Basic Degrees and the Common Basic Cycle

• Basic degrees are shared foundational curricula in engineering and sciences that serve as differential filters rather than uniform gateways.
• Longitudinal analysis reveals significant drop-out variations, with subject-level failures in early mathematics amplifying the risk.
• Multi-major enrollment acts as an adaptive exploration strategy that correlates with improved progression compared to single-major tracks.

Basic degrees in engineering and exact sciences are often organized around a Common Basic Cycle (CBC), a shared initial stage intended to function as a neutral levelling mechanism before entry into upper-cycle specialization. Longitudinal evidence from a Faculty of Engineering and Exact Sciences indicates that this characterization is misleading: across 24,017 entrants observed over twenty years, the CBC operates not as a uniform gateway but as a strongly differential filter, with outcomes that vary sharply by destination major, by subject-level failure patterns, and by the possibility of enrolling in more than one major during the CBC (Paz, 3 Dec 2025).

1. Common Basic Cycle as an institutional form

In the studied setting, the CBC is the segment of the curriculum defined through subjects with year level $\leq 1$. It is formally shared by several degree programmes in engineering and exact sciences, which encourages an interpretation of the CBC as a common academic foyer in which students acquire foundational knowledge before diverging into distinct professional and disciplinary tracks. The empirical record, however, shows that this shared formal structure does not imply uniform effects across programmes (Paz, 3 Dec 2025).

The central analytic distinction is between a neutral foundational stage and a differential filter. The evidence supports the second description. Outcomes are not stable across programmes or over time, and the same curricular space produces substantially different probabilities of upper-cycle progression and CBC drop-out depending on the targeted degree. This suggests that a “common” curricular architecture can remain institutionally unified while functioning as a structurally differentiated sorting mechanism.

A recurring misconception is that the CBC equalizes incoming heterogeneity in preparation and therefore should be evaluated only in aggregate. The findings contradict that view. Aggregate indicators obscure sharp between-program differences, especially between traditional engineering degrees and shorter or more applied programmes.

2. Data and analytical framework

The underlying study reconstructs trajectories from twenty years of longitudinal administrative records for 24,017 entrants. For each trajectory, it identifies CBC subjects, destination major, time to exit from the CBC, and final outcome, classified as progression to upper cycle, drop-out, or right-censoring (Paz, 3 Dec 2025).

The analysis combines several complementary statistical procedures. Transition matrices are used to quantify three-year outcome probabilities by destination major and by pre/post-2006 cohorts. Kaplan-Meier survival curves estimate the probability of remaining in the CBC over time, measured in months after entry and stratified by destination major. Stratified Cox proportional hazards models evaluate how early performance variables affect time to CBC exit while allowing different baseline hazards by major. Subject-level logistic models estimate the odds of drop-out after failure in specific subjects, incorporating major-specific interactions and controls.

The Cox specification is given as

$$h_i(t) = h_{0, g(i)}(t) \exp(\beta_1 X_{1i} + \beta_2 X_{2i} + \cdots),$$

where $h_i(t)$ is the hazard of exit from the CBC at time $t$ for student $i$, $h_{0,g(i)}(t)$ is the baseline hazard specific to destination major $g(i)$, $X_{1i}, X_{2i}$ are covariates such as CBC pass rate, grades, and the number of subjects passed in the first year, and $\beta_j$ are estimated effect parameters.

The subject-level drop-out model is written as

$$\log \left( \frac{P(\text{Dropout}=1)}{P(\text{Dropout}=0)} \right) = \alpha + \beta_1 \cdot \mathbf{1}(\text{FailSubject}=1) + \beta_2 \cdot \text{Major} + \beta_3 \cdot (\text{FailSubject} \times \text{Major}) + \text{Controls}.$$

Here the outcome is drop-out versus progression or censoring, the key predictor is failing a subject at least once, and the controls include CBC pass rate, mean grade, and entry year.

These methods are extended with multi-major enrolment data and with a pre/post-2006 curriculum reform comparison. Methodologically, the design is notable because it links programme-level sorting, time-to-event dynamics, and subject-level failure effects within a single longitudinal framework.

3. Differential filtering across majors

The most direct evidence of differential filtering appears in progression and drop-out probabilities. Overall drop-out during the CBC exceeds 60%, and after the 2006 reform the probability of progressing to the upper cycle in the same major ranges from about 0.20 to 0.70 across programmes (Paz, 3 Dec 2025).

Transition matrices show that progression to the upper cycle in the same major varies from roughly 20% in shorter programmes to more than 50% in some engineering degrees. Shorter or applied degrees show the harshest filtering, with drop-outs up to 80%. Kaplan-Meier curves further indicate a rapid decline in CBC retention within the first 18–30 months, and most students either progress or drop out within about two years. The shape and position of the survival curves differ by major: more permeable engineering degrees have faster, more successful exits, whereas applied or shorter degrees exhibit steeper early drop-out.

