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Axolotl Data*

Critical Essay · 2025 Qiyun Wang

This week's readings did not arrive to me as an "encounter" in the usual sense. No. More precisely: they arrived as a crime scene. The sentences I had written in my week-one response were already waiting there, like an uninvited detective. I should clarify first that what I'm about to discuss is actually a research question and model currently being developed in my other course this semester, linear regression. The word "linear" is worth lingering on for a moment. I keep thinking that nothing in the world is truly linear, not even time, though we pretend otherwise out of courtesy. But I find myself increasingly unable to think about statistical modeling without invoking the critical frameworks I have been building in this class. The dialogue between these two fields has become so deeply intertwined that I am no longer sure whether that's a problem or precisely the point.

This week's ethnographic material centers on Ms. Q, whose empathy operates not as something infinitely divisible, but according to a hidden geometry, one visible in the stark fact that 99% of her students are Black while the Child Study Team is entirely white. I don't know how to model that, but I suspect anyone who tries will have to confront a prior question: when the variables themselves carry the weight of history, what does residual mean?† The students are quietly displaced to the back of the classroom. I see them in my mind, though I have never seen them. That itself is either one of ethnography's miracles or one of its debts. These accounts provide the moral urgency and theoretical scaffolding for my regression design. To formalize these disparities, I use the Early Childhood Longitudinal Study, Kindergarten Class (ECLS-K), tracking early schooling through cognitive and behavioral assessments, teacher evaluations, and school-level structural factors. It offers the empirical terrain to investigate how the "punitive gaze" manifests within large-scale longitudinal trajectories.

The SAT score comparisons in the material struck me most. Andre and Jimmy, the two Black students categorized as "behavioral problems," scored in only the 2nd percentile for reading, yet received no sympathy, no "learning frustration" framing, and no medicalized exemptions. In contrast, Juan scored at the 25th percentile in reading and Francisco at the 17th, but their classroom friction was interpreted as learning disability frustration, earning them leniency never extended to the Black students whose academic needs were measurably greater. This inversion is more than a moral scandal. In statistical terms, race is associated with both teacher perceptions and interpretive opportunities, shaping observed relationships in ways that cannot be read as neutral. To focus solely on high-stakes testing, however, is to mistake the symptom for the pathology. The architecture of exclusion is not built in high school; its foundation is poured in the early years, camouflaged as developmental evaluation. Farkas (1990) originally demonstrated that teachers assign lower ratings to minoritized students based on habits, dress, and compliance even when controlling for cognitive scores. Yet his later work (Farkas, 2003; Farkas & Beron, 2004) was mobilized in "gap" literatures that invite the deficit-leaning framings his early findings should have preempted (Buckingham et al., 2013; Hindman et al., 2016). This echoes what Allen and Spencer (2022) describe as the racialized governance of behavioral norms. Constructs like "self-control" operate as culturally loaded proxies that recode conformity to white middle-class norms as evidence of competence. This is the fissure my research attempts to formalize. I conceptualize the "punitive teacher gaze" as the systematic divergence between objective cognitive scores and subjective behavioral ratings. I operationalize this by regressing the ARS against the DCCS and treating the residual not as a fully purified gaze, but as the portion of the teacher rating unexplained by measured cognitive performance and included controls. I then enter this divergence into the primary model, interacted with race. This follows Lavy (2008) and echoes Hinnant (2009), with the goal of testing whether negative divergence in teacher perception carries a structurally magnified penalty for minoritized children. However, I am concerned that two-stage residual extraction may invite generated-regressor complications for inference (Pagan, 1984). I am therefore considering a single-equation alternative. By fully specifying DCCS×Race alongside ARS×Race, the model may isolate a racially differentiated association between teacher ratings and outcomes net of cognitive performance within a single coefficient. I would welcome your pushback on whether this maneuver captures the divergence with greater inferential clarity, or risks burying the sociological friction I am trying to describe.

