge et al., [<reflink idref="bib7" id="ref58">7</reflink>]), multiple representations (the use of multiple models of the same concept help students grasp the underlying mathematical concept; Siegler &amp; Opfer, [<reflink idref="bib71" id="ref59">71</reflink>]), concreteness fading (the process of introducing a concept with concrete models that are then faded to iconic representations that are then faded to abstract or symbolic representations; Fyfe et al., [<reflink idref="bib25" id="ref60">25</reflink>]), gestures (the use of hand motions or animations to promote learning; Alibali &amp; Nathan, [<reflink idref="bib1" id="ref61">1</reflink>]), side-by-side solutions (displaying two or more ways of solving problems side by side to promote flexibility; Richland et al., [<reflink idref="bib57" id="ref62">57</reflink>]), and distributed and interleaved practice (spacing out practice over time and providing a variety of problems rather than one problem type in a single practice session; Rohrer et al., [<reflink idref="bib60" id="ref63">60</reflink>]).</p> <p>Practices that support motivation underlie some of these practices that support cognitive understanding. For example, anchored instruction is based on using real-life context, which is similar to supporting utility value, or helping students find connections between content and their personal life. Also, concreteness fading in math promotes student self-efficacy, as it fosters self-regulation and self-confidence, which ultimately builds self-efficacy (Grothérus et al., [<reflink idref="bib31" id="ref64">31</reflink>]). Including motivational aspects as part of a fractions intervention may have potential to increase students' fraction achievement and is worthy of future research.</p> <p>Last, teacher language affects student learning and motivation (Denton, [<reflink idref="bib15" id="ref65">15</reflink>]; Rimm-Kaufman et al., 2014). In her book, Denton ([<reflink idref="bib15" id="ref66">15</reflink>]) describes the principles of teacher language to help students learn. One of these principles is to express confidence in the capabilities and intentions of children. She states that teacher expectations directly influence student expectations for themselves. Using praise and encouragement through language is one way of communicating to students the faith their teacher has in their success. Rimm-Kaufman and colleagues ([<reflink idref="bib58" id="ref67">58</reflink>]) implemented a longitudinal study examining these principles' effect on student achievement in mathematics. They observed teachers' fidelity in the implementation of these principles and found that teachers who used these practices with greater fidelity in their teaching had greater student achievement. The potential impact that teacher language has on student motivation and achievement informs the focus and process of this study on teacher language.</p> <hd id="AN0186290813-7">Present Study</hd> <p>Prior research in SEVT in mathematics has largely focused on a specific course (e.g., college algebra) or mathematics in general (Gaspard et al., [<reflink idref="bib27" id="ref68">27</reflink>]; Hulleman &amp; Harackiewicz, [<reflink idref="bib39" id="ref69">39</reflink>]). This research has shown the importance of connecting academic content to students' personal and professional goals to increase their motivation and interest. We have also learned that interventions situated in SEVT can be an effective way of boosting students' motivation in science and math classes (e.g., Hulleman, Godes, et al., [<reflink idref="bib38" id="ref70">38</reflink>].; Newton et al., [<reflink idref="bib51" id="ref71">51</reflink>]; Schmidt et al., [<reflink idref="bib64" id="ref72">64</reflink>]). We have not yet learned in what other contexts and for which type of students these interventions are effective. Given the foundational role of fractions in higher mathematics, grounding this SEVT project in fraction learning can demonstrate broad potential of SEVT-supporting messaging for subsequent mathematics. In addition, focusing this work on middle school students with MLD targets an age and population that are in extra need of fraction learning and motivation support (Newton et al., [<reflink idref="bib52" id="ref73">52</reflink>]). By studying this population, we can understand boundary conditions of SEVT-type interventions, even without directly testing the intervention on MLD versus non-MLD populations (see discussion of <emph>utos</emph> in Shadish et al., [<reflink idref="bib66" id="ref74">66</reflink>]).</p> <p>The present study is part of a larger project investigating the effectiveness of a fraction sense intervention (FSI) for sixth-grade students who are performing at least 2 years below grade level in math. The present study focuses on math learning difficulties, which, as a term, encompasses those with math learning disabilities. The difference between math learning disabilities and math learning difficulties is not clear in the literature (Raghubar et al., [<reflink idref="bib55" id="ref75">55</reflink>]). We use <emph>learning difficulties</emph> in this article as a broader term encompassing any learning hindrance that may affect a student's math performance, not limited to only those students with a disability diagnosis.</p> <p>The FSI was designed to increase conceptual understanding of fractions. Although motivation was not an originally targeted outcome of the intervention, aspects of the intervention (e.g., supportive language and personal connections to students) may support motivation. Therefore, the aim of the present exploratory study is to analyze observed teacher language for evidence of language that supports a positive fraction-learning environment. We developed a coding framework that investigates teacher usage of utility value, interest, and self-efficacy (i.e., encouragement, discouragement, and praise) while they teach fraction lessons in their sixth-grade students' intervention classes. The findings compare the language of intervention teachers who implemented the FSI lessons and control teachers who taught business-as-usual (BAU), to see whether the intervention bolstered teachers' use of motivational language. Understanding the degree to which teachers communicate messages promoting utility value, interest, and self-efficacy may be pivotal for learners with MLD because these motivational constructs are closely tied to overcoming disengagement and low confidence, which are disproportionately prevalent in this population. To understand whether and how the intervention influenced teachers' motivationally supportive language, we ask:</p> <p></p> <p>• 1.</p> <p></p> <ulist> <item> How do teachers communicate the utility value of fractions, convey interest, and promote self-efficacy of fraction learning to students with MLD?</item> <p></p> </ulist> <p>• 2.</p> <p></p> <ulist> <item> Do teachers implementing the FSI have a greater frequency and quality of these messages than the BAU teachers?</item> </ulist> <hd id="AN0186290813-8">Method</hd> <p></p> <hd id="AN0186290813-9">Research Design</hd> <p>This study is an embedded, qualitative mixed-methods design (Creswell &amp; Plano Clark, [<reflink idref="bib11" id="ref76">11</reflink>]) in which qualitative data collection and analysis took place, followed by quantitative analysis of the qualitative findings. Interpretation of the qualitative and quantitative analyses is jointly presented in the results and discussion. Through audio recordings, the project team gathered qualitative data about teachers' use of SEVT language in their classrooms. Figure 1 outlines the design of this study. The purposes for using mixed methods in this study include complementarity and expansion, to connect results from both qualitative and quantitative methods and relate the outcomes, and to expand our findings to show a bigger picture (Greene, [<reflink idref="bib30" id="ref77">30</reflink>]).</p> <p>Graph: Figure 1. Using mixed-methods to explore motivational messaging while teaching fractions. MMR = mixed-methods research.</p> <hd id="AN0186290813-10">Participants</hd> <p>Participants included five teachers (six classrooms) of sixth-grade mathematics Response to Intervention (RTI) classes. The classes are designed to provide students who test at least two grade levels below in mathematics with extra teaching support. Three teachers were in the intervention condition and taught their class using the FSI (Barbieri et al., [<reflink idref="bib5" id="ref78">5</reflink>]; Dyson et al., [<reflink idref="bib16" id="ref79">16</reflink>]; Jordan et al., 2023), and the other two teachers (one of whom taught two sections) were in the control condition and taught their mathematics RTI class in a BAU manner. In the intervention group, there were 2 White men and 1 White woman, with teaching experience ranging from 8 to 18 years. The class sizes ranged from 8 to 10 students. In the control group, there was 1 White man and 1 White woman, with teaching experience ranging from 3 to 17 years. Their class sizes ranged from 10 to 14 students. Teachers were recruited via email after permission and access were granted through the mathematics administrator of the district and schools. Two schools within the same district participated, and the teachers within each school were randomly assigned to either the intervention or control condition.</p> <p>These public middle schools were situated in a mid-Atlantic state in mixed economic areas. The participating students' demographic information at School 1 included 25% White, 38% Black, 7% Hispanic, 17% with disabilities status, and 21% with low-income status. Student demographics at School 2 included 42% White, 45% Black, 21% Hispanic, 25% with disabilities status, and 40% with low-income status. Disability status was determined by school, meaning students who received special services and had an Individualized Education Plan. Some 40% of the 47 consenting students in this study had disability status. Low-income status was reported by the district's participation in free or reduced-price lunch programs. Consent from all teachers and 47 students was obtained prior to the start of the intervention.