A framework to assess the impact of matriculation requirements on academic performance

Predicting academic performance is a critical concern for educators, policymakers and institutions worldwide. With the increasing demand for higher education and the diversification of student populations, accurately forecasting student success has become more complex yet essential. Effective prediction models can enhance educational outcomes by enabling timely interventions, tailored support and informed admission decisions.

Historically, researchers have explored various factors influencing academic performance in higher education, such as language proficiency, socio-demographic variables and prior academic achievements. For instance, Stephen, Welman, and Jordaan (2004) investigated the impact of English language proficiency on the academic success of first-year students, identifying multiple inhibiting factors such as cultural influences and language skills. Similarly, Osmanbegovic and Suljic (2012) applied data mining techniques to predict academic success, emphasizing the importance of socio-demographic factors and high school achievements in developing predictive models. These studies highlight the multifaceted nature of academic performance and the need for comprehensive models that consider a wide range of variables.

Further research has delved into the role of entry qualifications and their correlation with university-level performance. Amasuomo (2014) compared the academic achievements of students with different entry certificates in Nigeria, revealing significant disparities based on entry qualifications. Thiele et al. (2016) expanded this investigation by examining the influence of socio-economic status and school type on academic outcomes, advocating for the inclusion of contextual data in university admissions. These findings underscore the limitations of traditional admission criteria and the potential benefits of incorporating additional contextual factors to ensure fair access and support for students.

The debate over standardized admission tests and their predictive validity has also been a focal point in recent studies. Sulphey, Al-Kahtani, and Syed (2018) analyzed the relationship between admission grades and academic success among business students in Saudi Arabia, confirming a strong correlation between high school grade point average (GPA), standardized test scores and future academic achievement. Similarly, Alamoudi et al. (2021) examined the correlation between admission exam scores and academic performance in health science programs, highlighting the need for tailored preparatory tracks to enhance student outcomes. These studies illustrate the ongoing need to refine admission criteria and consider alternative metrics to better predict and support student success.

Similar to the regions above, a complex mix of individual and demographic factors influences academic performance in the Caribbean. Gender consistently stands out, with females generally outperforming males in primary assessments and most subjects (Bailey, 2004; Kutnick et al., 1997; Kutnick & Jules, 1988). Interestingly, males who remain in the system tend to excel in science and technology (Bailey, 2004). Another key factor is socio-economic status. Students from higher socio-economic backgrounds tend to have an advantage in participation and performance (Bailey, 2004). In fact, socio-economic status, poverty and social class are frequently more strongly linked to educational outcomes than gender, with privileged boys sometimes outperforming less privileged girls (Cobbett & Younger, 2012; Kutnick et al., 1997).

Apart from personal traits, in the Caribbean, there are various institutional and environmental factors that also influence academic achievement. Specifically, school type is a dominating factor. Generally, single-sex, private or church-run institutions generally yield better results than coeducational or state-run schools (Cobbett & Younger, 2012; Kutnick et al., 1997; Kutnick & Jules, 1988). School locality also impacts performance, as urban areas often see better outcomes than rural ones (Cobbett & Younger, 2012; De Lisle, 2006; Kutnick & Jules, 1988). External factors such as home socialization practices, financial constraints and community or school violence also contribute to male “under-performance” (Bailey, 2004).

Based on these challenges, this paper seeks to investigate the following questions: (1) What impact does individual matriculation requirements have on student placement and academic success? (2) How can removing traditional matriculation requirements maximize enrollment and reduce mismatch issues in student admissions? Specifically, it proposes a personalized recommender system to optimize student placement and improve academic outcomes. It also discusses how departments can remove traditional matriculation requirements by leveraging a novel regression algorithm. The proposed approach aims to match applicants with suitable disciplines based on their entry grades, thereby maximizing enrollment and reducing mismatch issues. This personalized approach not only enhances the accuracy of predictions but also ensures a fair and transparent admission process, ultimately contributing to a more supportive and effective educational environment.

This paper is organized as follows: Section 2 reviews related work on predicting academic performance, highlighting key studies and their findings. Section 3 presents the proposed recommender system, detailing its methodology and potential benefits. Subsequent sections discuss the implementation, evaluation and implications of the proposed system. This paper seeks to advance the understanding of academic performance prediction and contribute to the development of more effective educational strategies and systems.

