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Junior High School Students' Self-Confidence during Transition to Above-Grade-Level Mathematics Courses

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Title: Junior High School Students' Self-Confidence during Transition to Above-Grade-Level Mathematics Courses
Language: English
Authors: Schuh, Kathy L. (ORCID 0000-0003-0799-9972), Meiners, Amanda J. (ORCID 0000-0003-0062-8781), Ferguson, Cheryl, Hageman, Kara, George, Salim, Cox, Michala, Zou, Yuqing, Lin, Chang-Jen
Source: Journal of Educational Research. 2023 116(2):61-76.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 16
Publication Date: 2023
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Elementary Education
Grade 7
Grade 8
Descriptors: Junior High School Students, Self Esteem, Mathematics Instruction, Advanced Courses, Student Attitudes, Stress Variables, Self Management, Student Adjustment, Grade 7, Grade 8, Algebra, Student Placement, Barriers, Coping
DOI: 10.1080/00220671.2023.2186338
ISSN: 0022-0671
1940-0675
Abstract: This qualitative study examined the mathematics self-confidence of eight junior high school students who were moved to an above-grade-level mathematics class through a nontraditional process. Teachers were concerned about how this transition may impact students' beliefs about their abilities to succeed in mathematics. Data were collected through interviews that included solving challenging mathematical tasks as a means to consider how students expressed their self-confidence in mathematics in general. Using a socio-constructivist lens with a focus on mediation, findings included themes about tensions given students' initial placement, changes in the role of self-confidence as a mediator, feelings of belonging as having multiple mediator roles, workarounds as mediators, and self-regulation strategies as internalized mediators that students brought with them to their transition. These findings point to solutions and supports for students who enroll in above-grade-level courses to view themselves as successful.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1393195
Database: ERIC
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  Value: <anid>AN0164054144;ere01mar.23;2023Jun05.07:29;v2.2.500</anid> <title id="AN0164054144-1">Junior high school students' self-confidence during transition to above-grade-level mathematics courses </title> <p>This qualitative study examined the mathematics self-confidence of eight junior high school students who were moved to an above-grade-level mathematics class through a nontraditional process. Teachers were concerned about how this transition may impact students' beliefs about their abilities to succeed in mathematics. Data were collected through interviews that included solving challenging mathematical tasks as a means to consider how students expressed their self-confidence in mathematics in general. Using a socio-constructivist lens with a focus on mediation, findings included themes about tensions given students' initial placement, changes in the role of self-confidence as a mediator, feelings of belonging as having multiple mediator roles, workarounds as mediators, and self-regulation strategies as internalized mediators that students brought with them to their transition. These findings point to solutions and supports for students who enroll in above-grade-level courses to view themselves as successful.</p> <p>Keywords: Belonging; junior high students; mathematics pipeline; mathematics self-confidence; mediation; workarounds</p> <hd id="AN0164054144-2">Introduction</hd> <p>Placement into above-grade-level courses as a means to college preparation has been done in subject areas such mathematics and science (Linnenbrink-Garcia et al., [<reflink idref="bib34" id="ref1">34</reflink>]). Furthermore, placement into mathematics courses has been shown to lead to higher postsecondary enrollment rates when foundational mathematics curricula are accessible during the junior-high-school years (Carpenter & Clayton, [<reflink idref="bib13" id="ref2">13</reflink>]). Students who have not successfully completed algebra or pre-algebra in ninth grade are less likely to take four years of mathematics in high school (Reyes & Domina, [<reflink idref="bib53" id="ref3">53</reflink>]) and may have less motivation for mathematics than students taking algebra in seventh or eighth grade (Simzar et al., [<reflink idref="bib60" id="ref4">60</reflink>]). Although early enrollment in algebra may support persistent mathematics enrollment in high school, moving students to above-grade-level mathematics courses is not without potential complications (Bush & Karp, [<reflink idref="bib10" id="ref5">10</reflink>]; Cortes et al., [<reflink idref="bib17" id="ref6">17</reflink>]; Domina et al., [<reflink idref="bib19" id="ref7">19</reflink>]; Perna & Loughan, [<reflink idref="bib51" id="ref8">51</reflink>]). While mathematics placement is important as it places students on a trajectory for future academic work, when students seem to not be placed appropriately, it may also limit further opportunities. Yet, alternatives to change trajectories are limited when a student begins in a sequential content area. Whether in mathematics or another content area, moving students in nontraditional means such as skipping years, taking an accelerated year, or moving mid-year, supports advancing students in the trajectory but may produce some psychological residue such as a decrease in self-confidence regarding their abilities to engage with the work and be successful. In an above-grade-level curriculum, students need a reasonable belief in their mathematical ability to view themselves as successful (Boaler & Dweck, [<reflink idref="bib7" id="ref9">7</reflink>]; Boaler & Sengupta-Irving, [<reflink idref="bib8" id="ref10">8</reflink>]; Dweck, [<reflink idref="bib20" id="ref11">20</reflink>]).</p> <p>In this study we consider students' self-confidence as they move from courses in which they have seen success to a more challenging course. The purpose of this qualitative study was to look specifically at the mathematics self-confidence of junior high school students who transitioned to pre-algebra or algebra classrooms through a process other than that involving the district procedure typically used for placement. The significance of our study provides support toward the noticed inequitable placement of some students into above-grade-level courses. The implications of our study can provide student-directed guidance about how to undo the typical student placement into above-grade-levels courses.</p> <hd id="AN0164054144-3">Background</hd> <p></p> <hd id="AN0164054144-4">Mathematics self-confidence</hd> <p>Self-confidence is a belief that an individual has that the outcome of an event or a behavior will occur as expected, which is based on past experience or past evidence (Oney & Oksuzoglu-Guven, [<reflink idref="bib49" id="ref12">49</reflink>]). Confidence, as defined in the context of studying mathematics, is a general concept pointing to an estimate of how well the student expects to do (Morony et al., [<reflink idref="bib38" id="ref13">38</reflink>]), including their ability to learn and perform well on mathematics tasks (Kiwanuka et al., [<reflink idref="bib30" id="ref14">30</reflink>]). Mathematics self-confidence (Çiftçi & Yildiz, [<reflink idref="bib16" id="ref15">16</reflink>]), a specific type of self-confidence (Oney & Oksuzoglu-Guven, [<reflink idref="bib49" id="ref16">49</reflink>]), is one component of a students' multifaceted attitude toward mathematics, which may also include perceived value and enjoyment of mathematics (Kiwanuka et al., [<reflink idref="bib30" id="ref17">30</reflink>]). Oftentimes, confidence is tied to a particular task, i.e., a learners' self-assessment of confidence is captured immediately after they complete a mathematics problem (Morony et al., [<reflink idref="bib38" id="ref18">38</reflink>]); with self-confidence being within the boundary of one's own self (Oney & Oksuzoglu-Guven, [<reflink idref="bib49" id="ref19">49</reflink>]). Specific self-confidence is more predictive of information-seeking behavior than overall self-confidence which is not domain or content specific. In the current study self-confidence in mathematics was defined as the students' expression of how they believe(d) they will do/did on mathematics tasks. Self-confidence is malleable, in that it can change over time (Bandura, [<reflink idref="bib3" id="ref20">3</reflink>]).</p> <p>Self-beliefs such as self-confidence do affect students' achievement and even their decisions to continue in particular mathematics courses (Sheldrake et al., [<reflink idref="bib58" id="ref21">58</reflink>]). Further, specific self-confidence, such as self-confidence in mathematics, is more predictive of positive outcomes (Oney & Oksuzoglu-Guven, [<reflink idref="bib49" id="ref22">49</reflink>]). For example, using multivariable and multilevel analysis Kiwanuka et al. ([<reflink idref="bib30" id="ref23">30</reflink>]) generated connections between students' mathematics self-confidence and greater enjoyment of mathematics, which connected to classrooms that endorsed the perceived usefulness of mathematics questions. In a meta-analysis of TIMSS data (Çiftçi & Yildiz, [<reflink idref="bib16" id="ref24">16</reflink>]) that included analysis of 336 independent studies from 76 countries, self-confidence was found to affect mathematics achievement (a moderate effect size of.59). Results did not vary by country or by grade level (fourth versus eighth grade). In a study of 3057 Finnish students in grades 5 and 7, self-confidence at grade 7 was predicted by the students' earlier beliefs (Hannula et al., [<reflink idref="bib24" id="ref25">24</reflink>]). Kiwanuka et al. ([<reflink idref="bib30" id="ref26">30</reflink>]) found no differences in self-confidence based on gender in a study of 7<sups>th</sups> grade students in Africa but did note a significant effect based on age with older students being more confident. Social-economic status was not significantly associated. In a study that included PISA data, Morony et al. ([<reflink idref="bib38" id="ref27">38</reflink>]) noted that self-confidence in mathematics was the single most important predictor of student accuracy among the self-belief constructs included in their regression model.</p> <hd id="AN0164054144-5">Self-confidence as mediator</hd> <p>In our consideration of self-confidence in the context of these students' transition in mathematics classes, we focus on it as a mediator in the learning process when described from a socio-constructivist perspective. Socio-constructivism, a theory of learning often linked to the work of Vygotsky, posits that learning is a shared rather than an individual experience (Prawat & Floden, [<reflink idref="bib52" id="ref28">52</reflink>]) and includes the interaction among individual, artifacts, and tools to achieve some outcome (Yamagata-Lynch, [<reflink idref="bib67" id="ref29">67</reflink>]). When considering the activity of solving math problems, the goal of the activity—finding an answer—is referred to as the object or objective; it is the reason why the activity is taking place (Wells, [<reflink idref="bib65" id="ref30">65</reflink>]). The object, the process of finding the answer, is transformed by the activity (Engeström, [<reflink idref="bib21" id="ref31">21</reflink>]; Nardi et al., [<reflink idref="bib40" id="ref32">40</reflink>]; Wells, [<reflink idref="bib65" id="ref33">65</reflink>], Yamagata-Lynch, [<reflink idref="bib67" id="ref34">67</reflink>]). In addition to the object, there is also a consequential outcome that emerges from the activity. In the case of a student solving a mathematics problem it might be a good score, a developed understanding of mathematical concepts, or even some non-cognitive outcome such as an increase in self-confidence. In Oney and Oksuzoglu-Guven's ([<reflink idref="bib49" id="ref35">49</reflink>]) summary of definitions of confidence, they note that confidence can be depleted when there are feelings of doubt or frustration with an object. When considering the larger timescale of our participants, we also consider the implicit intended outcome to be students' success in their transition. Within that, we wonder about the role of the self-confidence as a mediator in that process.