</p> <hd id="AN0186290813-11">Conditions</hd> <p></p> <hd id="AN0186290813-12">Intervention</hd> <p>The FSI was created by a team of researchers to develop an intervention for middle school students who struggle with fraction understanding, which has proven to be very effective in increasing students' understanding of fractions (Jordan et al., 2024). The FSI seeks to make explicit mathematical connections using the following validated learning strategies: multiple representations, gestures, concreteness fading, delayed and immediate interleaved practice, and feedback. These cognitive approaches are implemented via 24 animated PowerPoint lessons that are scripted for the teachers to easily administer to their students.</p> <p>The intervention consists of 24 lessons designed to be taught during a typical 30-minute mathematics RTI class. The lessons are set against the backdrop of an ongoing story about helping a student plan a 3-mile "color run." The unifying theme provides a real-life context for the lessons, which helps to engage students' interest throughout the lessons (Bottge et al., [<reflink idref="bib7" id="ref80">7</reflink>]; Dyson et al., 2020; Rodrigues et al., [<reflink idref="bib59" id="ref81">59</reflink>]).</p> <p>Each FSI lesson includes five short, consistent sections with corresponding activities. The activities are meant to reinforce the new fraction concepts being taught in the lesson or serve as a review of concepts from previous lessons. Breaking the lessons into shorter activities helps to hold students' attention and provides them with a variety of contexts for learning the targeted concepts (Gersten et al., [<reflink idref="bib28" id="ref82">28</reflink>]). The names given to the five lesson sections tie in thematically to the story of preparing for the color run (e.g., Warm-up and Cool-down).</p> <p>The intervention was not originally designed to include motivational messaging but is set up in a way that could help students succeed in developing self-efficacy in their fraction knowledge. The FSI coincidentally included components (i.e., provided examples of how fractions are used in daily life, activities to promote interest and engagement, and messages focused on effort and learning rather than perfection) theorized to benefit student motivation. Teachers were solely trained to use the cognitive approaches; therefore, we saw the opportunity to evaluate how the intervention includes motivational messaging as well (e.g., promoting the utility value of fractions).</p> <hd id="AN0186290813-13">Control</hd> <p>The control teachers taught their mathematics RTI classes BAU. These lessons were also focused on teaching elements of fractions to their students, with one teacher using the Mathematics 180 program and the other teacher using a teacher-driven approach supported by the Illustrative Mathematics curriculum. The lessons used in this study included all of the mathematics lessons the control teachers taught during the same time range that the intervention teachers taught the FSI lessons. One teacher in the BAU group used the same instructional strategies that the FSI teachers used in the lessons (e.g., gestures, visual representations) consistently, whereas the other teacher rarely used these strategies and had the students working on iReady independently in 45% of the classes.</p> <hd id="AN0186290813-14">Procedures</hd> <p>All participating teachers taught their RTI class while wearing an audio recorder around their neck to capture what was said by the teachers and students. Teachers' 24 fraction lessons were audio recorded and then transcribed via Otter AI (transcription software) and edited by two graduate and five undergraduate research assistants to capture everything said by the teacher and students.</p> <p>Students took pre- and postfractions assessments to test their understanding of fraction concepts and arithmetic. The pretest occurred over the span of 2 weeks in January/February due to scheduling and volume of students. The intervention followed immediately after the pretesting was completed. The posttest occurred 1 week after the end of the intervention in May. The main data sources for this project include audio recordings and the FSI PowerPoint lessons. After matching across data sources, the teacher transcripts were deidentified and stored on the university's secure server. Prior to the beginning of this project, approval was obtained from the Institutional Review Board of the University of Delaware.</p> <hd id="AN0186290813-15">Data Analysis</hd> <p></p> <hd id="AN0186290813-16">Coding framework</hd> <p>Teacher transcripts and FSI lessons were analyzed by trained researchers unaware of teacher condition. Qualitative coding with a theory-driven approach was used to code the lessons and transcripts (DeCuir-Gunby et al., [<reflink idref="bib13" id="ref83">13</reflink>]). This approach was used to deductively connect themes to the existing theoretical framework, SEVT. A deductive coding framework was created to assess the data for aspects of SEVT and related constructs, including utility value, situational interest, and self-efficacy (Bandura, [<reflink idref="bib4" id="ref84">4</reflink>]; Eccles, [<reflink idref="bib19" id="ref85">19</reflink>]; Hidi &amp; Renninger, [<reflink idref="bib34" id="ref86">34</reflink>]). This framework was chosen and created after an initial cycle of open coding, to see what motivational aspects were present in the data. We collaborated with three motivation researchers to create the final coding scheme. This process of feedback and collaboration was to ensure that we were defining the codes in a way that reflected accurate measurement of the SEVT constructs.</p> <p>The researchers assessed utility value–supporting language through teacher talk of relevance, because relevance increases utility value (Schmidt et al., [<reflink idref="bib64" id="ref87">64</reflink>]). The language included statements or activities that had the potential of students relating fractions or math to their lives, or so they understood the usefulness of the topic. Situational interest was assessed by analyzing teachers' use of engaging the student's interest or sense of fun in learning mathematics (Machlev &amp; Karlin, [<reflink idref="bib48" id="ref88">48</reflink>]), such as when a teacher used humor or enthusiasm to engage the students in the learning. Self-efficacy-supporting language was assessed through teachers' encouragement by giving praise (to the class or individually; Siegle &amp; McCoach, [<reflink idref="bib69" id="ref89">69</reflink>]), as well as comments promoting growth mindset (Dweck, [<reflink idref="bib17" id="ref90">17</reflink>]). Given the previous categories, we also coded for discouragement, or teacher criticism of students' work or understanding, to see if it was used in the absence of encouragement, and whether it had a potential opposite effect. It was coded the same way as the previous categories (Skipper &amp; Douglas, [<reflink idref="bib72" id="ref91">72</reflink>]). Table A1 in the Appendix provides the coding scheme with definitions and quotes from the data for each code as examples.</p> <hd id="AN0186290813-17">Qualitative analysis</hd> <p></p> <hd id="AN0186290813-18">PowerPoint lessons</hd> <p>All 24 PowerPoint lesson scripts/materials were coded using the first two codes of this coding scheme (relevance statements and situational interest), because the goal for coding these lessons was to see whether they demonstrated the utility value of fractions and provided engaging content to keep students' interest.</p> <p>Following the coding of the PowerPoint lessons, we strategically selected 10 FSI lessons and then analyzed the corresponding transcripts for each teacher. The chosen lessons were selected based on full coverage of the content of the 24 lessons to make sure all aspects of the intervention and variety of content were represented in the coding. We also chose lessons that included the relevance and situational interest codes to determine whether they encouraged additional, off-script teacher use of motivational messages.</p> <hd id="AN0186290813-19">Transcripts</hd> <p>The transcripts chosen for coding were aligned with 10 selected FSI PowerPoint lessons. Once these FSI lessons were identified, control teacher lessons were selected by first creating a pool of lessons focused on the same content (fractions). Subsequently, control lessons were matched to the 10 FSI lessons based on the date they were taught. The analysis covered a total of 60 teacher transcripts, with 10 transcripts from each of the 6 classrooms. The coding specifically focused on teacher interactions and additional dialogue, including any off-script talk by FSI teachers, because the scripted content from the PowerPoint presentations had already been coded.</p> <p>Each piece of data was coded twice, by two different researchers. The unit of analysis was a "turn of talk" (Pomerantz &amp; Fehr, [<reflink idref="bib54" id="ref92">54</reflink>]), defined as a conversation between teacher and student. A turn of talk was coded if it applied to one of the codes and a new turn of talk was coded whenever a new topic, new turn, or new code was presented. After coding each transcript and lesson using the framework, the researchers met for a consensus meeting to discuss instances where there was not full agreement, to determine final codes and definitions used for subsequent analyses. Consensus meetings were held weekly until all the data were coded. The interrater agreement prior to consensus meetings was calculated via Cohen's kappa statistic. Between the four sets of two coders, Cohen's kappa statistics included 0.6, 0.5, 0.7, and 0.9. Disagreements primarily arose due to ambiguities in initial code definitions and interpretational variability. Coding was refined through consensus meetings to discuss the disagreements in depth until each set of coders came to 100% agreement, and no further consensus meeting was needed.</p> <p>Using NVivo software (version 1.71), we compared the types of motivational-supportive messaging that the teachers used when teaching fractions for each code. To answer the second research question, we compared the frequency of codes across individual teachers in intervention and control groups. The first research question focuses on qualitative analysis of types of motivational messaging teachers used while teaching fractions, portrayed with direct quotes. The second research question focuses on the number of comparisons between the FSI and BAU groups, and how motivational content differed between the groups.