This section gives a summary of studies conducted on predicting academic performance globally. These summaries aim to highlight the impact that different contextual variables have on predicting academic performance across various regions, cultures and educational settings. Stephen et al. (2004) investigated the impact of English language proficiency on the academic success of first-year Black and Indian students in human resources management at a tertiary institution. Rural environment, school teacher English proficiency, cultural influences, learning and memorizing strategies, problems regarding verbal comprehension, problems regarding transferability of language skills, problems regarding reading proficiency and problems related to written English were the factors that impacted English language proficiency.

The work done by Osmanbegovic and Suljic (2012) explored the application of data mining techniques to predict academic success among first-year students at the University of Tuzla’s Faculty of Economics. The study compares various methods of data mining to develop a predictive model for students' success, using data collected from surveys during the summer session of the academic year 2010–2011, alongside enrollment data. Factors such as socio-demographic variables, high school achievements, entrance examination scores and attitudes towards studying were investigated. Three supervised data mining algorithms were employed to predict course success, with the Naïve Bayes classifier outperforming decision tree and neural network methods. The study emphasizes the importance of developing accurate and comprehensible models for professors. Although conducted in traditional classroom settings, the methodology holds promise for improving student performance and reducing failure rates through timely interventions. Key questions for future research include the user-friendliness of predictive models for non-expert users and the integration of university data collection systems with data mining tools. Future work could expand the experiment with more attributes for enhanced accuracy and explore additional data mining algorithms for broader insights. The review highlights the potential for using diverse software and factors to refine predictive models and improve student learning outcomes.

Amasuomo (2014) studied the academic performance levels of two distinct groups of students enrolled in the Nigeria Certificate in Education (NCE) Technical Program, differing in their entry certificates. The research focused on 70 first-year technical students at the Federal College of Education (Technical), Omoku, during the 2011–2012 academic year. Raw scores from five courses were collected and analyzed using arithmetic means and a t-test, with the reliability of the t-test results confirmed through an f-test of group variances. The findings of the study revealed a significant disparity in academic performance between students with secondary school certificates and those with City and Guilds certificates. Moreover, notable differences were observed in various facets of academic achievement between the two groups. This underscores the potential influence of entry certificate type on academic outcomes within the NCE technical program.

Following this, Thiele, Singleton, Pope, and Stanistreet (2016) investigated the relationship between various background characteristics and academic achievement at a British university. It explores how school qualifications, socio-economic status, school type and demographic factors influence students' academic performance. Findings indicate that while school grades are important predictors of academic potential, contextual factors such as socio-economic deprivation and school type also play significant roles. The study advocates for the inclusion of contextual data alongside traditional school grades in the admissions process to ensure fair access to higher education and improve student outcomes. The study underscores the importance of considering contextual factors in university admissions to address limitations associated with relying solely on examination marks. By identifying students whose academic potential may not be fully reflected in their school qualifications, universities can better support them to succeed in higher education. Moreover, integrating contextual data into admissions processes can enhance fairness and inclusivity, ultimately improving the overall student experience and academic attainment levels. Further research is needed to inform evidence-based policies that promote equitable access to higher education and support students in realizing their full potential.

Sulphey et al. (2018) noted that the use of standardized admission tests in college admissions has long been a topic of debate. Supporters cite predictive validity, and critics highlight concerns about fairness and the impact on educational systems. While such tests are widely used globally, including in the USA, where they face criticism for perceived biases and inequities, their efficacy remains under scrutiny. This study examines the relationship between admission grades and academic achievement among business students in Saudi Arabia, filling a gap in the literature. Findings indicate a strong correlation between high school GPA, standardized test scores and future academic success. The study underscores the importance of considering both academic performance and standardized test scores in college admissions. Furthermore, it suggests the need for ongoing research to refine admission criteria and address dropout rates, with potential areas of study including re-enrollment strategies and the implementation of e-learning platforms to enhance educational outcomes.