</p> <p>Mediators can be of various types (Kozulin, [<reflink idref="bib31" id="ref36">31</reflink>]; Vygotsky, [<reflink idref="bib63" id="ref37">63</reflink>]). Generally, when considering socio-constructivism and the role of mediators, typical interpretations often consider the role of a human mediator—that "more knowledgeable other" who supports the learning process (Kozulin, [<reflink idref="bib31" id="ref38">31</reflink>]). Physical or technical tools are those that are directed outward and impact or change the environment (such as using a calculator in solving a mathematics task). In the current study, we considered that self-confidence may be a cultural or psychological mediator, which is directed inward. Cultural and psychological tools that student internalize and are then enabled while they engage with challenging tasks. These are typically thought of as processes or techniques that someone might use, i.e., "higher order thinking processes," and are beyond lower processing such as perception and attention (Vygotsky, [<reflink idref="bib63" id="ref39">63</reflink>]). In mathematics, a psychological tool might be knowing the standard procedure to simplify an equation. While self-confidence is not considered a type of psychological tool in the way that having a strategy is, the role of self-confidence for these learners may be better understood when considering it as a mediator of the learning process.</p> <p>Further, the complexities of learning environments also point to the use of Cultural Historical Activity Theory (CHAT) as an expansion of socio-cultural theory. CHAT further elaborates the description of other elements of a system to be understood as mediators and how relationships among elements of the system may note tensions within the system. A tension may disrupt successful engagement in the activity (Yamagata-Lynch, [<reflink idref="bib67" id="ref40">67</reflink>]) and can be a driving force to prompt change. These additional mediators are the community, rules, and division of labor (see Figure 1). Rules govern the various elements of the system and division of labor notes how aspects of work are divided among those in the system (Yamagata-Lynch, [<reflink idref="bib67" id="ref41">67</reflink>]). Communities can be many and varied and affect the activity of the learner. The tool at the top of the pyramid (Figure 1) seems positioned as a primary mediator; that said, any of the elements in the system may serve as mediators. For example, a community many mediate the process between the learner and the outcome, such as a particular class that is developed to help students transition to a higher-level course. The elements on the bottom of the graphic prompt one to consider something larger than the students' work itself, considering how the student came to be positioned in the trajectory to start. For example, community can be broad reaching as noted in our own study in that broader community, as well as the rules within the larger system, indicate how these students were initially positioned in a mathematics pipeline. We position the mathematics pipeline within the larger community through which these students have engaged in their mathematics work, as well as systemic rules by which students may be placed in that pipeline. The larger community sets the parameters of who may participate and when. In this, it is a tension between elements within the system that prompted a need for this study. It is from this framework that we interpret the self-confidence of the learners.</p> <p>Graph: Figure 1. CHAT figure of general mediators as well as specific mediators prompting a tension that undergirds the study.</p> <p>In the current study we explored the self-confidence of eight junior high school students who were moved to an advanced mathematics classroom placement. Through this process, the students shifted their position in the mathematics pipeline.</p> <hd id="AN0164054144-6">Mathematics pipeline</hd> <p>Instilling algebraic ideas and concepts, particularly at the junior high level, has been a part of U.S. K-12 school systems for over three decades (Simzar & Domina, [<reflink idref="bib59" id="ref42">59</reflink>]) and recently has been called a pipeline after Linnenbrink-Garcia et al.'s ([<reflink idref="bib34" id="ref43">34</reflink>]) definition. The mathematics pipeline path is cemented within the Common Core Standards of Mathematics (CCSS-M) with the integration of algebraic concepts viewed as a longitudinal process intended to be continuous and embedded throughout a student's K-12 experience (National Council of Teachers of Mathematics, [<reflink idref="bib41" id="ref44">41</reflink>], [<reflink idref="bib42" id="ref45">42</reflink>]; National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], 2010). The push for taking above-grade-level courses places students on a path to engage with calculus and typical post-secondary mathematics courses during high school years (Balfanz et al., [<reflink idref="bib2" id="ref46">2</reflink>]; National Research Council, [<reflink idref="bib45" id="ref47">45</reflink>]; Oakes, [<reflink idref="bib48" id="ref48">48</reflink>]). Without this conceptual fluidity, the notion of a continuous K-12 mathematics pipeline is stalled or truncated for some students, noting a tension within the system.</p> <p>NCTM ([<reflink idref="bib43" id="ref49">43</reflink>]) has proposed a shift from a deficit view of mathematical abilities to a focus on students' strengths while engaging with mathematical tasks. In NCTM's view, students should no longer be cemented into a specific start and finish line within the mathematics pipeline merely by the progression of courses offered in junior or senior high school. Traditional coursework typically follows this order: algebra I, geometry, algebra II, pre-calculus, and calculus. If students take one course each year of high school (i.e., algebra in ninth grade), they will not reach calculus until college entrance. Hence, there is a push for students to complete pre-algebra and algebra in junior high so that calculus can be reached in high school. Once in the pipeline, slowing down (retaking a course) is possible; however, trying to advance at a faster pace might mean completing both algebra I and geometry in a single school year. While this ambitious path may provide for mathematics learning, it continues to perpetuate mathematics anxieties, fears, and lower self-efficacy (Boaler & Dweck, [<reflink idref="bib7" id="ref50">7</reflink>]). Specifically, the current mathematics pipeline in the United States greatly affects students' mathematics self-confidence and how they view their ability and capacity to engage with mathematics in and out of the classroom (Boaler, [<reflink idref="bib6" id="ref51">6</reflink>]).</p> <hd id="AN0164054144-7">Our study</hd> <p>Our study seeks to provide direct insight into how a small group of junior high mathematics students talked about their self-confidence and challenges when moved within the mathematics pipeline.</p> <p>We gathered data from eight students who excelled in their grade-level mathematics class and had been placed into higher-level mathematics courses in a way that was different for this school district, positioning them for a higher-level mathematics path in high school. These students were selected to change course enrollments in the summer prior to or following the start of the academic year based on teachers' perceptions of students not being challenged in the grade-level course. The question that guided this research study was: How did students who changed placement from a grade-level to an above-grade-level course through non-typical means portray their self-confidence about mathematics?</p> <hd id="AN0164054144-8">Methods</hd> <p></p> <hd id="AN0164054144-9">Participants</hd> <p>Eight seventh- and eighth-grade pre-algebra and algebra students who were moved to above-grade-level mathematics courses via teacher recommendation agreed to participate in this qualitative study. Demographics and pseudonyms for these eight students are included in Table 1. At this junior high, which included grades seven and eight, 42.8% of students were eligible for the Free or Reduced-Price Lunch Program. The following is a breakdown of the school based on race/ethnicity: Asian (1.4%), Black or African American (18.8%), Hispanic or Latino (17.4%), Multiracial (4.4%), and White (59%). The study spanned two years, with three students participating in the spring of year 1, one in the fall of year 2, and four students participating in the spring of year 2. These eight students do not comprise the entire group of students who were invited to move to an above-grade-level mathematics classes in the two school years of the study (we are unaware of the full number). The eight students who participated in this study were the ones for whom we received parental and student consent.</p> <p>Table 1. Student demographics.</p> <p> <ephtml> <table><thead><tr><td>Pseudonym</td><td>M/F</td><td>Grade/Age at interview</td><td>Race</td><td>Mostly speaks this language at home</td><td>Class sequence and support</td></tr></thead><tbody valign="top"><tr><td>Heather</td><td>F</td><td char=".">7th/13</td><td>Black or African-American </td><td>English</td><td char=".">7<sup>th</sup> grade: Math 7 (2 mo), then Pre-algebra</td></tr><tr><td>Barrett</td><td>M</td><td char=".">8th/14</td><td>White</td><td>English</td><td char=".">8<sup>th</sup> grade: Pre-algebra<xref ref-type="table-fn" rid="tfn1">*</xref> (1<sup>st</sup> trimester), then Algebra </td></tr><tr><td>Kevin</td><td>M</td><td char=".">8th</td><td>Black or African-American </td><td>Unsure, ELL</td><td char=".">8<sup>th</sup> grade: Pre-algebra<xref ref-type="table-fn" rid="tfn1">*</xref> (1<sup>st</sup> trimester), then Algebra</td></tr><tr><td>Michael</td><td>M</td><td char=".">8th/13</td><td>White</td><td>English</td><td char=".">7<sup>th</sup> grade: Math 7 (2 mo), then Pre-algebra 8<sup>th</sup> grade: Algebra </td></tr><tr><td>Armella</td><td>F</td><td char=".">8th/13</td><td>Black or African-American </td><td>French</td><td char=".">7<sup>th</sup> grade: Math 7 with advisory support 8<sup>th</sup> grade: summer camp, Algebra</td></tr><tr><td>Ray</td><td>M</td><td char=".">8th/13</td><td>White</td><td>English</td><td char=".">7<sup>th</sup> grade: Math 7 with advisory support 8<sup>th</sup> grade: summer camp, Algebra </td></tr><tr><td>Amber</td><td>F</td><td char=".">8th/14</td><td>White</td><td>English</td><td char=".">7<sup>th</sup> grade: Math 7 8<sup>th</sup> grade: summer camp, Algebra </td></tr><tr><td>Jenica</td><td>F</td><td char=".">8th/13</td><td>Hispanic, Latino/a, or Spanish</td><td>English and Spanish</td><td char=".">7<sup>th</sup> grade: Math 7 8<sup>th</sup> grade: summer camp, Algebra</td></tr></tbody></table> </ephtml> </p> <p>1 Throughout our analysis we will refer to all students as having moved from "grade-level" to "above-grade-level" classes, despite these two students being moved from pre-algebra to algebra in grade 8 when they participated in the study.</p> <p>One mathematics teacher from the school served as a secondary participant. She had 16 years of teaching experience including 12 years of teaching high school and college students. Classes she had taught at the high school level included advanced placement level statistics and dual credit calculus 1; while college level classes were primarily mathematics teaching methods courses. In her four years at the junior high school, she had taught above-grade-level courses including algebra and geometry, adding grade-level courses to her teaching load in the last two years (beginning in year 1 of the study).</p> <p>Typically, in the school district, junior high students begin their mathematics sequence in grade 7 math. The criteria for being placed in an above-grade-level course (i.e., not being placed in grade 7 math as a seventh grader) included a number of assessments (including a district mathematics exam) that provides a combined score, along with math scores consistently above average for daily work and assessments, emotional and social maturity, strong work and study habits, a strong interest in math, and the desire to do challenging work. While the entry criteria did restrict all the students in this study from an early entry into the above-grade-level course, the staff at the school perceived that, in some cases, the criteria also acted as an equity barrier. As will be noted in the findings, some students were well aware of their score and its implications for placement. It was possible for parents to petition a placement of their child; however, for this study we did not collect information about attempts to do so. For these eight students, a teacher (and in at least two cases, the student) advocated for the change to an above-grade-level course.