</p> <hd id="AN0186290813-20">Quantitative analysis</hd> <p>Frequencies of codes were counted through NVivo and are reported in Figure 2. A chi-square test for independence was run to determine whether there was a statistically significant difference between the frequency of motivational codes between the FSI and BAU groups. This nonparametric test was used because the frequency data (with a small sample size) were categorical. The assumptions for using a chi-square test were met. Data analyses were conducted in R (version 2022.12.0). To address the concern of potential correlation among lessons taught by the same teacher, we analyzed lesson data aggregated by the teacher, ensuring that our statistical test reflects teacher-level units rather than individual lessons.</p> <p>Graph: Figure 2. Frequency counts of motivational messages. BAU = business-as-usual, FSI = fraction sense intervention.</p> <hd id="AN0186290813-21">Results</hd> <p>The forthcoming sections present findings from the teacher transcripts. Refer to Table A1 in the Appendix for the definitions of each motivation code described in this section.</p> <hd id="AN0186290813-22">RQ1. Motivational Messaging</hd> <p>Our first research question asked about the kind of motivational messaging teachers use when teaching fraction lessons. This section is structured by type of motivational messaging, and direct examples from the teacher transcripts are presented from a range of topics and teachers.</p> <hd id="AN0186290813-23">Relevance</hd> <p>Some teachers used relevance messages to explicitly talk about why fractions are useful to learn (<emph>high relevance</emph>), whereas some used relevance messages by relating content to general examples (<emph>low relevance</emph>; e.g., food). When teaching the students how to identify partitions on a ruler, one teacher used statements of high relevance in discussing how fractions are important in the future and outside of school. They said: "This is what my uncles were telling me: 'Please teach these kids before they learn to trade how to use a ruler. This is a great life skill.' And the interesting thing is on a handyman's measuring tape ... it has wholes, halves, eighths, and even something even smaller—sixteenths."</p> <p>Low relevance messages were also provided when teachers used general fraction examples that students could relate to. For example, one teacher said: "If this were a candy bar, what are you taking—the three of the nine, or the one half? You're takin' the one half, because it's bigger! It's more candy."</p> <p>Other teachers used relevance statements by situating fraction content in a realistic scenario for students. For example, a teacher said the following when comparing fraction sizes:</p> <p>Here's the scenario: You go to a birthday party ... they serve pizza. You are the last person in line.... So you walk up to the pizza boxes, and there are two pizza boxes, and you open the left box there's one piece in there. You open the right box, there's one piece in there, and you're starving. You're only allowed to take one piece. I now want you to look at the board. The left is the left pizza piece, and the right is the right box pizza piece. Which one of those pieces are you going to take? Which one are you takin'? The one on the left. Why!? It's a bigger piece!</p> <p>The types of relevance statements used when teaching fractions usually consisted of relating things that could be fractioned that students could envision from their prior experience. The use of food was a common example source teachers used to teach students about portions and fraction comparisons.</p> <hd id="AN0186290813-24">Situational interest</hd> <p>Some teachers attempted to incite situational interest by using humor, and others attempted the same by exhibiting excitement about a topic. During one fraction lesson, one teacher stated: "Pretty cool, huh? I mean, come on, who doesn't like stickers?" when using stickers to identify students' correct work. They also broke into song, singing, "Matchmaker, matchmaker, let's make me a match" when observing students during a fractions "matching" activity.</p> <p>This teacher tried to elicit interest in students to complete their assignments by rewarding them with stickers. As the students worked, the teacher also sang a song from a musical that they connected to creating equivalent fractions. Rewarding students with candy, stickers, or public praise was a common way teachers tried to garner student engagement. In addition, although this was not formally observed, anecdotal observations during coding suggested that when the teachers used a tone of voice that appeared warm and positive, they were attempting to engage their students' attention and elicit student interest in the content or activity.</p> <p>Another teacher frequently used humor as a way to engage their students. For example, when providing feedback on student work, they said:</p> <p>Teacher:</p> <p>They're all totally wrong.</p> <p>Student:</p> <p>How?</p> <p>Teacher:</p> <p>Today's opposite day!</p> <p>Other times, teachers used hand gestures and metaphors to help students understand and make sense of fraction concepts. One teacher said, "This is where you do the alligator mouth, and you eat the bigger amount" to teach students how to determine which inequality sign (&lt; or &gt;) students should use to determine which fraction was bigger than the other. Overall, teachers commonly used humor, tone of voice, and rewards to elicit situational interest in their students for learning fraction material in both conditions.</p> <hd id="AN0186290813-25">Encouragement and discouragement</hd> <p>Some teachers used encouragement to instill the importance of effort over perfection. For example, one teacher stated the following: "We can learn from our mistakes" and "We want to see what you can do yourself. So just continue trying your best. That's all we're asking." Another teacher responded to students' negative beliefs about their mathematical abilities through encouragement during independent work. They remarked:</p> <p>Teacher:</p> <p>You ready? How confident do you feel on this?</p> <p>Student:</p> <p>Not confident.</p> <p>Teacher:</p> <p>Because you suck at math? Or did you say math or fractions?</p> <p>Student:</p> <p>Both.</p> <p>Teacher:</p> <p>So I don't know why you have this thought. Because it just so happens that every single one of those is right. So apparently you don't suck at math or fractions. Apparently your attitude is just terrible. Pull it together! Go get two pieces of candy!</p> <p>In another example of this, one teacher said the following to a student after they responded to an answer: "What you just said is still not incorrect. It's still correct, right? It's just not the simplest form. That's all. The number lines give us the simplest form. So don't doubt yourself. That's still ... you're still solid. That was still awesome."</p> <p>In contrast, teachers used some instances of discouragement when teaching fractions.[<reflink idref="bib2" id="ref93">2</reflink>] However, these instances were rare, and judging by the teachers' tone, were not meant to be harmful to the students but rather to engage them, elicit effort from the students, or redirect their behavior. Some teachers used humor or teasing, which could appear discouraging to students, even though that did not seem to be the teachers' intention. Overall, teachers generally gave similar encouragement to their students, which included the importance of giving your best effort and not doubting your abilities to learn math/fractions. When teachers used discouragement, it usually involved noting students' lack of effort or teasing students for making mistakes.</p> <hd id="AN0186290813-26">Praise</hd> <p>Some teachers used praise in a specific context, whereas some gave general praise to their students. One teacher gave specific praise to a student, thanking them for using the particular strategies they had been taught: "Good, great. You guys are awesome. Thank you for using our strategies." Another teacher gave specific praise on student's participation: "I will say that I love the participation today. I'm a little worried on the other days because you guys are normally pretty bubbly and volunteer a lot and have things to say, and the other classes were getting a little quiet, so starting to worry me."</p> <p>All of the teachers also gave general praise including: "Good job guys," "Excellent," "Look at you guys. Yes. Rockin' this out," and "All right. Kudos to you." Another important distinction is the praise that was given to the class as a whole and to individual students. Some teachers gave more personal praise than others who used more praise to the whole class, rather than individually.</p> <hd id="AN0186290813-27">RQ2. Comparing Frequency and Content of Motivational Messages Between Groups</hd> <p>Our second research question asked about the statistical difference in frequency and content of motivational messages between teachers participating in the FSI and their nonparticipating peers in the BAU group. This section is also structured by motivational message type, with frequency comparisons reported between groups and direct examples of motivational messages from each group. Figure 2 provides the frequencies of each code among both groups.</p> <hd id="AN0186290813-28">Relevance</hd> <p>In the FSI PowerPoint lessons themselves, there were 23 instances of relevance messages. Including these instances and the teachers' additional messaging, FSI teachers provided 37 instances of relevance messages overall to their students. Among the BAU teachers, there were 21 instances of relevance messages. Teachers in the FSI group tended to expand their use of relevance statements from the ones provided in the PowerPoint lessons. The lessons allowed teachers to share examples based on the content provided, such as the usefulness of fractions in driving, sports, cooking, and music. For example, after the content of one lesson included examples of how fractions are used in sports, one FSI teacher said:</p> <p>Teacher:</p> <p>Give me an example for sports. How could you use a fraction for sports? There's something big happening this weekend. Anybody know what's big this weekend? Nobody knows this weekend?! The 10 of you sitting in this room have no idea what's happening this weekend? It's the Super Bowl! What's the biggest thing that happens at the Super Bowl that like, everyone talks about and actually, it will be the best performance in years because it's actual music. What happens in the middle of the game?</p> <p>Student:</p> <p>Halftime.