AP Calculus Success Without STEM Continuation

AP Calculus Success Without STEM Continuation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article AP Calculus Success Without STEM Continuation David Bond This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9044668/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract AP Calculus is widely positioned as a gateway to STEM, yet many students who earn qualifying scores do not continue into STEM majors. This qualitative hermeneutic phenomenological study examines how eight first- and second-year undergraduates (AP Calculus score ≥ 3) made sense of AP Calculus while choosing non-STEM pathways. Drawing on mathematical autobiographies and in-depth interviews, findings present AP Calculus as a meaning-laden transition point where students negotiated competence, belonging, and future participation. Three integrated themes emerged: (1) AP Calculus calibrated mathematical identity—students affirmed capability while distinguishing competence from identification; (2) rigor was lived as relational and temporal, mediated by teacher practices, peer norms, and pacing; and (3) non-continuation functioned as agentic alignment rather than “leakage,” with students using Calculus success to clarify values and coherent futures. Implications for mathematics teacher education include preparing teachers to recognize how everyday instructional decisions shape students’ interpretations of belonging and to support multiple legitimate post-Calculus trajectories. AP Calculus mathematics teacher education hermeneutic phenomenology mathematical identity rigor STEM persistence Figures Figure 1 Figure 2 1.0 Introduction Calculus occupies a powerful symbolic and structural position in secondary and post-secondary mathematics education. In the United States, Advanced Placement (AP) Calculus is widely regarded as both an indicator of academic rigor and a gateway to science, technology, engineering, and mathematics (STEM) pathways. Nationally, nearly 286,000 students sat for an AP Calculus examination in 2025, with over 180,000 earning a score of 3 or higher, commonly interpreted as evidence of college-level readiness (College Board, 2025b ). Despite its symbolic power and its association with STEM preparation, a substantial proportion of students who successfully complete AP Calculus do not pursue STEM majors. National datasets indicate that approximately 28% of students earning qualifying AP Calculus scores do not declare STEM majors (Avery et al., 2018 ). These patterns complicate prevailing assumptions that mathematical achievement reliably translates into STEM persistence. Historically, Calculus has functioned as both a prerequisite and a gatekeeper to STEM disciplines (Seymour & Hewitt, 1997 ; Bressoud, Mesa, & Rasmussen, 2015 ). Research on Calculus and STEM persistence has primarily focused on failure, withdrawal, and under-preparation in college-level courses. Far less attention has been given to students who have already met conventional benchmarks of readiness, such as earning a 3 or higher on the AP Calculus exam yet choose not to continue in Calculus or STEM. When such decisions are interpreted through pipeline metaphors, they are often framed as “leakage” or attrition. These framing risks locating the problem within students rather than examining how institutional narratives, identity negotiations, and affective experiences shape postsecondary trajectories. Emerging research in mathematics education suggests that identity, belonging, and affect frequently exert stronger influence on persistence than achievement alone (Carlone & Johnson, 2007 ; Eccles, 2009 ; Boaler, 2016 ). Students who demonstrate competence may nonetheless experience Calculus as alienating, exhausting, or misaligned with their developing sense of self. Without qualitative inquiry into how students interpret their AP Calculus experiences, efforts to strengthen STEM participation risk remaining narrowly focused on access and performance while overlooking meaning-making processes that influence continuation. This study addresses this gap by examining how students who earned a score of 3 or higher on the AP Calculus examination make sense of their lived experiences and decision-making processes surrounding their choice not to pursue STEM majors as undergraduates. Rather than asking why capable students “leave” Calculus, the study investigates how AP Calculus functions as a critical interpretive site in which competence, belonging, and future possibilities are negotiated. 1.1 Relevance for Mathematics Teacher Education Mathematics educators play a central role in shaping how advanced mathematics is framed, valued, and interpreted. Secondary teachers often advise students about course trajectories and implicitly signal who “belongs” in advanced mathematics. Teacher education programs prepare educators who will participate in constructing the meanings attached to AP Calculus and STEM pathways. If AP Calculus is implicitly framed as a STEM litmus test, teachers may unintentionally reinforce narrow definitions of success and equate continuation with validation. Understanding how successful students interpret their Calculus experiences, even when they choose non-STEM trajectories has direct implications for how teachers are prepared to: Frame advanced mathematics beyond sorting mechanisms, Attend to identity dimensions of participation, Support multiple legitimate post-Calculus pathways. By centering students’ retrospective interpretations, this study contributes to mathematics teacher education research by reframing AP Calculus as a site of meaning-making rather than merely a gatekeeping mechanism. 1.2 Research Question How do students who earn a score of 3 or higher on the AP Calculus exam make sense of their lived experiences and decision-making processes surrounding their choice not to pursue a STEM major as undergraduates? 1.3 Conceptual Framework This study is grounded primarily in social constructivism, informed by sociocultural theory and scholarship on mathematical identity. Subsequently, meaning is understood as socially produced through participation in communities, discourse, and institutional structures rather than located solely within individuals. 1.3.1 Social Constructivism and the Production of Meaning From a social constructivist perspective, mathematical knowledge and legitimacy are co-constructed through classroom norms, assessment practices, peer comparison, and institutional messaging (Vygotsky, 1978 ; Cobb & Yackel, 1996 ; Ernest, 1991 ). Achievement, such as earning a qualifying AP Calculus score, does not carry inherent meaning. Rather, its significance is interpreted within social and cultural contexts. In many educational settings, AP Calculus is positioned as both an academic pinnacle and a gateway to STEM. Students encounter narratives that equate Calculus completion with intellectual distinction, perseverance, and future scientific participation. These narratives are mediated through grades, weighted GPA systems, college admissions discourse, and advising practices. As a result, AP Calculus may function not only as coursework but as symbolic capital within competitive schooling environments (Geiser & Santelices, 2007 ). Within this framework, decisions not to continue in STEM are not treated as simple preference shifts or indicators of diminished ability. Instead, they are interpreted as meaning-making acts shaped by interactions with teachers, peers, family expectations, institutional structures, and broader cultural discourses about who belongs in STEM (Fig. 1 ). 1.3.2 Mathematical Identity and Competence Without Identification Central to this study is the concept of mathematical identity, understood as relational, dynamic, and socially negotiated (Sfard & Prusak, 2005 ; Nasir, 2002 ). Mathematical identity emerges through recognition by others, self-appraisal of competence, participation in valued practices, and alignment with imagined future selves. Research has demonstrated that competence does not automatically translate into disciplinary identification (Carlone & Johnson, 2007 ). Students may achieve high levels of performance while simultaneously experiencing disidentification with a field. For students who earn qualifying AP Calculus scores yet choose non-STEM majors, tensions may arise between demonstrated capability and feelings of alienation, fatigue, or misalignment with STEM cultures. Affective experiences, including stress, anxiety, exhaustion, pride, or validation, are not peripheral but central to identity development (Boaler & Greeno, 2000 ). Even when students succeed, they may interpret the emotional cost of participation as unsustainable or inconsistent with their values. Thus, AP Calculus may affirm competence while simultaneously destabilizing identification. 1.3.3 Hermeneutic Phenomenology and Retrospective Meaning The study adopts a hermeneutic phenomenological stance, recognizing that understanding emerges through interpretation and is shaped by language, context, and temporality (Gadamer, 1975 ; van Manen, 2016 ). Participants’ accounts are treated not as objective reports, but as meaning-laden narratives constructed in retrospect. Students’ interpretations of AP Calculus often evolve after the experience has concluded. Through reflective dialogue and autobiographical writing, participants articulate how Calculus shaped their sense of capability, belonging, and future possibility. Meaning is therefore not fixed after exam completion but reconstructed across time. This interpretive stance enables the study to examine how AP Calculus, despite being academically “passed,” may be remembered as alienating, exhausting, affirming, or misaligned. By situating participants’ Calculus narratives within their broader mathematical autobiographies, the study explores how success is reinterpreted and how those interpretations inform postsecondary decisions (Fig. 2 , Monero, 2014). 1.3.4 Framing the AP Calculus → Non-STEM Trajectory Taken together, social constructivism, mathematical identity theory, and hermeneutic phenomenology position the AP Calculus-to-non-STEM transition not as a pipeline failure but as an outcome of socially mediated meaning-making. Calculus achievement becomes a critical transition point at which students negotiate: Whether STEM participation feels imaginable Whether belonging is perceived as durable Whether the emotional and identity costs align with future aspirations By centering these interpretive processes, the study shifts attention from deficit narratives of attrition to systemic considerations of how advanced mathematics is framed and experienced within educational institutions. 2.0 Theoretical and Empirical Background 2.1 AP Calculus as Gateway and Credential Advanced Placement (AP) Calculus occupies a distinctive place in U.S. mathematics schooling as both a curricular culmination and an institutional signal. As Seymour and Hewitt ( 1997 ) and Bressoud, Mesa, and Rasmussen ( 2015 ) note, Calculus has historically functioned as a prerequisite and gateway to STEM disciplines. AP Calculus is widely treated as evidence of readiness for college-level quantitative study and positioned as an entry point into STEM majors requiring Calculus. Yet its meaning extends beyond content mastery. Geiser and Santelices ( 2007 ) demonstrate that AP coursework functions simultaneously as preparation and credential, conferring weighted GPA advantages, admissions signaling, and college credit, often alongside of intrinsic mathematical interest. This dual function complicates a simple readiness narrative: advanced course completion does not necessarily indicate commitment to continued mathematical participation. Large-scale research documents positive associations between AP performance and college outcomes (Geiser & Santelices, 2007 ), yet access to AP Calculus and its benefits remains uneven, mediated by disparities in teacher preparation and instructional conditions (Bressoud et al., 2015 ). Most critically, Avery et al. ( 2018 ) show that a substantial proportion of students meeting conventional readiness benchmarks do not pursue STEM majors. This paradox calls for research that examines not only what AP Calculus predicts, but how students interpret its meaning when deciding what comes next. 2.2 Beyond “STEM Leakage”: Persistence, Choice, and Meaning STEM persistence is often framed through pipeline metaphors in which students either advance or “leak” out (Cannady, Greenwald, & Harris, 2014 ). While such language highlights structural inequities, Adiredja and Louie ( 2020 ) caution that it can also reproduce deficit assumptions by positioning non-continuation as failure. Research critiquing attrition framings argues that educational trajectories are rarely linear and that continuation depends on value alignment, identity coherence, and cultural meanings (Eccles, 2009 ; Carlone & Johnson, 2007 ). Leaving STEM may therefore reflect agency and discernment rather than inability. For students who have already succeeded in AP Calculus, pipeline interpretations become especially reductive. Expectancy–value theory (Eccles & Wigfield, 2002 ) and identity-based accounts (Carlone & Johnson, 2007 ) emphasize that students weigh utility, belonging, and alignment alongside competence. As Boaler ( 2016 ) and Martin ( 2000 ) show, advanced mathematics can signal particular ways of being; speed, competition, narrow definitions of “smart” that some students choose not to inhabit, even when capable. The analytic focus thus shifts from “Why did they leave?” to “How did they interpret participation, and what did that interpretation mean for their futures?” 2.3 Mathematical Identity, Belonging, and Recognition in Advanced Courses Mathematics education scholarship posits identity and belonging as central to persistence. Sfard and Prusak ( 2005 ) conceptualize identity as narratively constructed, while Wenger ( 1998 ) frames it as participation in communities of practice. Mathematical identity is therefore relational, shaped by recognition, classroom discourse, peer comparison, and institutional narratives (Martin, 2000 ; Nasir, 2002 ). In advanced courses, public markers such as AP labels and exam scores intensify both affirmation and vulnerability (Boaler, 2002 ). Students may experience competence and insecurity simultaneously, particularly in environments privileging speed and correctness (Boaler, 2016 ). Importantly, competence does not guarantee identification (Carlone & Johnson, 2007 ). Students may achieve highly yet not claim mathematics as a future domain of belonging. Identification depends on cultural fit, values, and legitimacy and not ability alone (Eccles, 2009 ; Martin, 2009 ). AP Calculus may recalibrate what it means to be a “math person,” shifting identity from effortless performance toward effortful, relational participation. Such recalibration may support persistence for some while enabling others to pursue non-STEM pathways without perceiving themselves as deficient. Teachers and peer communities are pivotal in these processes. Cobb and Yackel ( 1996 ) argue that classroom norms define legitimate participation. Instructional practices that normalize revision, reasoning, and sense-making expand belonging (Boaler, 2002 ), while rushed pacing and competitive climates narrow it (Boaler, 2016 ; Martin, 2000 ). AP Calculus is therefore experienced not as content alone but as lived pedagogy and lived community. 2.4 Transitions and Lived Experience: Why Interpretive Methods Are Needed Research on secondary-to-postsecondary transitions highlights discontinuities in norms, assessment practices, and expectations for independence (Seymour & Hewitt, 1997 ; Bressoud et al., 2015 ). Such shifts can destabilize previously successful identities and reshape perceptions of what mathematical participation demands (Eccles, 2009 ). Yet much AP research relies on quantitative indicators (Avery et al., 2018 ; Geiser & Santelices, 2007 ), leaving lived experiences of rigor, belonging, and interpretation underexamined. Hermeneutic phenomenology, as articulated by Gadamer ( 1975 /2004) and van Manen ( 1990 , 2016 ), treats meaning as historically situated and emerging through reflection. Students’ understandings of AP Calculus may crystallize only after the experience, as they reinterpret it through college transition and major selection. Integrating autobiographical writing with dialogic interviews enables exploration of how students construct coherence between demonstrated competence and evolving selfhood (Sfard & Prusak, 2005 ). Together, this scholarship positions AP Calculus as a meaning-laden transition point rather than a deterministic filter. It underscores the need to reframe “leakage” by centering student interpretation and agency, particularly among those who have already met conventional definitions of readiness (Adiredja & Louie, 2020 ). 2.5 Mathematics Education Affectations Because AP Calculus is enacted through teachers’ instructional decisions and classroom participation norms, the phenomenon of “AP Calculus success → non-STEM redirection” is also a mathematics teacher education issue, not only a student pathway issue. AP Calculus teachers are positioned as mediators of what counts as legitimate mathematical work (e.g., speed versus sense-making), how rigor is lived (e.g., pacing pressures versus opportunities for revision and conceptual exploration), and who is recognized as belonging in advanced mathematics (through discourse practices, assessment norms, and peer culture). Participants in this study repeatedly interpreted AP Calculus through these teacher-mediated conditions, with the teacher as interpretive anchor, peer belonging as a condition for learning, and rigor as relational, all suggesting that teacher education must explicitly prepare prospective and practicing teachers to recognize how everyday instructional decisions (e.g., pacing, public comparison, error treatment, discourse authority) mediate students’ interpretations of belonging and future participation. Framed this way, the study offers teacher-educative insights about how advanced mathematics instruction can cultivate durable mathematical agency and “competence without identification,” supporting multiple post-AP futures without defaulting to deficit pipeline narratives (Boaler, 2002 , 2016 ; Cobb & Yackel, 1996 ; Martin, 2000 , 2009 ; Wenger, 1998 ; Carlone & Johnson, 2007 ; van Manen, 1990 , 2014 ; Gadamer, 1975 /2004). 3.0 Methods 3.1 Design and methodological orientation This qualitative study used hermeneutic phenomenology to interpret how students who earned a score of 3 or higher on the AP Calculus examination make sense of their AP Calculus experiences and their subsequent decision to pursue non-STEM undergraduate majors. Phenomenological inquiry in mathematics education prioritizes depth over breadth to illuminate the complexity of students lived experiences, the intersectionality of emotions, identity negotiations, institutional messages, and sense-making, often obscured in achievement-centered research (Moustakas, 1994; van Manen, 2016; Vagle, 2018). A hermeneutic approach was appropriate because the phenomenon under study is not simply behavioral (e.g., course-taking decisions) but interpretive: participants’ decisions are understood as meaning-laden responses shaped through experience, reflection, and context (Heidegger, 1962; van Manen, 2016). The study was epistemologically aligned with a social constructivist stance that conceptualizes knowledge and identity as socially produced and mediated through language, interaction, and institutional narratives (Cobb, 1994; Ernest, 1998). Consistent with Gadamer’s view of understanding as historically situated and dialogic, participant accounts were treated as interpretive “texts” shaped by prior schooling, peer interactions, assessment structures, and broader cultural messages about Calculus as a gatekeeper to STEM (Gadamer, 1975). Rather than attempting to bracket the researcher’s prior experience, hermeneutic phenomenology acknowledges positionality as integral to interpretation and emphasizes the “fusion of horizons” through which new understandings emerge (Gadamer, 1975; van Manen, 2016). 