</p> <p>All of the participants in this study began their junior high mathematics in grade 7 math (i.e., grade-level). All of the students made a change that allowed them to complete algebra in the eighth grade. For half of these students, the change came midyear. For the other four students, the decision for the change was made late in year 1 or during the summer and the students enrolled in the above-grade-level course at the beginning of the new school year (Table 1 includes the students' mathematics sequences).</p> <p>In this particular district, students in junior and senior high school have a scheduled, approximately 30-minute, advisory time four days per week. During this time, students may visit a teacher for additional support, make-up work, etc. The students who participated in this study, as well as similar students who chose to not participate, were encouraged to visit their math teacher for extra support. In year 1, above-grade-level teachers made a point to visit during the advisory time students who would move to above-grade-level classes the following year; the focus was on working with students to develop skills in taking risks to try mathematics tasks that they did not know how to solve so they could learn to build from mistakes. In addition, the students who participated in the study during year 2 also attended a "boot camp" in the summer prior to their first enrollment in the above-grade-level courses. In the one-day boot camp, students were presented with challenging problems, again practicing "feeling uncomfortable."</p> <hd id="AN0164054144-10">Procedure and data collection tools</hd> <p>Following approval by the host university's IRB of all study protocols and upon receiving parental consent to participate in the study, students completed two brief questionnaires about their self-efficacy and confidence related to math, which were delivered via Qualtrics. The Math Confidence Scale (MCS) included seven questions in which students responded on a five-point Likert-type scale (Hendy et al., [<reflink idref="bib25" id="ref52">25</reflink>]). The questions in the scale are about confidence in math generally that perhaps points to accompanying persistence; e.g., "Even if I do not understand a math problem at first, I am confident I will get it eventually." Internal reliability for this instrument in a sample of college students was 0.85 (Hendy et al., [<reflink idref="bib25" id="ref53">25</reflink>]). In the sample for this study, the reliability was approximately 0.74.</p> <p>The Math Self-Efficacy Scale (MSES) included nine questions on a five-point Likert-type scale (Nielsen & Moore, [<reflink idref="bib46" id="ref54">46</reflink>]) and was chosen because of its focus on confidence within self-efficacy. Students are asked to rate their confidence in working with specific mathematical concepts; e.g., "[How confident are you that you can perform each of the following tasks in the classroom?] an algebra problem." Reliability for this instrument for similar age students was 0.86 (Nielsen & Moore, [<reflink idref="bib46" id="ref55">46</reflink>]). In the sample for this study, the reliability was approximately 0.80. For this qualitative study, we considered these student scores as demographic information (Table 2) as the quantitative data was not robust in its own right for use of specific analysis methods (Creswell & Plano-Clark, [<reflink idref="bib18" id="ref56">18</reflink>]).</p> <p>Table 2. Student math confidence and math self-efficacy scores.</p> <p> <ephtml> <table><thead><tr><td>Pseudonym</td><td>Math confidence scale<xref ref-type="table-fn" rid="tfn2">a</xref></td><td>Mathematics self-efficacy scale<xref ref-type="table-fn" rid="tfn3">b</xref></td></tr></thead><tbody valign="top"><tr><td>Heather</td><td char=".">3.86</td><td char=".">2.44</td></tr><tr><td>Barrett</td><td char=".">3.57</td><td char=".">3.67</td></tr><tr><td>Kevin</td><td>Not available</td><td>Not available</td></tr><tr><td>Michael</td><td char=".">3.86</td><td char=".">4</td></tr><tr><td>Armella</td><td char=".">2.29</td><td char=".">2.56</td></tr><tr><td>Ray</td><td char=".">4</td><td char=".">4</td></tr><tr><td>Amber</td><td char=".">4</td><td char=".">4.67</td></tr><tr><td>Jenica</td><td char=".">4.14</td><td char=".">2.56</td></tr><tr><td>Mean (SD)</td><td char=".">3.67 (0.64)</td><td char=".">3.41 (0.89)</td></tr></tbody></table> </ephtml> </p> <ulist> <item>2 Math Confidence Scale (MCS); Hendy et al., [<reflink idref="bib25" id="ref57">25</reflink>] - General Confidence. Internal reliability for this instrument in a sample of college students was 0.85 (Hendy et al., [<reflink idref="bib25" id="ref58">25</reflink>]). In the sample for this study, the reliability was approximately 0.74.</item> <item>3 Mathematics Self-Efficacy Scale: Class (MSES); Nielsen & Moore, [<reflink idref="bib46" id="ref59">46</reflink>] - Specific tasks. Reliability for this instrument for similar age students was 0.86 (Nielsen & Moore, [<reflink idref="bib46" id="ref60">46</reflink>]). In the sample for this study, the reliability was approximately 0.80.</item> </ulist> <p>To understand how student's self-confidence potentially changed during their transition to an above-grade-level mathematics course, we conducted a semi-structured individual interview with each participant that included two sections. In the first section (about 5 minutes), the students were asked about their confidence in math now and prior to changing classes. Examples of topics included how their mathematics course was currently going, their confidence while in their past and current math course, what changes occurred between their past and current math course, what the student does when seeing an unfamiliar mathematics task, and what advice they would give future students taking the course.</p> <p>In the second part of the interview (about 20 minutes) students talked aloud as they completed several math problems. During this phase, we were interested in how students talked about solving the problems relative to their abilities and self-confidence rather than if they were solving problems correctly. In other words, we considered the role of their own talk during problem solving and how it mediated their own problem-solving processes.</p> <p>The six mathematics tasks used in the second part of the interview were selected from sections in the students' current algebra book (Charles, [<reflink idref="bib15" id="ref61">15</reflink>]) that they had not yet, or had only recently, covered in class. Because some students were interviewed near the end of the spring semester in year 1, and some interviewed in the fall and near the beginning of the calendar year in year 2, two different sets of mathematics tasks were used. No specific tasks overlapped between the two years, although they shared similar task content foci. That task content varied based on the time of year in which the interview was conducted allowed the task difficulty levels to be similar for each student, regardless of when they participated in the study. We selected tasks to be challenging, yet potentially answerable based on material covered in class up to the date of the interview; further we used the curricular sequence within the students' mathematics text to guide our problem selection. Year 1 mathematics tasks focused on end-of-year understanding of concepts, as interviews were conducted at the end of the school year; whereas year 2 mathematics tasks focused on the expected concepts taught by the 25th week of the school year. Year 1 tasks were abstract and symbolic, focusing on using computations that embedded contextual or real-world situations and asked for multiple representations. The year 2 tasks retained some of this focus, but more so focused on making connections between multiple representations of problem-solving situations, rather than symbolic to abstract connections (Table 3).</p> <p>Table 3. Challenging task types and programs for year 1 and year 2.</p> <p> <ephtml> <table><thead><tr><td>Mathematics topic/concept</td><td>Year 1 task #</td><td>Task</td><td>Year 2 tasks #</td><td>Task</td></tr></thead><tbody valign="top"><tr><td>Simplifying expressions</td><td>#1</td><td>Factor completely: <p id="ilm0001"><graphic href="vjer_a_2186338_ilm0001.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mn xmlns="">15</mn><msup xmlns=""><mrow><mi>t</mi></mrow><mrow><mn>3</mn></mrow></msup><mo xmlns="">+</mo><mn xmlns="">2</mn><msup xmlns=""><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo xmlns="">−</mo><mn xmlns="">45</mn><mi xmlns="">t</mi><mo xmlns="">−</mo><mn xmlns="">6</mn></math></p></td><td>#4</td><td>Write an expression in simplest form for the area of the rectangle. <p id="ilm0003"><graphic href="vjer_a_2186338_ilg0002.jpg" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mn xmlns="">15</mn><mo stretchy="false" xmlns="">(</mo><mi xmlns="">x</mi><mo xmlns="">−</mo><mn xmlns="">5</mn><mo stretchy="false" xmlns="">)</mo></math></p></td></tr><tr><td>Solve when there are multiple variables</td><td>#2</td><td>Solve this system: <p id="ilm0004"><graphic href="vjer_a_2186338_ilm0004.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">y</mi><mo xmlns="">=</mo><mi xmlns="" /><msup xmlns=""><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo xmlns="">+</mo><mn xmlns="">2</mn><mi xmlns="">x</mi><mo xmlns="">−</mo><mn xmlns="">2</mn></math></p><p id="ilm0005"><graphic href="vjer_a_2186338_ilm0005.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">y</mi><mo xmlns="">=</mo><mi xmlns="">x</mi><mo xmlns="">+</mo><mn xmlns="">10</mn></math></p></td><td>#2</td><td>Solve <p id="ilm0006"><graphic href="vjer_a_2186338_ilm0006.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mn xmlns="">8</mn><mi xmlns="">n</mi><mo xmlns="">=</mo><mi xmlns="" /><mo xmlns="">−</mo><mn xmlns="">3</mn><mi xmlns="">m</mi><mo xmlns="">+</mo><mn xmlns="">1</mn></math></p> when <p id="ilm0007"><graphic href="vjer_a_2186338_ilm0007.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">n</mi><mo xmlns="">=</mo><mi xmlns="" /><mo xmlns="">−</mo><mn xmlns="">2</mn><mo xmlns="">,</mo><mi xmlns="" /><mn xmlns="">2</mn><mo xmlns="">,</mo><mi xmlns="" /><mi mathvariant="italic" xmlns="">and</mi><mi xmlns="" /><mn xmlns="">4</mn></math></p>.</td></tr><tr><td>Graph a linear or quadradic function</td><td>#3</td><td>Solve by graphing: <p id="ilm0008"><graphic href="vjer_a_2186338_ilm0008.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">y</mi><mo xmlns="">=</mo><mi xmlns="" /><msup xmlns=""><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo xmlns="">+</mo><mi xmlns="">x</mi><mo xmlns="">−</mo><mn xmlns="">6</mn></math></p></td><td>#1</td><td>The table below shows the relationship between the number of teachers and the number of students going on a field trip. How can the relationship be described using words, an equation, and a graph? Field TripTeachers 2 3 4 5 6Students 34 51 68 85 102</td></tr><tr><td>Simplify the expression</td><td>#4</td><td>Simplify the radical expression: <p id="ilm0009"><graphic href="vjer_a_2186338_ilm0009.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac xmlns=""><mrow><mo>√</mo><mn>2</mn></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>3</mn></mrow></mfrac></math></p></td><td>#4</td><td>Write an expression in simplest form for the area of the rectangle. <p id="ilm0015"><graphic href="vjer_a_2186338_ilg0001.jpg" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mn xmlns="">15</mn><mo stretchy="false" xmlns="">(</mo><mi xmlns="">x</mi><mo xmlns="">−</mo><mn xmlns="">5</mn><mo stretchy="false" xmlns="">)</mo></math></p></td></tr><tr><td>Rational Expressions</td><td>#5</td><td><p id="ilm0011"><graphic href="vjer_a_2186338_ilm0011.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac xmlns=""><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mi /><mo>−</mo><mi /><mn>4</mn></mrow><mrow><mi>x</mi><mi /><mo>+</mo><mi /><mn>3</mn></mrow></mfrac><mo xmlns="">×</mo><mfrac xmlns=""><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mi /><mo>+</mo><mi /><mn>7</mn><mi>x</mi><mi /><mo>+</mo><mi /><mn>12</mn></mrow><mrow><mi>x</mi><mi /><mo>−</mo><mi /><mn>2</mn></mrow></mfrac></math></p></td><td>#3</td><td>If <p id="ilm0012"><graphic href="vjer_a_2186338_ilm0012.