</p> <p>Teacher:</p> <p>Halftime. Right. Fractions. Halftime. Halfway through a game. How many quarters are there in a football game?</p> <p>Class:</p> <p>Four.</p> <p>Teachers in the control group often referred to examples of pizza when discussing how fractions are relevant. For example, one teacher likened their fraction example to a local pizza place the students knew: "So I know it's not a circle pizza but you like Pat's pizza, right? Yeah, I like Pat's. Their square piece is better than a circle piece anyway. So, five out of six is this much for this one? Five out of 12, is that much. Which one do you get more pizza for? It's totally this one."</p> <p>The FSI lessons seemed to provide the teachers with a variety of relevance examples that they could expand on, whereas the teachers without the aid of the lessons generally referred to pizza as an example.</p> <hd id="AN0186290813-29">Situational interest</hd> <p>In the FSI PowerPoint lessons themselves, there were 45 instances of situational interest messages. Including these instances and the teachers' additional messaging, FSI teachers provided 69 instances of situational interest messages overall to their students. Among the BAU teachers, there were 28 instances of situational interest messages or activities. Like the relevance messages, teachers in the FSI group tended to expand their commentary on the situational interest content of the lessons. When a lesson introduced a color run as the context for fractions on a number line, one teacher garnered student interest by stating: "My kids did this one time. The color didn't come out of their hair for like a while." Another teacher explained it to their students by sharing the following:</p> <p>Teacher:</p> <p>Anybody know what a color run is?</p> <p>Class:</p> <p>No.</p> <p>Teacher:</p> <p>No?! Have you ever seen pictures like this? Yeah? Some? Yeah, sometimes they do them in Philadelphia. They do like big summer runs. And they do like a color run through, like, Philadelphia, down by like the art museum and the Rocky steps. It's like powder they throw into the air that's like nontoxic, safe, but it just sticks to your clothes. It's super fun. [Teacher name] wants to plan one to do here in the spring.</p> <p>Of the BAU teachers, only one of the two teachers appeared to attempt to engage student situational interest while teaching. This teacher used a lot of humor and incentives to get their students to want to put forth effort toward learning fractions. For example, when students were encouraged to complete a fraction comparison worksheet, the teacher said: "When you finish, if they're all right, I got candy for ya. While you're focused on your work, I'll do some incredible juggling up here." When the students finished the worksheet, the teacher said: "You can come up and grab any two things out of the bag. Because I know you're super focused after my juggling, because it was incredible. You may grab two pieces of candy. Two of them! Perfect paper gets two." The use of humor appeared to enhance teacher-student connections and increase engagement in the classroom, though it was generally unrelated to mathematical content.</p> <hd id="AN0186290813-30">Encouragement and discouragement</hd> <p>Among the FSI teachers, there were 62 instances of encouragement messages. Among the BAU teachers, there were 55 instances of encouragement messages. The FSI lessons provided statements, such as "do your best," and the FSI teachers generally encouraged their students to learn from their mistakes and to put effort in their work rather than being perfect when answering questions or solving problems. One FSI teacher focused on correcting students' negative talk and complimenting their efforts. For instance, the teacher said, "I don't want to hear us putting ourselves down" and "Thank you for your patience and hard work today."</p> <p>The control teachers also focused on encouraging student effort and confidence. One teacher emphasized, "OK, so go ahead and try both through them and keep trying so remember your grade is going to be on if you are showing you work and you are participating." Another teacher encouraged students' efforts by trying to make learning fun. When giving feedback to a student, they said, "I found one mistake. The rest are perfect. There's one little mistake in there, you gotta find it."</p> <p>Among the FSI teachers, there were 13 instances that could be perceived as discouraging, and 19 instances among the BAU teachers. These messages tended to be ones of humor.</p> <hd id="AN0186290813-31">Praise</hd> <p>Among the FSI teachers, there were 214 instances of praise. Among the BAU teachers, there were 154 instances of praise. Overall, the teachers gave similar kinds of praise, usually when providing students feedback on their work, responses, or effort, as described by the results for the first research question (e.g., "You're exactly correct!" "I'm proud of you," "Nicely done," "I like your confidence!"). One teacher in the control group gave the most praise of any of the teachers (115 instances), and the other BAU teacher gave the least praise (7 instances). The teachers in the FSI group all gave similar amounts of praise to their students.</p> <hd id="AN0186290813-32">Comparing frequencies</hd> <p>To determine whether differences in motivational code frequencies between groups were statistically significant, a chi-square test for independence was run. The relation between treatment group and frequency of motivational messages was statistically significant, χ<sups>2</sups> (<reflink idref="bib4" id="ref94">4</reflink>) = 67.031, <emph>p</emph> &lt;.001. This test shows that the pattern of motivational codes was different for the intervention versus the control group. Post hoc comparisons with a Bonferroni adjustment revealed that FSI teachers were more likely than BAU teachers to use messages of relevance, situational interest, encouragement, and praise, whereas the BAU teachers were more likely to use messages of discouragement. Table 1 provides the descriptive statistics and <emph>p</emph>-values for each code in both groups.</p> <p>Table 1. Descriptive and Significant Statistics of Codes</p> <p> <ephtml> &lt;table&gt;&lt;thead&gt;&lt;tr&gt;&lt;th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1" /&gt;&lt;th align="center" style="border-bottom: solid thin black" colspan="2" valign="bottom" scope="colgroup" rowspan="1"&gt;FSI&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" colspan="2" valign="bottom" scope="colgroup" rowspan="1"&gt;Control&lt;/th&gt;&lt;th align="center" valign="bottom" scope="col" rowspan="1" colspan="1" /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;&lt;italic&gt;M&lt;/italic&gt;&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;&lt;italic&gt;SD&lt;/italic&gt;&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;&lt;italic&gt;M&lt;/italic&gt;&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;&lt;italic&gt;SD&lt;/italic&gt;&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;&lt;italic&gt;p&lt;/italic&gt;&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Relevance&lt;/th&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;27.67&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;4.04&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;7.00&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;1.73&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;.011&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Interest&lt;/th&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;53.00&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;10.44&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;9.33&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;15.31&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;&amp;#60;.001&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Encouragement&lt;/th&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;20.67&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;17.67&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;18.33&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;14.01&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;.018&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Discouragement&lt;/th&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;4.33&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;5.77&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;6.33&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;9.29&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;.023&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Praise&lt;/th&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;71.00&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;13.08&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;51.33&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;56.54&lt;/td&gt;&lt;td char="." valign="bottom" rowspan="1" colspan="1"&gt;&amp;#60;.001&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>Graph</p> <p>1 Note. The reported means (<emph>M</emph>) represent the mean of the motivational message frequencies of the three classrooms in each condition, and the <emph>p</emph> values represent the statistical significance of the difference in total frequencies between each condition derived from chi-square tests and post hoc comparisons. FSI = fraction sense intervention, <emph>SD</emph> = standard deviation.</p> <hd id="AN0186290813-33">Discussion</hd> <p>Our results reveal a number of interesting observations about the different ways teachers use motivational language when teaching fractions. We discuss motivational methods used by the teachers and their connection to math content. We also consider how the FSI may have supported the use of motivational messages. Compared with the BAU teachers, the FSI teachers tended to use more high relevance messages (messages that explicitly state how or why fractions are useful to learn) and situational interest messages that directly related to the fraction content, usually supported by the motivational messaging included in the FSI PowerPoint lessons. Our findings contribute to the existing literature by showing that an intervention designed to boost students' knowledge of fraction concepts also shifted the types and frequencies of motivational messages that teachers provided. We conclude with implications for research and instructional practice, along with limitations and recommendations for future research.