Readings on hyper-segregated school contexts have pushed me to deepen my second research question. It asks whether the reading growth trajectories of high-risk minoritized students deviate from their white peers by the end of first grade and to what extent structural deprivation drives this deviation. My HLM models individual growth trajectories at the student level. It then asks at the school level how these slopes vary with racial composition and resource scarcity. Crucially, I borrow the methodological architecture of Fish (2019) to examine whether the school context moderates the relationship between student race and growth trajectory. Fish demonstrated that school racial composition rarely exerts a universal effect. Instead, it interacts specifically with student race to dictate institutional sorting. This cross-level interaction forms the theoretical heart of my model. It tests whether the deceleration in reading growth is an inherent attribute of Black students or a structural amplification produced by hyper-segregated schools. In Berlant's terms, this is a slow death written into a slope. Fish convinced me that school context must operate as an active moderator rather than a passive background variable. I remain less certain how to operationalize school segregation itself. A continuous variable captures gradations but may mask threshold effects. A binary cutoff is theoretically clearer yet feels arbitrary. A composite index combining racial composition, poverty rates, and teacher turnover might be more honest. However, it increases interpretative difficulty and raises concerns regarding multicollinearity.

The third insight concerns a more insidious operation: the erasure of the denominator. One of the special education teachers who took solace in a 50/50 racial split among students labeled with learning disabilities was not observing equity. In reality, she was ignoring the fact that Black students made up only 17 percent of the school's total population. This is precisely why measures of relative risk exist: to forcibly make the suppressed denominator visible. My third research question seeks to operationalize this reversal by dragging those structural proportions back into the analytic frame. It asks whether traditional deficit predictors like the home literacy environment lose their explanatory power over first grade reading scores once behavioral self-control is re-situated within its subjective measurement context and structural inequalities are controlled. To test this, I plan to design a blocked hierarchical regression. Block 1 will include traditional "deficit" predictors such as SES, home literacy, and family structure. Block 2 will then introduce the institutional mechanisms formalized in my prior models, including the cognitive and behavioral divergence terms capturing the punitive gaze and the segregation metrics from the growth models. The inferential target is not significance theater, but reallocation. If the coefficients for Block 1 attenuate after Block 2 enters, this pattern is consistent with the possibility that so called deficit predictors were partially proxying for omitted structural processes. At the same time, I will not treat attenuation or loss of significance as uniquely diagnostic of misspecification, since it can also reflect collinearity, changes in precision, or measurement error in the Block 1 constructs. For that reason, I plan to pair coefficient shifts with model level evidence such as incremental R² and information criteria comparisons, and, if feasible, relative importance metrics that quantify how much explanatory share is carried by the structural block versus the deficit block. I would greatly appreciate your guidance on whether this is the most defensible way to formalize the claim, and on what diagnostics you would want to see to distinguish genuine proxying for institutional processes from a mere loss of precision due to collinearity. The goal is to show, in measurable terms, whether explanatory power that appears to belong to the home is in fact borrowed from the institution once the institutional denominator is made visible.

When viewing the three research questions together, I harbor a broader concern. Has the critical framework truly permeated the model design or is it merely a theoretical label pasted onto a traditional regression? This week's readings made me feel more clearly than ever that the project has a central claim: special education disproportionality is manufactured by institutional architecture rather than individual deficit. I want the quantitative design to carry this argument as a whole rather than in fragments. In this sense, I am trying to build a "reverse panopticon" where the spotlight of judgment no longer falls on the child's self-control, but on the institutional gaze of the educational apparatus itself.

References

* Inspired by Cortázar's Axolotl, finished just days before this response. Like the story's total inversion of observer and observed, this paper seeks an ontological flip: to transform the "objects" of data back into subjects who gaze at the system that categorized them.

† See Lucretius, De Rerum Natura, II. Atoms falling in parallel lines create only a "world of nothing" — the sterile monotony of the linear regression. Existence requires the clinamen: a spontaneous swerve in the void. What the poet calls a swerve, we politely call the "residual" (e).