3.2 Setting, participants, and sampling Participants were recruited from a small, southern liberal arts college using purposeful criterion sampling (Patton, 2015) to ensure each participant had directly experienced the phenomenon of interest. Eligibility criteria were: (a) completion of AP Calculus AB and/or BC in high school; (b) an AP Calculus exam score of 3+; (c) current enrollment as a first- or second- year college student; (d) formal declaration of a non-STEM major; and (e) no enrollment in any college-level Calculus course since matriculation. (Table 1). Table 1: Participant List and Demographic Characteristics Participant Gender Year in School Undergraduate Major Participant #1 Female Freshman Accounting Participant #2 Female Freshman Exercise Science Participant #3 Male Freshman Philosophy & Religion Participant #4 Male Sophomore Business Participant #5 Male Freshman Business Participant #6 Female Freshman Theatre & Communication Participant #7 Male Freshman Business Participant #8 Male Sophomore History This sampling strategy supported interpretive depth rather than representativeness, consistent with hermeneutic phenomenology’s emphasis on richly described experience (van Manen, 2016). The final sample consisted of eight participants (N = 8). 3.3 Recruitment and consent Following Institutional Review Board (IRB) approval, eligible participants were recruited via email outreach facilitated through the Registrar’s office. Interested students received information about the study, the voluntary nature of participation, and the focus on meaning-making rather than evaluating their decisions or mathematical ability. Students who agreed to participate completed informed consent procedures prior to data collection. Pseudonyms were assigned and identifying details were removed from interview transcripts and autobiographical texts. 3.4 Data sources Data were generated through two complementary sources: mathematical autobiographies and semi-structured hermeneutic phenomenological interviews. The study treated these sources as methodologically complementary rather than as triangulation for convergence; autobiographies provided reflective, self-authored narratives, and interviews enabled dialogic elaboration and interpretive deepening. 3.4.1 Mathematical autobiographies Each participant composed a mathematical autobiography narrating their experiences with mathematics across time, including early memories, moments of success and struggle, relationships with teachers and peers, motivations for enrolling in AP Calculus, and reflections on how AP Calculus shaped identity, affect, and post-secondary decisions. Mathematical autobiographies are well established in mathematics education research as tools for surfacing identity development and affective dimensions of mathematical participation that may not emerge immediately in interviews (Boaler, 2002; Sfard & Prusak, 2005; Clandinin & Connelly, 2000). Within a hermeneutic phenomenological orientation, the autobiography was treated not as a neutral record of events but as an interpretive text through which participants constructed meanings about competence, belonging, and future trajectories. 3.4.2 Hermeneutic phenomenological interviews Primary data were generated through semi-structured, in-depth interviews lasting approximately 60–90 minutes. Interviews were conducted via secure video conferencing, audio recorded, and transcribed verbatim. Hermeneutic phenomenological interviewing aims to elicit reflective accounts of lived experience; how events were felt, interpreted, and understood, rather than to extract factual reports (van Manen, 1990, 2014). Accordingly, interview prompts were open-ended and experiential, inviting participants to describe their AP Calculus classroom experiences, the transition to college, advising/placement messages, peer comparison, affective responses to Calculus, and evolving mathematical identity. Follow-up questions were used flexibly to deepen descriptions of tensions, turning points, and meaning rather than to solicit justification for major choice (Finlay, 2011; Gadamer, 1975). Participants were offered the opportunity to review their transcripts for reflection, clarification, or elaboration. 3.4.3 Data collection sequence and rationale Data collection followed a two-stage sequence: (1) mathematical autobiography, followed by (2) individual interview. This sequence was intentional. Autobiographical writing provided participants time and space to reflect on emotionally complex experiences prior to dialogic interviewing and served as an “anchor text” for interpretive conversation (Hauk, 2005; Kaasila, 2007; McCulloch et al., 2013). The subsequent interview enabled probing of silences, contradictions, and pivotal moments in the written narrative, supporting the hermeneutic movement between parts (specific episodes, metaphors, emotions) and the whole (participants’ broader meaning structures and trajectories) (van Manen, 1990; Seidman, 2019; Zahavi, 2019). Together, the two methods supported rich, contextualized accounts of the paradox central to the study: demonstrated Calculus readiness alongside non-STEM trajectories. 3.5 Analytic approach Analysis proceeded as an iterative, interpretive process guided by the hermeneutic circle, emphasizing ongoing movement between individual texts and emerging shared meanings (Heidegger, 1962; Gadamer, 2004; van Manen, 2016). The analytic goal was to develop thematic interpretations that illuminated how AP Calculus success was experienced, reinterpreted over time, and decoupled from STEM continuation. Analysis began with sustained immersion in both autobiographies and interview transcripts. Each participant’s texts were first read holistically to develop an initial sense of the narrative arc, and how the participant positioned AP Calculus within their broader mathematical history and self-concept. Subsequent readings attended to language and meaning-making features emphasized in hermeneutic work: metaphors, emotional tone, moments of rupture or affirmation, and identity-relevant positioning (e.g., being “a math person,” feeling legitimate/illegitimate, experiencing Calculus as belonging or alienation). Rather than coding for frequency or treating themes as fixed categories, the study used selective and thematic reading to identify interpretive insights regarding how participants constructed the meaning of Calculus success in relation to identity, affect, belonging, and perceived futures (van Manen, 2016; Vagle, 2018). To support organization and retrieval of interpretive materials, NVivo 15 was used to manage transcripts and autobiographies and to document clusters of salient passages and analytic memos (Churchill & Wertz, 2015). Coding was used as a tool for locating meaning-rich segments and organizing interpretive work; however, theme development remained grounded in iterative interpretive writing, memoing, and repeated returns to the full texts to check coherence and resonance with participants’ accounts (Lincoln & Guba, 1985; Zahavi, 2019). Across cases, provisional thematic statements were drafted, tested against the dataset (including discrepant moments), refined, and rewritten in interpretive form. Final themes were developed to preserve both convergence and variation, enabling the findings to represent shared meanings without collapsing differences across participants. 3.6 Researcher positionality and reflexivity Hermeneutic phenomenology treats the researcher’s horizon of understanding as inseparable from interpretation. The researcher’s background as a Calculus educator across secondary and postsecondary contexts shaped initial pre-understandings about Calculus as a marker of readiness and STEM possibility. Rather than bracketing these assumptions, reflexive practice made them explicit and treated them as an analytic resource to be examined and potentially unsettled through engagement with participants’ texts (Gadamer, 2004; van Manen, 2016). Reflexive memoing documented how interpretations were influenced by professional experiences and how those preconceptions shifted as participants’ accounts challenged conventional narratives of persistence, achievement, and belonging (Lincoln & Guba, 1985). This reflexive stance also is due to power dynamics that can emerge when a mathematics educator interviews students about mathematics-related experiences. 3.7 Trustworthiness Trustworthiness was established using criteria aligned with qualitative inquiry (Lincoln & Guba, 1985). Credibility was supported through immersive engagement with participants’ narratives across two complementary sources (interviews and autobiographies) and through opportunities for participant reflection. In addition to transcript review, the study included member checking beyond transcript verification, in which participants were invited to respond to the researcher’s developing interpretive claims (e.g., thematic summaries and/or interpretive statements) and to clarify, extend, or complicate those interpretations (Maxwell, 2013). This process was used to strengthen interpretive resonance while remaining consistent with hermeneutic commitments: participants’ feedback informed refinement of themes without treating participant agreement as the sole criterion of “truth.” Dependability was strengthened through an audit trail documenting analytic decisions, memoing, iterative theme drafts, and interpretive shifts across the hermeneutic process (Dey, 1993). Confirmability was supported through ongoing reflexive journaling to surface assumptions and track how interpretations were produced (Lincoln & Guba, 1985). Transferability was enhanced through rich, contextualized description of participants’ experiences and the AP Calculus-to-college transition, allowing readers to determine relevance to similar settings. Where feasible, peer debriefing was used to interrogate interpretations and identify potential blind spots (Ahmed, 2004; Richards, 2015). Consistent with hermeneutic and constructivist traditions, “validity” was treated as interpretive credibility, grounded in participant texts, coherence of interpretations, and the capacity of findings to illuminate the phenomenon for readers (van Manen, 2016). 3.8 Ethical considerations and emotional risk mitigation Ethical approval was obtained prior to data collection. Pseudonyms were used, and identifying information was removed from all materials. Because recalling advanced mathematics experiences can surface anxiety, shame, or perceived threats to identity, particularly where Calculus is culturally positioned as a marker of intelligence and STEM belonging, interviews were conducted using non-evaluative language and participant-centered prompts emphasizing meaning-making rather than justification (van Manen, 2016). Participants were reminded they could pause, redirect, or discontinue participation at any time without consequence and could decline to elaborate on experiences that felt uncomfortable or unresolved. The researcher remained attentive to signs of distress and prioritized participant well-being over data completeness, treating silence, hesitation, and partial recall as meaningful dimensions of lived experience rather than deficiencies to be corrected (Heidegger, 1962; Lincoln & Guba, 1985). 4.0 Integrated Findings 4.1 Overview of the Findings as Interpretive Account This study examined how students who earned a score of 3 or higher on the AP Calculus exam made sense of their AP Calculus experiences and their subsequent choice not to pursue STEM majors or further collegiate mathematics. Consistent with a hermeneutic phenomenological orientation, the findings are presented as interpretations of lived experience rather than causal explanations or predictive claims. Meaning was approached as historically situated and dialogically produced, emerging through iterative movement between participants’ mathematical autobiographies (self-authored recollections) and semi-structured interviews (interpretive dialogue), as well as through the researcher’s reflexive engagement with these texts (Gadamer, 1975/2004; van Manen, 1990, 2014). Across this fusion of horizons, AP Calculus appeared not as a neutral curricular milestone but as a meaning-laden transition point where participants negotiated identity, belonging, and future possibility. All eight participants completed AP Calculus successfully and met an institutional marker of readiness through an AP score of 3+. Yet each pursued an undergraduate major outside of STEM (accounting, exercise science, philosophy & religion, business, theatre & communication, history). Participants described AP Calculus as a high-intensity course shaped by coverage demands, frequent assessments, and the cultural positioning of Calculus as a capstone of secondary mathematics and a gateway to STEM futures. Importantly, participants did not narrate non-continuation as incapacity. Instead, they described competence alongside discernment: AP Calculus served as a site where they learned what they could do, what it cost them, what it meant to belong, and what they wanted next. This non-deficit stance aligns with scholarship challenging “leakage” metaphors and emphasizing that non-participation can reflect meaningful negotiation of identity, value, and coherence rather than academic deficiency (Brown & McNamara, 2011; Solomon, 2007; Walshaw, 2017). To render the findings legible for mathematics teacher education audiences, the chapter is organized into three integrated interpretive themes. Each theme synthesizes patterns that became visible only through reading autobiographies and interviews together: (1) AP Calculus as identity calibration rather than identity sorting, (2) rigor as relational and interpretive rather than inherent, and (3) non-continuation as agentic alignment rather than pipeline loss. Throughout, participant quotations are used not as “evidence fragments,” but as language through which experience becomes visible and interpretable. 4.2 Theme 1: AP Calculus Calibrated Mathematical Identity Without Necessarily Producing Mathematical Identification Participants commonly entered AP Calculus with a confident identity narrative, often framed as being “good at math,” “a math person,” or someone for whom mathematics had previously felt natural. Their autobiographies were saturated with earlier markers of validation: accelerated placement, high grades, and recognition from teachers and peers. One participant recalled the affective security of prior success: “knowing I was probably the best in the class was so nice” (Participant 1). Another described the social status of enrollment itself: “I honestly felt really smart being an AP Calculus student” (Participant 5). In these accounts, mathematical identity initially appeared stable and trait-like, grounded in a history of doing school mathematics successfully. Yet across interviews, this “math person” identity did not remain intact as a simple label. Instead, AP Calculus recalibrated what participants understood mathematical competence to require. Several described an encounter with difficulty that disrupted the relationship between confidence and ease. Participant 1 narrated the shift as a humbling but formative reorientation: AP Calculus “knocked [me] down a few pegs,” revealing “a new world of difficulty.” Rather than narrating this as identity collapse, she narrated it as a change in the terms of competence, moving from confidence built on speed and effortless recall toward confidence built on effort, vulnerability, and persistence. Participant 7 similarly rejected the notion that success reflected innate giftedness, explaining that others may see him as naturally strong, but “I work for it and don’t give up when things get hard.” In this recalibration, AP Calculus was experienced as an identity event: not a course that sorted who belonged and who did not, but a course that altered what “belonging” meant in the first place (Martin, 2000; Wenger, 1998). This calibration was not uniform. For some, it solidified pride in capability precisely because it required sustained struggle. Participant 4 framed the course as a rare experience of intellectual disruption that he ultimately valued: it was “one of the first times in my entire life that I got my [butt] kicked in a class.” The force of this statement was not only about difficulty; it signaled that AP Calculus made him confront a new relationship to learning, one that included failure, recovery, and endurance. Others framed their entry into AP Calculus as less intentional (“the next class in order,” Participant 5; a “natural inclination,” Participant 8), yet in retrospect, even habitual enrollment became meaningful as participants interpreted what the course revealed about themselves. Across these variations, the shared interpretive movement was from identity-as-achievement to identity-as-situated participation. Participants could still claim competence, but they often did so in new language: competence as something enacted through practice, supported by others, and sustained across time. This was especially visible in the way participants talked about learning itself. Participant 1 contrasted earlier mathematics courses, where she “would just memorize techniques” with AP Calculus, which “really taught me that it is important to apply the work and PRACTICE a ton.” The capitalization in her written account functioned like an embodied emphasis: practice was not a study tip; it was a new moral of what it means to learn. Crucially, this identity calibration did not automatically produce mathematical identification or a desire to continue participating in mathematics as a future domain. Participants repeatedly illustrated what might be described as competence without identification: they learned they could succeed in demanding mathematics yet did not necessarily want to keep living the version of mathematical participation that AP Calculus represented. For some, this distinction was explicit in how they narrated selfhood. Participant 6 simultaneously acknowledged success and resisted identity labeling: “No I don’t think I consider myself a math person… I’m a performing arts person,” while also describing AP Calculus as a source of “academic validation.” Her narrative reveals a tension between categorical identity (“performing arts person”) and demonstrated competence (“academic validation”), suggesting that mathematics success can function as recognition without becoming a stable self-concept. Participant 8 described a different tension: he now “miss[es] math,” not necessarily as a major, but as a way of thinking: “figuring things out” with clarity and resolution. Even in absence, mathematics remained meaningful as an orientation, not a pipeline. 4.2.1 Synthesis of Theme 1: Self-Understanding as a Mathematics Person From a mathematics teacher education perspective, the significance of this theme lies in how AP Calculus acted as a calibration mechanism for students’ understandings of themselves as mathematical learners. Participants did not narrate AP Calculus as merely “hard content”; they narrated it as the experience that redefined what counts as legitimate mathematical work and what kinds of selves can sustain it (Martin, 2000; Wenger, 1998). The course did not simply confer or deny identity; it reshaped the meanings attached to “being good at math,” making visible that achievement can coexist with disidentification and that identity claims are negotiated through lived participation rather than determined by scores alone. 4.3 Theme 2: Rigor Was Experienced as Relational and Interpretive, Mediated by Teachers, Peers, and Time Participants consistently described AP Calculus as rigorous, but they did not treat rigor as a fixed property of the curriculum. Instead, rigor appeared as a lived phenomenon shaped by instructional decisions, peer culture, and the temporal pressures of students’ broader lives. Participants repeatedly returned to the same experiential ingredients, including pace, assessment rhythms, opportunities (or lack of opportunities) to revisit ideas, and narrated how those conditions made Calculus feel either possible or overwhelming. In this sense, rigor was not simply “difficulty”; it was how difficulty was organized, distributed, and interpreted across relationships and time (van Manen, 1990; Hiebert & Grouws, 2007). 