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">x</mi><mo xmlns="">=</mo><mo xmlns="">−</mo><mfrac xmlns=""><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math></p> and <p id="ilm0013"><graphic href="vjer_a_2186338_ilm0013.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">y</mi><mo xmlns="">=</mo><mi xmlns="" /><mfrac xmlns=""><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></math></p>, what is the value of <p id="ilm0014"><graphic href="vjer_a_2186338_ilm0014.gif" content-type="Graph" /><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">−</mo><mn xmlns="">2</mn><mi xmlns="">x</mi><mi xmlns="">y</mi></math></p>?</td></tr><tr><td>Use rates to determine information for further use</td><td>#6</td><td>A camper takes 2 h to ride a bike around a reservoir at 10 mi/h at the beginning of the summer. By the end of the summer, she can ride around the reservoir in 1½ h. The time to travel around the reservoir varies inversely with the speed she pedals. What is her speed at the end of the summer? </td><td>#5</td><td>A child takes a nap averaging three hours and gets an average of 12 hours of sleep at night. Nap time and nighttime sleep can each vary by 30 minutes. What are the possible time lengths for the child's nap and nighttime sleep? </td></tr><tr><td /><td /><td /><td>#6</td><td>A student reads an average of 34 page per day. The number of pages they read per day varies from the average by up to 8 pages. a. Write an absolute value inequality that represents the range of the number of pages she reads per day. b. Solve your inequality. </td></tr></tbody></table> </ephtml> </p> <p>4 Problem directions that were provided to the student are omitted in this table. All problems are from Algebra I Common Core Edition by Charles ([<reflink idref="bib15" id="ref62">15</reflink>]).</p> <p>Following completion of student data collection during the spring semester of 2020, the teacher participated in a semi-structured interview. Questions focused on why and how the change of courses was implemented for these students and general information about the mathematics department. All interviews were recorded and transcribed verbatim.</p> <hd id="AN0164054144-11">Analysis</hd> <p>Because of the small data set for the two quantitative instruments that students completed regarding their self-confidence, we use those scores only as descriptive statistics. The qualitative data gathered were analyzed in two different waves, using the constant comparative method (Merriam & Tisdell, [<reflink idref="bib37" id="ref63">37</reflink>]; Saldaña, [<reflink idref="bib54" id="ref64">54</reflink>]). First, two members of the research team reviewed the data from the first part of the interview in which the students were asked about their class transition. summaries were created for each individual participant that focused on the student responses to their move, their perceptions of their move, and their self-confidence both in their earlier class and their current class. From these summaries we developed a number of categories that supported our further analysis and articulation of the findings. These included aspects of self-confidence and other verbal expressions that reflected the experience for these students, such as perceptions of why they moved, attributions, belonging, changes in confidence, self-regulation and persistence, help seeking, and the role of the teacher. At this point we returned to the original transcripts, in the spirit of the constant-comparative method, to ensure that all categories had been applied to each student's transcript and also to see that all elements of the students' talk that were of interest had been included in the coding. As each of these categories were summarized through the writing process (Wolcott, [<reflink idref="bib66" id="ref65">66</reflink>]), they were combined and refined in the following themes: Tensions given placement in the pipeline, the role of prior self-confidence as an outcome, changing role a self-confidence as a mediator that produced barriers, belonging as multiple mediating types, workarounds as mediators in problem solving, and self-regulation strategies as internalized mediators.</p> <p>Concurrently with the data analysis of the first part of the interview, a second group of researchers reviewed the talk-aloud data from the students' problem solving, focusing on how they talked about their problem solving, particularly when they were challenged. While we were interested in expressions of their self-confidence while solving the problems, we initially considered their general success in solving the problem. For example, "Tried, but incorrect answer in the end"; "tried, but partly correct answer in the end"; "tried but no solution/no official answer in the end"; "no try"; "correct answer and understanding"; and "End of ZPD" (even with strong support from the researcher, the student was unable to make any progress). This provided a context for our understanding of their expressions about self-confidence and to what they attributed their struggles or success in solving a problem. These were then integrated as examples of how their problem-solving talk fit into categories that were developed from the first part of the interview. Given this process, the data from the problem-solving analysis were used to provide triangulation of data by type (Stake, [<reflink idref="bib61" id="ref66">61</reflink>]) and further illuminate categories that emerged in the first phase of analysis.</p> <p>The teacher was considered a secondary informant and the data from her interview was used to provide context for the students' class transitions as well as clarification regarding students' comments about class happenings and typical procedures. The teacher interview data were analyzed for confirmatory and disconformity evidence based on what student participants mentioned.</p> <hd id="AN0164054144-12">Findings</hd> <p>As we considered these students' self-confidence during their mathematics class placement transition, we noted themes about their placement in the pipeline, the role of prior self-confidence as an outcome, changing role a self-confidence as a mediator that produced barriers, belonging as multiple mediating types, workarounds as mediators in problem solving, and self-regulation strategies as internalized mediators.</p> <hd id="AN0164054144-13">Placement in the mathematics pipeline: Tensions</hd> <p>For all the students in the study, their initial placement in their grade-level class was perhaps by default—they had not been identified to move to the above-grade-level course. In the district, students were identified for the above-grade-level sequence through a combination of exam scores and personal characteristics. For students, the critical element was the composite exam score. Two of the students interviewed in year 2 (Michael and Amber) indicated that they missed the benchmark exam score by one point. Michael attributed his missing the cutoff to his test-taking skills.</p> <p>Some students were identified for moving because being academically unchallenged prompted classroom issues. As the teacher shared, "it was sort of interesting, the students that we first started identifying were kids who—they were actually acting out in grade-level classes. And so, we first tried to identify kids like, 'OK, is the behavior problem because you're bored or because you're lost?'" For example, year 1 participant Barrett attributed his potential struggles in mathematics to paying attention, "Oh, no. I was horrible at math. Whenever I did math, I would either pay very much attention or no attention at all.... It would go well if I actually paid attention."</p> <p>For others, the student implied that they had advocated for themselves. Heather, who was transitioned from Math 7 to Pre-Algebra in the seventh grade, indicated in her interview that she self-selected changing classes: "I was getting all A's. I talked to a teacher about it, and she said that I could move up."</p> <p>Students had mixed feelings about their initial transitions to the above-grade-level course. One view expressed the appropriate placement into their grade-level course. For example, Jenica, who was in math 7 as a seventh grader and then moved to Algebra at the start of grade 8, described feeling that it was "unfair" to be moved from their grade-level course where they felt they belonged. In contrast, two students (Michael and Heather) felt that their appropriate placement was in the above-grade-level course that they were initially denied. Michael felt he should have been placed into the above-grade-level course from the start. He shared, "It didn't seem like there was any shame or anything in that but it was just, um, I was a little disappointed 'cuz I feel like I coulda got that one last point to get into pre-al, uh, so I was a little disappointed in myself for that, but then it wasn't that big of a deal." His justification to remain at grade level implicitly projecting that it was perhaps shameful (at least for him having missed that one point that he felt he could have gotten). Regardless of why they were moved, these students largely experienced similar challenges to their self-confidence regarding mathematics once they had moved.</p> <p>While placement in the pipeline itself via rules of the larger system can mediate the students' learning outcomes and opportunities, we consider the added layer of self-confidence and how it may have been coupled with their prior success and if it may be considered an outcome of the at-grade-level experience.</p> <hd id="AN0164054144-14">Prior self-confidence as an outcome</hd> <p>Students had expressed self-confidence regarding their ability to do mathematics while in their grade-level courses; yet they generally expressed that they had not been challenged there. Some indicated that it was because the mathematics covered was "pretty easy." Heather commented, "It didn't take them long to move me up, because I had all A's and I was doing good in Math 7." For some like Jenica, the content in their grade-level course was viewed as review, she described "in Math 7, I knew like everything that we were doing, it was just like review to me, so like, I remember that from sixth." They were able to complete the mathematics with ease. Barrett was clear, "And I transferred because I was getting like every question right. And I said over and over that I already knew all of this. Every new lesson, I was like, 'oh this is easy,' and I would just write it all down."</p> <p>While the focus of this qualitative study was on the students' expressions of their self-confidence given their move, these eight students also completed two surveys related to math self-efficacy and confidence prior to the start of their interview (Table 2). In general, averages on both surveys for this group of students indicated moderate levels of math confidence and self-efficacy (MCS = 3.67 and MSES = 3.41 respectively; see Table 2). We noted that for all but one student (Armella) their scores on the MSES were quite similar. We also noted that the MCS scores for Armella, Heather, and Jenica were lower than the other students (Figure 2).</p> <p>Graph: Figure 2. Students' scores on the MCS and the MESE.</p> <p>Whether the grade-level class seemed a review or easy, these eight students, even those that indicated lower mathematics confidence in the survey, were generally confident about their ability to do mathematics in their previous grade-level course; they indicated a belief in their abilities to do the work. As Jenica shared, "I was really confident I—math wasn't really a problem for me back then." For all of the students, the opportunity to move to an above-grade-level mathematics course came because they had been doing well or were viewed as unchallenged. In this, we viewed self-confidence as an outcome of their prior coursework, and a potential mediator for future learning processes.