</p> <p>When using instances of relevance, some teachers used high relevance messaging, explicitly stating why and in what circumstances fractions were useful for students to understand. Other teachers used lower relevance messages, such as comparing different fractions of a candy bar or a pizza. Past research has found similar trends regarding high or low specificity of relevance between content and student experiences or goals (Schmidt et al., [<reflink idref="bib64" id="ref95">64</reflink>]). The FSI teachers tended to use more high relevance messages compared with the control teachers. These instances usually followed content included in the FSI lessons themselves, which suggests that the lessons scaffolded the teachers' use of high relevance teaching. Drawing on relevance while teaching fractions is important in increasing students' understanding of their usefulness, because research has shown that students have negative views of fractions despite having positive views of whole numbers (Sidney et al., [<reflink idref="bib68" id="ref96">68</reflink>]). Thus, the FSI lessons' use of relevance messages may lead to students having more positive views of fractions if they understand why they are important to learn. Although we did not test this hypothesis with the current data, future research should investigate whether the FSI lessons' use of relevance messages leads to students having more positive views of fractions.</p> <p>Situational interest also varied by group and by teacher. Some teachers consistently used humor to engage their students. FSI teachers were more likely than control teachers to use situational interest related to the fraction content, supported by the activities and prompts provided in the FSI lessons (e.g., hands-on practice with fraction magnet bars, stickers for feedback and to identify fractions on a color run racecourse). These activities (hands-on, modeling, novelty, narrative, and humor) are among the ones outlined by Bergin ([<reflink idref="bib6" id="ref97">6</reflink>]) as situational factors that positively influence student interest.</p> <p>Recent research confirms that teacher humor and student engagement are closely, positively related (Lu'mu et al., [<reflink idref="bib47" id="ref98">47</reflink>]; Machlev &amp; Karlin, [<reflink idref="bib48" id="ref99">48</reflink>]). Furthermore, Machlev and Karlin ([<reflink idref="bib48" id="ref100">48</reflink>]) made the distinction between relevant and nonrelevant humor, the former being humor that is related to the material being taught and the latter being humor used that has no connection to the material. They found that the more relevant humor used, the more students had interest in course materials. Contrastingly, the more nonrelevant humor used, the less students reported interest in course materials. The FSI teachers' use of greater connection between fraction content and situational interest messaging may have led to students' greater interest in fractions compared with the students in the control group. Although student interest was not measured in this study, future research should measure the effects of the FSI on students' interest in fractions.</p> <p>Other teachers relied on tone of voice and rewards to elicit student effort in ways that were more deeply connected to the math content. Tone of voice has been shown to affect students' sense of well-being, engagement, perceived relationship with their teacher, and their psychological need satisfaction (Paulmann &amp; Weinstein, [<reflink idref="bib53" id="ref101">53</reflink>]). Informal observations indicated that teachers employed a warm and positive tone of voice. Furthermore, providing incentives, such as candy for completed work, also appeared to be an attempt to increase student engagement and situational interest in the activity. Research has shown that external awards, such as this, can increase students' motivation and conceptual understanding (e.g., Hoffman &amp; Woehr, [<reflink idref="bib35" id="ref102">35</reflink>]), although there has been controversy concerning the use of external rewards and their consequences on student learning and motivation (Cameron et al., [<reflink idref="bib10" id="ref103">10</reflink>]). The use of external rewards might also cause students to focus more on obtaining the reward than the learning itself.</p> <p>Each teacher used similar methods of encouragement and praise, regardless of their intervention assignment. Overall, each teacher focused on students putting forth effort and doing their best. These characteristics are those of a <emph>mastery-oriented</emph> classroom, in which there is an emphasis on learning and understanding, effort, and improvement, whereas a <emph>performance-oriented</emph> classroom emphasizes grades, ability, and comparison (Ames, [<reflink idref="bib2" id="ref104">2</reflink>]; Newton et al., [<reflink idref="bib51" id="ref105">51</reflink>]). These findings may suggest that a mastery-oriented teaching approach is prevalent in middle school math classrooms, but future research is needed to test the possibility of the plausible explanation for the lack of difference between groups in methods of encouragement and praise.</p> <p>Instances of discouragement were relatively rare. Interestingly, the teachers who gave the most discouragement also gave the most praise to their students. These teachers tended to focus more on relationship-building through humor and individual praise compared with the other teachers. This observation supports recent research showing that teacher use of humor leads to greater perceived teacher-student relationship quality (Lu'mu et al., [<reflink idref="bib47" id="ref106">47</reflink>]). This may be one reason the teachers felt comfortable enough with their relationship with their students that they could use sarcastic humor to engage their students (Cahyadi &amp; Ramli, [<reflink idref="bib9" id="ref107">9</reflink>]).</p> <p>These motivational messages occur more frequently in the classrooms that emphasize multiple representations, gestures, concreteness fading, delayed and interleaved practice, and immediate feedback through the FSI. This finding shows the synergistic relationship between effective instructional methods and teacher communication. Classrooms that use these teaching strategies may create conditions that naturally encourage the use of motivationally supportive messages. This is portrayed by the distinction between the FSI and BAU classes, not just in the frequency of motivational messages, but in their depth and alignment with pedagogical goals.</p> <hd id="AN0186290813-34">Limitations and Future Directions</hd> <p>Despite the contributions of these findings, there are several limitations that should be acknowledged. Although suggestive, the sample size in this study was small. The study was conducted in mathematics RTI classes in two schools in one district, which limits the generalizability of the results. The design of this study includes classes solely made up of students with MLD and does not include students without MLD. Therefore, the results of this study should be interpreted with caution. Further research with more teachers and students with diverse backgrounds is needed to validate these findings.</p> <p>Because we aggregated our analysis to the teacher level, we did not investigate variations within teacher across time or across students. Future research should also measure student motivation outcomes to add robustness to the effectiveness of teachers' use of motivational messages. The present study focused on types of motivational messages used and how the FSI supported the use of those messages, but because of the small sample size, student outcomes were not included in this analysis. Future research should include measures of student motivation to better understand the relationship between motivation and teacher actions, with a larger sample size of classrooms. Our team is currently undergoing these next steps, to include student achievement and motivation outcomes in the context of the intervention and teacher language.</p> <hd id="AN0186290813-35">Implications</hd> <p>The present study provides valuable insights into the ways teachers use messages of motivation when teaching fractions, such as through explaining the usefulness of understanding the content, engaging students through humor, activities, or incentives, and encouraging students with praise and challenges to increase their effort. The findings of this study can be used to guide future research in this area and ultimately to inform instructional practices in similar settings.</p> <p>Our study not only highlights the potential for increased fraction understanding through the intervention but also uncovers collateral motivational benefits, demonstrating that teacher language can be modified in ways aligned with supporting positive student motivation. That is, findings of this study contribute to our understanding of how teachers might effectively motivate their students to learn fractions, as well as how a structured intervention can support this process. For example, teachers in the intervention group used more relevance and situational interest messages while teaching about fractions compared with the teachers in the control group, and these messages were made explicit and directly related to the content. The common examples of pizza used by the teachers in the control group may limit students' motivation and understanding, whereas the FSI uses representations that easily connect to a number line, which is an effective tool for learning fractions (Gersten et al., [<reflink idref="bib29" id="ref108">29</reflink>]). The practice of using examples better connected to students' interests and lives can increase students' engagement in the content (Harackiewicz et al., [<reflink idref="bib33" id="ref109">33</reflink>]).</p> <p>Teachers can incorporate the strategies and techniques (i.e., using relevance in their teaching, enhancing student interest through dialogue and activities, encouraging student effort, and providing specific praise) identified in this study into their instructional practices to provide additional support to struggling students. By identifying these effective strategies and techniques, and providing evidence of the effectiveness of a specific intervention for improving motivational messages, this research provides valuable insights for both researchers and practitioners. One of the insights this study provides is that teachers do not have to choose between being motivational or providing strong mathematical content—the FSI intervention succeeded at providing both.