Alamoudi et al. (2021) explored the correlation between admission exam scores and preparatory year GPA with academic performance in basic science subjects in health science colleges at King Abdulaziz University. The research encompassed four cohort studies from nursing and clinical nutrition programs. Results reveal weak correlations between admission exam scores and academic achievement in clinical biochemistry and clinical pharmacology. However, a significant positive correlation was found between the two subjects. The findings suggest a need to reevaluate admission criteria and consider tailored preparatory year tracks for health science students. The study emphasizes the importance of continuously assessing and developing admission criteria for health science colleges, particularly amidst increasing applicant numbers and evolving teaching methodologies. The weak correlations between admission examination scores and academic performance underscore the need for reevaluation. Tailored preparatory year tracks could better equip students with the specific skills and knowledge necessary for success in health science programs. Further research is warranted to refine admission criteria and ensure optimal student outcomes in health science education at King Abdulaziz University.

In 2021, Aciro et al. (2021) investigated the relationship between pre-university academic achievements and university-level performance, drawing on a systematic review of 53 relevant articles primarily from America and Europe, with limited representation from Asia, Latin America and Africa. Findings reveal varying correlations between entry grades and academic outcomes, with some studies indicating positive, negative or mixed associations, while others suggest gender differences. The review underscores the lack of consensus regarding the predictive value of pre-university academic performance on university success, highlighting the need for further research to inform admission criteria and policies at the undergraduate and graduate levels globally. This literature review examines the relationship between entry grades and university academic performance, highlighting positive, negative and mixed correlations identified in existing research. Additionally, it underscores significant gaps and weaknesses in current university admission criteria, emphasizing the need for attention from stakeholders, educational planners and policymakers. The review also addresses contradictory findings regarding gender's impact on academic performance, emphasizing the necessity for evidence-based studies to inform admission policies for undergraduate and graduate programs worldwide. Recommendations from such research have the potential to enhance admission practices and improve student outcomes globally.

Barroso, Cainday, Sedon, and Tilanduca (2022) concluded that in order to predict academic success, college admission tests and high school GPA are essential requirements for admission to both board and non-board programs. But not for the board course; the high school strand may have an impact on an individual's academic achievement in the non-board course. Based on a quantitative analysis of 286 respondents – 153 from the board course program and 133 from the non-board course program – this conclusion was drawn. Furthermore, results indicated a moderate correlation between students' high school GPA and their college academic achievement in the non-board course Bachelor of Science in Information Technology (BSIT). A similar association was found between the variables on the college admission test and GPA. In the meantime, Bachelor of Science in Electrical Engineering (BSEE), admission exams and high school GPA were indicators of future academic success for the board course.

In the context of the Caribbean, Anderson, Devonish, Bailey, and Daley (2014) analyzed undergraduate admissions to the University of the West Indies (Mona) between 1983 and 2010. They examined the relationship between student characteristics and their impact on academic performance. Their study highlighted that uneven academic performance was something associated with variables such as age, gender, urban-rural residence, registration status (part-time or full-time), previous schooling and faculty. Specifically, Anderson et al. (2014) found that social class and geographic location significantly influenced access to tertiary education, with notable disparities observed in enrollment rates across different income levels and regions. Another issue observed was a significant change in the age structure towards a younger student population. Thus, they concluded that there is a need for enhanced support services to foster broader academic success among a diverse student body.

Browne and Shen (2017) studied the challenges associated with low output and the availability of higher education institutions in the Eastern Caribbean. They found that factors affecting higher education in this region include accessibility, location, quality of education, institutional costs and graduate unemployment. Although access to higher education has increased significantly due to technological advancements, globalization and reduced travel costs, several challenges persist. Specifically, these include insufficient funding, low government revenues and increased privatization. These issues, coupled with high tuition fees, brain drain and a mismatch between educational output and labor market needs, contribute to low student performance and high dropout rates. Additionally, they proposed that a lack of a strong research culture and limited highly qualified human resources further hinder academic performance and overall educational development in the region.

In the Caribbean, most higher education institutions rely heavily on the Caribbean Examinations Council (CXC) grades for matriculation. Griffith (2017) discussed how these institutions can enhance quality assurance by adopting an outcomes-based model that prioritizes the student experience, drawing lessons from the CXC. Based on the CXC's practices, the key variables affecting academic performance are clearly defined educational standards and learning outcomes in syllabi, effective teaching enabled by pedagogical guidance, teacher training and accessible resources and rigorous assessment procedures featuring standardized marking and detailed feedback to students and teachers. Collectively, these elements contribute to improved student preparation and achievement of expected outcomes. Although Griffith (2017) doesn't explicitly state a direct statistical correlation between specific CXC grades and university GPA, his report emphasizes that CXC's quality assurance mechanisms in its examinations prepare students for higher education, which implies that students with good CXC performance should have a smoother academic progression at the university level.

