Deep learning-based model for predicting student learning behavior: A pathway to early intervention and enhanced outcomes

Abstract

In the realm of educational data science, the utilization of advanced analytical techniques is increasingly pivotal for optimizing pedagogical methods and implementing early interventions. This study introduces a predictive model employing deep learning technology for the analysis of student learning behavior. The model’s primary objective is to detect potential learning impediments at nascent stages, thereby facilitating timely and effective educational strategies to augment learning outcomes. Despite strides in behavioral prediction, challenges persist due to the dynamic and complex nature of educational data. Addressing these challenges, the proposed model integrates sequence pattern recognition with time-series analysis. The application of the PrefixSpan algorithm initiates the process, identifying sequential patterns in student learning behaviors and elucidating their temporal progression. Subsequently, an advanced ordered funnel analysis algorithm is employed, unveiling directional associations among diverse learning patterns. The final phase involves applying independent component analysis (ICA) to enhance the multi-layer long short-term memory (Multi-LSTM) network’s structure, thus enabling precise predictions of student outcomes in the context of early interventions. The results underscore the efficacy of deep learning in deciphering intricate behavioral patterns and underscore its potential in personalized educational interventions. This comprehensive approach demonstrates the model’s capacity to harness the intricacies of educational data, thereby contributing significantly to the field of personalized education and precise teaching methodologies. The innovative aspect of this study lies in the comprehensive application of the PrefixSpan algorithm, the ordered funnel analysis algorithm, and the Multi-LSTM network architecture. A holistic model for predicting student learning behavior is proposed, coupled with early interventions, which enables educators to better understand student learning conditions and implement effective measures to enhance student learning outcomes.

Keywords

deep learning student learning behavior sequence pattern recognition ordered funnel analysis multi-layer long short-term memory network early intervention learning outcome prediction

Introduction

The advent of sophisticated educational technologies has ushered in an era where data on student learning behaviors are increasingly recognized as invaluable for educational research.^1,2 These data, encapsulating students’ learning habits, provide insights into multifaceted patterns prevalent in the educational process.^3–5 In this context, deep learning emerges as a robust tool for data analysis, capable of extracting profound insights from voluminous data related to student learning behaviors. Such insights are imperative for the formulation of personalized teaching strategies and the implementation of early intervention measures.^6–8 Nonetheless, the effective prediction of students’ learning outcomes and the timely execution of interventions require an in-depth understanding of the intricacies and dynamics inherent in student behavior.

The prediction of student learning behavior not only facilitates personalized learning experiences but also aids educators in pinpointing potential challenges in pedagogy. This capability enables the prompt adaptation of teaching methods and content to suit evolving educational needs.^2,9 Central to enhancing student learning outcomes is the concept of early intervention. Such interventions, by providing requisite support during the learning process, mitigate frustration and thereby augment learning efficiency and performance.^10,11 In light of these considerations, the development of a precise model for predicting student learning behavior represents a critical endeavor in the field of educational research.

Prevailing approaches to predicting learning behavior have predominantly concentrated on static data analysis, thereby neglecting the temporal aspects and the dynamic progression of student behavior patterns.^12,13 Additionally, conventional analytical methods often struggle to interpret complex data structures, thus limiting their effectiveness in forecasting student learning trajectories and outcomes.^14–18 Consequently, it is imperative to develop a predictive model that holistically integrates sequence patterns and dynamic variations.

The objective of this study is to introduce a comprehensive predictive model for student learning behavior, utilizing the capabilities of deep learning technology. The initial phase involves deploying technology based on the PrefixSpan algorithm to discern sequential patterns in student learning behaviors, thereby accurately tracing their temporal development. This is followed by the application of an advanced ordered funnel analysis algorithm, aimed at investigating the directed associations among student learning patterns and uncovering the underlying linkages between different learning behaviors. The final phase amalgamates ICA with the Multi-LSTM network architecture, facilitating the prediction of student learning effectiveness in the context of early intervention. This research not only addresses the deficiencies of existing methodologies but also provides educators and policymakers with a novel perspective. It enables the scientific monitoring, analysis, and intervention of the learning process, ultimately contributing to the enhancement of educational quality and student learning outcomes.

The impact of this study on educational practice is reflected in the insights provided by the model, which guide teachers in targeted early interventions. By analyzing patterns and trends in student learning behavior, teachers can promptly identify potential learning difficulties and implement personalized intervention measures. This enhances student learning outcomes and the quality of education, thereby rendering educational practices more targeted and effective.

Sequence pattern recognition in student learning behavior

In this study, the focus is placed on identifying sequence patterns in student learning behavior utilizing the PrefixSpan algorithm, a technique renowned for its proficiency in sequence pattern mining. The application of the PrefixSpan algorithm is instrumental in handling extensive datasets and extracting frequent patterns, thereby enabling the extraction of valuable insights from substantial educational data. The algorithmic process involves initially utilizing the PrefixSpan algorithm to identify sequential patterns in student learning behavior, capturing the temporal variations in student actions. Subsequently, an enhanced ordered funnel analysis algorithm is employed to explore the directed associations among student learning patterns, revealing the intrinsic connections between different learning behaviors. Finally, the Multi-LSTM network architecture, incorporating ICA, is applied to predict student learning outcomes under early intervention.