4.3.1 Teacher as interpretive anchor: Calculus was experienced as “Calculus-as-taught” Across autobiographies and interviews, the teacher emerged as a primary medium through which Calculus became meaningful. When teachers were described as relational, enthusiastic, and responsive, participants narrated Calculus as approachable and enjoyable. Participant 4 linked confidence explicitly to his teacher’s presence: “I remember feeling confident… because of the energy of my teacher… her catchy songs.” Participant 6 described the class as “homey and comfortable,” suggesting that affective safety was not supplemental to learning but part of how learning became livable. In interviews, this teacher-mediated experience became even more pronounced. Participant 6 said the class “felt like a club” because the teacher knew students personally and “talked us through” confusion. Participant 8 recalled that the teacher “would try and make sure everyone understood,” framing instruction as an ethic of inclusion rather than an expectation of self-sufficiency. In contrast, when instructional clarity or relational care was perceived as absent, the same Calculus curriculum was narrated as alienating. Participant 1 described how instructional errors and disengagement “made the content much more confusing,” and Participant 3 recalled peer mistreatment that “was not discouraged by my teacher,” leading him to “dislike the class.” These accounts did not position the teacher as a mere contextual variable; they positioned pedagogy as the lived reality of Calculus. AP Calculus was not encountered as abstract mathematics; it was encountered as pacing, responsiveness, examples offered or withheld, norms for questions, and what happened when students were confused (Boaler, 2002; van Manen, 2014). A key dimension of this teacher-mediated rigor was time. Participants described moments when pace functioned as a boundary between sense-making and survival. Participant 1 contrasted her experience across semesters, describing the BC portion as “rushed” and cognitively overwhelming. She described the experience of holding too many procedures at once: remembering when to use “9 or 10 different tests,” and the embodied residue of this pressure: “my head hurt… I still got to remember it.” Importantly, she interpreted this not only as content load but as a time condition: “we were just in a hurry rushing to get through that and into graduation.” Rigor here was temporal saturation; moving forward before meaning could settle. Participant 2 similarly described embodied rigor: headaches and migraines during heavy workload periods. This language matters: the “difficulty” of Calculus was felt in the body and carried into students’ lives. Yet she also framed herself as “lucky with my teacher,” indicating that relational support could coexist with overwhelming pace. In other words, teacher care did not eliminate rigor, but it shaped how rigor was interpreted—as possible, purposeful, or simply punishing. 4.3.2 Peer community as belonging and vulnerability: struggle became shared or shameful Peer relationships were equally central to how rigor was lived. When classrooms were experienced as collaborative, struggle became a shared practice rather than private evidence of inadequacy. Participant 1 described classmates who would “constantly ‘huddle up’… to learn and remember the formulas,” suggesting that understanding was socially distributed and that collective effort normalized difficulty. Participant 8 described collaboration as one of his favorite aspects of advanced mathematics: “working together with students to figure out the content was honestly some of my favorite times in high school.” He also described teaching peers as deepening his own understanding: “I would be explaining things to them… this helped my understanding.” Here, peer interaction was not only emotional support; it was epistemic—talking mathematics became a way of learning mathematics (Lave & Wenger, 1991; Wenger, 1998). Participant 4’s interview described a classroom ethic that institutionalized peer support: “help your neighbors,” with structures such as redo assignments that reframed error as part of collective improvement. In these contexts, participants did not narrate rigor as isolating; they narrated it as relationally buffered and even identity-supporting, because struggle was interpreted as normal rather than stigmatizing. In contrast, when peer culture became unsafe, rigor took on a different meaning. Participant 3 described classmates who “made fun of me when I asked a question,” and this ridicule reshaped his experience into alienation: he came to “dislike being in class.” Notably, the content difficulty in such narratives was often less prominent than the social penalty for confusion. The lived meaning of Calculus shifted from “hard but learnable” to “hard and humiliating.” This contrast illustrates how rigor was interpreted through belonging: the same struggle could be experienced as productive or as evidence of not belonging, depending on whether the social world made questions legitimate (Boaler, 2016; Lave & Wenger, 1991). 4.3.3 Competing demands and the structure of schooling: rigor was situated in life context Participants’ narratives also show that rigor was not limited to classroom time; it was experienced in the collision between AP Calculus and students’ broader commitments. Several participants described late nights, athletics, employment, and performance obligations. Participant 2 recalled “staying up very late finishing homework” during the second semester, which became “very stressful.” Another participant described the feeling that “the amount of work… felt like it never ended.” Participant 6 narrated a particularly revealing tension: late-night rehearsals led to missed online assignments that “tanked my grade,” even though she described strong conceptual understanding. This account makes visible how rigor is produced not only by mathematical complexity but by assessment systems and deadline structures that convert life circumstances into academic consequences (Hiebert & Grouws, 2007; van Manen, 1990). Across these stories, rigor was experienced as contingent: it could validate endurance, strengthen confidence, and create pride; it could also generate exhaustion, stress, and discouragement. What determined these meanings was not the Calculus content alone, but the relational and temporal design of the course. 4.3.4 Synthesis of Theme 2 This theme reframes rigor as something students interpret through teacher mediation, peer belonging, and temporal constraints. For mathematics teacher education, this matters because it locates “rigor” not primarily in curriculum documents or exam blueprints, but in everyday instructional decisions that participants experienced as identity- and future-shaping: pacing, error treatment, opportunities to revise, norms for questions, and whether comparison and ranking were made public or implicit. Participants’ accounts suggest that when these decisions supported sense-making and belonging, rigor was experienced as purposeful and formative; when they emphasized coverage, speed norms, or social vulnerability, rigor was experienced as overwhelming or alienating (Boaler, 2002, 2016; van Manen, 1990, 2014; Wenger, 1998). 4.4 Theme 3: Non-Continuation Functioned as Agentic Alignment—AP Calculus as a Site of Discernment Rather Than Pipeline Loss A central paradox structured every narrative: participants succeeded in one of the most institutionally valorized mathematics courses yet did not continue into STEM majors or collegiate Calculus. Read through a pipeline lens, this would be coded as “leakage.” Participants, however, narrated their trajectories as discernment, an interpretive process of aligning ability, interest, identity, and future imagination. They did not describe themselves as pushed out by inability. They described themselves as learning something about what mathematical participation demanded and deciding whether that demanded self-fit the person they were becoming (Brown & McNamara, 2011; Solomon, 2007; Walshaw, 2017). 4.4.1 AP Calculus produced evidence of capability—even when it also produced closure Participants repeatedly described completion as pride and relief. Participant 1 described finishing as “one of the best feelings in the world… utter relief” and feeling “super proud of myself.” Participant 2 called completion “an accomplishment and a burden that I no longer had at the same time.” These statements hold a double meaning: Calculus completion conferred accomplishment yet also signaled the end of a period of sustained pressure. The affective residue, described as relief, exhaustion, or pride, became part of how participants interpreted what it would mean to continue. Some participants narrated Calculus credit instrumentally, as a way to avoid college mathematics. Participant 6 described being “extremely excited” to be excused from future math courses. Participant 7 described taking AP Calculus to “get it out of the way,” implying that the course functioned as both credential and closure. In autobiographical form, these accounts may be interpreted as aversion. Yet the interviews complicated this “closure” narrative by surfacing a second layer: participants often reclaimed Calculus as a marker of capability that made future options feel open, even if they chose not to take them. Participant 1, who wrote that Calculus “scared me away from math a little bit,” resisted the idea that Calculus determined her major choice, saying “Not at all,” when asked whether AP Calculus shaped her decision to study business (in that interview moment). She later said she would “absolutely” take Calculus again in college. Here, the apparent contradiction functions hermeneutically as temporal reframing: the autobiography preserved affective residue (“scared away… a little bit”), while the interview produced a re-narration of agency (“absolutely”). Rather than inconsistency, this reveals how meaning changed when participants returned to their experiences in dialogue and from new horizons of identity (Gadamer, 1975/2004; Ricoeur, 1984). Participant 8 similarly framed returning to mathematics as an option rather than a closed door. Although he chose a non-STEM pathway, he described still enjoying mathematics “for the discovery of it.” He also described missing the certainty and resolution of mathematical problem-solving in his current coursework. In this sense, not continuing in mathematics did not erase mathematical value; it re-situated it. 4.4.2 Non-STEM trajectories were narrated as coherent futures, not losses Participants also narrated non-STEM choices as morally or vocationally coherent rather than as a retreat. Participant 3 attributed his pathway to a “calling to the ministry,” emphasizing that his decision “did not involve my experiences in AP Calculus.” Yet in interview reflection, he also described how AP Calculus affirmed his capacity to handle rigor, suggesting that even when Calculus was vocationally “irrelevant,” it was still identity-relevant: it confirmed that leaving STEM was not compelled by incapacity. Participant 1 described “miss[ing] numbers,” moving toward accounting, where mathematics persisted as a valued practice even if not labeled STEM. These narratives suggest that AP Calculus success can travel into non-STEM domains as confidence, credibility, or a way of thinking, rather than as a ticket that must be cashed only through STEM persistence. Participant 8 articulated an especially direct critique of deficit framing: even if he had failed, universities would respect that “they still tried.” His statement reframes participation itself as meaningful—not because it guarantees continuation, but because it signifies willingness to engage with challenge. In a pipeline narrative, “trying” without continuing can be framed as waste; in his narrative, it is evidence of character and capability. This interpretive stance undercuts the idea that leaving STEM after Calculus success is irrational. Instead, it suggests that AP Calculus can function as a boundary experience where students test alignment between capacities and futures and then decide with authority. 4.4.3 Learning to struggle as transferable outcome supported agency to choose differently Participants described AP Calculus as teaching them how to learn, not only what to learn. They frequently described a shift from memorization to sense-making, from passive technique to active practice. Participant 7 emphasized understanding the “‘why’ behind” procedures, describing how application and repetition helped ideas “click.” Participant 3 described daily quizzes with correction opportunities as assignments “there to help you not hurt you,” suggesting that error and revision were interpreted as part of learning rather than as evidence of deficiency. Participant 8 emphasized “trial and error… all the repetition I had to do” as what made learning real. These narratives position Calculus as a metacognitive and dispositional threshold—an experience that taught endurance, practice, and tolerance for confusion. Critically, participants narrated these outcomes as transferable beyond mathematics. Participant 5 likened the course to athletics, describing it as evidence he could take unfamiliar information and “produce a product that I’m proud of.” Others described carrying persistence habits into college. Even when participants chose not to continue mathematics, they did not narrate Calculus as wasted. They narrated it as formative: it produced confidence, discipline, and a changed understanding of how learning works. From a teacher education perspective, this theme matters because it reframes the purpose of advanced mathematics: the value of AP Calculus may include identity and agency outcomes that do not depend on STEM continuation (Skemp, 1976). 4.4.4 Remembered mathematics as meaning: what endured were relationships and thresholds Finally, participants’ memories of AP Calculus were often relational and experiential rather than procedural. In autobiographies, participants frequently ended with gratitude for teachers, peers, and personal growth; interviews illuminated why these memories endured. Participant 6 recalled apologizing on an AP free-response question; an act that symbolized humility, care, and the felt presence of evaluation. She also described the class as “a club,” emphasizing belonging over content. Participant 2 described missing her teacher more than mathematics itself. Participant 8 mourned the loss of “figuring things out” in environments with clear right answers. These recollections suggest that what persisted was not the mechanics of Calculus but the remembered self in relation to challenge: supported, pressured, affirmed, exhausted, proud. This matters for interpreting non-continuation. If what students carry forward is primarily the meaning of who they were in Calculus, rather than the content they mastered, then decisions about continuing mathematics are likely shaped by whether that remembered self feels sustainable and desirable. Participants’ narratives suggest that many experienced Calculus as “worth having” even when they chose not to repeat it, which reframes non-continuation as a coherent response to a meaning-laden experience rather than as loss of talent. 4.4.5 Synthesis of Theme 3 Across participants, AP Calculus success did not function as a deterministic feeder into STEM. Instead, AP Calculus acted as a site of discernment where students learned: (a) they could do hard things, (b) the conditions under which mathematics felt livable or alienating, and (c) whether continued participation aligned with who they were becoming. In these accounts, leaving STEM after Calculus success was not narrated as inability. It was narrated as agentic alignment, a decision made from a position of demonstrated competence and newly clarified values. This theme challenges “leakage” framings by showing that redirection can reflect coherence and self-knowledge rather than attrition (Adiredja & Louie, 2020; Brown & McNamara, 2011). 4.5 Concluding Integrative Statement: AP Calculus as Meaning-Making Crucible at a Transition Point Taken together, the three themes show AP Calculus functioning less as a pipeline checkpoint and more as a meaning-making crucible where identity, rigor, belonging, and future imagination were negotiated over time. First, AP Calculus calibrated students’ mathematical identities by redefining competence as effortful, relational, and practiced, yet this calibration did not require ongoing identification with mathematics as a future domain (Martin, 2000; Wenger, 1998). Second, rigor was experienced as relational and interpretive, mediated by teacher practices, peer culture, and the temporal structure of schooling; students did not simply “face Calculus,” they faced Calculus-as-lived through pacing, error treatment, discourse norms, and support (Boaler, 2002, 2016; van Manen, 1990, 2014). Third, non-continuation emerged as agentic alignment: students interpreted AP Calculus as evidence of capability and used that evidence to choose futures that felt coherent, including non-STEM pathways that still carried mathematical confidence and ways of thinking. For mathematics teacher education, these findings reframe the AP Calculus → non-STEM trajectory as a teacher-educative problem of practice rather than a student deficit: participants’ accounts suggest that teachers’ everyday instructional decisions and the classroom participation norms those decisions produce, mediate how students interpret belonging and future participation in advanced mathematics. In other words, AP Calculus “works” on students not only through content, but through the meanings students construct about what mathematics participation requires and whether they want to become (or remain) that kind of participant. 5.0 Discussion: Beyond the Pipeline — AP Calculus as Identity Work, Not STEM Sorting This study began with a deceptively simple question: How do students who successfully complete AP Calculus make sense of choosing not to pursue STEM majors? The dominant policy discourse would frame such students as “leakage” from the STEM pipeline. Yet participants’ narratives resist this framing. Across autobiographies and interviews, AP Calculus was experienced not as a sorting mechanism that determined who belongs in STEM, but as a formative encounter that recalibrated identity, clarified values, and strengthened agency. Rather than producing attrition, AP Calculus produced interpretation. Three interpretive claims extend mathematics education scholarship and challenge deficit-oriented pipeline logics: (1) AP Calculus functioned as an identity-calibrating experience rather than an identity-sorting one; (2) rigor was lived and relational rather than inherent; and (3) non-continuation was frequently narrated as agentic discernment grounded in demonstrated competence. Together, these claims reposition AP Calculus from a pipeline checkpoint to a meaning-making site. 5.1 AP Calculus as Identity Calibration, Not Identity Sorting Participants entered AP Calculus with established mathematical identities often grounded in speed, recognition, and prior success. Yet Calculus destabilized simplistic notions of being a “math person.” Struggle became unavoidable, and competence was renegotiated as effortful rather than effortless. Importantly, this renegotiation did not collapse identity. Instead, it recalibrated it. This distinction is critical. Pipeline metaphors assume that advanced coursework reveals who “truly belongs.” However, participants’ narratives suggest that AP Calculus did not sort identities; it refined them. Students who ultimately chose non-STEM majors did not describe themselves as incapable. They described themselves as clarified. They learned what sustained engagement in advanced mathematics required, perceived cognitively, emotionally, and socially, and assessed whether that form of participation aligned with their broader sense of self. This finding aligns with sociocultural theories positioning identity as participation rather than possession (Wenger, 1998 ; Martin, 2000 ). Competence alone did not guarantee identification. Students demonstrated ability (AP scores ≥ 3), yet identification with mathematics as a future domain remained conditional. This articulates what this study conceptualizes as competence without identification, a theoretically generative distinction for mathematics education research. For teacher education, this reframing disrupts the assumption that successful students will persist in STEM. Mathematical success does not obligate mathematical continuation. Identity is negotiated through meaning, not determined by performance. 