</p> <hd id="AN0186290813-36">Conclusion</hd> <p>The present study describes the use of motivational language during fraction instruction for students with math learning difficulties. Our results suggested that the FSI increases teachers' use of relevance and situational interest, and it allows for more deep connections between the content and students' personal lives compared with the control teachers' use of shallow instances of relevance and interest. The findings of this study can be used to inform instructional practices and interventions aimed at enhancing student motivation and improving learning outcomes in fractions instruction through incorporating messages of relevance of content to student lives, using engaging activities or humor to enhance student interest in content, encouraging students to put forth effort, and using specific praise when providing feedback.</p> <hd id="AN0186290813-37">Appendix</hd> <p>Table A1. Expectancy-Value Theory (EVT) Coding Scheme</p> <p> <ephtml> &lt;table&gt;&lt;thead&gt;&lt;tr&gt;&lt;th style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;Code&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;Definition&lt;/th&gt;&lt;th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"&gt;Example&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;th valign="top" scope="row" rowspan="1" colspan="1"&gt;Relevance (utility value)&lt;/th&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;Statements/activities that provide real-world context that has the potential of students relating fractions/math to their lives or so they understand the usefulness&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;Teacher says "It is important that we learn how to use rulers, &lt;italic&gt;because&lt;/italic&gt; some of you may get a job as a contractor in the future."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th rowspan="4" valign="top" scope="rowgroup" colspan="1"&gt;Situational interest&lt;/th&gt;&lt;td rowspan="4" valign="top" colspan="1"&gt;Engaging the student's interest or sense of fun of learning fractions/math (&lt;italic&gt;teacher commentary&lt;/italic&gt;)&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;When a teacher uses humor to engage students.&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;&lt;italic&gt;Teacher:&lt;/italic&gt; "They're all totally wrong."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;&lt;italic&gt;Student&lt;/italic&gt;: "How?"&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;&lt;italic&gt;Teacher&lt;/italic&gt;: "Today's opposite day."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th rowspan="2" valign="top" scope="row" colspan="1"&gt;Encouragement (self-efficacy)&lt;/th&gt;&lt;td rowspan="2" valign="top" colspan="1"&gt;Teacher talks about learning from mistakes, trying/effort, gives helpful feedback&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;"If you don't know, it's OK. Just do your best."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;"Try using this strategy instead."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th rowspan="2" valign="top" scope="row" colspan="1"&gt;Discouragement&lt;/th&gt;&lt;td rowspan="2" valign="top" colspan="1"&gt;Teacher gives vague criticism or sends messages that convey that students are not good at math&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;"Not everyone is a math person."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign="top" rowspan="1" colspan="1"&gt;"Work harder."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="bottom" scope="row" rowspan="1" colspan="1"&gt;Praise to class (self-efficacy)&lt;/th&gt;&lt;td valign="top" rowspan="1" colspan="1"&gt;Teachers give praise to the whole class&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1" /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="top" scope="row" rowspan="1" colspan="1"&gt; &amp;#8226; General or specific&lt;/th&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;Identify whether the praise is general or specific (includes when referencing something specific)&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;"Good job, everyone" (general) vs. "Great job on improving your multiplication skills" (specific).&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th valign="top" scope="row" rowspan="1" colspan="1"&gt;Individual praise (self-efficacy)&lt;/th&gt;&lt;td valign="top" rowspan="1" colspan="1"&gt;Teachers give praise or positive feedback to students individually; recognizes students' strengths&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;Student says "I am so dumb" when he can't figure out a problem. Teacher says "No you are not, you are doing great at the addition problems."&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th align="left" valign="top" scope="row" rowspan="1" colspan="1"&gt; &amp;#8226; Vague or specific&lt;/th&gt;&lt;td valign="top" rowspan="1" colspan="1"&gt;Identify whether the praise is vague or specific&lt;/td&gt;&lt;td valign="bottom" rowspan="1" colspan="1"&gt;Teacher says to a student "You are doing great at the addition problems" (specific) vs. "nice work today" (vague).&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>Graph</p> <ref id="AN0186290813-38"> <title> Notes </title> <blist> <bibl id="bib1" idref="ref61" type="bt">1</bibl> <bibtext> No potential conflict of interest was reported by the authors. Megan Botello is a PhD candidate at the University of Delaware; Nancy Dyson is research faculty at the University of Delaware; Teomara Rutherford is an associate professor in the Education Department at the University of Delaware; and Nancy C. Jordan is a professor in the Education Department at the University of Delaware. Megan Botello (ORCID: https://orcid.org/0000-0002-6258-6620). Correspondence may be sent to Megan Botello at mbotello@udel.edu.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref42" type="bt">2</bibl> <bibtext> To protect the identity of the teachers, comments coded as "discouraging" were not included as quotes in the article.</bibtext> </blist> </ref> <ref id="AN0186290813-39"> <title> References </title> <blist> <bibtext> Alibali, M. W., &amp; Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners' and teachers' gestures. Journal of the Learning Sciences, 21(2), 247–286.</bibtext> </blist> <blist> <bibtext> Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84(3), 261.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref6" type="bt">3</bibl> <bibtext> Anderman, L., Andrzejewski, C. E., &amp; Allen, J. (2011). How do teachers support students' motivation and learning in their classrooms? Teachers College Record, 113(5), 969–1003.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref14" type="bt">4</bibl> <bibtext> Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref78" type="bt">5</bibl> <bibtext> Barbieri, C. A., Rodrigues, J., Dyson, N., &amp; Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref23" type="bt">6</bibl> <bibtext> Bergin, D. A. (1999). Influences on classroom interest. Educational Psychologist, 34(2), 87–98.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref58" type="bt">7</bibl> <bibtext> Bottge, B. A., Ma, X., Gassaway, L., Toland, M. D., Butler, M., &amp; Cho, S. J. (2014). Effects of blended instructional models on math performance. Exceptional Children, 80(4), 423–437.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref8" type="bt">8</bibl> <bibtext> Burić, I., &amp; Kim, L. E. (2020). Teacher self-efficacy, instructional quality, and student motivational beliefs: An analysis using multilevel structural equation modeling. Learning and Instruction, 66, 101302.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref107" type="bt">9</bibl> <bibtext> Cahyadi, A., &amp; Ramli, M. (2023). Perceived related humor in the classroom, student–teacher relationship quality, and engagement: Individual differences in sense of humor among students. Heliyon, 9(1), e13035.</bibtext> </blist> <blist> <bibtext> Cameron, J., Pierce, W. D., Banko, K. M., &amp; Gear, A. (2005). Achievement-based rewards and intrinsic motivation: A test of cognitive mediators. Journal of Educational Psychology, 97(4), 641.</bibtext> </blist> <blist> <bibtext> Creswell, J. W., &amp; Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). Sage.</bibtext> </blist> <blist> <bibtext> Deci, E. L., &amp; Ryan, R. M. (2012). Self-determination theory. Handbook of Theories of Social Psychology, 1(20), 416–436.</bibtext> </blist> <blist> <bibtext> DeCuir-Gunby, J. T., Marshall, P. L., &amp; McCulloch, A. W. (2011). Developing and using a codebook for the analysis of interview data: An example from a professional development research project. Field Methods, 23(2), 136–155.</bibtext> </blist> <blist> <bibtext> De La Paz, S., &amp; Butler, C. (2018). Promoting motivated writers: Suggestions for teaching and conducting research with students with learning disabilities and struggling learners. Learning Disabilities: A Multidisciplinary Journal, 23(2), 56–69.</bibtext> </blist> <blist> <bibtext> Denton, P. (2013). The power of our words: Teacher language that helps children learn. Center for Responsive Schools.</bibtext> </blist> <blist> <bibtext> Dyson, N. I., Jordan, N. C., Rodrigues, J., Barbieri, C., &amp; Rinne, L. (2020). A fraction sense intervention for sixth graders with or at risk for mathematics difficulties. Remedial and Special Education, 41(4), 244–254.</bibtext> </blist> <blist> <bibtext> Dweck, C. (2015). Carol Dweck revisits the growth mindset. Education Week, 35(5), 20–24.</bibtext> </blist> <blist> <bibtext> Dweck, C. S., &amp; Leggett, E. L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95(2), 256.</bibtext> </blist> <blist> <bibtext> Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. Handbook of Competence and Motivation, 105, 121.</bibtext> </blist> <blist> <bibtext> Eccles, J. S. (2009). Who am I and what am I going to do with my life? Personal and collective identities as motivators of action. Educational Psychologist, 44(2), 78–89.</bibtext> </blist> <blist> <bibtext> Eccles, J. S., &amp; Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132.</bibtext> </blist> <blist> <bibtext> Eccles, J. S., &amp; Wigfield, A. (2020). From expectancy-value theory to situated expectancy-value theory: A developmental, social cognitive, and sociocultural perspective on motivation. Contemporary Educational Psychology, 61, 101859.