In summary, the literature shows that many researchers are interested in investigating the factors that influence academic performance. It also highlights that both globally and within the Caribbean, in all educational settings, there are many variables (academic and non-academic), which can influence academic performance. Which subset of these variables is best suited for algorithms predicting academic performance is a complex and vital area of study. Generally, departments in higher education within the Caribbean base their matriculation requirements on academic variables they believe are the best indicator of a candidate's readiness to pursue a degree. However, such requirements introduce two challenges. Firstly, they limit the size of a department cohort, which impacts the potential to earn revenue from paying students. Secondly, a department may unintentionally mismatch applicants with degree options if they do not monitor the influence of matriculation requirements on graduating GPAs closely. Both scenarios result in frustrated students and staff and reduce the department's average graduating GPA and throughput. Therefore, there is a need for a continuous monitoring framework that can quantify the impact that entry requirements have on academic performance over time. This quantification enables personalized recommendations that are likely to be mutually beneficial to both faculty and students.

This section proposes a personalized recommender system in response to the challenges identified in Section 2. Using this system, a department can counteract the reduced cohort size and unintentional student-degree mismatch issues. To illustrate the key ideas, let us consider the fictional case of an idealistic Faculty of Innovation and Digital Transformation (FIDT).

Let’s suppose that the FIDT removes all its matriculation requirements from all departments and matches applicants to departments with help from a recommender system instead. This approach allows departments to consider enrollment from all applicants, maximizing their respective cohorts and revenues. The challenge for FIDT now shifts to accurately matching its applicants to a suitable department using the recommender system. For each applicant, the system must rank all departments by the expected graduating GPA based on the applicant's entry grades. These personalized rankings will solve any mismatch issues.

For transparency, the system must quantify the influence that any entry grade will likely have on an applicant's graduating GPA for any department. With this level of detail, the FIDT's staff can meaningfully advise applicants on making their final choice of department, ensuring a fair and transparent process. This process maximizes the FIDT's fairness to departments and applicants by enrolling students into departments where they are likely to excel, thereby enhancing the overall academic environment.

Another advantage of this quantification is monitoring influence. As more applicants with a specific entry subject enroll, the FIDT can detect whether the subject's influence on graduating GPAs changes. These alerts allow the FIDT to react proactively when factors outside of its control affect students' success.

A key challenge for this recommender system is data quality. The previously used matriculation requirements would have skewed the entry grades and graduating GPAs dataset available to the system. If a department receives a traditional applicant (who matches the traditional matriculation requirements), the recommender system has enough historical data to make a robust and personalized prediction. However, if it is a new type of applicant (who does not match the traditional departmental requirements), the recommender system must estimate a personalized GPA based on how similar applicants performed. This notation of similarity is essential for this recommender system. Otherwise, the best prediction would be the simple average of that department's graduating GPAs. This data quality issue will become less significant as the department's dataset diversifies. This diversification may take a few years since the number of applicants enrolling is typically higher than the number of students graduating annually. Hence, even with a personalized ranking, the FIDT would still need to provide some advising sessions to applicants before they make their final choice. Figure 1 summarizes the FIDT's new workflow.

In this study, we utilized a recent novel regression algorithm proposed by Hosein (2023) to quantify the level of personalization each entry subject has on graduating GPA prediction. This algorithm can quantify the robustness vs personalization tradeoff and works well with small datasets. Also, other studies by Gooljar, Manohar, and Hosein (2023), Manohar, Manohar, and Hosein (2023), Moore, Baboolal, and Hosein (2023), Harrykissoon, Persaud, Manohar, and Hosein (2023) and Manohar and Hosein (2023) demonstrated that this algorithm performs well with various datasets and improves the performance of popular clustering, classification and regression algorithms.

The key idea of Hosein's algorithm is to express every prediction as a weighted average using non-linear weights. Every prediction is robust because it utilizes information from every training sample. Every prediction is personalized because the non-linear weights can effectively capture the similarity between every sample. The hyperparameter κ determines the level of personalization.