5.2 Rigor as Lived, Relational, and Interpretive Policy discourse frequently treats rigor as a fixed curricular attribute, an objective measure of challenge. Participants’ accounts complicate this assumption. Rigor was experienced as temporal pressure, cognitive saturation, and emotional regulation. Yet whether that rigor was interpreted as empowering or alienating depended heavily on relational and pedagogical conditions. Teachers functioned as interpretive anchors. When instruction included modeling, relational care, revision opportunities, and normalized error, difficulty was narrated as productive. When pacing was rushed or relational signals were thin, similar content demands were experienced as isolating. Peers also mediated rigor. Collaborative environments reframed struggle as shared sense-making (Lave & Wenger, 1991 ; Boaler, 2016 ). In contrast, peer ridicule or competition amplified vulnerability even when achievement remained high. These findings reinforce phenomenological accounts of difficulty as lived and embodied (van Manen, 1990 ). Rigor is not merely what is taught; it is how difficulty is experienced within social worlds. For mathematics educators, this has direct implications. If rigor is relational, then preparing teachers involves more than content knowledge and task design. It involves preparing teachers to cultivate interpretive environments where struggle is framed as growth rather than deficiency. Without this mediation, advanced coursework may unintentionally narrow belonging even among high-achieving students. 5.3 Non-Continuation as Agentic Discernment Perhaps the most significant contribution of this study lies in reframing non-STEM trajectories. Participants did not narrate their decisions as being pushed out. Instead, many described AP Calculus as providing clarity about what they valued and how they wished to live their education. They distinguished between: “I can do this.” “I want this.” This distinction echoes expectancy–value theory’s emphasis on subjective task value (Eccles & Wigfield, 2002 ) yet extends it hermeneutically. Understanding emerged after the experience, not during it. Autobiographical writing often captured stress residue and relief, while interviews revealed reclaimed agency and reopened possibility. Meaning unfolded temporally, consistent with Gadamer’s ( 1975 /2004) account of understanding as historically situated. From this perspective, labeling these students as “leakage” mischaracterizes their trajectories. They did not exit due to incapacity, but redirected from a position of demonstrated capability. This challenges deficit models that equate persistence with success and departure with failure (Cannady et al., 2014 ). For mathematics education research, this suggests the need to examine not only who persists, but how students interpret participation itself. 5.4 Implications for Mathematics Teacher Education If AP Calculus is a meaning-making crucible rather than a deterministic filter, what does this mean for teacher education? Three implications follow. 5.4.1 Reframing Success Beyond Continuation Teacher preparation programs should explicitly interrogate the assumption that advanced mathematics exists primarily to produce STEM majors. When AP Calculus is framed solely as a gateway, students who choose alternative pathways may interpret themselves as deviations from a normative trajectory. Teacher educators can instead prepare teachers to frame AP Calculus as: An intellectual encounter with powerful ideas A site for learning how to struggle productively An opportunity for identity exploration A credential of capability independent of future major Such framing expands success beyond continuation and aligns with broader humanistic purposes of mathematics education (Wenger, 1998 ). 5.4.2 Preparing Teachers to Mediate Rigor Relationally Given that rigor was experienced as relational and interpretive, teacher education must foreground: How classroom discourse signals belonging How pacing shapes interpretation of struggle How public comparison and speed norms affect identity How revision structures reframe error Preparing teachers to notice and intentionally design these relational conditions may prevent advanced mathematics from becoming unintentionally alienating, even for capable students. Rigor need not be softened; it must be mediated. 5.4.3. Supporting Agency in Postsecondary Advising Narratives Mathematics teacher education often intersects with advising cultures that implicitly equate AP success with STEM obligation. Teacher educators can help future teachers recognize that students may use AP Calculus to clarify what they do not wish to pursue, and that this clarification is educationally legitimate. Affirming multiple post-AP trajectories, including humanities, business, arts, and interdisciplinary fields, honors students’ agency without diminishing mathematical accomplishment. An equity-oriented stance requires not only access to advanced mathematics but autonomy in interpreting its meaning. 5.4 Contributions to Mathematics Education Research This study contributes to mathematics education scholarship in four primary ways. First, it challenges deficit framings of STEM leakage by accentuating interpretive agency. Second, it reconceptualizes AP Calculus as a sense-making site rather than solely a gatekeeping mechanism. Third, it advances the construct of competence without identification, offering a theoretical distinction between achievement and disciplinary belonging. Fourth, methodologically, it demonstrates how integrating mathematical autobiographies with hermeneutic phenomenology surfaces temporal shifts in meaning that cross-sectional or quantitative approaches may overlook. By centering lived experience and retrospective interpretation, this study expands how researchers might conceptualize advanced mathematics participation beyond enrollment and persistence metrics. 6.0 Conclusion: Listening to Students Who Succeeded and Still Chose Otherwise AP Calculus is a powerful educational experience. It affirms competence, confers symbolic capital, and signals academic distinction. Yet it is fundamentally non-deterministic. Participants in this study did not fail Calculus. They succeeded. And then, from that position of success, some chose differently. Listening to these students reframes the question from “How do we prevent leakage?” to “How do students interpret what participation means?” When mathematics education attends to that question, success becomes broader, more humane, and more aligned with identity coherence rather than institutional expectation. AP Calculus, then, need not be defended as a flawless pipeline mechanism. It can instead be understood as a formative space where students encounter challenge, renegotiate identity, and author futures, in STEM or beyond. Declarations The author did not receive any funding support from any organization for the submitted work. Data Availability Statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. Ethics Approval and Consent to Participate Kennesaw State University Ethics Approval Approval for the research conducted by Kennesaw State University’s Office of Research and Research Compliance. This office follows the The Federal Wide Assurance (FWA) granted by the Department of Health and Human Service's (DHHS) Office for Human Research Protections (OHRP). It is the only type of assurance of compliance accepted and approved by OHRP for institutions engaged in non-Exempt human subjects research conducted or supported by DHHS. Under an FWA, an institution commits to DHHS that it will comply with the requirements set forth in 45 CFR Part 46, as well as the Terms of Assurance. Berry College Ethics Approval Additional approval was receive by the Berry College Institutional Review Board Institutional Review Board for Human Subjects Research (IRB), which is charged with reviewing all research activities involving human subjects, in compliance with the Code of Federal Regulations, Title 45, Part 46. All research involving human participants must be submitted for review by the IRB, and must be approved before initiating any research activities. By definition, research is “any systematic investigation, including research development, testing, and evaluation, designed to develop or contribute to generalizable knowledge.” (45 CRF 46.102d). To ensure compliance with federal regulations, researchers must follow the Berry College [policy on human subjects research]. Those who fail to follow this policy may receive up to a one-year suspension of all research activities from the IRB. Consent to Participate For all research involving human participants, informed consent to participate in the study was obtained from participants that was signed by both the participant and researcher, with one copy for the participant and one copy for the researcher. All participants were anonymized as to not trace back individual participants to any identifiable characteristics, and consent to publish is not necessary. IRB Approval given by both Berry College, where the participants were students resided, and at Kennesaw State University, where the researcher is employed. Ethical requirements are under the guidelines of the IRBs of both Berry College and Kennesaw State University to ensure compliance with federal regulations follow the Berry College and Kennesaw State University policies on human subject research. 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University of Chicago Press. Seidman, I. (2019). Interviewing as qualitative research: A guide for researchers in education and the social sciences (5th ed.). Teachers College Press. Seymour, E., & Hewitt, N. M. (1997). Talking about leaving: Why undergraduates leave the sciences. Westview Press. Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34 (4), 14–22. https://doi.org/10.3102/0013189X03400401 Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77 , 20–26. https://doi.org/10.5951/MTMS.12.2.0088 Solomon, Y. (2007). Experiencing mathematics classes: Ability grouping, gender and the selective development of participative identities. International Journal of Educational Research, 43 (1–2), 8–16. https://doi.org/10.1016/j.ijer.2007.07.002 Unnikrishnan, A. (2016). E – learning: An individual learning perspective: An Analysis. International Journal of Engineering Research and Technology, 5(11), 53-56. http://dx.doi.org/10.17577/IJERTV5IS110062 Vagle, M. D. (2018). Crafting phenomenological research (2nd ed.). Routledge. van Manen, M. (2016). Researching lived experience : Human science for an action sensitive pedagogy (2nd ed.). Routledge. van Manen, M. (2014). Phenomenology of practice . Routledge. van Manen, M. (1990). Researching lived experience . State University of New York Press. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes . Harvard University Press. Walshaw, M. (2017). Understanding mathematical identity: Theory, method, and practice . Springer. Wenger, E. (1998). Communities of practice: Learning, meaning, and identity . Cambridge University Press. Zahavi, D. (2019). The practice of phenomenology: The case of Max van Manen. Nursing Philosophy, 20 (2), e12276. https://doi.org/10.1111/nup.12276 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 04 May, 2026 Reviews received at journal 04 May, 2026 Reviewers agreed at journal 04 May, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers invited by journal 16 Apr, 2026 Editor invited by journal 27 Mar, 2026 Editor assigned by journal 27 Mar, 2026 Submission checks completed at journal 24 Mar, 2026 First submitted to journal 24 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9044668","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628104131,"identity":"9d5c6f3e-fc4a-4034-bca6-748839278d06","order_by":0,"name":"David Bond","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYDCCG0DMYyAhJ4EkZkCElgIbY1K1fEhLnEG0Fr7bzccevDE4nD6zvffYgw9/7BIb2Ju3SeDTInnnWLrhHIPDubN5zqUbzmxLTmzgOVaGV4vBjRwzaR6glnkSQAZvA3NuA5BBlJZ0Ofk3ZtJ//tTnNgAZxGhJS5CW4DGTZmA7DLSFB78WoF/SJOcY2BjO7Mkxk+xtO17fxpNWbIFPCyjEJN78kZCXOH7GTOLHn2pjfvbDG2/g04IJ2EhTPgpGwSgYBaMAGwAAEOpIveulnmoAAAAASUVORK5CYII=","orcid":"","institution":"Kennesaw State University","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"","lastName":"Bond","suffix":""}],"badges":[],"createdAt":"2026-03-06 00:23:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9044668/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9044668/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107755887,"identity":"bef79289-6647-4758-8434-99509c33501e","added_by":"auto","created_at":"2026-04-24 19:05:35","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":156869,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSocial Constructivism Framework for Mathematics\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9044668/v1/5e4dd965edbfe54a58c81559.jpeg"},{"id":107755888,"identity":"67706688-66ab-4b7e-9976-5b9a3f8b274f","added_by":"auto","created_at":"2026-04-24 19:05:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":152584,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHermeneutic Circle\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9044668/v1/e4ff4d22d34a739c0c444e85.png"},{"id":109067592,"identity":"61ffdf12-507c-4fd3-a0fe-ce409588e01b","added_by":"auto","created_at":"2026-05-12 09:57:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":701292,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9044668/v1/e217a15b-fe88-4ccc-b126-5708de4e4ddd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"AP Calculus Success Without STEM Continuation","fulltext":[{"header":"1.0 Introduction","content":"\u003cp\u003eCalculus occupies a powerful symbolic and structural position in secondary and post-secondary mathematics education. In the United States, Advanced Placement (AP) Calculus is widely regarded as both an indicator of academic rigor and a gateway to science, technology, engineering, and mathematics (STEM) pathways. Nationally, nearly 286,000 students sat for an AP Calculus examination in 2025, with over 180,000 earning a score of 3 or higher, commonly interpreted as evidence of college-level readiness (College Board, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDespite its symbolic power and its association with STEM preparation, a substantial proportion of students who successfully complete AP Calculus do not pursue STEM majors. National datasets indicate that approximately 28% of students earning qualifying AP Calculus scores do not declare STEM majors (Avery et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). These patterns complicate prevailing assumptions that mathematical achievement reliably translates into STEM persistence.\u003c/p\u003e \u003cp\u003eHistorically, Calculus has functioned as both a prerequisite and a gatekeeper to STEM disciplines (Seymour \u0026amp; Hewitt, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bressoud, Mesa, \u0026amp; Rasmussen, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Research on Calculus and STEM persistence has primarily focused on failure, withdrawal, and under-preparation in college-level courses. Far less attention has been given to students who have already met conventional benchmarks of readiness, such as earning a 3 or higher on the AP Calculus exam yet choose not to continue in Calculus or STEM. When such decisions are interpreted through pipeline metaphors, they are often framed as \u0026ldquo;leakage\u0026rdquo; or attrition. These framing risks locating the problem within students rather than examining how institutional narratives, identity negotiations, and affective experiences shape postsecondary trajectories.\u003c/p\u003e \u003cp\u003eEmerging research in mathematics education suggests that identity, belonging, and affect frequently exert stronger influence on persistence than achievement alone (Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Eccles, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Boaler, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Students who demonstrate competence may nonetheless experience Calculus as alienating, exhausting, or misaligned with their developing sense of self. Without qualitative inquiry into how students interpret their AP Calculus experiences, efforts to strengthen STEM participation risk remaining narrowly focused on access and performance while overlooking meaning-making processes that influence continuation.\u003c/p\u003e \u003cp\u003eThis study addresses this gap by examining how students who earned a score of 3 or higher on the AP Calculus examination make sense of their lived experiences and decision-making processes surrounding their choice not to pursue STEM majors as undergraduates. Rather than asking why capable students \u0026ldquo;leave\u0026rdquo; Calculus, the study investigates how AP Calculus functions as a critical interpretive site in which competence, belonging, and future possibilities are negotiated.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Relevance for Mathematics Teacher Education\u003c/h2\u003e \u003cp\u003eMathematics educators play a central role in shaping how advanced mathematics is framed, valued, and interpreted. Secondary teachers often advise students about course trajectories and implicitly signal who \u0026ldquo;belongs\u0026rdquo; in advanced mathematics. Teacher education programs prepare educators who will participate in constructing the meanings attached to AP Calculus and STEM pathways.\u003c/p\u003e \u003cp\u003eIf AP Calculus is implicitly framed as a STEM litmus test, teachers may unintentionally reinforce narrow definitions of success and equate continuation with validation. Understanding how successful students interpret their Calculus experiences, even when they choose non-STEM trajectories has direct implications for how teachers are prepared to:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eFrame advanced mathematics beyond sorting mechanisms,\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAttend to identity dimensions of participation,\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSupport multiple legitimate post-Calculus pathways.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eBy centering students\u0026rsquo; retrospective interpretations, this study contributes to mathematics teacher education research by reframing AP Calculus as a site of meaning-making rather than merely a gatekeeping mechanism.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2 Research Question\u003c/h2\u003e \u003cp\u003eHow do students who earn a score of 3 or higher on the AP Calculus exam make sense of their lived experiences and decision-making processes surrounding their choice not to pursue a STEM major as undergraduates?\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Conceptual Framework\u003c/h2\u003e \u003cp\u003eThis study is grounded primarily in social constructivism, informed by sociocultural theory and scholarship on mathematical identity. Subsequently, meaning is understood as socially produced through participation in communities, discourse, and institutional structures rather than located solely within individuals.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e1.3.1 Social Constructivism and the Production of Meaning\u003c/h2\u003e \u003cp\u003eFrom a social constructivist perspective, mathematical knowledge and legitimacy are co-constructed through classroom norms, assessment practices, peer comparison, and institutional messaging (Vygotsky, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e1978\u003c/span\u003e; Cobb \u0026amp; Yackel, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Ernest, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1991\u003c/span\u003e). Achievement, such as earning a qualifying AP Calculus score, does not carry inherent meaning. Rather, its significance is interpreted within social and cultural contexts.