This study developed and evaluated a Machine Learning classification model for early detection of academic risk in the development of projective spatial thinking. Academic and sociodemographic variables from 153 students in basic and secondary education were analyzed using a Gradient Boosting Classifier algorithm. The model was trained to identify predictors of low performance and classify students according to their risk level. The results showed a good predictive performance (ROC AUC = 0.866). We conclude that the classification system is an efective tool for teachers, facilitating proactive identification of at-risk students and enabling the design of early, personalized pedagogical interventions to strengthen this fundamental cognitive skill.
The development of spatial thinking is a fundamental cognitive skill for academic success in various
disciplines; however, there is evidence of persistent low performance in this area among primary and
secondary school students [
Faced with this challenge, Educational Data Mining and Machine Learning (ML) techniques emerge
as a powerful approach, capable of analyzing large datasets to identify patterns and make predictions
[
The development of models capable of early detecting students at risk of low performance has
proven to be an efective application for predicting dropout and student success. Building on this,
the present article addresses a gap in the literature by detailing the development and evaluation of a
Machine Learning classification model specifically designed for the early detection of academic risk
in the development of the projective space of spatial thinking. The study’s objective is to answer the
following research question: To what extent do sociodemographic and academic variables, analyzed
with Machine Learning techniques, allow for the prediction of risk in the development of projective
spatial thinking [
This paper is structured as follows. Section 2 describes the theoretical framework related to this study. Section 3 presents the methodology used to develop the work. Section 4 explains the results obtained from the work. Section 5 presents a discussion of the most insightful elements. Section 6 presents the future work. Some recommendations are ofered in section 7. Finally, Section 8 concludes the work.
Spatial thinking is defined as the set of cognitive processes through which an individual mentally
constructs, represents, and manipulates objects in space, as well as their relationships and transformations
[
The Piagetian theory, which underpins this study, distinguishes a hierarchy in the development of
spatial relations, each with direct implications for the student’s capacity for abstraction:
• Topological Relations: These constitute the first understanding of space, focused on qualitative
properties such as proximity, separation, order, and enclosure. At this stage, the child understands
basic concepts of the object itself, without yet considering metrics or external perspectives [
This cognitive development does not occur in a vacuum; it is profoundly influenced by the student’s physical, social, and cultural environment. The quality of pedagogical strategies and the richness of interactive experiences with the environment are decisive for the student to successfully transition through these stages.
The prediction of academic performance is a complex task due to the multiplicity of factors that afect
it, from the family environment to pedagogical strategies. Educational Data Mining (EDM) emerges as
a research field that applies computational methods to explore large volumes of educational data and
discover patterns that would otherwise remain hidden [
Within EDM, Machine Learning (ML) ofers a set of techniques for building predictive models from
data [
To ensure a systematic and reproducible process, this research adopted the CRISP-DM (Cross-Industry
Standard Process for Data Mining) methodological framework [
The phases of CRISP-DM, followed in this work, are: 1. Business Understanding, where the objectives are defined 2. Data Understanding, for an initial exploratory analysis 3. Data Preparation, which includes cleaning and transformation 4. Modeling, where ML algorithms are selected and trained 5. Evaluation, to measure the model’s performance 6. Deployment, which involves integrating the model into a functional system
This research adopted a quantitative, correlational approach with the objective of determining the relationship between academic and sociodemographic variables and the prediction of performance in projective spatial thinking. The entire analysis and modeling process was structured following the CRISP-DM (Cross-Industry Standard Process for Data Mining) methodological framework. Figure 2 visually summarizes the complete workflow, from data collection to the final evaluation of the model.
The study was conducted at the Institución Educativa Departamental General Carlos Albán, located in Albán, Cundinamarca (Colombia). The total population consisted of 599 students from urban and rural sectors. For this research, a non-probabilistic convenience sample of 153 students who voluntarily participated during the 2019 academic year was selected. The sample was distributed across the eighth, ninth, tenth, and eleventh grades, with ages ranging from 12 to 18 years.
• Mock Test: A 15-question spatial reasoning test, adapted from the 2010 entrance examination of the National University of Colombia, was administered. This instrument was designed to assess the students’ level of development in projective space.
• Sociodemographic Factors Survey: A survey composed of 33 groups of questions was designed and administered to characterize the sociodemographic conditions of the students. The survey variables were based on the dictionary of associated factors from the Colombian Institute for the Evaluation of Education (ICFES).
The data processing and the construction of the predictive model were carried out in several stages, using the Python programming language and specialized libraries such as Pandas, Scikit-learn, and PyMC3. 3.3.1. Data Preparation The initial dataset, composed of 119 variables, underwent an exploratory analysis. Missing values were imputed using the mean for numerical data and the mode for categorical data. Given the limited size of the original sample, a statistical simulation based on the Monte Carlo method was applied to generate a more robust synthetic dataset, preserving the original distributions of the variables. 3.3.2. Feature Selection To optimize the model’s performance and avoid overfitting, a feature selection process was carried out. A Random Forest Classifier algorithm was used to evaluate and rank the predictive importance of each variable. A final subset of 63 variables was selected, which together explained 95% of the model’s predictive capacity, a practice recommended in the literature for optimizing classifiers. 3.3.3. Model Building and Evaluation Several supervised classification algorithms were evaluated, with the Gradient Boosting Classifier ofering the best performance for this problem. The dataset was split into a training set (80%) and a test set (20%) to validate the model. The final performance was measured using the ROC (Receiver Operating Characteristic) curve and the area under it (AUC), a standard metric for evaluating the discriminative ability of a binary classifier.