To better explain the value of κ, suppose that we have an input sample x. When κ = 0, every sample is considered identical to x, all the non-linear weights are 1, and the prediction becomes the simple average over all samples, which is robust but not personalized. When κ = ∞, only samples that match x's input features have a weight of 1. The algorithm assigns a weight of 0 to all other samples, and the prediction becomes the simple average of only those samples that are identical to x, which is personalized but not necessarily robust. When κ is some value other than these extremes, the algorithm's weighted average computation exploits samples in the neighborhood of x. The nearer the sample, the closer the non-linear weight is to one. This computation helps in cases where a class has a few samples, but there are samples in its neighborhood, which can help improve the prediction's robustness at a small cost to personalization. The higher the κ, the better the personalization. Features with some influence will have a κ value that reduces the prediction error compared to when κ = 0.

We selected this algorithm because it simplifies the measurement of an entry subject's value in predicting graduating GPAs. Specifically, we compared the product of the normalized prediction error and normalized κ values. Products closer to 1 maximize the probability that the entry subject improves prediction accuracy and personalization. For example, if two subjects offer similar reductions in GPAs, the subject with a higher κ value is better. Similarly, if both subjects match in personalization, the subject with the lower prediction error adds more value. Notably, a product of 0 does not necessarily mean the entry subject is unimportant. It just means that this algorithm could not extract any value from the subject's grade.

An even distribution across all samples is ideal for any entry subject. When 50% of the samples have the subject and 50% do not, the mean graduating GPAs are robust, and their absolute difference, Δμ, quantifies the subject's impact on graduating GPA. Thus, for every entry subject, we have four concerns – the graduating GPA prediction error, the level of personalization κ, Δμ the absolute difference in the means of graduating GPAs with and without the entry subject and how robust these means are.

We combined these objectives into a single score by generating four scores for each concern and taking their product. Each score measures an entry's subject similarity to the ideal case, with a value between 0 and 1. The prediction error score divides the mean absolute error (MAE) for a specific κ by the MAE when κ = 0 (MAE_κ = 0). The personalization score divides the κ value by κ_max = 30 (the largest κ used in our experiments). The Δμ score divides Δμ by 4.3 (the maximum difference in GPA). The sample size score compares the entry subject's distribution to a 50–50 split. The score is 1 when exactly half the samples have a grade for the subject and 0 when all or none do. Otherwise, it scales linearly based on how many more or fewer samples have a grade for the entry subject. Intuitively, a product of 1 implies that all four objectives are fully satisfied, while a product of 0 implies that at least one objective is not satisfied.

The dataset used in this study contains 1,114 samples of applicants' entry grades and graduating GPAs from 5 departments in a Caribbean university. Table 1 shows the distribution across departments A through E. These applicants' entry subjects and grades are further distributed across 31 Caribbean Advanced Proficiency Examination (CAPE) subjects, each with 2 units for 62 possible entry grades. A typical applicant from the dataset has grades for both units of four to six CAPE subjects. Each department's entry grade distribution was highly skewed to its matriculation requirements. Table 2 illustrates this by listing the eight most popular entry subjects by department.

In our first set of experiments, we investigated the impact individual entry subject grades have on academic performance. These experiments used a randomized 80–20 train-test split and computed the optimal κ_opt ∈ [0, 30]. Table 3 lists the top 10 entry subjects for all departments according to our score. The experimental data presented in Table 3 and Figure 2 suggest that our score was an effective mechanism to balance the four concerns identified in Section 3.

For example, consider the top two entry subjects for department A, Pure Mathematics Units 1 and 2, with scores of 1617 × 10⁻⁶ and 1238.653 × 10⁻⁶, respectively. Unit 1 achieved better κ_opt and NMAE values, while Unit 2 achieved an ideal 50–50 distribution and a better Δμ value. These values show that Unit 1 is more useful for prediction accuracy, while Unit 2 is better for quantifying academic performance between groups with and without the subjects. In this case, our score ranked Unit 2 as better because the gain in quantifying academic performance outweighed the gain in predicting it.