\u003c/p\u003e \u003cp\u003eIn many educational settings, AP Calculus is positioned as both an academic pinnacle and a gateway to STEM. Students encounter narratives that equate Calculus completion with intellectual distinction, perseverance, and future scientific participation. These narratives are mediated through grades, weighted GPA systems, college admissions discourse, and advising practices. As a result, AP Calculus may function not only as coursework but as symbolic capital within competitive schooling environments (Geiser \u0026amp; Santelices, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWithin this framework, decisions not to continue in STEM are not treated as simple preference shifts or indicators of diminished ability. Instead, they are interpreted as meaning-making acts shaped by interactions with teachers, peers, family expectations, institutional structures, and broader cultural discourses about who belongs in STEM (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e1.3.2 Mathematical Identity and Competence Without Identification\u003c/h2\u003e \u003cp\u003eCentral to this study is the concept of mathematical identity, understood as relational, dynamic, and socially negotiated (Sfard \u0026amp; Prusak, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Nasir, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Mathematical identity emerges through recognition by others, self-appraisal of competence, participation in valued practices, and alignment with imagined future selves. Research has demonstrated that competence does not automatically translate into disciplinary identification (Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Students may achieve high levels of performance while simultaneously experiencing disidentification with a field. For students who earn qualifying AP Calculus scores yet choose non-STEM majors, tensions may arise between demonstrated capability and feelings of alienation, fatigue, or misalignment with STEM cultures. Affective experiences, including stress, anxiety, exhaustion, pride, or validation, are not peripheral but central to identity development (Boaler \u0026amp; Greeno, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Even when students succeed, they may interpret the emotional cost of participation as unsustainable or inconsistent with their values. Thus, AP Calculus may affirm competence while simultaneously destabilizing identification.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e1.3.3 Hermeneutic Phenomenology and Retrospective Meaning\u003c/h2\u003e \u003cp\u003eThe study adopts a hermeneutic phenomenological stance, recognizing that understanding emerges through interpretation and is shaped by language, context, and temporality (Gadamer, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1975\u003c/span\u003e; van Manen, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Participants\u0026rsquo; accounts are treated not as objective reports, but as meaning-laden narratives constructed in retrospect. Students\u0026rsquo; interpretations of AP Calculus often evolve after the experience has concluded. Through reflective dialogue and autobiographical writing, participants articulate how Calculus shaped their sense of capability, belonging, and future possibility. Meaning is therefore not fixed after exam completion but reconstructed across time. This interpretive stance enables the study to examine how AP Calculus, despite being academically \u0026ldquo;passed,\u0026rdquo; may be remembered as alienating, exhausting, affirming, or misaligned. By situating participants\u0026rsquo; Calculus narratives within their broader mathematical autobiographies, the study explores how success is reinterpreted and how those interpretations inform postsecondary decisions (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Monero, 2014).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e1.3.4 Framing the AP Calculus \u0026rarr; Non-STEM Trajectory\u003c/h2\u003e \u003cp\u003eTaken together, social constructivism, mathematical identity theory, and hermeneutic phenomenology position the AP Calculus-to-non-STEM transition not as a pipeline failure but as an outcome of socially mediated meaning-making. Calculus achievement becomes a critical transition point at which students negotiate:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eWhether STEM participation feels imaginable\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWhether belonging is perceived as durable\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWhether the emotional and identity costs align with future aspirations\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eBy centering these interpretive processes, the study shifts attention from deficit narratives of attrition to systemic considerations of how advanced mathematics is framed and experienced within educational institutions.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"2.0 Theoretical and Empirical Background","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.1 AP Calculus as Gateway and Credential\u003c/h2\u003e \u003cp\u003eAdvanced Placement (AP) Calculus occupies a distinctive place in U.S. mathematics schooling as both a curricular culmination and an institutional signal. As Seymour and Hewitt (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) and Bressoud, Mesa, and Rasmussen (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) note, Calculus has historically functioned as a prerequisite and gateway to STEM disciplines. AP Calculus is widely treated as evidence of readiness for college-level quantitative study and positioned as an entry point into STEM majors requiring Calculus. Yet its meaning extends beyond content mastery. Geiser and Santelices (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) demonstrate that AP coursework functions simultaneously as preparation and credential, conferring weighted GPA advantages, admissions signaling, and college credit, often alongside of intrinsic mathematical interest. This dual function complicates a simple readiness narrative: advanced course completion does not necessarily indicate commitment to continued mathematical participation.\u003c/p\u003e \u003cp\u003eLarge-scale research documents positive associations between AP performance and college outcomes (Geiser \u0026amp; Santelices, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), yet access to AP Calculus and its benefits remains uneven, mediated by disparities in teacher preparation and instructional conditions (Bressoud et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Most critically, Avery et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) show that a substantial proportion of students meeting conventional readiness benchmarks do not pursue STEM majors. This paradox calls for research that examines not only what AP Calculus predicts, but how students interpret its meaning when deciding what comes next.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Beyond \u0026ldquo;STEM Leakage\u0026rdquo;: Persistence, Choice, and Meaning\u003c/h2\u003e \u003cp\u003eSTEM persistence is often framed through pipeline metaphors in which students either advance or \u0026ldquo;leak\u0026rdquo; out (Cannady, Greenwald, \u0026amp; Harris, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). While such language highlights structural inequities, Adiredja and Louie (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) caution that it can also reproduce deficit assumptions by positioning non-continuation as failure. Research critiquing attrition framings argues that educational trajectories are rarely linear and that continuation depends on value alignment, identity coherence, and cultural meanings (Eccles, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Leaving STEM may therefore reflect agency and discernment rather than inability.\u003c/p\u003e \u003cp\u003eFor students who have already succeeded in AP Calculus, pipeline interpretations become especially reductive. Expectancy\u0026ndash;value theory (Eccles \u0026amp; Wigfield, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) and identity-based accounts (Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) emphasize that students weigh utility, belonging, and alignment alongside competence. As Boaler (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) and Martin (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) show, advanced mathematics can signal particular ways of being; speed, competition, narrow definitions of \u0026ldquo;smart\u0026rdquo; that some students choose not to inhabit, even when capable. The analytic focus thus shifts from \u0026ldquo;Why did they leave?\u0026rdquo; to \u0026ldquo;How did they interpret participation, and what did that interpretation mean for their futures?\u0026rdquo;\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Mathematical Identity, Belonging, and Recognition in Advanced Courses\u003c/h2\u003e \u003cp\u003eMathematics education scholarship posits identity and belonging as central to persistence. Sfard and Prusak (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) conceptualize identity as narratively constructed, while Wenger (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) frames it as participation in communities of practice. Mathematical identity is therefore relational, shaped by recognition, classroom discourse, peer comparison, and institutional narratives (Martin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Nasir, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). In advanced courses, public markers such as AP labels and exam scores intensify both affirmation and vulnerability (Boaler, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Students may experience competence and insecurity simultaneously, particularly in environments privileging speed and correctness (Boaler, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eImportantly, competence does not guarantee identification (Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Students may achieve highly yet not claim mathematics as a future domain of belonging. Identification depends on cultural fit, values, and legitimacy and not ability alone (Eccles, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Martin, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). AP Calculus may recalibrate what it means to be a \u0026ldquo;math person,\u0026rdquo; shifting identity from effortless performance toward effortful, relational participation. Such recalibration may support persistence for some while enabling others to pursue non-STEM pathways without perceiving themselves as deficient.\u003c/p\u003e \u003cp\u003eTeachers and peer communities are pivotal in these processes. Cobb and Yackel (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1996\u003c/span\u003e) argue that classroom norms define legitimate participation. Instructional practices that normalize revision, reasoning, and sense-making expand belonging (Boaler, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), while rushed pacing and competitive climates narrow it (Boaler, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Martin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). AP Calculus is therefore experienced not as content alone but as lived pedagogy and lived community.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Transitions and Lived Experience: Why Interpretive Methods Are Needed\u003c/h2\u003e \u003cp\u003eResearch on secondary-to-postsecondary transitions highlights discontinuities in norms, assessment practices, and expectations for independence (Seymour \u0026amp; Hewitt, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bressoud et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Such shifts can destabilize previously successful identities and reshape perceptions of what mathematical participation demands (Eccles, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Yet much AP research relies on quantitative indicators (Avery et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Geiser \u0026amp; Santelices, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), leaving lived experiences of rigor, belonging, and interpretation underexamined. Hermeneutic phenomenology, as articulated by Gadamer (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1975\u003c/span\u003e/2004) and van Manen (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1990\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), treats meaning as historically situated and emerging through reflection. Students\u0026rsquo; understandings of AP Calculus may crystallize only after the experience, as they reinterpret it through college transition and major selection. Integrating autobiographical writing with dialogic interviews enables exploration of how students construct coherence between demonstrated competence and evolving selfhood (Sfard \u0026amp; Prusak, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Together, this scholarship positions AP Calculus as a meaning-laden transition point rather than a deterministic filter. It underscores the need to reframe \u0026ldquo;leakage\u0026rdquo; by centering student interpretation and agency, particularly among those who have already met conventional definitions of readiness (Adiredja \u0026amp; Louie, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Mathematics Education Affectations\u003c/h2\u003e \u003cp\u003eBecause AP Calculus is enacted through teachers\u0026rsquo; instructional decisions and classroom participation norms, the phenomenon of \u0026ldquo;AP Calculus success \u0026rarr; non-STEM redirection\u0026rdquo; is also a mathematics teacher education issue, not only a student pathway issue. AP Calculus teachers are positioned as mediators of what counts as legitimate mathematical work (e.g., speed versus sense-making), how rigor is lived (e.g., pacing pressures versus opportunities for revision and conceptual exploration), and who is recognized as belonging in advanced mathematics (through discourse practices, assessment norms, and peer culture). Participants in this study repeatedly interpreted AP Calculus through these teacher-mediated conditions, with the teacher as interpretive anchor, peer belonging as a condition for learning, and rigor as relational, all suggesting that teacher education must explicitly prepare prospective and practicing teachers to recognize how everyday instructional decisions (e.g., pacing, public comparison, error treatment, discourse authority) mediate students\u0026rsquo; interpretations of belonging and future participation. Framed this way, the study offers teacher-educative insights about how advanced mathematics instruction can cultivate durable mathematical agency and \u0026ldquo;competence without identification,\u0026rdquo; supporting multiple post-AP futures without defaulting to deficit pipeline narratives (Boaler, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Cobb \u0026amp; Yackel, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Martin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2000\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Wenger, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Carlone \u0026amp; Johnson, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; van Manen, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1990\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Gadamer, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1975\u003c/span\u003e/2004).\u003c/p\u003e \u003c/div\u003e"},{"header":"3.0 Methods","content":"\u003cp\u003e\u003cstrong\u003e3.1 Design and methodological orientation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis qualitative study used hermeneutic phenomenology to interpret how students who earned a score of 3 or higher on the AP Calculus examination make sense of their AP Calculus experiences and their subsequent decision to pursue non-STEM undergraduate majors. Phenomenological inquiry in mathematics education prioritizes depth over breadth to illuminate the complexity of students lived experiences, the intersectionality of emotions, identity negotiations, institutional messages, and sense-making, often obscured in achievement-centered research (Moustakas, 1994; van Manen, 2016; Vagle, 2018). A hermeneutic approach was appropriate because the phenomenon under study is not simply behavioral (e.g., course-taking decisions) but interpretive: participants\u0026rsquo; decisions are understood as meaning-laden responses shaped through experience, reflection, and context (Heidegger, 1962; van Manen, 2016).\u003c/p\u003e\n\u003cp\u003eThe study was epistemologically aligned with a social constructivist stance that conceptualizes knowledge and identity as socially produced and mediated through language, interaction, and institutional narratives (Cobb, 1994; Ernest, 1998). Consistent with Gadamer\u0026rsquo;s view of understanding as historically situated and dialogic, participant accounts were treated as interpretive \u0026ldquo;texts\u0026rdquo; shaped by prior schooling, peer interactions, assessment structures, and broader cultural messages about Calculus as a gatekeeper to STEM (Gadamer, 1975). Rather than attempting to bracket the researcher\u0026rsquo;s prior experience, hermeneutic phenomenology acknowledges positionality as integral to interpretation and emphasizes the \u0026ldquo;fusion of horizons\u0026rdquo; through which new understandings emerge (Gadamer, 1975; van Manen, 2016).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2 Setting, participants, and sampling\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants were recruited from a small, southern liberal arts college using purposeful criterion sampling (Patton, 2015) to ensure each participant had directly experienced the phenomenon of interest. Eligibility criteria were: (a) completion of AP Calculus AB and/or BC in high school; (b) an AP Calculus exam score of 3+; (c) current enrollment as a first- or second- year college student; (d) formal declaration of a non-STEM major; and (e) no enrollment in any college-level Calculus course since matriculation. (Table 1).\u003c/p\u003e\n\u003cp id=\"_Toc221883900\"\u003e\u003cstrong\u003eTable 1: Participant List and Demographic Characteristics\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" title=\"Figure 4: Participant List and Demographic Characteristics\" summary=\"A list of the 8 participants who were interviewed and wrote mathematical autobiographies, with their gender, year in school, and major for each individual.\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eParticipant\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eGender\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eYear in School\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUndergraduate Major\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eFemale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eAccounting\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eFemale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eExercise Science\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003ePhilosophy \u0026amp; Religion\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eSophomore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eBusiness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eBusiness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eFemale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eTheatre \u0026amp; Communication\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eFreshman\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eBusiness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParticipant #8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 120px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eSophomore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 216px;\"\u003e\n \u003cp\u003eHistory\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis sampling strategy supported interpretive depth rather than representativeness, consistent with hermeneutic phenomenology\u0026rsquo;s emphasis on richly described experience (van Manen, 2016). The final sample consisted of eight participants (N = 8).