</p> <hd id="AN0164054144-15">Changing role of mediator: New barriers</hd> <p>While some students questioned whether they were in the right class, for all of the students we noted a trajectory of changing self-confidence. In their interviews, students indicated early self-confidence, or a gain in self-confidence, in working in their grade-level mathematics course, which was easy or for which they had a strong skill set. Then, self-confidence dropped in the new above-grade-level class. For example, Armella, who had taken Math 7 as a seventh grader and was moved to algebra at the start of eighth grade, explained, "it's getting a little harder and harder;" her survey scores indicating comparatively low confidence and low self-efficacy in math at the time of the survey. Ray, also with a grade 7 to algebra transition, agreed that some of the work was "more confusing," whereas Amber commented, "this year it feels like more new stuff." As they continued in their above-grade level course, students did regain some of their self-confidence, although Armella and Jenica did not indicate the level of self-confidence that their peers in the study did. Armella was an English language learner (ELL) and spoke of increased confidence as being language-related, rather than mathematics-related. "In the first tri[mester] it was really, really hard because you know, a lot of English, and, but in ... the second tri it kinda get really easy and, was, I was more confident in it." Thus, Armella's mathematical self-confidence was also intertwined with language self-efficacy. Jenica expressed her trajectory of self-confidence in her interview when she stated: "So at the beginning, I was not confident, and right now I'm like, getting a bit more confident..."</p> <p>We noted this trajectory of self-confidence as a qualitative change as students shared how they felt in their grade-level course, their above-grade-level course, and about transitioning. All students believed they were still on the continuing path in regaining their self-confidence. Other than Armella, no student indicated the positive self-confidence and the ease of math about their above-grade-level class that they had experienced in their previous grade-level class. Rather than self-confidence being an outcome as with success in earlier classes, the outcome was a change in self-confidence, which then provided a different mediator for the students' problem solving than they had in the past. Rather that supporting the process, it appeared to provide a barrier.</p> <p>We asked the students to solve challenging tasks in the second part of their interview. Given the small timescale of the problems, we did not expect to see large patterns of self-confidence talk. Problems were of the same type but different in scope given the different time of the school year in which the students participated in the study. In total, 48 problems were attempted by the students (8 students solving 6 problems each). Only one problem was solved correctly by a student who had transitioned mid-year (Barrett, with Heather, Kevin, and Michael solving none correctly). Of the students who transitioned at the start of the school year, nine problems were solved correctly (one by Armella, three by Ray, two by Amber, and three by Jenica). We were not interested in their ability to correctly solve the problems, but rather how what they said during their problem solving related to self-confidence. Of the 48 problems we noted that three included "math talk" only—no indicators of questioning themselves, unsureness, or frustration. For the vast majority of the problems, their problem-solving processes that would mediate their activity were not wholly about how to solve the problems but indicated other non-cognitive elements that we interpreted as evidence of self-confidence (or lack thereof) mediating their work.</p> <p>Through these data, we were able to observe what their lack of self-confidence looked like. When students were unsure about how to begin a task, they were often hesitant to even attempt the tasks. Challenges to getting started included unfamiliar or unremembered vocabulary, procedures, or mathematical syntax. For example, Ray thought aloud as he worked on a linear problem (Table 3, Y2P1) that included a proportionate reasoning element (i.e., as one item varies X amount the other also varies in a proportional amount),</p> <p>So I'm supposed to just describe it using words and equation and graph? Well, for every student there's 17, or for every teacher, there are 17 students. So like, so. [pause] An equation. [long pause] How would I write this as an equation? Just like. [long pause] [researcher: What are you thinking about?] I'm trying to think about how I would write this as an equation 'cause I really, I don't know how I would ... For a graph would I just like mark the points?"</p> <p>Jenica ended a similar task (Y2P5) stating after struggling with the definition of "vary" in her problem solving, "We haven't really used that word I think the last time I used it was in 7th grade, so I don't, I don't really remember."</p> <p>While this may appear as lack of knowledge, it seemed there was more to it, given what they shared. Without recent use of concepts or ideas, students similar to Jenica engaged with tasks, but were not confident about presenting their final answer. Jenica exhibited lower self-confidence again when engaged with a different task that involved area, a concept taught and explored in junior high, but was challenged when the task presented mathematical expressions (e.g., x + 5, y − 2 etc.) instead of only numerical values (i.e., 5, 7, 8, etc.).</p> <p>So, this one... length times width, right? That's length times width times height, wait, yeah um just [erases, realizes doesn't need height] .... I'll do 15 times x minus 5, that's...um, wait, how do you do the expressions? Ok I don't, I don't know I don't remember about this one.</p> <p>Although Jenica was correct in her initial evaluation of how she would proceed in evaluating the task presented, the use of the expressions involved prompted her unsureness. While these students were unsure about some of the mathematics, they were also unsure about being in the right place.</p> <hd id="AN0164054144-16">Belonging as multiple mediating types</hd> <p>Changing courses, whether two months into the school year or as the school year began, presented challenges related to students' belonging—whether because of skills or their beliefs about who legitimately belonged in the class.</p> <p>As students talked about their class transition, we noted points about comfort and the perceptions of the other students about the class that prompted them to feel that they did not belong. Within individuals there seemed to be tensions about belonging. Some sense of belonging hinged on preparation. Kevin and Jenica indicated that they were not prepared, having skipped parts of the grade-level class and thus were not skilled in working with particular concepts. Whether or not actual mathematical competencies were missed was not divulged, but from the students' perspectives they felt mathematical skills were lacking.</p> <p>More troubling than the missing skills about particular concepts were these students' feelings of being an outsider. The teacher commented on this, "some students indicated that the others seemed to have something different or were something different than what they were." Amber indicated this feeling as well.</p> <p>Yeah, I just feel like since there's, it's like a higher class, I feel like you're supposed to be like one of the smarter ones and supposed to get most of them right, even though messing up is what makes you smarter and stuff and our teacher does a good job of reminding us of that.</p> <p>As Heather, after moving from Math 7 to pre-algebra midyear, indicated, "They [those in Math 7] all were like, 'how come she got to move? She doesn't even know anything.' They were all doubting me. But those are the same people who were trying to distract me the whole time." For Heather, the new class was not welcoming either. "At first the students in there were kind of like, 'why is she moving up? Is she just new here?' None of them knew me, I didn't have any classes with them." Given this example, belonging was also an element of the community in which there was a tension in allowing the transitioned student membership. That said, Kevin, who moved midyear from pre-algebra to algebra, said that the kids in the new class were "not at all" confused with him moving up. For those moved during the year, Heather and Kevin saw the awkwardness of advancing into the above-grade-level courses from different perspectives; and for a number of students, feeling they did not belong played into their lack of self-confidence.</p> <p>Some students who transitioned felt they did not belong because they lacked the mathematical skills required and expressed feelings of being an outsider coming into the new peer group during their interview. One way this was exhibited was in a hesitancy to speak up in class. For example, Amber shared that "... I have less confidence talking to the whole group 'cause I'm—more worried I'll mess up." The teacher elaborated the idea of not speaking up in her interview as an element of the façade that non-transitioned students present. She recalled sharing with a student,</p> <p>And the thing I said to him was, do you feel like you're the only person in the room who doesn't understand what's going on? And he said, yes. And I said, the unwritten rule that you have to understand is in above-grade-level classes, everybody pretends that they know what's going on, and so you just have to understand that, you know, everyone's pretending that they know what's going on. Everyone feels like you feel. No one will speak up and ask the question.</p> <p>Further, according to the teacher, even though transitioned students perceived they lacked the skills and did not belong, their skills were on-par with students in the above-grade-level course. The teacher saw commonalities between grade-level and above-grade-level students, such as the reluctance to speak up. Students in the above-grade-level courses had some of the same challenges or shortcomings as those in the grade-level course. The students were not so different, she explained, "Some of the kids who were in the advanced track from the beginning had some of those same characteristics that they were sort of just like explained away." For example, students in the above-grade-level course were also challenged by basic mathematics skills. The teacher explained, "... in the advanced classes ..., those kids didn't know how to do arithmetic with fractions either. But the difference was that in above-grade-level classes, they were allowed to use calculators. And so that skill deficit got hidden." Students in both courses encountered struggles with arithmetic tasks, but two different scenarios occurred when addressing their stalled progress: students in the above-grade-level course were encouraged to use a calculator or a similar mathematical tool to allow the student to proceed with the task, whereas the students in the grade-level courses were not encouraged to use these tools and instead instruction was stopped while the arithmetic skills were retaught. The teacher elaborated this differential effect,</p> <p>And I would say in the above-grade-level classes, it's sort of like, the focus is really on teaching kids how to work around, you know. In an above-grade-level class, if we're teaching kids how to solve two-step equations and we find out they don't know how to add and subtract with fractions, we're giving them a calculator and saying like, OK, this is the arithmetic that you don't know how to do. We're not going to stop class to teach this to you. But in a grade-level class, that would happen.</p> <p>This differential approach between the two classes prompted the use of what the teacher called "workarounds," an artifact of group membership.</p> <hd id="AN0164054144-17">Workarounds: Seeking mediators</hd> <p>Workarounds were necessary to mediate the learning process, it seemed, in the above-grade-level course. The problem-solving tasks provided an illustration of the transitioned student's appropriation of workarounds. Multiple students asked to use a calculator or indicated that not having a calculator was the explanation for being unsuccessful on a task. Kevin talked aloud, "I wish I had a calculator right now. Mental math is... I think I did that wrong," while he engaged in solving a linear task focused on rates (Y1P6), needing a workaround and also indicating his limited self-confidence. Likewise, Barrett illustrated this point in his interview during a task (Y1P2) that focused on simplifying using fractions, "Is a calculator needed for this problem? I know how to do it, but it's a sort of -problem. Want me to tell you how to do the problem?" Barrett could describe in detail how and why steps were taken but could not reach a final, numerical answer without using a calculator. According to the teacher, when faced with arithmetic challenges, students in above-grade-level courses were allowed to use calculators; however, students in grade-level mathematics classes were not provided this same allowance. The use of workarounds filled in the gaps in the above-grade-level class and allowed those students to move beyond what they could do alone. While students had indicated that they perhaps had missed some mathematical skills that fostered a feeling of not belonging, workarounds were a remedy for that. In this, students sought physical tools to mediate their problem solving, and in some cases seemed to rely on them. When these tools were used to mediate the process, the students indicated they had a chance of completing the problem, but without it, lack of self-confidence mediated the process, or at least how they talked about it. The workarounds provided potential support when skills and self-confidence may have not been effective on their own.