The administration of the mock test to the sample of 153 students revealed a widespread low performance
in the development of projective spatial thinking. The results indicated that a high percentage of students
across all evaluated grades fell into the "Low Level" category. Specifically, it was found that 88% of
eighthgrade students, 76% of ninth-grade, 98% of tenth-grade, and 84% of eleventh-grade students obtained
an insuficient score. These findings empirically validated the existence of a significant educational
problem in the area of study and provided the baseline performance data for training the model [
To build a robust model, a feature importance analysis was first conducted to identify the variables with the greatest predictive power. As shown in Figure 3, the most influential variables were not academic but rather sociodemographic and related to personal habits. The top five predictors were the time the student spends reading, the number of siblings, the number of people in the household, the time spent browsing the internet, and the Sisbén score.
Subsequently, four classification algorithms were evaluated to select the most suitable one. Table 1 summarizes the performance of each. The Gradient Boosting Classifier was selected as the final model due to its superior performance (AUC of 0.86) on the test dataset.
The final Gradient Boosting Classifier model was optimized by tuning its hyperparameters, determining that 100 estimators ofered the best balance between performance and overfitting (see Figure 4). The ifnal evaluation of the optimized model yielded an AUC = 0.86, as observed in the ROC Curve in Figure 5, confirming a high discriminatory power.
The confusion matrix (Figure 6) details this performance on the 5060 samples of the test set. The model correctly identified 1626 students at risk (True Positives) and 2354 students not at risk (True Negatives). The classification report (Table 2) summarizes the key metrics, highlighting a Recall of 0.71 for the "Risk" class and an overall Accuracy of 79%.
The results of this research demonstrate that it is feasible to predict the risk of academic performance in projective spatial thinking with a high degree of certainty (AUC = 0.86) using a Machine Learning model. Beyond the technical validation of the model, the findings ofer a deep insight into the factors that modulate cognitive development in primary and secondary school students.
A first significant finding emerges when contrasting the students’ low performance on the diagnostic
test with Piaget’s theoretical framework [
The model’s feature importance analysis (Figure 3) strongly reinforces this idea. The model did not
identify previous grades as the strongest predictors, but rather sociodemographic variables and personal
habits such as time spent reading, the number of people in the household, and the Sisbén score. This
result aligns with studies that have demonstrated the profound influence of cultural and economic
capital on academic performance [
Finally, the model’s performance as a classification tool has direct practical implications for teaching.
The classifier’s ability to identify students "At Risk" (Recall = 0.71) and those "Not at Risk" (Recall = 0.85),
as detailed in Table 2, makes it an efective early warning system [
It is essential to acknowledge a methodological limitation of this study: the use of synthetic data generated from a small original sample to achieve suficient volume for model training. Although this technique allowed for the construction of a robust classifier and the validation of the hypothesis, it introduces a potential bias, as the generated data inherits the characteristics and distribution of the initial sample.
Therefore, while the model has shown high potential, the generalization of these results should be considered with caution. The reproducibility of the use case in other populations or educational contexts will require empirical validation with a larger and more diverse organic dataset. Future lines of research should focus on applying and retraining this model with data collected on a larger scale to confirm and expand upon the findings presented here.
Based on the findings and limitations identified, the following recommendations are proposed:
• Prioritize Organic Data in Future Iterations: The most important recommendation is that
future replications of this study prioritize the use of non-synthetic data. To validate and generalize
the findings, it is essential to train and test the model on a larger and more diverse organic dataset,
thereby eliminating the bias inherent in the simulation technique used.
• Adopt a "Data Culture": It is recommended that educational institutions foster an organizational
culture that values data as a strategic asset. This involves the systematic and ethical collection of
information to use predictive models like the one presented here and thus design personalized
and proactive pedagogical strategies.
• Deepen Causal Analysis: Future research should go beyond prediction and delve into the causal
analysis of the most influential variables. Understanding why "time spent reading" is such a
strong predictor, for example, could generate valuable pedagogical knowledge.
• Integration into Educational Systems: Work should be done to integrate the predictive model
into an interactive module within school information systems (SIS) or learning management
systems (LMS). This would allow teachers and counselors to consult risk predictions in real-time,
transforming the model from a research artifact into a daily support tool for decision-making
[
This study afirmatively answers the research question, demonstrating that the application of Machine Learning techniques is an efective tool for predicting the risk of academic performance in the development of projective spatial thinking. The classification model validated the hypothesis that sociodemographic variables and personal habits are highly significant predictors. However, it is imperative to contextualize these good results, acknowledging that they were achieved using a dataset augmented through synthetic simulation. While this was a necessary methodological strategy for the analysis in this use case due to the small size of the original sample, it introduces a potential bias that must be considered.
Therefore, it is also concluded that the success of such projects depends on robust interdisciplinary collaboration, where education experts guide the interpretation of the context and technical results. The model should not be seen as an end in itself, but as a starting point for deeper inquiry.
Finally, it is crucial to address the ethical dimension raised by the high predictive power of socioeconomic variables, such as the Sisbén score. While efective for the model, their uncritical use risks reinforcing systemic biases and potentially stigmatizing students from vulnerable backgrounds. Therefore, it is emphatically concluded that the model must not be used as an automatic labeling tool. Instead, it should function as an early warning system that serves as a starting point for a teacher’s inquiry. Its role is to complement, not replace, the professional judgment of the educator, who provides the indispensable human context and understanding required for any fair and efective intervention.