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.3 Recruitment and consent\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFollowing Institutional Review Board (IRB) approval, eligible participants were recruited via email outreach facilitated through the Registrar\u0026rsquo;s office. Interested students received information about the study, the voluntary nature of participation, and the focus on meaning-making rather than evaluating their decisions or mathematical ability. Students who agreed to participate completed informed consent procedures prior to data collection. Pseudonyms were assigned and identifying details were removed from interview transcripts and autobiographical texts.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4 Data sources\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData were generated through two complementary sources: mathematical autobiographies and semi-structured hermeneutic phenomenological interviews. The study treated these sources as methodologically complementary rather than as triangulation for convergence; autobiographies provided reflective, self-authored narratives, and interviews enabled dialogic elaboration and interpretive deepening.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4.1 Mathematical autobiographies\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEach participant composed a mathematical autobiography narrating their experiences with mathematics across time, including early memories, moments of success and struggle, relationships with teachers and peers, motivations for enrolling in AP Calculus, and reflections on how AP Calculus shaped identity, affect, and post-secondary decisions. Mathematical autobiographies are well established in mathematics education research as tools for surfacing identity development and affective dimensions of mathematical participation that may not emerge immediately in interviews (Boaler, 2002; Sfard \u0026amp; Prusak, 2005; Clandinin \u0026amp; Connelly, 2000). Within a hermeneutic phenomenological orientation, the autobiography was treated not as a neutral record of events but as an interpretive text through which participants constructed meanings about competence, belonging, and future trajectories.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4.2 Hermeneutic phenomenological interviews\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePrimary data were generated through semi-structured, in-depth interviews lasting approximately 60\u0026ndash;90 minutes. Interviews were conducted via secure video conferencing, audio recorded, and transcribed verbatim. Hermeneutic phenomenological interviewing aims to elicit reflective accounts of lived experience; how events were felt, interpreted, and understood, rather than to extract factual reports (van Manen, 1990, 2014). Accordingly, interview prompts were open-ended and experiential, inviting participants to describe their AP Calculus classroom experiences, the transition to college, advising/placement messages, peer comparison, affective responses to Calculus, and evolving mathematical identity. Follow-up questions were used flexibly to deepen descriptions of tensions, turning points, and meaning rather than to solicit justification for major choice (Finlay, 2011; Gadamer, 1975). Participants were offered the opportunity to review their transcripts for reflection, clarification, or elaboration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4.3 Data collection sequence and rationale\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData collection followed a two-stage sequence: (1) mathematical autobiography, followed by (2) individual interview. This sequence was intentional. Autobiographical writing provided participants time and space to reflect on emotionally complex experiences prior to dialogic interviewing and served as an \u0026ldquo;anchor text\u0026rdquo; for interpretive conversation (Hauk, 2005; Kaasila, 2007; McCulloch et al., 2013). The subsequent interview enabled probing of silences, contradictions, and pivotal moments in the written narrative, supporting the hermeneutic movement between parts (specific episodes, metaphors, emotions) and the whole (participants\u0026rsquo; broader meaning structures and trajectories) (van Manen, 1990; Seidman, 2019; Zahavi, 2019). Together, the two methods supported rich, contextualized accounts of the paradox central to the study: demonstrated Calculus readiness alongside non-STEM trajectories.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.5 Analytic approach\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAnalysis proceeded as an iterative, interpretive process guided by the hermeneutic circle, emphasizing ongoing movement between individual texts and emerging shared meanings (Heidegger, 1962; Gadamer, 2004; van Manen, 2016). The analytic goal was to develop thematic interpretations that illuminated how AP Calculus success was experienced, reinterpreted over time, and decoupled from STEM continuation.\u003c/p\u003e\n\u003cp\u003eAnalysis began with sustained immersion in both autobiographies and interview transcripts. Each participant\u0026rsquo;s texts were first read holistically to develop an initial sense of the narrative arc, and how the participant positioned AP Calculus within their broader mathematical history and self-concept. Subsequent readings attended to language and meaning-making features emphasized in hermeneutic work: metaphors, emotional tone, moments of rupture or affirmation, and identity-relevant positioning (e.g., being \u0026ldquo;a math person,\u0026rdquo; feeling legitimate/illegitimate, experiencing Calculus as belonging or alienation). Rather than coding for frequency or treating themes as fixed categories, the study used selective and thematic reading to identify interpretive insights regarding how participants constructed the meaning of Calculus success in relation to identity, affect, belonging, and perceived futures (van Manen, 2016; Vagle, 2018).\u003c/p\u003e\n\u003cp\u003eTo support organization and retrieval of interpretive materials, NVivo 15 was used to manage transcripts and autobiographies and to document clusters of salient passages and analytic memos (Churchill \u0026amp; Wertz, 2015). Coding was used as a tool for locating meaning-rich segments and organizing interpretive work; however, theme development remained grounded in iterative interpretive writing, memoing, and repeated returns to the full texts to check coherence and resonance with participants\u0026rsquo; accounts (Lincoln \u0026amp; Guba, 1985; Zahavi, 2019). Across cases, provisional thematic statements were drafted, tested against the dataset (including discrepant moments), refined, and rewritten in interpretive form. Final themes were developed to preserve both convergence and variation, enabling the findings to represent shared meanings without collapsing differences across participants.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.6 Researcher positionality and reflexivity\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eHermeneutic phenomenology treats the researcher\u0026rsquo;s horizon of understanding as inseparable from interpretation. The researcher\u0026rsquo;s background as a Calculus educator across secondary and postsecondary contexts shaped initial pre-understandings about Calculus as a marker of readiness and STEM possibility. Rather than bracketing these assumptions, reflexive practice made them explicit and treated them as an analytic resource to be examined and potentially unsettled through engagement with participants\u0026rsquo; texts (Gadamer, 2004; van Manen, 2016). Reflexive memoing documented how interpretations were influenced by professional experiences and how those preconceptions shifted as participants\u0026rsquo; accounts challenged conventional narratives of persistence, achievement, and belonging (Lincoln \u0026amp; Guba, 1985). This reflexive stance also is due to power dynamics that can emerge when a mathematics educator interviews students about mathematics-related experiences.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.7 Trustworthiness\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTrustworthiness was established using criteria aligned with qualitative inquiry (Lincoln \u0026amp; Guba, 1985). Credibility was supported through immersive engagement with participants\u0026rsquo; narratives across two complementary sources (interviews and autobiographies) and through opportunities for participant reflection. In addition to transcript review, the study included member checking beyond transcript verification, in which participants were invited to respond to the researcher\u0026rsquo;s developing interpretive claims (e.g., thematic summaries and/or interpretive statements) and to clarify, extend, or complicate those interpretations (Maxwell, 2013). This process was used to strengthen interpretive resonance while remaining consistent with hermeneutic commitments: participants\u0026rsquo; feedback informed refinement of themes without treating participant agreement as the sole criterion of \u0026ldquo;truth.\u0026rdquo;\u003c/p\u003e\n\u003cp\u003eDependability was strengthened through an audit trail documenting analytic decisions, memoing, iterative theme drafts, and interpretive shifts across the hermeneutic process (Dey, 1993). Confirmability was supported through ongoing reflexive journaling to surface assumptions and track how interpretations were produced (Lincoln \u0026amp; Guba, 1985). Transferability was enhanced through rich, contextualized description of participants\u0026rsquo; experiences and the AP Calculus-to-college transition, allowing readers to determine relevance to similar settings. Where feasible, peer debriefing was used to interrogate interpretations and identify potential blind spots (Ahmed, 2004; Richards, 2015). Consistent with hermeneutic and constructivist traditions, \u0026ldquo;validity\u0026rdquo; was treated as interpretive credibility, grounded in participant texts, coherence of interpretations, and the capacity of findings to illuminate the phenomenon for readers (van Manen, 2016).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.8 Ethical considerations and emotional risk mitigation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthical approval was obtained prior to data collection. Pseudonyms were used, and identifying information was removed from all materials. Because recalling advanced mathematics experiences can surface anxiety, shame, or perceived threats to identity, particularly where Calculus is culturally positioned as a marker of intelligence and STEM belonging, interviews were conducted using non-evaluative language and participant-centered prompts emphasizing meaning-making rather than justification (van Manen, 2016). Participants were reminded they could pause, redirect, or discontinue participation at any time without consequence and could decline to elaborate on experiences that felt uncomfortable or unresolved. The researcher remained attentive to signs of distress and prioritized participant well-being over data completeness, treating silence, hesitation, and partial recall as meaningful dimensions of lived experience rather than deficiencies to be corrected (Heidegger, 1962; Lincoln \u0026amp; Guba, 1985).\u003c/p\u003e"},{"header":"4.0 Integrated Findings","content":"\u003cp\u003e\u003cstrong\u003e4.1 Overview of the Findings as Interpretive Account\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study examined how students who earned a score of 3 or higher on the AP Calculus exam made sense of their AP Calculus experiences and their subsequent choice not to pursue STEM majors or further collegiate mathematics. Consistent with a hermeneutic phenomenological orientation, the findings are presented as interpretations of lived experience rather than causal explanations or predictive claims. Meaning was approached as historically situated and dialogically produced, emerging through iterative movement between participants\u0026rsquo; mathematical autobiographies (self-authored recollections) and semi-structured interviews (interpretive dialogue), as well as through the researcher\u0026rsquo;s reflexive engagement with these texts (Gadamer, 1975/2004; van Manen, 1990, 2014). Across this fusion of horizons, AP Calculus appeared not as a neutral curricular milestone but as a meaning-laden transition point where participants negotiated identity, belonging, and future possibility.\u003c/p\u003e\n\u003cp\u003eAll eight participants completed AP Calculus successfully and met an institutional marker of readiness through an AP score of 3+. Yet each pursued an undergraduate major outside of STEM (accounting, exercise science, philosophy \u0026amp; religion, business, theatre \u0026amp; communication, history). Participants described AP Calculus as a high-intensity course shaped by coverage demands, frequent assessments, and the cultural positioning of Calculus as a capstone of secondary mathematics and a gateway to STEM futures. Importantly, participants did not narrate non-continuation as incapacity. Instead, they described competence alongside discernment: AP Calculus served as a site where they learned what they could do, what it cost them, what it meant to belong, and what they wanted next. This non-deficit stance aligns with scholarship challenging \u0026ldquo;leakage\u0026rdquo; metaphors and emphasizing that non-participation can reflect meaningful negotiation of identity, value, and coherence rather than academic deficiency (Brown \u0026amp; McNamara, 2011; Solomon, 2007; Walshaw, 2017).\u003c/p\u003e\n\u003cp\u003eTo render the findings legible for mathematics teacher education audiences, the chapter is organized into three integrated interpretive themes. Each theme synthesizes patterns that became visible only through reading autobiographies and interviews together: (1) AP Calculus as identity calibration rather than identity sorting, (2) rigor as relational and interpretive rather than inherent, and (3) non-continuation as agentic alignment rather than pipeline loss. Throughout, participant quotations are used not as \u0026ldquo;evidence fragments,\u0026rdquo; but as language through which experience becomes visible and interpretable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2 Theme 1: AP Calculus Calibrated Mathematical Identity Without Necessarily Producing Mathematical Identification\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants commonly entered AP Calculus with a confident identity narrative, often framed as being \u0026ldquo;good at math,\u0026rdquo; \u0026ldquo;a math person,\u0026rdquo; or someone for whom mathematics had previously felt natural. Their autobiographies were saturated with earlier markers of validation: accelerated placement, high grades, and recognition from teachers and peers. One participant recalled the affective security of prior success: \u0026ldquo;knowing I was probably the best in the class was so nice\u0026rdquo; (Participant 1). Another described the social status of enrollment itself: \u0026ldquo;I honestly felt really smart being an AP Calculus student\u0026rdquo; (Participant 5). In these accounts, mathematical identity initially appeared stable and trait-like, grounded in a history of doing school mathematics successfully.\u003c/p\u003e\n\u003cp\u003eYet across interviews, this \u0026ldquo;math person\u0026rdquo; identity did not remain intact as a simple label. Instead, AP Calculus recalibrated what participants understood mathematical competence to require. Several described an encounter with difficulty that disrupted the relationship between confidence and ease. Participant 1 narrated the shift as a humbling but formative reorientation: AP Calculus \u0026ldquo;knocked [me] down a few pegs,\u0026rdquo; revealing \u0026ldquo;a new world of difficulty.\u0026rdquo; Rather than narrating this as identity collapse, she narrated it as a change in the \u003cem\u003eterms\u003c/em\u003e of competence, moving from confidence built on speed and effortless recall toward confidence built on effort, vulnerability, and persistence. Participant 7 similarly rejected the notion that success reflected innate giftedness, explaining that others may see him as naturally strong, but \u0026ldquo;I work for it and don\u0026rsquo;t give up when things get hard.\u0026rdquo; In this recalibration, AP Calculus was experienced as an identity event: not a course that sorted who belonged and who did not, but a course that altered what \u0026ldquo;belonging\u0026rdquo; meant in the first place (Martin, 2000; Wenger, 1998).\u003c/p\u003e\n\u003cp\u003eThis calibration was not uniform. For some, it solidified pride in capability precisely because it required sustained struggle. Participant 4 framed the course as a rare experience of intellectual disruption that he ultimately valued: it was \u0026ldquo;one of the first times in my entire life that I got my [butt] kicked in a class.\u0026rdquo; The force of this statement was not only about difficulty; it signaled that AP Calculus made him confront a new relationship to learning, one that included failure, recovery, and endurance. Others framed their entry into AP Calculus as less intentional (\u0026ldquo;the next class in order,\u0026rdquo; Participant 5; a \u0026ldquo;natural inclination,\u0026rdquo; Participant 8), yet in retrospect, even habitual enrollment became meaningful as participants interpreted what the course revealed about themselves.\u003c/p\u003e\n\u003cp\u003eAcross these variations, the shared interpretive movement was from identity-as-achievement to identity-as-situated participation. Participants could still claim competence, but they often did so in new language: competence as something enacted through practice, supported by others, and sustained across time. This was especially visible in the way participants talked about learning itself. Participant 1 contrasted earlier mathematics courses, where she \u0026ldquo;would just memorize techniques\u0026rdquo; with AP Calculus, which \u0026ldquo;really taught me that it is important to apply the work and PRACTICE a ton.\u0026rdquo; The capitalization in her written account functioned like an embodied emphasis: practice was not a study tip; it was a new moral of what it means to learn.\u003c/p\u003e\n\u003cp\u003eCrucially, this identity calibration did not automatically produce mathematical identification or a desire to continue participating in mathematics as a future domain. Participants repeatedly illustrated what might be described as competence without identification: they learned they could succeed in demanding mathematics yet did not necessarily want to keep living the version of mathematical participation that AP Calculus represented. For some, this distinction was explicit in how they narrated selfhood. Participant 6 simultaneously acknowledged success and resisted identity labeling: \u0026ldquo;No I don\u0026rsquo;t think I consider myself a math person\u0026hellip; I\u0026rsquo;m a performing arts person,\u0026rdquo; while also describing AP Calculus as a source of \u0026ldquo;academic validation.\u0026rdquo; Her narrative reveals a tension between categorical identity (\u0026ldquo;performing arts person\u0026rdquo;) and demonstrated competence (\u0026ldquo;academic validation\u0026rdquo;), suggesting that mathematics success can function as recognition without becoming a stable self-concept. Participant 8 described a different tension: he now \u0026ldquo;miss[es] math,\u0026rdquo; not necessarily as a major, but as a way of thinking: \u0026ldquo;figuring things out\u0026rdquo; with clarity and resolution. Even in absence, mathematics remained meaningful as an orientation, not a pipeline.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.1 Synthesis of Theme 1: Self-Understanding as a Mathematics Person\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFrom a mathematics teacher education perspective, the significance of this theme lies in how AP Calculus acted as a calibration mechanism for students\u0026rsquo; understandings of themselves as mathematical learners. Participants did not narrate AP Calculus as merely \u0026ldquo;hard content\u0026rdquo;; they narrated it as the experience that redefined what counts as legitimate mathematical work and what kinds of selves can sustain it (Martin, 2000; Wenger, 1998). The course did not simply confer or deny identity; it reshaped the meanings attached to \u0026ldquo;being good at math,\u0026rdquo; making visible that achievement can coexist with disidentification and that identity claims are negotiated through lived participation rather than determined by scores alone.