The following post-2006 outcomes are reported as illustrative:

Major	CBC Dropout (%)	Progression to Upper Cycle (Same Major) (%)
Ingeniería Industrial	52.3	~48
Ingeniería en Computación	75.8	~24
Programador Universitario	76.5	~23
Ingeniería Eléctrica	60.0	~40
Ingeniería Electrónica	67.2	~33

The stratified Cox results reinforce this pattern. Each additional CBC subject passed in the first year increases the hazard of exit, interpreted here as faster progression, and higher CBC GPA also predicts faster, more successful exits. Because the baseline hazard is stratified by destination major, these effects are estimated against programme-specific temporal dynamics rather than an assumed common exit process.

The broader significance is that “shared entry” does not imply shared risk. A plausible implication is that curricular commonality and institutional openness at admission can coexist with deeply unequal progression structures once subject sequencing, assessment patterns, and programme-specific tolerances are taken into account.

4. Early mathematics as a structural bottleneck

Introductory Calculus, Algebra, and Analytic Geometry emerge as structural bottlenecks in the CBC. Their global pass rates are below 40% for the whole faculty, and failing these subjects at least once is associated with a 2–3× higher hazard of drop-out in the survival and logistic analyses (Paz, 3 Dec 2025).

The study characterizes these mathematics modules as structural rather than merely difficult. They combine low pass rates with strong downstream consequences for persistence. In the logistic models, failing mathematics modules increases drop-out odds 2–4 fold, with the largest impact in shorter or applied degrees. Severity is not homogeneous across programmes: pass rates in these modules exceed 80–90% in traditional engineering degrees classified as more permeable, but can be below 40% in shorter or more applied degrees classified as selective or exclusionary.

The paper also identifies “sentinel subjects,” defined operationally through major-specific logistic effects whose failure almost guarantees drop-out in some programmes. Examples include “Representación Gráfica” in Tech Lighting and “Cálculo I” for University Programmer, with odds ratios on the order of ~4–8. This indicates that the same formal CBC includes subjects that behave differently depending on the degree trajectory to which they are attached.

The finding has a substantive implication beyond local pedagogy. Early mathematics acts as a structural amplifier of risk: it does not merely register prior preparation but reorganizes the probability of continuation in programme-specific ways. This suggests that curricular bottlenecks should be analyzed jointly through pass rates and post-failure transition risks rather than through pass rates alone.

5. Multi-major trajectories and adaptive exploration

Between 10% and 15% of students enrolled in two or more majors during the CBC. This pattern is often treated administratively as indecision, yet the observed outcome structure points in the opposite direction: single-major students have the highest drop-out, at about 64%, whereas those enrolled in two or more majors have substantially lower drop-out, around 47%, together with higher progression rates (Paz, 3 Dec 2025).

Drop-out decreases as the number of enrolled majors increases. The study therefore interprets multi-major enrolment as adaptive exploration rather than indecision. Students who can re-route among alternatives appear better able to withstand programme-specific bottlenecks, especially when their initial major corresponds to a structurally fragile starting choice.

This result is important because it shifts the interpretation of flexibility. Administrative systems frequently code movement across majors as noise, lack of commitment, or failed preference formation. The longitudinal evidence instead portrays multi-major enrolment as a resilience mechanism. A plausible implication is that institutional flexibility in programme affiliation can partially offset the sorting pressure produced by bottleneck subjects and highly selective progression structures.

The point is not that all exploration is beneficial in itself, but that the opportunity to explore alternative majors changes the risk environment of the CBC. In that sense, flexibility is not external to academic success; it is part of the architecture through which success or attrition is produced.

6. The 2006 reform and implications for programme design

The pre/post-2006 comparison shows that filtering intensifies after the curriculum reform. CBC drop-out rises post-2006, and progression to the upper cycle falls by 10–20 percentage points in most programmes, even though the filtering profiles remain sharply differentiated by major (Paz, 3 Dec 2025).

This persistence matters analytically. It indicates that curricular restructuring did not eliminate the programme-specific mechanisms through which the CBC sorts students. Instead, those mechanisms remained stable enough to preserve major-specific filtering profiles while producing harsher aggregate outcomes. The reform therefore appears to have altered intensity more than structure.

Several policy implications follow directly from the evidence. CBC performance should be analyzed at the programme and subject level rather than only in aggregate. Early mathematics should be treated as a structural amplifier of risk rather than as a neutral screening device. Multi-major flexibility should be supported rather than discouraged. Targeted interventions are needed at curricular points where the hazard of drop-out spikes, including academic support and revised assessment at bottleneck subjects.

Taken together, these results redefine the CBC within exact sciences and engineering degrees. Rather than a neutral initial platform, it is a structured sorting device whose consequences depend sharply on the targeted degree and on the institutional availability of alternative trajectories.