</p> <p>Given that the students who transitioned had earlier success in their grade-level course, they did not need the workarounds in their earlier grade-level courses that were used in above-grade-level courses. Because of that, transitioned students did not <emph>know</emph> that workarounds, such as calculators, were part of doing mathematics until they were in the above-grade-level courses. The teacher indicated that it was important to figure out what the student did not know how to do, so that "we can, you know, sort of like get you up to speed," or telling the students "the rules of the game that [they] didn't even know existed." The availability and encouragement of workarounds indicated knowing the rules, and perhaps a different way to apply those rules in the above-grade-level course, and were then useful in addressing issues with self-confidence.</p> <hd id="AN0164054144-18">People as workarounds</hd> <p>According to the teacher, perhaps the biggest workaround was the use of other people such as students' peers, their parents, or other teachers in the building.</p> <p>Honestly, the biggest workaround was that if I taught something in class that they didn't understand, a lot of them had parents they could go home to that could either help them understand or knew someone who could help them understand. And grade-level kids didn't really have that sort of extra support. So, traditionally, above-grade-level kids sort of had ways they could cover up these holes in understanding that grade-level kids, those were just really exposed.</p> <p>The notion of students covering up holes in their understanding is not uncommon (Canning et al., [<reflink idref="bib12" id="ref67">12</reflink>]; Yeager & Dweck, [<reflink idref="bib68" id="ref68">68</reflink>]). Workarounds point to the appropriateness of filling the holes rather than covering them up. Nearly every student we interviewed (all but Barrett) talked about other people, those more-knowledgeable others who can mediate a learning process, as resources that they would use when they did not understand a mathematical concept. The students we interviewed had learned to draw on resources such as peers, parents, and teachers; resources that they did not need to use when they were in grade-level mathematics courses. Who they asked usually depended on where they were working when they needed help. Heather used her peer group in class, explaining "there's two other girls at my table and we all work together. Another girl at my table also got moved up. We all work together." Barrett and Armella stated they would talk to their table groupmates. During her interview Armella also shared she would "Just ask a friend that [got] it." Ray, Kevin, Amber, and Jenica mentioned asking parents. Jenica elaborated about working together at home, "... when I take [homework] home, I try to figure it out by myself, but my stepmom is really good at math, so, sometimes I ask her for help." Kevin specifically mentioned that he would ask his parents if at home, but his teacher if at school.</p> <p>The teacher was to be a last resource for the students. The teacher explained, "we have the kids make lists in the front of your math notebook, 'you need to list what are five resources you are gonna consult before you consult the teacher. It can be the Internet. It could be your textbook. It can be a friend.'" Perhaps because they were in school during the interview, for a number of the students, their first choice was the teacher. For example, Kevin, Ray, and Jenica mentioned they would be asking their teacher for help at the particular point where they were stuck in our problem solving tasks. Specifically, Jenica mentioned during a challenging task (Y2P4) that she would ask her teacher, "how you write an expression," and then would "just plug in the numbers." As Ray indicated, he would typically solve tasks that included multiple representations using linear concepts with a symbolic equation. When given a chart/table of data (Y2P1), he needed a workaround.</p> <p>I would try. I would ask a teacher. What I can't decide is like—I just don't know how I would write it like. So, I would ask the teacher like what format or something. [What's your best guess for the format? If you had to try] If I would like... [Sighed] Like. [Pause] [Researcher: Remember it doesn't have to be perfect, so.] Yeah. I don't really know, what I would write.</p> <p>Ray mentioned he would need to reach out to his teacher to ensure that the format was correct rather than having the self-confidence to know his approach. Ray's lack of self-confidence was met with a need for a workaround (the teacher) and a sigh. Yet despite his insecurity about solving the problem, his work was generally correct. We found this interesting in that self-confidence was not an outcome of correct work, which was believed to be the norm for these students as all but one indicated that they expected to receive an A or a B in the class; Barrett expecting a C. The lack of self-confidence continued to mediate the learning processes. As Oney and Oksuzoglu-Guven ([<reflink idref="bib49" id="ref69">49</reflink>]) noted, what mattered was the strength of the belief rather than the level of perceived competence.</p> <p>While these students had varying views of their transition to an above-grade-level mathematics course, their trajectory of self-confidence, which started high in their grade-level class, plummeted, and then showed a gradual increase in self-confidence, seldom allowed the students to confidently complete challenging mathematics tasks that we presented. While the workarounds were helpful, when they were not available, students lacked self-confidence in shorter timescales—many struggled with the challenging tasks and half of the students asked about workarounds while solving the problems. Yet, these students did bring with them skills that helped with the transition.</p> <hd id="AN0164054144-19">Self-regulation strategies: Internalized mediators</hd> <p>In addition to using workarounds such as asking people or using a calculator, students identified self-regulation strategies that supported their transition to an above-grade-level mathematics class. We considered that students knowing they could ask other people for help and knew they could ask different people in different environments, part of their self-regulatory processes for their learning. Consider Jenica's process of first trying on her own and then asking for help when needed. Heather saw asking questions of the people around her, e.g., "I feel like I have people to go ask," as a strategy. Once students knew of workarounds, their own self-regulatory processes monitored and prompted as needed; for example, knowing that a calculator would be useful for multiplying fractions. Students shared other processes when asked in their interviews to give advice to other students. For example, two students (Barrett and Kevin) indicated the importance of paying closer attention in class. As Barrett described, "It would go well if I actually paid attention. I'm trying to pay more attention now, but at the beginning when I was first transferred—well, in the first part after I was transferred, I did pay attention. But the middle segment, I just didn't pay attention. Just let everything go."</p> <p>Amber's focus was on taking her time, knowing her tendency to rush on tests. "I normally try to think back in my notes and like work it out, like slower cuz I normally tend to rush on tests. So, I take my time more and think about it more." When Amber worked at the challenging tasks, we noted how she brought a strong sense of self-regulation and knowledge of her abilities. She shared that she "was very much a visual learner" and that she "prefer[red] word problems." Throughout her work she pointed to strategies that would help her learn in visual ways such as "I like to write to help me remember" or sharing that "when I heard 'range' I think of number line." She was active in pointing to prior learning, whether she noted that she had not "done that one in a while" or pointing to when she had done the work (e.g., 6<sups>th</sups> grade). All in all, Amber brought strong skills with her to aid in her above-grade level work, solving two problems correctly: a graphing problem (Y2P3) and a word problem (Y2P6), indicating not only self-confidence, but self-efficacy (note her strong MSES score, Table 2).</p> <p>Michael, likewise, brought a strong skill set; his strength was self-assessment. He had a variety of phrases that pointed to his unsureness, but also positioned his work. He shared what happens when solving a challenging problem, "I get frustrated sometimes when I can't figure it out and then, normally I'll skip it and then I'll come back to it, I'm not very good at like timed tests, I get stressed out about that kinda stuff." It seemed that for some of these students, their self-regulation came from a self-awareness of their mathematical limitations. Michael talked about how he approached challenging mathematics tasks when struggling,</p> <p>If you actually don't understand a problem, if you put down a number, you'll at least have a chance of getting it right, but if you leave it blank then it's impossible like to get it remotely right, and sometimes, you know, a teacher will give you credit for at least putting down a number than just leaving it blank and not even trying.</p> <p>This strategy reiterated the skills that the teacher indicated they wanted students to gain prior to their transfer via advisory sessions and the one-day boot camp for the year 2 students, to learn to feel uncomfortable. Michael's advice echoed his own self-assessment, "I used to be that guy who just gives up on things, but now I just wanna figure this out, I don't like leaving pages blank and stuff."</p> <p>As indicated in the Math Confidence Scale, their confidence included a serving of persistence. Students should "just stick with it" (Ray). Armella was more inspirational in her advice, "That you never lose hope on yourself in math ... Even though it's really hard you should never give up." All of these students were able to talk about regulatory tactics to get their work done, support their understanding, and lead to potential success in the mathematics pipeline.</p> <hd id="AN0164054144-20">Summary</hd> <p>In considering the self-confidence of these students who were moved to an above-grade-level mathematics course in a manner that differed from their school district's norm for mathematics class placement, we found that their self-confidence moved from an outcome to a more explicit mediator of their problem-solving processes when students were presented with challenging tasks. They indicated a drop in self-confidence, moving from "ease" and "familiarity" regarding their grade-level work, and at the point of the study had not returned to the self-confidence they had in the at-grade-level mathematics course. While some felt they belonged at the above-level class initially, some struggled with comments from new peers and those they had left behind who questioned their ability. All struggled and lost self-confidence with the transition, yet all had moved from that initial lack of self-confidence that the change in course sequence had brought. While it seemed that the move to the above-grade-level class did not present an insurmountable obstacle in terms of mathematics learning, more problematic was their perception of belonging, the various ways in which it manifested, and how it linked to their self-confidence. Those in above-grade-level classes were believed to have some special, perhaps unknown, characteristics that superseded how they acted. Despite our participants' own perceptions, they had useful skill sets, but needed to understand that they were not so different and that they brought useful personal attributes with them. Attributes that fostered their developing return in self-confidence included persistence and self-regulation strategies. Further, they needed to become comfortable with drawing on workarounds that they were either not allowed to use before or did not previously need because of the ease of math in the grade-level course.