Another interesting observation for Department A is the scores for Chemistry Unit 1 and Applied Mathematics Unit 2. The NMAE for applied mathematics is close to one, which says that we could not extract any useful information from this subject to help with prediction accuracy. However, the Δμ values suggest that the GPAs of graduating students, with and without either subject, are significantly better for applied mathematics. Since the dataset only has 38 and 42 grades for the applied mathematics and chemistry subjects, respectively, we do not know how reliable these Δμ′s are because both subjects’ distributions are far from the ideal 50–50 distribution. Based on the current dataset, chemistry is the better choice for Department A because it has four more samples, and its information is more useful for reducing prediction errors. Curious cases like this, which require more samples, can be monitored over time as the dataset grows and entry subject scores begin to shift.

Table 3 shows that for each department, the most impactful entry subjects are different. For example, Biology Unit 2 is in the top ten entry subjects for Departments B, C and E but not others. Results like these demonstrate that the algorithm can extract the most relevant entry-level subjects for departments that have different areas of focus and expertise. The data in Table 3 indicate that pure mathematics is universally important, regardless of the departmental focus. This observation is interesting because not every department has mathematics as a key area of focus or listed in their matriculation requirements. Table 3 suggests that applicants weak in or missing pure mathematics would be mismatched to Departments A through E, if they do not also have one or more of the other impactful subjects.

Another benefit of scoring entry subjects is monitoring for changes over time. For example, currently, Biology Unit 2 is the most important entry subject for Department B but is not in the top 10 entry subjects for Departments A and D. Table 3 shows that biology is the second most influential subject across all graduates from all faculties. Therefore, over time, if more students with grades in Biology Unit 2 do well in Departments A and D, their scores will be updated and move Biology Unit 2 up in the rankings.

The value of a specific entry subject to both department and applicant can be estimated from the experimental results. Consider the example of Biology Unit 2. Based on the current dataset, it is difficult for Department A to decide if an applicant with Biology Unit 2 is a good match. According to Table 4, on average, graduates with biology from Department A performed better than those without it. However, this observation is not robust because only 21 graduates had Biology Unit 2 grades. However, if the department considers the academic performance of all 438 graduates with biology across all departments, it can obtain a robust prediction for the Δμ on average. This value indicates that on average, a person's graduating GPA with biology is expected to be higher than someone without it by 0.058. Table 5 estimates the graduating GPA of applicants from Department A, who enter with a specific grade in CAPE Biology. Together, these results quantify the expected value of biology to the department and student better than the simple average of 21 samples. Specifically, on average, an applicant with biology is expected to graduate with a GPA of 3.368 from any department. Therefore, Department A would need to carefully consider applicants with biology grades of 2 or lower since they are predicted to perform on average closer to an applicant without biology from any department. Careful consideration is required because enrolling such students into Department A may potentially be unfair to both faculty and students.

A typical graduate would usually have grades that reflect three areas of focus. In our next experiment, we demonstrate how departments can quantify the potential impact of various entry subject combinations on graduating GPA. Table 6 compares the impact of popular combinations like mathematics, physics and chemistry and mathematics, physics and applied mathematics, with less popular mathematics, biology and applied mathematics and mathematics, physics and biology. These results indicate the more mathematics an applicant has on entry, the better for their graduating GPA, regardless of department. This observation is consistent with the impact of single-entry subjects in Table 3, where pure mathematics and applied mathematics were in the top 10 subjects for every department and 3 of 5 departments, respectively. Another interesting result is the pairing of biology with other subjects. On average, applicants who have biology are expected to perform better if they do more mathematics. However, at the departmental level, this may not be the case. For example, for Departments A and B, it is better if biology is paired with physics instead of applied mathematics, whereas for Departments C and D, more mathematics with biology is better. The associated score with the combinations also gives faculty a level of confidence in the recommendations. For example, in Department A, we are more confident about pairing biology with physics instead of applied mathematics since the scores are 91.7 × 10⁻⁶ and 22.0 × 10⁻⁶, respectively, than in Department B, where both combinations are predicted to have the same impact with scores of 350.9 × 10⁻⁶ and 344.0 × 10⁻⁶, respectively.