</bibtext> </blist> <blist> <bibtext> Eccles, W. J. (1983). The Canadian frontier, 1534–1760. UNM Press.</bibtext> </blist> <blist> <bibtext> Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R., &amp; Changas, P. (2013). Improving at-risk learners' understanding of fractions. Journal of Educational Psychology, 105(3), 683.</bibtext> </blist> <blist> <bibtext> Fyfe, E. R., McNeil, N. M., Son, J. Y., &amp; Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26, 9–25.</bibtext> </blist> <blist> <bibtext> Gafoor, K. A., &amp; Kurukkan, A. (2015, August 18–19). Why high school students feel mathematics difficult? An exploration of affective beliefs. Paper presented at the UGC Sponsored National Seminar on Pedagogy of Teacher Education, Trends and Challenges, Kozhikode, Kerala, India..</bibtext> </blist> <blist> <bibtext> Gaspard, H., Dicke, A. L., Flunger, B., Brisson, B. M., Häfner, I., Nagengast, B., &amp; Trautwein, U. (2015). Fostering adolescents' value beliefs for mathematics with a relevance intervention in the classroom. Developmental Psychology, 51(9), 1226.</bibtext> </blist> <blist> <bibtext> Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., &amp; Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202–1242.</bibtext> </blist> <blist> <bibtext> Gersten, R., Schumacher, R. F., &amp; Jordan, N. C. (2017). Life on the number line: Routes to understanding fraction magnitude for students with difficulties learning mathematics. Journal of Learning Disabilities, 50(6), 655–657.</bibtext> </blist> <blist> <bibtext> Greene, J. C. (2007). Mixed methods in social inquiry (Vol. 9). Wiley.</bibtext> </blist> <blist> <bibtext> Grothérus, A., Jeppsson, F., &amp; Samuelsson, J. (2019). Formative scaffolding: How to alter the level and strength of self-efficacy and foster self-regulation in a mathematics test situation. Educational Action Research, 27(5), 667–690.</bibtext> </blist> <blist> <bibtext> Harackiewicz, J. M., Rozek, C. S., Hulleman, C. S., &amp; Hyde, J. S. (2012). Helping parents to motivate adolescents in mathematics and science: An experimental test of a utility-value intervention. Psychological Science, 23(8), 899–906.</bibtext> </blist> <blist> <bibtext> Harackiewicz, J. M., Smith, J. L., &amp; Priniski, S. J. (2016). Interest matters: The importance of promoting interest in education. Policy Insights from the Behavioral and Brain Sciences, 3(2), 220–227.</bibtext> </blist> <blist> <bibtext> Hidi, S., &amp; Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111–127.</bibtext> </blist> <blist> <bibtext> Hoffman, B. J., &amp; Woehr, D. J. (2009). Disentangling the meaning of multisource performance rating source and dimension factors. Personnel Psychology, 62(4), 735–765.</bibtext> </blist> <blist> <bibtext> Holstermann, N., Grube, D., &amp; Bögeholz, S. (2010). Hands-on activities and their influence on students' interest. Research in Science Education, 40, 743–757.</bibtext> </blist> <blist> <bibtext> Hulleman, C. S., &amp; Barron, K. E. (2013, April). Teacher perceptions of student motivational challenges and best strategies to enhance motivation. Paper presented in symposium, J. Turner (Chair), Bridging the Theory-Practice Divide: Teacher Approaches to Motivating Students, at the annual meeting of the American Educational Research Association, San Francisco, CA.</bibtext> </blist> <blist> <bibtext> Hulleman, C. S., Godes, O., Hendricks, B. L., &amp; Harackiewicz, J. M. (2010). Enhancing interest and performance with a utility value intervention. Journal of Educational Psychology, 102(4), 880.</bibtext> </blist> <blist> <bibtext> Hulleman, C. S., &amp; Harackiewicz, J. M. (2021). The utility-value intervention. In In G. M. Walton &amp; A. J. Crum (Eds.), Handbook of wise interventions: How social psychology can help people change (pp. 100–125). Guilford.</bibtext> </blist> <blist> <bibtext> Hulleman, C. S., Schrager, S. M., Bodmann, S. M., &amp; Harackiewicz, J. M. (2010). A meta-analytic review of achievement goal measures: Different labels for the same constructs or different constructs with similar labels? Psychological Bulletin, 136(3), 422.</bibtext> </blist> <blist> <bibtext> Jacobs, J. E., Lanza, S., Osgood, D. W., Eccles, J. S., &amp; Wigfield, A. (2002). Changes in children's self-competence and values: Gender and domain differences across grades one through twelve. Child Development, 73(2), 509–527.</bibtext> </blist> <blist> <bibtext> Jordan, N. C., Dyson, N. I., Devlin, B. L., &amp; Gesuelli, K. A. (2023). Developing fraction sense in students with mathematics learning difficulties: From research to practice. In K. M. Robinson, A. K. Dubé, &amp; D. Kotsopoulos (Eds.), Mathematical cognition and understanding: Perspectives on mathematical minds in the elementary and middle school years (pp. 259–280). Springer International.</bibtext> </blist> <blist> <bibtext> Jordan, N. C., Dyson, N., Guba, T. P., Botello, M., Suchanec-Cooper, H., &amp; May, H. (2024). Exploring the impact of a fraction sense intervention in authentic school environments: An initial investigation. Journal of Experimental Child Psychology, 244, 105954.</bibtext> </blist> <blist> <bibtext> Konrad, M., Fowler, C. H., Walker, A. R., Test, D. W., &amp; Wood, W. M. (2007). Effects of self-determination interventions on the academic skills of students with learning disabilities. Learning Disability Quarterly, 30(2), 89–113.</bibtext> </blist> <blist> <bibtext> Louick, R. (2021). Teacher beliefs about factors that influence motivation among adolescents with learning disabilities. Journal of Educational Studies and Multidisciplinary Approaches, 2(1), 110–130.</bibtext> </blist> <blist> <bibtext> Lovett, M. W., Frijters, J. C., Steinbach, K. A., Sevcik, R. A., &amp; Morris, R. D. (2020). Effective intervention for adolescents with reading disabilities: Combining reading and motivational remediation to improve outcomes. Journal of Educational Psychology, 113(4), 656.</bibtext> </blist> <blist> <bibtext> Lu'mu, Cahyadi, A., Ramli, M. Ruslan, &amp; Hendryadi. (2023). Perceived related humor in the classroom, student–teacher relationship quality, and engagement: Individual differences in sense of humor among students. Heliyon, 9(1), e13035.</bibtext> </blist> <blist> <bibtext> Machlev, M., &amp; Karlin, N. J. (2017). The relationship between instructor use of different types of humor and student interest in course material. College Teaching, 65(4), 192–200.</bibtext> </blist> <blist> <bibtext> Main, N. (2016). The power of praise: Supporting all students in mathematics. Saint Mary's College of California.</bibtext> </blist> <blist> <bibtext> Marsh, H. W. (1990). The structure of academic self-concept: The Marsh/Shavelson model. Journal of Educational Psychology, 82(4), 623.</bibtext> </blist> <blist> <bibtext> Newton, K. J., Jansen, A., &amp; Puleo, P. (2022). Elements of instruction that motivate students with learning disabilities to learn fractions. Mathematical Thinking and Learning, 26(3), 238–257.</bibtext> </blist> <blist> <bibtext> Newton, K. J., Willard, C., &amp; Teufel, C. (2014). An examination of the ways that students with learning disabilities solve fraction computation problems. Elementary School Journal, 115(1), 1–21.</bibtext> </blist> <blist> <bibtext> Paulmann, S., &amp; Weinstein, N. (2022). Teachers' motivational prosody: A pre-registered experimental test of children's reactions to tone of voice used by teachers. British Journal of Educational Psychology, 93(2), 437–452.</bibtext> </blist> <blist> <bibtext> Pomerantz, A., &amp; Fehr, B. J. (2011). Conversation analysis: An approach to the analysis of social interaction. Discourse Studies: A Multidisciplinary Introduction, 2, 165–190.</bibtext> </blist> <blist> <bibtext> Raghubar, K., Cirino, P., Barnes, M., Ewing-Cobbs, L., Fletcher, J., &amp; Fuchs, L. (2009). Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties. Journal of Learning Disabilities, 42(4), 356–371.</bibtext> </blist> <blist> <bibtext> Resnick, I., Jordan, N. C., Hansen, N., Rajan, V., Rodrigues, J., Siegler, R. S., &amp; Fuchs, L. S. (2016). Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade. Developmental Psychology, 52, 746–757.</bibtext> </blist> <blist> <bibtext> Richland, L. E., Stigler, J. W., &amp; Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189–203.</bibtext> </blist> <blist> <bibtext> Rimm-Kaufman, S. E., Larsen, R. A., Baroody, A. E., Curby, T. W., Ko, M., Thomas, J. B., Merritt, E. G., Abry, T., &amp; DeCoster, J. (2014). Efficacy of the responsive classroom approach: Results from a 3-year, longitudinal randomized controlled trial. American Educational Research Journal, 51(3), 567–603.</bibtext> </blist> <blist> <bibtext> Rodrigues, J., Dyson, N. I., Hansen, N., &amp; Jordan, N. C. (2016). Preparing for algebra by building fraction sense. Teaching Exceptional Children, 49(2), 134–141.</bibtext> </blist> <blist> <bibtext> Rohrer, D., Dedrick, R. F., &amp; Burgess, K. (2014). The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problems. Psychonomic Bulletin and Review, 21, 1323–1330.</bibtext> </blist> <blist> <bibtext> Rosenzweig, E. Q., Wigfield, A., &amp; Eccles, J. S. (2019). Expectancy-value theory and its relevance for student motivation and learning. In K. A. Renninger &amp; S. E. Hidi (Eds.), The Cambridge handbook of motivation and learning (pp. 617–644). Cambridge University Press. https://doi.org/10.1017/9781316823279.026</bibtext> </blist> <blist> <bibtext> Rutherford, T., Liu, A. S., &amp; Wagemaker, M. (2021). "I chose math because ...": Cognitive interviews of a motivation measure. Contemporary Educational Psychology, 66, 101992.</bibtext> </blist> <blist> <bibtext> Sadler, P. M., &amp; Tai, R. H. (2007). Advanced placement exam scores as a predictor of performance in introductory college biology, chemistry and physics courses. Science Educator, 16(2), 1–19.</bibtext> </blist> <blist> <bibtext> Schmidt, J. A., Kafkas, S. S., Maier, K. S., Shumow, L., &amp; Kackar-Cam, H. Z. (2019). Why are we learning this? Using mixed methods to understand teachers' relevance statements and how they shape middle school students' perceptions of science utility. Contemporary Educational Psychology, 57, 9–31.</bibtext> </blist> <blist> <bibtext> Schunk, D. H., &amp; Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel &amp; D. B. Miele (Eds.), Handbook of motivation at school (pp. 49–68). Routledge.