</p> <hd id="AN0164054144-21">Discussion</hd> <p>This study explored junior high school students' self-confidence transitioning to above-grade-level mathematics courses through a lens of how self-confidence may mediate the process. As previous research demonstrates (Bush & Karp, [<reflink idref="bib10" id="ref70">10</reflink>]; Cortes et al., [<reflink idref="bib17" id="ref71">17</reflink>]; Domina et. al, 2014; Perna & Loughan, [<reflink idref="bib51" id="ref72">51</reflink>]) advanced mathematical course trajectories can be sought when algebra or another above-grade-level coursework takes place in junior high. The mathematics department at the school attended by our participants had moved beyond their traditional means of selecting students for above-level mathematics courses. Student's self-concept was the strength of the belief, that indicated their level of believed competence (Oney & Oksuzoglu-Guven, [<reflink idref="bib49" id="ref73">49</reflink>]).</p> <p>Our findings indicated that, in addition to changing these students' mathematics path, they also exhibited a trajectory that included a change in self-confidence in mathematics. In their previous grade-level-course they engaged with the content with ease; the transition to the new class brought a drop in self-confidence. While we did not have data regarding the students' grade-level mathematics grade, we consider the Simzar et al. ([<reflink idref="bib60" id="ref74">60</reflink>]) finding that prior mathematical achievement will moderate a decrease in the self-confidence students have about their mathematics abilities once enrolled in algebra. The participants in this study all noted a decrease; could that be an artifact of their initial placement? Were they not academically ready to avoid this decrease? Or that they were ready enough so that they did not have a greater decrease in self-confidence? We tend to believe that they were ready but needed extra support as was shown in our data—through introduction of workarounds and developing a sense of belonging that included understanding their similarities to their above-grade-level peers rather than differences. Our findings indicate that these students did benefit from being placed in the highest-level mathematics course in which they were capable of succeeding given their prior mathematics achievement (Simzar et al., [<reflink idref="bib60" id="ref75">60</reflink>]), but their self-confidence was impacted (Huang et al., [<reflink idref="bib26" id="ref76">26</reflink>]) as we noted in how they talked about their problem-solving processes. Bandura ([<reflink idref="bib4" id="ref77">4</reflink>]) suggested the beliefs students hold about their capabilities influences their self-confidence to start and continue a successful mathematics trajectory. Martin et al. ([<reflink idref="bib36" id="ref78">36</reflink>]) agreed in their fifth grade to eighth grade study that declines in mathematics engagement were related to student factors, including the value of mathematics confidence that aligned with student's self-efficacy. These results also align with previous research on secondary school students that reported strong positive relationships between students' mathematics self-efficacy and achievement in mathematics (Ayotola & Adedeji, [<reflink idref="bib1" id="ref79">1</reflink>]).</p> <p>Given our theoretical lens, we observed that self-confidence, as well as the tools (workarounds), seemed to mediate the learners' mathematical processes. We noted a change in the role of self-confidence given the students' transition. While self-confidence developed as an outcome of prior work, that outcome was insufficient to be an effective mediator in students new (above-grade-level) classes. Self-confidence is malleable (Bandura, [<reflink idref="bib5" id="ref80">5</reflink>]), and given the circumstances of their moving to the new class, despite the supports available, we noted how it became part of their talk in solving challenging mathematics tasks. In this way, while self-confidence may be an outcome of good work, and may implicitly mediate the process (e.g., self-confidence helps them approach challenging tasks), our data indicate the lack of self-confidence will also mediate their processes in explicit ways, particularly in self-talk.</p> <hd id="AN0164054144-22">Workarounds</hd> <p>Some workarounds come about through interacting with a more knowledgeable other, such as a parent, teacher, or peer. Guidance from peers, parents, and teachers influenced the way transitioned students reasoned through problem-solving tasks. In grade-level courses, content was process based instead of conceptual. As such, transitioning students to an above-grade-level course disrupted how they viewed their mathematical abilities. As Dweck ([<reflink idref="bib20" id="ref81">20</reflink>]) described, students need to have a reasonable belief in their mathematical abilities. Students who find an outlet, such as human supports, are likely to have increased self-efficacy and improved performance compared to students who are placed into above-grade-level courses without supports (Simzar et al., [<reflink idref="bib60" id="ref82">60</reflink>]).</p> <p>While a lack of self-confidence mediated their process, workarounds that the students sought were peppered with tensions from the larger system in which their mathematics learning was situated (Liljedahl, [<reflink idref="bib33" id="ref83">33</reflink>]). Workarounds were the mathematical tools students have the privilege to effectively use. In a meta-analysis, Bray and Tangney ([<reflink idref="bib9" id="ref84">9</reflink>]) noted differences between mathematical classroom tools, how they were used across classrooms, and teachers approaches that could optimize and further enhance mathematics education. However, tools such as calculators have long been used as a means of supporting or accommodating students while scaffolding mathematics learning. Yet, contrasting views persist on the use of tools such as calculators, when and where they may be used, whether they are privileged, and that their use is often teacher dependent (Walen et al., [<reflink idref="bib64" id="ref85">64</reflink>]). Given a successful workaround, the new outcome can then be used by other activity systems (see, for example, Schuh et al., [<reflink idref="bib56" id="ref86">56</reflink>]), meaning that the result of a particular activity can take on a new role in that or another system (Schul, [<reflink idref="bib55" id="ref87">55</reflink>], Yamagata-Lynch, [<reflink idref="bib67" id="ref88">67</reflink>]). Our results demonstrated that these types of tools may provide appropriate scaffolds to allow for students' success in above-level mathematics courses, but system rules may get in the way. Students may need permission to use them (given an assumption that workarounds are not allowed) and understand that they may be the norm for working in above-grade-level mathematics courses.</p> <p>Campbell ([<reflink idref="bib11" id="ref89">11</reflink>]) characterized workarounds as, "...tak[ing] place in bureaucratic settings where formal rules and regulations guide and constrain the behavior of personnel throughout the chain of command" (p. 409). While junior high school mathematics classes may not seem like a bureaucratic setting, the availability of workarounds may function in much the same way. As the teacher indicated, in grade-level courses the use of calculators was a privilege, the alterative was an entire class being stopped to relearn computations (i.e., constraining behavior). Whereas, in the above-grade level course she sought to assist the students, providing what was readily available as the necessary workaround to maintain course pace and learning standards. If the goal is to enrich and remove the limitations, bureaucratic or not (Campbell, [<reflink idref="bib11" id="ref90">11</reflink>]) of calculations (for example), equitable use of workarounds may be appropriate. While larger communities and their rules play into the role of workarounds, smaller communities such as the class itself can limit a students' self-confidence (Liljedahl, [<reflink idref="bib32" id="ref91">32</reflink>]).</p> <hd id="AN0164054144-23">Belonging</hd> <p>In the emergent theme of belonging, both in terms of preparation, peer acceptance, and individual comfort in a new, perhaps challenging situation, we find that self-determination theory (SDT) with its focus on basic psychological needs supports our understanding of its role. Relatedness, in SDT, along with autonomy and competence, is a basic psychological need that supports an individual's experience of well-being. It is the desire by individuals to be valued and respected by those they view as important to them, and have meaningful relationships with them (Cerasoli et al., [<reflink idref="bib14" id="ref92">14</reflink>]). As such, we view the students' need to belong (in terms of the competence given preparation and believing peers accept them) as an element of relatedness. As we consider that the students were to develop new processes (i.e., the use of workarounds) and come to understand the norms of above-grade-level classrooms, they may be better positioned to do this should they feel connected or that they belong (Niemiec & Ryan, [<reflink idref="bib47" id="ref93">47</reflink>]). In a meta-analysis, relatedness showed a modest relationship with performance for a diverse collection of students (<emph>r<sups>2</sups></emph> =.25; Cerasoli et al., [<reflink idref="bib14" id="ref94">14</reflink>]; Gniewosz & Watt, [<reflink idref="bib22" id="ref95">22</reflink>]).</p> <hd id="AN0164054144-24">Marginalized students</hd> <p>Although we did not set out to study the effect of course transition, given mathematics placement, on students who are typically marginalized, we would be remiss to not acknowledge the selection of some of the students to move to an above-grade-level course based on equity as well as the demographic characteristics of the students who participated in this study. Our findings, generally, support the challenges that marginalized students might experience in courses that they may not typically be placed. In Jaeger et al.'s ([<reflink idref="bib28" id="ref96">28</reflink>]) reflective study, doctoral students who recalled barriers experienced as younger students noted the role of race and ethnicity in their future career choices, as well as isolation, that pointed to a need for community building. We had identified that three female nonwhite students in the study scored lower on the MSES (one also scoring lower on the MCS) than their peers. A limitation of the study is, certainly, that we did not have greater data through which to understand these students' experiences, yet we agree our study points to the underlying tensions of who may be allowed into particular classes given particular rules and procedures for placement and pipeline mobility.</p> <p>Gender differences in mathematics achievement through high school have diminished. Yet, gender differences in self-beliefs and attitudes toward learning mathematics remain strong (Huang et al., [<reflink idref="bib26" id="ref97">26</reflink>]; Luis, [<reflink idref="bib35" id="ref98">35</reflink>]; Seo et al., [<reflink idref="bib57" id="ref99">57</reflink>]). Generally, male students rated themselves as having better self-confidence in mathematical adjacent items than female students (Steinmayr & Spinath, [<reflink idref="bib62" id="ref100">62</reflink>]). Accordingly, gender and race play an intricate part in the leaky pipeline (e.g., Linnenbrink-Garcia et al., [<reflink idref="bib34" id="ref101">34</reflink>]) and the loss of motivation within mathematics occurs during adolescence (Jacobs et al., [<reflink idref="bib27" id="ref102">27</reflink>]).