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3 Theme 2: Rigor Was Experienced as Relational and Interpretive, Mediated by Teachers, Peers, and Time\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants consistently described AP Calculus as rigorous, but they did not treat rigor as a fixed property of the curriculum. Instead, rigor appeared as a lived phenomenon shaped by instructional decisions, peer culture, and the temporal pressures of students\u0026rsquo; broader lives. Participants repeatedly returned to the same experiential ingredients, including pace, assessment rhythms, opportunities (or lack of opportunities) to revisit ideas, and narrated how those conditions made Calculus feel either possible or overwhelming. In this sense, rigor was not simply \u0026ldquo;difficulty\u0026rdquo;; it was how difficulty was organized, distributed, and interpreted across relationships and time (van Manen, 1990; Hiebert \u0026amp; Grouws, 2007).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3.1 Teacher as interpretive anchor: Calculus was experienced as \u0026ldquo;Calculus-as-taught\u0026rdquo;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAcross autobiographies and interviews, the teacher emerged as a primary medium through which Calculus became meaningful. When teachers were described as relational, enthusiastic, and responsive, participants narrated Calculus as approachable and enjoyable. Participant 4 linked confidence explicitly to his teacher\u0026rsquo;s presence: \u0026ldquo;I remember feeling confident\u0026hellip; because of the energy of my teacher\u0026hellip; her catchy songs.\u0026rdquo; Participant 6 described the class as \u0026ldquo;homey and comfortable,\u0026rdquo; suggesting that affective safety was not supplemental to learning but part of how learning became livable. In interviews, this teacher-mediated experience became even more pronounced. Participant 6 said the class \u0026ldquo;felt like a club\u0026rdquo; because the teacher knew students personally and \u0026ldquo;talked us through\u0026rdquo; confusion. Participant 8 recalled that the teacher \u0026ldquo;would try and make sure everyone understood,\u0026rdquo; framing instruction as an ethic of inclusion rather than an expectation of self-sufficiency.\u003c/p\u003e\n\u003cp\u003eIn contrast, when instructional clarity or relational care was perceived as absent, the same Calculus curriculum was narrated as alienating. Participant 1 described how instructional errors and disengagement \u0026ldquo;made the content much more confusing,\u0026rdquo; and Participant 3 recalled peer mistreatment that \u0026ldquo;was not discouraged by my teacher,\u0026rdquo; leading him to \u0026ldquo;dislike the class.\u0026rdquo; These accounts did not position the teacher as a mere contextual variable; they positioned pedagogy as the lived reality of Calculus. AP Calculus was not encountered as abstract mathematics; it was encountered as pacing, responsiveness, examples offered or withheld, norms for questions, and what happened when students were confused (Boaler, 2002; van Manen, 2014).\u003c/p\u003e\n\u003cp\u003eA key dimension of this teacher-mediated rigor was time. Participants described moments when pace functioned as a boundary between sense-making and survival. Participant 1 contrasted her experience across semesters, describing the BC portion as \u0026ldquo;rushed\u0026rdquo; and cognitively overwhelming. She described the experience of holding too many procedures at once: remembering when to use \u0026ldquo;9 or 10 different tests,\u0026rdquo; and the embodied residue of this pressure: \u0026ldquo;my head hurt\u0026hellip; I still got to remember it.\u0026rdquo; Importantly, she interpreted this not only as content load but as a time condition: \u0026ldquo;we were just in a hurry rushing to get through that and into graduation.\u0026rdquo; Rigor here was temporal saturation; moving forward before meaning could settle.\u003c/p\u003e\n\u003cp\u003eParticipant 2 similarly described embodied rigor: headaches and migraines during heavy workload periods. This language matters: the \u0026ldquo;difficulty\u0026rdquo; of Calculus was felt in the body and carried into students\u0026rsquo; lives. Yet she also framed herself as \u0026ldquo;lucky with my teacher,\u0026rdquo; indicating that relational support could coexist with overwhelming pace. In other words, teacher care did not eliminate rigor, but it shaped how rigor was interpreted\u0026mdash;as possible, purposeful, or simply punishing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3.2 Peer community as belonging and vulnerability: struggle became shared or shameful\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePeer relationships were equally central to how rigor was lived. When classrooms were experienced as collaborative, struggle became a shared practice rather than private evidence of inadequacy. Participant 1 described classmates who would \u0026ldquo;constantly \u0026lsquo;huddle up\u0026rsquo;\u0026hellip; to learn and remember the formulas,\u0026rdquo; suggesting that understanding was socially distributed and that collective effort normalized difficulty. Participant 8 described collaboration as one of his favorite aspects of advanced mathematics: \u0026ldquo;working together with students to figure out the content was honestly some of my favorite times in high school.\u0026rdquo; He also described teaching peers as deepening his own understanding: \u0026ldquo;I would be explaining things to them\u0026hellip; this helped my understanding.\u0026rdquo; Here, peer interaction was not only emotional support; it was epistemic\u0026mdash;talking mathematics became a way of learning mathematics (Lave \u0026amp; Wenger, 1991; Wenger, 1998).\u003c/p\u003e\n\u003cp\u003eParticipant 4\u0026rsquo;s interview described a classroom ethic that institutionalized peer support: \u0026ldquo;help your neighbors,\u0026rdquo; with structures such as redo assignments that reframed error as part of collective improvement. In these contexts, participants did not narrate rigor as isolating; they narrated it as relationally buffered and even identity-supporting, because struggle was interpreted as normal rather than stigmatizing.\u003c/p\u003e\n\u003cp\u003eIn contrast, when peer culture became unsafe, rigor took on a different meaning. Participant 3 described classmates who \u0026ldquo;made fun of me when I asked a question,\u0026rdquo; and this ridicule reshaped his experience into alienation: he came to \u0026ldquo;dislike being in class.\u0026rdquo; Notably, the content difficulty in such narratives was often less prominent than the social penalty for confusion. The lived meaning of Calculus shifted from \u0026ldquo;hard but learnable\u0026rdquo; to \u0026ldquo;hard and humiliating.\u0026rdquo; This contrast illustrates how rigor was interpreted through belonging: the same struggle could be experienced as productive or as evidence of not belonging, depending on whether the social world made questions legitimate (Boaler, 2016; Lave \u0026amp; Wenger, 1991).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3.3 Competing demands and the structure of schooling: rigor was situated in life context\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants\u0026rsquo; narratives also show that rigor was not limited to classroom time; it was experienced in the collision between AP Calculus and students\u0026rsquo; broader commitments. Several participants described late nights, athletics, employment, and performance obligations. Participant 2 recalled \u0026ldquo;staying up very late finishing homework\u0026rdquo; during the second semester, which became \u0026ldquo;very stressful.\u0026rdquo; Another participant described the feeling that \u0026ldquo;the amount of work\u0026hellip; felt like it never ended.\u0026rdquo; Participant 6 narrated a particularly revealing tension: late-night rehearsals led to missed online assignments that \u0026ldquo;tanked my grade,\u0026rdquo; even though she described strong conceptual understanding. This account makes visible how rigor is produced not only by mathematical complexity but by assessment systems and deadline structures that convert life circumstances into academic consequences (Hiebert \u0026amp; Grouws, 2007; van Manen, 1990).\u003c/p\u003e\n\u003cp\u003eAcross these stories, rigor was experienced as contingent: it could validate endurance, strengthen confidence, and create pride; it could also generate exhaustion, stress, and discouragement. What determined these meanings was not the Calculus content alone, but the relational and temporal design of the course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3.4 Synthesis of Theme 2\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis theme reframes rigor as something students interpret through teacher mediation, peer belonging, and temporal constraints. For mathematics teacher education, this matters because it locates \u0026ldquo;rigor\u0026rdquo; not primarily in curriculum documents or exam blueprints, but in everyday instructional decisions that participants experienced as identity- and future-shaping: pacing, error treatment, opportunities to revise, norms for questions, and whether comparison and ranking were made public or implicit. Participants\u0026rsquo; accounts suggest that when these decisions supported sense-making and belonging, rigor was experienced as purposeful and formative; when they emphasized coverage, speed norms, or social vulnerability, rigor was experienced as overwhelming or alienating (Boaler, 2002, 2016; van Manen, 1990, 2014; Wenger, 1998).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4 Theme 3: Non-Continuation Functioned as Agentic Alignment\u0026mdash;AP Calculus as a Site of Discernment Rather Than Pipeline Loss\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA central paradox structured every narrative: participants succeeded in one of the most institutionally valorized mathematics courses yet did not continue into STEM majors or collegiate Calculus. Read through a pipeline lens, this would be coded as \u0026ldquo;leakage.\u0026rdquo; Participants, however, narrated their trajectories as discernment, an interpretive process of aligning ability, interest, identity, and future imagination. They did not describe themselves as pushed out by inability. They described themselves as learning something about what mathematical participation demanded and deciding whether that demanded self-fit the person they were becoming (Brown \u0026amp; McNamara, 2011; Solomon, 2007; Walshaw, 2017).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4.1 AP Calculus produced evidence of capability\u0026mdash;even when it also produced closure\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants repeatedly described completion as pride and relief. Participant 1 described finishing as \u0026ldquo;one of the best feelings in the world\u0026hellip; utter relief\u0026rdquo; and feeling \u0026ldquo;super proud of myself.\u0026rdquo; Participant 2 called completion \u0026ldquo;an accomplishment and a burden that I no longer had at the same time.\u0026rdquo; These statements hold a double meaning: Calculus completion conferred accomplishment yet also signaled the end of a period of sustained pressure. The affective residue, described as relief, exhaustion, or pride, became part of how participants interpreted what it would mean to continue.\u003c/p\u003e\n\u003cp\u003eSome participants narrated Calculus credit instrumentally, as a way to avoid college mathematics. Participant 6 described being \u0026ldquo;extremely excited\u0026rdquo; to be excused from future math courses. Participant 7 described taking AP Calculus to \u0026ldquo;get it out of the way,\u0026rdquo; implying that the course functioned as both credential and closure. In autobiographical form, these accounts may be interpreted as aversion.\u003c/p\u003e\n\u003cp\u003eYet the interviews complicated this \u0026ldquo;closure\u0026rdquo; narrative by surfacing a second layer: participants often reclaimed Calculus as a marker of capability that made future options feel open, even if they chose not to take them. Participant 1, who wrote that Calculus \u0026ldquo;scared me away from math a little bit,\u0026rdquo; resisted the idea that Calculus determined her major choice, saying \u0026ldquo;Not at all,\u0026rdquo; when asked whether AP Calculus shaped her decision to study business (in that interview moment). She later said she would \u0026ldquo;absolutely\u0026rdquo; take Calculus again in college. Here, the apparent contradiction functions hermeneutically as temporal reframing: the autobiography preserved affective residue (\u0026ldquo;scared away\u0026hellip; a little bit\u0026rdquo;), while the interview produced a re-narration of agency (\u0026ldquo;absolutely\u0026rdquo;). Rather than inconsistency, this reveals how meaning changed when participants returned to their experiences in dialogue and from new horizons of identity (Gadamer, 1975/2004; Ricoeur, 1984).\u003c/p\u003e\n\u003cp\u003eParticipant 8 similarly framed returning to mathematics as an option rather than a closed door. Although he chose a non-STEM pathway, he described still enjoying mathematics \u0026ldquo;for the discovery of it.\u0026rdquo; He also described missing the certainty and resolution of mathematical problem-solving in his current coursework. In this sense, not continuing in mathematics did not erase mathematical value; it re-situated it.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4.2 Non-STEM trajectories were narrated as coherent futures, not losses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants also narrated non-STEM choices as morally or vocationally coherent rather than as a retreat. Participant 3 attributed his pathway to a \u0026ldquo;calling to the ministry,\u0026rdquo; emphasizing that his decision \u0026ldquo;did not involve my experiences in AP Calculus.\u0026rdquo; Yet in interview reflection, he also described how AP Calculus affirmed his capacity to handle rigor, suggesting that even when Calculus was vocationally \u0026ldquo;irrelevant,\u0026rdquo; it was still identity-relevant: it confirmed that leaving STEM was not compelled by incapacity. Participant 1 described \u0026ldquo;miss[ing] numbers,\u0026rdquo; moving toward accounting, where mathematics persisted as a valued practice even if not labeled STEM. These narratives suggest that AP Calculus success can travel into non-STEM domains as confidence, credibility, or a way of thinking, rather than as a ticket that must be cashed only through STEM persistence.\u003c/p\u003e\n\u003cp\u003eParticipant 8 articulated an especially direct critique of deficit framing: even if he had failed, universities would respect that \u0026ldquo;they still tried.\u0026rdquo; His statement reframes participation itself as meaningful\u0026mdash;not because it guarantees continuation, but because it signifies willingness to engage with challenge. In a pipeline narrative, \u0026ldquo;trying\u0026rdquo; without continuing can be framed as waste; in his narrative, it is evidence of character and capability. This interpretive stance undercuts the idea that leaving STEM after Calculus success is irrational. Instead, it suggests that AP Calculus can function as a boundary experience where students test alignment between capacities and futures and then decide with authority.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4.3 Learning to struggle as transferable outcome supported agency to choose differently\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants described AP Calculus as teaching them how to learn, not only what to learn. They frequently described a shift from memorization to sense-making, from passive technique to active practice. Participant 7 emphasized understanding the \u0026ldquo;\u0026lsquo;why\u0026rsquo; behind\u0026rdquo; procedures, describing how application and repetition helped ideas \u0026ldquo;click.\u0026rdquo; Participant 3 described daily quizzes with correction opportunities as assignments \u0026ldquo;there to help you not hurt you,\u0026rdquo; suggesting that error and revision were interpreted as part of learning rather than as evidence of deficiency. Participant 8 emphasized \u0026ldquo;trial and error\u0026hellip; all the repetition I had to do\u0026rdquo; as what made learning real. These narratives position Calculus as a metacognitive and dispositional threshold\u0026mdash;an experience that taught endurance, practice, and tolerance for confusion.\u003c/p\u003e\n\u003cp\u003eCritically, participants narrated these outcomes as transferable beyond mathematics. Participant 5 likened the course to athletics, describing it as evidence he could take unfamiliar information and \u0026ldquo;produce a product that I\u0026rsquo;m proud of.\u0026rdquo; Others described carrying persistence habits into college. Even when participants chose not to continue mathematics, they did not narrate Calculus as wasted. They narrated it as formative: it produced confidence, discipline, and a changed understanding of how learning works. From a teacher education perspective, this theme matters because it reframes the purpose of advanced mathematics: the value of AP Calculus may include identity and agency outcomes that do not depend on STEM continuation (Skemp, 1976).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4.4 Remembered mathematics as meaning: what endured were relationships and thresholds\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFinally, participants\u0026rsquo; memories of AP Calculus were often relational and experiential rather than procedural. In autobiographies, participants frequently ended with gratitude for teachers, peers, and personal growth; interviews illuminated why these memories endured. Participant 6 recalled apologizing on an AP free-response question; an act that symbolized humility, care, and the felt presence of evaluation. She also described the class as \u0026ldquo;a club,\u0026rdquo; emphasizing belonging over content. Participant 2 described missing her teacher more than mathematics itself. Participant 8 mourned the loss of \u0026ldquo;figuring things out\u0026rdquo; in environments with clear right answers. These recollections suggest that what persisted was not the mechanics of Calculus but the remembered self in relation to challenge: supported, pressured, affirmed, exhausted, proud.\u003c/p\u003e\n\u003cp\u003eThis matters for interpreting non-continuation. If what students carry forward is primarily the meaning of who they were in Calculus, rather than the content they mastered, then decisions about continuing mathematics are likely shaped by whether that remembered self feels sustainable and desirable. Participants\u0026rsquo; narratives suggest that many experienced Calculus as \u0026ldquo;worth having\u0026rdquo; even when they chose not to repeat it, which reframes non-continuation as a coherent response to a meaning-laden experience rather than as loss of talent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4.5 Synthesis of Theme 3\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAcross participants, AP Calculus success did not function as a deterministic feeder into STEM. Instead, AP Calculus acted as a site of discernment where students learned: (a) they could do hard things, (b) the conditions under which mathematics felt livable or alienating, and (c) whether continued participation aligned with who they were becoming. In these accounts, leaving STEM after Calculus success was not narrated as inability. It was narrated as agentic alignment, a decision made from a position of demonstrated competence and newly clarified values. This theme challenges \u0026ldquo;leakage\u0026rdquo; framings by showing that redirection can reflect coherence and self-knowledge rather than attrition (Adiredja \u0026amp; Louie, 2020; Brown \u0026amp; McNamara, 2011).