</bibtext> </blist> <blist> <bibtext> Shadish, W. R., Cook, T. D., &amp; Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference (2nd ed.). Cengage Learning.</bibtext> </blist> <blist> <bibtext> Sideridis, G. D. (2007). Goal orientations and classroom goal structures as predictors of classroom behaviors for Greek students with and without learning difficulties: Clarifying the differential role of motivational orientations. Advances in Learning and Behavioral Disabilities, 20, 101–137.</bibtext> </blist> <blist> <bibtext> Sidney, P. G., Thalluri, R., Buerke, M. L., &amp; Thompson, C. A. (2019). Who uses more strategies? Linking mathematics anxiety to adults' strategy variability and performance on fraction magnitude tasks. Thinking and Reasoning, 25(1), 94–131.</bibtext> </blist> <blist> <bibtext> Siegle, D., &amp; McCoach, D. B. (2007). Increasing student mathematics self-efficacy through teacher training. Journal of Advanced Academics, 18(2), 278–312.</bibtext> </blist> <blist> <bibtext> Siegler, R. S., Fazio, L. K., Bailey, D. H., &amp; Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19.</bibtext> </blist> <blist> <bibtext> Siegler, R. S., &amp; Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–250.</bibtext> </blist> <blist> <bibtext> Skipper, Y., &amp; Douglas, K. (2015). The influence of teacher feedback on children's perceptions of student–teacher relationships. British Journal of Educational Psychology, 85(3), 276–288.</bibtext> </blist> <blist> <bibtext> Wang, G., Zhang, S., &amp; Cai, J. (2019). Chinese high school students' mathematics-related beliefs and their perceived mathematics achievement: A focus on teachers' praise. EURASIA Journal of Mathematics, Science and Technology Education, 15(7), em1713.</bibtext> </blist> </ref> <aug> <p>By Megan Botello; Nancy Dyson; Teomara Rutherford and Nancy C. Jordan</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib24" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib70" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib63" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib41" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib37" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib26" firstref="ref7"></nolink> <nolink nlid="nl7" bibid="bib39" firstref="ref9"></nolink> <nolink nlid="nl8" bibid="bib56" firstref="ref10"></nolink> <nolink nlid="nl9" bibid="bib45" firstref="ref11"></nolink> <nolink nlid="nl10" bibid="bib23" firstref="ref12"></nolink> <nolink nlid="nl11" bibid="bib22" firstref="ref13"></nolink> <nolink nlid="nl12" bibid="bib50" firstref="ref15"></nolink> <nolink nlid="nl13" bibid="bib62" firstref="ref17"></nolink> <nolink nlid="nl14" bibid="bib65" firstref="ref19"></nolink> <nolink nlid="nl15" bibid="bib20" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib21" firstref="ref21"></nolink> <nolink nlid="nl17" bibid="bib61" firstref="ref22"></nolink> <nolink nlid="nl18" bibid="bib36" firstref="ref24"></nolink> <nolink nlid="nl19" bibid="bib27" firstref="ref25"></nolink> <nolink nlid="nl20" bibid="bib47" firstref="ref26"></nolink> <nolink nlid="nl21" bibid="bib48" firstref="ref27"></nolink> <nolink nlid="nl22" bibid="bib15" firstref="ref28"></nolink> <nolink nlid="nl23" bibid="bib49" firstref="ref29"></nolink> <nolink nlid="nl24" bibid="bib73" firstref="ref30"></nolink> <nolink nlid="nl25" bibid="bib32" firstref="ref34"></nolink> <nolink nlid="nl26" bibid="bib40" firstref="ref36"></nolink> <nolink nlid="nl27" bibid="bib64" firstref="ref37"></nolink> <nolink nlid="nl28" bibid="bib51" firstref="ref39"></nolink> <nolink nlid="nl29" bibid="bib12" firstref="ref41"></nolink> <nolink nlid="nl30" bibid="bib44" firstref="ref43"></nolink> <nolink nlid="nl31" bibid="bib67" firstref="ref44"></nolink> <nolink nlid="nl32" bibid="bib18" firstref="ref46"></nolink> <nolink nlid="nl33" bibid="bib46" firstref="ref51"></nolink> <nolink nlid="nl34" bibid="bib14" firstref="ref52"></nolink> <nolink nlid="nl35" bibid="bib16" firstref="ref55"></nolink> <nolink nlid="nl36" bibid="bib42" firstref="ref56"></nolink> <nolink nlid="nl37" bibid="bib43" firstref="ref57"></nolink> <nolink nlid="nl38" bibid="bib71" firstref="ref59"></nolink> <nolink nlid="nl39" bibid="bib25" firstref="ref60"></nolink> <nolink nlid="nl40" bibid="bib57" firstref="ref62"></nolink> <nolink nlid="nl41" bibid="bib60" firstref="ref63"></nolink> <nolink nlid="nl42" bibid="bib31" firstref="ref64"></nolink> <nolink nlid="nl43" bibid="bib58" firstref="ref67"></nolink> <nolink nlid="nl44" bibid="bib38" firstref="ref70"></nolink> <nolink nlid="nl45" bibid="bib52" firstref="ref73"></nolink> <nolink nlid="nl46" bibid="bib66" firstref="ref74"></nolink> <nolink nlid="nl47" bibid="bib55" firstref="ref75"></nolink> <nolink nlid="nl48" bibid="bib11" firstref="ref76"></nolink> <nolink nlid="nl49" bibid="bib30" firstref="ref77"></nolink> <nolink nlid="nl50" bibid="bib59" firstref="ref81"></nolink> <nolink nlid="nl51" bibid="bib28" firstref="ref82"></nolink> <nolink nlid="nl52" bibid="bib13" firstref="ref83"></nolink> <nolink nlid="nl53" bibid="bib19" firstref="ref85"></nolink> <nolink nlid="nl54" bibid="bib34" firstref="ref86"></nolink> <nolink nlid="nl55" bibid="bib69" firstref="ref89"></nolink> <nolink nlid="nl56" bibid="bib17" firstref="ref90"></nolink> <nolink nlid="nl57" bibid="bib72" firstref="ref91"></nolink> <nolink nlid="nl58" bibid="bib54" firstref="ref92"></nolink> <nolink nlid="nl59" bibid="bib68" firstref="ref96"></nolink> <nolink nlid="nl60" bibid="bib53" firstref="ref101"></nolink> <nolink nlid="nl61" bibid="bib35" firstref="ref102"></nolink> <nolink nlid="nl62" bibid="bib10" firstref="ref103"></nolink> <nolink nlid="nl63" bibid="bib29" firstref="ref108"></nolink> <nolink nlid="nl64" bibid="bib33" firstref="ref109"></nolink> |
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| Header | DbId: eric DbLabel: ERIC An: ED673973 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Teachers' Use of Motivational Messages While Teaching Fractions – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Megan+Botello%22">Megan Botello</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-6258-6620">0000-0002-6258-6620</externalLink>)<br /><searchLink fieldCode="AR" term="%22Nancy+Dyson%22">Nancy Dyson</searchLink><br /><searchLink fieldCode="AR" term="%22Teomara+Rutherford%22">Teomara Rutherford</searchLink><br /><searchLink fieldCode="AR" term="%22Nancy+C%2E+Jordan%22">Nancy C. Jordan</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22Grantee+Submission%22"><i>Grantee Submission</i></searchLink>. 2025 125(4). – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 25 – Name: DatePubCY Label: Publication Date Group: Date Data: 2025 – Name: SourceSuprt Label: Sponsoring Agency Group: SrcSuprt Data: National Center for Special Education Research (NCSER) (ED/IES) – Name: NumberContract Label: Contract Number Group: NumCntrct Data: R324A200140 – 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="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="DE" term="%22Fractions%22">Fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Comparative+Analysis%22">Comparative Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Intervention%22">Intervention</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Motivation%22">Student Motivation</searchLink><br /><searchLink fieldCode="DE" term="%22Motivation+Techniques%22">Motivation Techniques</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Student+Relationship%22">Teacher Student Relationship</searchLink><br /><searchLink fieldCode="DE" term="%22Transcripts+%28Written+Records%29%22">Transcripts (Written Records)</searchLink><br /><searchLink fieldCode="DE" term="%22Audio+Equipment%22">Audio Equipment</searchLink><br /><searchLink fieldCode="DE" term="%22Response+to+Intervention%22">Response to Intervention</searchLink><br /><searchLink fieldCode="DE" term="%22Relevance+%28Education%29%22">Relevance (Education)</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Problems%22">Learning Problems</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1086/735431 – Name: Abstract Label: Abstract Group: Ab Data: In this study, our team observed sixth grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy-Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed, comparing teachers taking part in the experimental fractions intervention and teachers teaching business-as-usual. The fraction lessons and motivational messages were coded via teachers' audio recordings over the span of 15 weeks (24 lessons). Findings revealed that teachers in the experimental group used significantly more motivationally-supportive messages than the teachers in the control group, as well as made deeper connections between content and students' lives. These results imply that the use of an intervention including motivational messages can further promote teachers' use of motivational strategies while teaching mathematical content. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: CodeSource Label: IES Funded Group: SrcInfo Data: Yes – Name: DateEntry Label: Entry Date Group: Date Data: 2025 – Name: AN Label: Accession Number Group: ID Data: ED673973 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1086/735431 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 25 Subjects: – SubjectFull: Grade 6 Type: general – SubjectFull: Fractions Type: general – SubjectFull: Mathematics Instruction Type: general – SubjectFull: Teaching Methods Type: general – SubjectFull: Comparative Analysis Type: general – SubjectFull: Intervention Type: general – SubjectFull: Student Motivation Type: general – SubjectFull: Motivation Techniques Type: general – SubjectFull: Teacher Student Relationship Type: general – SubjectFull: Transcripts (Written Records) Type: general – SubjectFull: Audio Equipment Type: general – SubjectFull: Response to Intervention Type: general – SubjectFull: Relevance (Education) Type: general – SubjectFull: Middle School Students Type: general – SubjectFull: Learning Problems Type: general Titles: – TitleFull: Teachers' Use of Motivational Messages While Teaching Fractions Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Megan Botello – PersonEntity: Name: NameFull: Nancy Dyson – PersonEntity: Name: NameFull: Teomara Rutherford – PersonEntity: Name: NameFull: Nancy C. Jordan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Type: published Y: 2025 Numbering: – Type: volume Value: 125 – Type: issue Value: 4 Titles: – TitleFull: Grantee Submission Type: main |
| ResultId | 1 |