</p> <p>In a study to explore underrepresented students' pathways to college, Perez-Felkner (2016) agree that students may sustain their self-confidence and feel less burnout when their (student's) efforts are valued and reflected beyond just the systematic climate of the school. Similar to what our teachers at this school had seen, Reyes and Domina ([<reflink idref="bib53" id="ref103">53</reflink>]) indicated that black and low-income students are often over-presented in lower-level (i.e., grade-level classes), thus limiting their potential given the mathematics pipeline. Further, students who are marginalized may have the illusion of a mathematics class as solely with specific and rigid rules they must anticipate and overcome to be successful (Gutstein, [<reflink idref="bib23" id="ref104">23</reflink>]), much as the students in this study shared.</p> <hd id="AN0164054144-25">Implications</hd> <p>As we consider the implications of our study, we first applaud this junior high school mathematics department for making opportunities for students to improve their positioning in the mathematics pipeline and supporting the students as they did so. Although our focus was on the students with only one teacher voice, in year 1 this school had moved students midyear, providing in-school support, and in year 2 students who were identified near the end of the previous school year had been provided a variety of supports to position the students for success. As such, they were developing a process, implementing iterations with small changes to better support the students. Seeking nontraditional ways, moving beyond the initial placement process (whatever they may be) may provide more equitable opportunities for all students. That said, supports must promote workarounds and resources as well as the social emotional effects of moving to above-grade-level courses and supporting students' academic success and self-confidence.</p> <p>Promoting the use of various types of workarounds seems helpful. Coupled with this, students need to become aware of what is usual support for tackling the conceptual abstractions that are found as they follow their mathematics path. While students can be expected to do basic mathematical functions, a workaround may provide the support needed to leap a hurdle and continue moving forward in their mathematics learning.</p> <p>The issue of belonging is a challenge because it is multi-faceted. Belonging moves beyond a classroom to the culture of the school and community. While it may be everyone's task to build community, initially it is placed in the hands of the teachers and administrators. We are of the mind that the transition should be shared and applauded—i.e., promoting communication such as "this student belongs in this mathematics class with us—let's all share the things that we've learned about how to be the best problem solvers we can be."</p> <hd id="AN0164054144-26">Limitations and future research</hd> <p>Given our qualitative study, our major limitation was in the paucity of the data gained from each participant. Additional interviews, perhaps across a year, with individuals who are repositioned in the mathematics pipeline would support data triangulation over time and would allow for better tracking the trajectory of self-confidence.</p> <p>Future research endeavors should consider more diverse groups of students using a variety of research methodologies; particularly if those students were selected to transition into an above-grade-level course using means other than a placement assessment. Given the reluctance that some parents and students may have to participate in studies, additional effort and support may be necessary to gain adequate data to better understand how these transitions might affect different groups of people.</p> <p>Finally, future research should investigate the process by which students are selected for above-grade-level course placement (i.e., what stakeholders are involved, what information is considered beyond the placement exam scores, timing of transition, etc.), how welcomed and/or supported students feel, particularly those who feel marginalized or underrepresented. Reducing inequalities for students transitioning into above-grade-level mathematics courses may help dissolve systematic and systemic educational barriers. Decision makers, teachers, and the students placed into above-grade-level courses need to consider that previous learning (i.e., students who have shown high positive strides in previous courses and have high self-confidence that has implicitly mediated their work) will be affected and supported as the student works through the process to realign their skills and self-confidence. Muenks et al. ([<reflink idref="bib39" id="ref105">39</reflink>]) noticed this with higher education students in STEM courses; and would seem to hold true for junior high students. To fill in this gap students may require workarounds and continued support of instructors. We cannot conclusively specify the implications of additional workarounds as they would depend on the systems in place and the nature of the students' above-grade-level placement.</p> <p>In conclusion, given the noted tension in the system based on systemic rules, these students participated in a change process to allow them a different trajectory in an academic pipeline. For these students, their self-confidence changed from an implicit mediator to an explicit mediator that was verbalized in their problem solving and may be viewed as a barrier to their learning. Further, their link to the classroom community to which they moved prompted feelings of not belonging, which further impacted their self-confidence. In addition, they lacked the understanding of the appropriateness of workarounds in solving mathematics problems and how the rules were different in the different courses. While challenges existed, these students brought persistence and self-regulation skills that would support their coursework. As would be expected, the work was more challenging, but not unobtainable.</p> <hd id="AN0164054144-27">Disclosure statement</hd> <p>We have no conflicts of interest to disclose.</p> <ref id="AN0164054144-28"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref79" type="bt">1</bibl> <bibtext> Amanda Meiners is currently employed at Northwest Missouri State University.</bibtext> </blist> </ref> <ref id="AN0164054144-29"> <title> References </title> <blist> <bibtext> Ayotola, A., & Adedeji, T. (2009). The relationship between mathematics self-efficacy and achievement in mathematics. Procedia-Social and Behavioral Sciences, 1 (1), 953 – 957. https://doi.org/10.1016/j.sbspro.2009.01.169</bibtext> </blist> <blist> <bibl id="bib2" idref="ref46" type="bt">2</bibl> <bibtext> Balfanz, R., Legters, N., & Jordan, W. (2004). 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  Data: Junior High School Students' Self-Confidence during Transition to Above-Grade-Level Mathematics Courses
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  Data: <searchLink fieldCode="AR" term="%22Schuh%2C+Kathy+L%2E%22">Schuh, Kathy L.</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0003-0799-9972">0000-0003-0799-9972</externalLink>)<br /><searchLink fieldCode="AR" term="%22Meiners%2C+Amanda+J%2E%22">Meiners, Amanda J.</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0003-0062-8781">0000-0003-0062-8781</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ferguson%2C+Cheryl%22">Ferguson, Cheryl</searchLink><br /><searchLink fieldCode="AR" term="%22Hageman%2C+Kara%22">Hageman, Kara</searchLink><br /><searchLink fieldCode="AR" term="%22George%2C+Salim%22">George, Salim</searchLink><br /><searchLink fieldCode="AR" term="%22Cox%2C+Michala%22">Cox, Michala</searchLink><br /><searchLink fieldCode="AR" term="%22Zou%2C+Yuqing%22">Zou, Yuqing</searchLink><br /><searchLink fieldCode="AR" term="%22Lin%2C+Chang-Jen%22">Lin, Chang-Jen</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Educational+Research%22"><i>Journal of Educational Research</i></searchLink>. 2023 116(2):61-76.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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  Label: Descriptors
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  Data: <searchLink fieldCode="DE" term="%22Junior+High+School+Students%22">Junior High School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Self+Esteem%22">Self Esteem</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Advanced+Courses%22">Advanced Courses</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Attitudes%22">Student Attitudes</searchLink><br /><searchLink fieldCode="DE" term="%22Stress+Variables%22">Stress Variables</searchLink><br /><searchLink fieldCode="DE" term="%22Self+Management%22">Self Management</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Adjustment%22">Student Adjustment</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+7%22">Grade 7</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+8%22">Grade 8</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Placement%22">Student Placement</searchLink><br /><searchLink fieldCode="DE" term="%22Barriers%22">Barriers</searchLink><br /><searchLink fieldCode="DE" term="%22Coping%22">Coping</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/00220671.2023.2186338
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0022-0671<br />1940-0675
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This qualitative study examined the mathematics self-confidence of eight junior high school students who were moved to an above-grade-level mathematics class through a nontraditional process. Teachers were concerned about how this transition may impact students' beliefs about their abilities to succeed in mathematics. Data were collected through interviews that included solving challenging mathematical tasks as a means to consider how students expressed their self-confidence in mathematics in general. Using a socio-constructivist lens with a focus on mediation, findings included themes about tensions given students' initial placement, changes in the role of self-confidence as a mediator, feelings of belonging as having multiple mediator roles, workarounds as mediators, and self-regulation strategies as internalized mediators that students brought with them to their transition. These findings point to solutions and supports for students who enroll in above-grade-level courses to view themselves as successful.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2023
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1393195
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1393195
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/00220671.2023.2186338
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 61
    Subjects:
      – SubjectFull: Junior High School Students
        Type: general
      – SubjectFull: Self Esteem
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Advanced Courses
        Type: general
      – SubjectFull: Student Attitudes
        Type: general
      – SubjectFull: Stress Variables
        Type: general
      – SubjectFull: Self Management
        Type: general
      – SubjectFull: Student Adjustment
        Type: general
      – SubjectFull: Grade 7
        Type: general
      – SubjectFull: Grade 8
        Type: general
      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Student Placement
        Type: general
      – SubjectFull: Barriers
        Type: general
      – SubjectFull: Coping
        Type: general
    Titles:
      – TitleFull: Junior High School Students' Self-Confidence during Transition to Above-Grade-Level Mathematics Courses
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Schuh, Kathy L.
      – PersonEntity:
          Name:
            NameFull: Meiners, Amanda J.
      – PersonEntity:
          Name:
            NameFull: Ferguson, Cheryl
      – PersonEntity:
          Name:
            NameFull: Hageman, Kara
      – PersonEntity:
          Name:
            NameFull: George, Salim
      – PersonEntity:
          Name:
            NameFull: Cox, Michala
      – PersonEntity:
          Name:
            NameFull: Zou, Yuqing
      – PersonEntity:
          Name:
            NameFull: Lin, Chang-Jen
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
          Identifiers:
            – Type: issn-print
              Value: 0022-0671
            – Type: issn-electronic
              Value: 1940-0675
          Numbering:
            – Type: volume
              Value: 116
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Journal of Educational Research
              Type: main
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