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.5 Concluding Integrative Statement: AP Calculus as Meaning-Making Crucible at a Transition Point\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTaken together, the three themes show AP Calculus functioning less as a pipeline checkpoint and more as a meaning-making crucible where identity, rigor, belonging, and future imagination were negotiated over time. First, AP Calculus calibrated students\u0026rsquo; mathematical identities by redefining competence as effortful, relational, and practiced, yet this calibration did not require ongoing identification with mathematics as a future domain (Martin, 2000; Wenger, 1998). Second, rigor was experienced as relational and interpretive, mediated by teacher practices, peer culture, and the temporal structure of schooling; students did not simply \u0026ldquo;face Calculus,\u0026rdquo; they faced Calculus-as-lived through pacing, error treatment, discourse norms, and support (Boaler, 2002, 2016; van Manen, 1990, 2014). Third, non-continuation emerged as agentic alignment: students interpreted AP Calculus as evidence of capability and used that evidence to choose futures that felt coherent, including non-STEM pathways that still carried mathematical confidence and ways of thinking.\u003c/p\u003e\n\u003cp\u003eFor mathematics teacher education, these findings reframe the AP Calculus \u0026rarr; non-STEM trajectory as a teacher-educative problem of practice rather than a student deficit: participants\u0026rsquo; accounts suggest that teachers\u0026rsquo; everyday instructional decisions and the classroom participation norms those decisions produce, mediate how students interpret belonging and future participation in advanced mathematics. In other words, AP Calculus \u0026ldquo;works\u0026rdquo; on students not only through content, but through the meanings students construct about what mathematics participation requires and whether they want to become (or remain) that kind of participant.\u003c/p\u003e"},{"header":"5.0 Discussion: Beyond the Pipeline — AP Calculus as Identity Work, Not STEM Sorting","content":"\u003cp\u003eThis study began with a deceptively simple question: How do students who successfully complete AP Calculus make sense of choosing not to pursue STEM majors? The dominant policy discourse would frame such students as \u0026ldquo;leakage\u0026rdquo; from the STEM pipeline. Yet participants\u0026rsquo; narratives resist this framing. Across autobiographies and interviews, AP Calculus was experienced not as a sorting mechanism that determined who belongs in STEM, but as a formative encounter that recalibrated identity, clarified values, and strengthened agency. Rather than producing attrition, AP Calculus produced interpretation.\u003c/p\u003e \u003cp\u003eThree interpretive claims extend mathematics education scholarship and challenge deficit-oriented pipeline logics: (1) AP Calculus functioned as an identity-calibrating experience rather than an identity-sorting one; (2) rigor was lived and relational rather than inherent; and (3) non-continuation was frequently narrated as agentic discernment grounded in demonstrated competence. Together, these claims reposition AP Calculus from a pipeline checkpoint to a meaning-making site.\u003c/p\u003e \u003cdiv id=\"Sec43\" class=\"Section2\"\u003e \u003ch2\u003e5.1 AP Calculus as Identity Calibration, Not Identity Sorting\u003c/h2\u003e \u003cp\u003eParticipants entered AP Calculus with established mathematical identities often grounded in speed, recognition, and prior success. Yet Calculus destabilized simplistic notions of being a \u0026ldquo;math person.\u0026rdquo; Struggle became unavoidable, and competence was renegotiated as effortful rather than effortless. Importantly, this renegotiation did not collapse identity. Instead, it recalibrated it. This distinction is critical.\u003c/p\u003e \u003cp\u003e Pipeline metaphors assume that advanced coursework reveals who \u0026ldquo;truly belongs.\u0026rdquo; However, participants\u0026rsquo; narratives suggest that AP Calculus did not sort identities; it refined them. Students who ultimately chose non-STEM majors did not describe themselves as incapable. They described themselves as clarified. They learned what sustained engagement in advanced mathematics required, perceived cognitively, emotionally, and socially, and assessed whether that form of participation aligned with their broader sense of self. This finding aligns with sociocultural theories positioning identity as participation rather than possession (Wenger, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Martin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Competence alone did not guarantee identification. Students demonstrated ability (AP scores\u0026thinsp;\u0026ge;\u0026thinsp;3), yet identification with mathematics as a future domain remained conditional. This articulates what this study conceptualizes as competence without identification, a theoretically generative distinction for mathematics education research. For teacher education, this reframing disrupts the assumption that successful students will persist in STEM. Mathematical success does not obligate mathematical continuation. Identity is negotiated through meaning, not determined by performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec44\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Rigor as Lived, Relational, and Interpretive\u003c/h2\u003e \u003cp\u003ePolicy discourse frequently treats rigor as a fixed curricular attribute, an objective measure of challenge. Participants\u0026rsquo; accounts complicate this assumption. Rigor was experienced as temporal pressure, cognitive saturation, and emotional regulation. Yet whether that rigor was interpreted as empowering or alienating depended heavily on relational and pedagogical conditions.\u003c/p\u003e \u003cp\u003eTeachers functioned as interpretive anchors. When instruction included modeling, relational care, revision opportunities, and normalized error, difficulty was narrated as productive. When pacing was rushed or relational signals were thin, similar content demands were experienced as isolating. Peers also mediated rigor. Collaborative environments reframed struggle as shared sense-making (Lave \u0026amp; Wenger, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Boaler, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). In contrast, peer ridicule or competition amplified vulnerability even when achievement remained high.\u003c/p\u003e \u003cp\u003eThese findings reinforce phenomenological accounts of difficulty as lived and embodied (van Manen, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1990\u003c/span\u003e). Rigor is not merely what is taught; it is how difficulty is experienced within social worlds. For mathematics educators, this has direct implications. If rigor is relational, then preparing teachers involves more than content knowledge and task design. It involves preparing teachers to cultivate interpretive environments where struggle is framed as growth rather than deficiency. Without this mediation, advanced coursework may unintentionally narrow belonging even among high-achieving students.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec45\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Non-Continuation as Agentic Discernment\u003c/h2\u003e \u003cp\u003ePerhaps the most significant contribution of this study lies in reframing non-STEM trajectories. Participants did not narrate their decisions as being pushed out. Instead, many described AP Calculus as providing clarity about what they valued and how they wished to live their education. They distinguished between:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e\u0026ldquo;I can do this.\u0026rdquo;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e\u0026ldquo;I want this.\u0026rdquo;\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis distinction echoes expectancy\u0026ndash;value theory\u0026rsquo;s emphasis on subjective task value (Eccles \u0026amp; Wigfield, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) yet extends it hermeneutically. Understanding emerged after the experience, not during it. Autobiographical writing often captured stress residue and relief, while interviews revealed reclaimed agency and reopened possibility. Meaning unfolded temporally, consistent with Gadamer\u0026rsquo;s (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1975\u003c/span\u003e/2004) account of understanding as historically situated. From this perspective, labeling these students as \u0026ldquo;leakage\u0026rdquo; mischaracterizes their trajectories. They did not exit due to incapacity, but redirected from a position of demonstrated capability. This challenges deficit models that equate persistence with success and departure with failure (Cannady et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). For mathematics education research, this suggests the need to examine not only who persists, but how students interpret participation itself.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec46\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Implications for Mathematics Teacher Education\u003c/h2\u003e \u003cp\u003eIf AP Calculus is a meaning-making crucible rather than a deterministic filter, what does this mean for teacher education? Three implications follow.\u003c/p\u003e \u003cdiv id=\"Sec47\" class=\"Section3\"\u003e \u003ch2\u003e5.4.1 Reframing Success Beyond Continuation\u003c/h2\u003e \u003cp\u003eTeacher preparation programs should explicitly interrogate the assumption that advanced mathematics exists primarily to produce STEM majors. When AP Calculus is framed solely as a gateway, students who choose alternative pathways may interpret themselves as deviations from a normative trajectory. Teacher educators can instead prepare teachers to frame AP Calculus as:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAn intellectual encounter with powerful ideas\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eA site for learning how to struggle productively\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAn opportunity for identity exploration\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eA credential of capability independent of future major\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eSuch framing expands success beyond continuation and aligns with broader humanistic purposes of mathematics education (Wenger, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec48\" class=\"Section3\"\u003e \u003ch2\u003e5.4.2 Preparing Teachers to Mediate Rigor Relationally\u003c/h2\u003e \u003cp\u003eGiven that rigor was experienced as relational and interpretive, teacher education must foreground:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eHow classroom discourse signals belonging\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eHow pacing shapes interpretation of struggle\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eHow public comparison and speed norms affect identity\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eHow revision structures reframe error\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003ePreparing teachers to notice and intentionally design these relational conditions may prevent advanced mathematics from becoming unintentionally alienating, even for capable students. Rigor need not be softened; it must be mediated.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec49\" class=\"Section3\"\u003e \u003ch2\u003e5.4.3. Supporting Agency in Postsecondary Advising Narratives\u003c/h2\u003e \u003cp\u003eMathematics teacher education often intersects with advising cultures that implicitly equate AP success with STEM obligation. Teacher educators can help future teachers recognize that students may use AP Calculus to clarify what they do \u003cem\u003enot\u003c/em\u003e wish to pursue, and that this clarification is educationally legitimate. Affirming multiple post-AP trajectories, including humanities, business, arts, and interdisciplinary fields, honors students\u0026rsquo; agency without diminishing mathematical accomplishment. An equity-oriented stance requires not only access to advanced mathematics but autonomy in interpreting its meaning.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec50\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Contributions to Mathematics Education Research\u003c/h2\u003e \u003cp\u003eThis study contributes to mathematics education scholarship in four primary ways. First, it challenges deficit framings of STEM leakage by accentuating interpretive agency. Second, it reconceptualizes AP Calculus as a sense-making site rather than solely a gatekeeping mechanism. Third, it advances the construct of competence without identification, offering a theoretical distinction between achievement and disciplinary belonging. Fourth, methodologically, it demonstrates how integrating mathematical autobiographies with hermeneutic phenomenology surfaces temporal shifts in meaning that cross-sectional or quantitative approaches may overlook. By centering lived experience and retrospective interpretation, this study expands how researchers might conceptualize advanced mathematics participation beyond enrollment and persistence metrics.\u003c/p\u003e \u003c/div\u003e"},{"header":"6.0 Conclusion: Listening to Students Who Succeeded and Still Chose Otherwise","content":"\u003cp\u003eAP Calculus is a powerful educational experience. It affirms competence, confers symbolic capital, and signals academic distinction. Yet it is fundamentally non-deterministic. Participants in this study did not fail Calculus. They succeeded. And then, from that position of success, some chose differently. Listening to these students reframes the question from \u0026ldquo;How do we prevent leakage?\u0026rdquo; to \u0026ldquo;How do students interpret what participation means?\u0026rdquo; When mathematics education attends to that question, success becomes broader, more humane, and more aligned with identity coherence rather than institutional expectation. AP Calculus, then, need not be defended as a flawless pipeline mechanism. It can instead be understood as a formative space where students encounter challenge, renegotiate identity, and author futures, in STEM or beyond.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eThe author did not receive any funding support from any organization for the submitted work.\u003c/p\u003e\n\u003cp\u003eData Availability Statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003eEthics Approval and Consent to Participate\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eKennesaw State University Ethics Approval\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eApproval for the research conducted by Kennesaw State University\u0026rsquo;s Office of Research and Research Compliance. This office follows the The Federal Wide Assurance (FWA) granted by the Department of Health and Human Service\u0026apos;s (DHHS) Office for Human Research Protections (OHRP). It is the only type of assurance of compliance accepted and approved by OHRP for institutions engaged in non-Exempt human subjects research conducted or supported by DHHS. Under an FWA, an institution commits to DHHS that it will comply with the requirements set forth in 45 CFR Part 46, as well as the Terms of Assurance.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eBerry College Ethics Approval\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAdditional approval was receive by the Berry College Institutional Review Board Institutional Review Board for Human Subjects Research (IRB), which is charged with reviewing all research activities involving human subjects, in compliance with the Code of Federal Regulations, Title 45, Part 46. All research involving human participants must be submitted for review by the IRB, and must be approved before initiating any research activities. By definition, research is \u0026ldquo;any systematic investigation, including research development, testing, and evaluation, designed to develop or contribute to generalizable knowledge.\u0026rdquo; (45 CRF 46.102d). To ensure compliance with federal regulations, researchers must follow the Berry College [policy on human subjects research]. Those who fail to follow this policy may receive up to a one-year suspension of all research activities from the IRB.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eConsent to Participate\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eFor all research involving human participants, informed consent to participate in the study was obtained from participants that was signed by both the participant and researcher, with one copy for the participant and one copy for the researcher. All participants were anonymized as to not trace back individual participants to any identifiable characteristics, and consent to publish is not necessary. IRB Approval given by both Berry College, where the participants were students resided, and at Kennesaw State University, where the researcher is employed. Ethical requirements are under the guidelines of the IRBs of both Berry College and Kennesaw State University to ensure compliance with federal regulations follow the Berry College and Kennesaw State University policies on human subject research.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eDeclarations\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eEthical approval\u003c/u\u003e: Ethical approval has been obtained from Kennesaw State University Kennesaw State University\u0026rsquo;s Office of Research and Research Compliance under Federal Wide Assurance under the U.S. Department of Health and Human Services. Ethical approval was also obtained from Berry College\u0026rsquo;s Institutional Review Board under Federal Wide Assurance under the U.S. Department of Health and Human Services.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eConsent to participate:\u003c/u\u003e All participants have signed agreements with consent to participate and remove themselves at any time.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eConsent to publish:\u003c/u\u003e All participants have signed agreements with consent that any data learned from the study may be published with anonymized results as to mask each participant\u0026rsquo;s identity.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAdiredja, A., \u0026amp; Louie, N. (2020). Untangling the web of deficit discourses in mathematics education. \u003cem\u003eFor the Learning of Mathematics, 40\u003c/em\u003e(1), 42-46. https://www.jstor.org/stable/27091140 \u003c/li\u003e\n\u003cli\u003eAhmed, S. (2004). 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The practice of phenomenology: The case of Max van Manen. \u003cem\u003eNursing Philosophy, 20\u003c/em\u003e(2), e12276. https://doi.org/10.1111/nup.12276 \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-education","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"diedu","sideBox":"Learn more about [Discover Education](https://www.springer.com/journal/44217)","snPcode":"44217","submissionUrl":"https://submission.nature.com/new-submission/44217/3","title":"Discover Education","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"AP Calculus, mathematics teacher education, hermeneutic phenomenology, mathematical identity, rigor, STEM persistence","lastPublishedDoi":"10.21203/rs.3.rs-9044668/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9044668/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAP Calculus is widely positioned as a gateway to STEM, yet many students who earn qualifying scores do not continue into STEM majors. This qualitative hermeneutic phenomenological study examines how eight first- and second-year undergraduates (AP Calculus score\u0026thinsp;\u0026ge;\u0026thinsp;3) made sense of AP Calculus while choosing non-STEM pathways. Drawing on mathematical autobiographies and in-depth interviews, findings present AP Calculus as a meaning-laden transition point where students negotiated competence, belonging, and future participation. Three integrated themes emerged: (1) AP Calculus calibrated mathematical identity\u0026mdash;students affirmed capability while distinguishing competence from identification; (2) rigor was lived as relational and temporal, mediated by teacher practices, peer norms, and pacing; and (3) non-continuation functioned as agentic alignment rather than \u0026ldquo;leakage,\u0026rdquo; with students using Calculus success to clarify values and coherent futures. 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