Most departmental matriculation requirements specify entry subjects and a minimum grade. For example, consider that Department A specified all applicants must have a grade of one in at least one CAPE science subject. The mean graduating GPA of students who did not satisfy this exact rule is 3.34 across all departments. Table 7 illustrates how this criterion may not be fair to every applicant. Consider the results for κ = 15. Department A can expect an applicant, Alice, who achieved grade ones in all subjects, to graduate with a GPA higher than 3.34. These predictions indicate that her entry grades were beneficial to her in the context of that department. In contrast, the department would expect an applicant, Bob, who achieved grade ones in all subjects except for his grade three in the Pure Mathematics Unit 2, to perform close to average. Bob's entry grades do not seem to benefit him in this department, because on average, Bob is likely to graduate with the same GPA as someone who does not have this combination. In this example, both applicants satisfied the matriculation requirement, but Bob would be better advised to enroll in a department where he is expected to perform above average with his current entry grades. It is possible that Bob's entry grades do not distinguish him in any department. In this case, if he does enroll in Department A, there should be some type of intervention by the department to bridge the predicted 0.19 GPA gap between Bob and Alice. Suppose Bob had achieved his grade of three in Pure Mathematics Unit 1 instead of Unit 2. Department A can expect Bob to perform better than average. This scenario illustrates that a higher grade in Unit 2 is more beneficial to applicants. Performing a similar type of analysis with more entry subjects and grade combinations, departments can better understand the impact their matriculation requirements have on a student's graduating GPAs.

In the above scenario, we reemphasize that it is ultimately Bob's decision whether to choose Department A or not. The benefit here is that now both Bob and Department A can utilize the recommendation system to make informed decisions based on the predicted GPAs. Since removing the traditional matriculation requirements gives both Bob and Department A more access to programs and students, respectively, both parties must carefully weigh these predictions against other predictors of academic performance, which the model does not currently capture, e.g. applicant interest, full-time versus part-time students, educational background, etc.

Failure to consider other predictors of academic performance could lead to a stratification system. In this extreme scenario, departments would only accept applicants who score above a certain threshold. This policy would reduce access instead of increasing it, as departments will now deny applicants whom they would traditionally accept because they scored below the threshold. Naturally, a question of fairness arises. For example, suppose a science, technology, engineering and mathematics (STEM) department sets a very high threshold. Although it increases the likelihood that all accepted applicants will graduate with above-average GPAs, it denies those who did not perform well in STEM classes the opportunity to advance further in the STEM field. Is it fair for a department to accept students, knowing it cannot adequately support them based on its allocated resources? Also, is it fair to deny a highly motivated STEM student an opportunity to grow? These are complex issues that require future study.

A more balanced approach involves both applicants and the departments utilizing the system's scores to take proactive actions. Departments can utilize an aggregate version of Table 7 to quantify the impact of lowering thresholds and understand the amount and type of supporting resources that need to be acquired and deployed to ensure student success. Similarly, students can also understand how much more effort is required and in what subject areas to fill in the gaps.

In this paper, we presented a framework that uses a recommender system for enrollment. Specifically, this system must be able to quantify the level of personalization and impact each entry subject grade and combinations has on an applicant's success in specific departments. The prediction error, personalization score, difference in means with and without the entry subject and subject distribution are all factors that affect the confidence of a recommendation. We proposed a scoring metric to combine these concerns into a score between 0 and 1, where one represents the ideal case. Our score allows the algorithm to rank eligible departments in a way that is fair.

We demonstrated the effectiveness of our approach with a dataset of 1,114 samples from a Caribbean university across 5 departments. The experimental results scored the influence individual CAPE subjects and popular subject combinations have on the graduating GPA of students. We demonstrated how the system can compare an applicant's estimated graduating GPA for a department to the average graduating GPA of applicants who do not match its entry subjects. This comparison allowed us to score departments by likelihood of success based on an individual applicant's entry grades. Thus, instead of allowing applicants who meet matriculation requirements to enroll in a department where they are likely to perform just as well as someone without their entry grades, we can recommend placement in departments where they are likely to excel instead. This type of personalized placement is the key to a university maximizing departmental revenue and its students' academic performance.

In the future, we would like to extend our experiments to more departments and faculties. Other areas of interesting work are refining the score to reflect individual departmental preferences and formalizing the matching problem as an optimization problem to maximize student preferences, departmental enrollment and the likelihood of students' academic success. Also expanding the feature set to capture student motivation would enhance the quality of our scores.