The process of mining frequent sequence patterns from student learning behavior data involves initially pinpointing single items that satisfy a predefined support threshold, which are essentially prefixes of length 1. These items constitute the foundation for the construction of more extended sequence patterns. Support is defined as the frequency of occurrence of a specific pattern within the entire dataset, and a pattern is deemed frequent only if it appears at a rate higher than the predetermined minimum support threshold. Practically, this translates to the algorithm assessing the occurrence frequency of each potential behavior (such as reviewing materials or submitting assignments) across all student behavior sequences. Behaviors exceeding the minimum support threshold are then selected as the starting points for the formation of frequent sequences. Figure 1 delineates the prefixes of length 1 and their corresponding projected databases, elucidating the initial step in the pattern mining process. The model structure initially employs the PrefixSpan algorithm to identify sequential patterns of student learning behavior, capturing the temporal dynamics of student actions. Subsequently, an enhanced ordered funnel analysis algorithm is utilized to delve deeper into the directed associations among student learning patterns, unveiling the intrinsic links between various learning behaviors. Finally, through the integration of ICA with the Multi-LSTM network architecture, the model predicts student learning outcomes under early intervention, enabling comprehensive prediction and analysis of student learning behavior.

Figure 1.

Illustration of length-1 prefixes and their corresponding projected databases.

In the subsequent phase of this study, each identified frequent prefix undergoes analysis within its respective projected database to discern additional frequent patterns. Projected databases are defined as subsets of behavior sequences that encompass a specific prefix, which are subsequently utilized to explore potential behavior patterns succeeding the prefix. During this analysis, the algorithm examines all conceivable behaviors that might be appended to the current prefix in the projected database and evaluates the support of these augmented sequences. Sequences whose support levels surpass the established minimum threshold are classified as frequent and are incorporated into the collection of frequent sequence patterns. This iterative and recursive procedure is perpetuated until the identification of new frequent sequences ceases. Figure 2 illustrates the methodology of iteratively generating prefixes for each projected database, providing a visual representation of this analytical stage.

Figure 2.

Methodology for iterative generation of prefixes in projected databases.

Specific explanations and definitions were utilized for identifying sequence patterns in student learning behaviors, based on the PrefixSpan algorithm.

(a) Recursive mining principle

The recursive mining principle, integral to the PrefixSpan algorithm, was employed for the identification of sequence patterns in student learning behaviors. This principle involves analyzing a sequence pattern, which could be a series of learning activities performed by a student over a period. Such activities may include engaging in video lectures, completing quizzes, and participating in discussions. For a student learning behavior sequence pattern denoted as β with a length m, a set expression is established.

τ_{m + 1} = {α_{1}, α_{2} \dots α_{l}}

(1)

This expression includes all student learning behavior sequences of length m+1 that commence with the prefix x, as illustrated in:

α_{u}, \forall u = {1 \dots l}

(2)

The process of recursive mining initiates with the identification of frequently occurring items, essentially recognizing single behaviors that appear recurrently. Upon identifying these frequent items, they are utilized as prefixes. The algorithm then recursively searches for behavior sequences following each prefix, thereby constructing more extended frequent sequence patterns. This iterative method continues, with each iteration treating the present frequent sequence as a new prefix, until the discovery of further frequent extensions ceases. Consequently, this unveils the hierarchical structure of the complete learning behavior sequence pattern. Figure 3 provides an algorithmic flowchart demonstrating the PrefixSpan process.

(b) Projected databases

Figure 3.

Flowchart of the PrefixSpan algorithm process.

Projected databases are defined as specific subsets of the original database containing sequences with particular prefixes. Upon the algorithm’s identification of a frequent prefix, a corresponding projected database is constituted. This database encompasses only those behavior sequences from the original dataset that proceed following the identified prefix. The employment of projected databases enables the algorithm to concentrate on more compact data subsets for the detection of frequent patterns succeeding a specified prefix. For instance, let β represent a sequence pattern within the student learning behavior sequence database T. The collection of all suffixes relative to x for each sequence in T is delineated as the projected database for the prefix β.

Support within projected databases is characterized by the occurrence frequency of a specific sequence pattern within a particular projected database. This measure is contextualized against the support metric in the entire original database. The computation of support in projected databases facilitates a more expedient recognition of frequent behavior sequences that succeed a designated prefix. This is because the algorithm is required to consider only those sequences encompassing the prefix. For a given sequence pattern β in the student learning behavior sequence database T, let α denote a student learning behavior sequence prefixed by β.

T |_{β} = {ε_{1}, ε_{2} \dots ε_{l}}

(3)

Subsequently, the quantity of ε_u that α must fulfill within the projected database is expressed by SU_T|β(α):

α \subseteq β \cdot ε_{u}

(4)

(d) Characteristics of projected databases

The initial step involves the recursive creation of projected databases. This approach is crucial in ensuring that no frequent sequence patterns are overlooked during the step-by-step analysis. Each recursive stage builds upon the frequent patterns identified in the preceding step, thus maintaining the integrity of the mining process. Specifically, when considering sequence patterns in the sequence database T, denoted as β and α where β is a prefix of α, the following relationship is established:

T |_{α} = (T |_{β}) |_{α}

(5)

Moreover, when a pattern is identified as frequent within a projected database, it is not only frequent in that specific subset but also across the entire original database. This occurrence stems from the fact that the projected database is derived from the original database based on a particular prefix. Consequently, any pattern that is frequent in this subset also constitutes a frequent pattern in the original database beginning with that prefix. This is exemplified in the case of any sequence b that has the prefix β:

S U_{T} (ε) = S U_{T |_{β}} (ε)

(6)

Lastly, considering the nature of projected databases, each contains only the portion of the original database that includes a specific prefix. Therefore, the size of a projected database will never surpass that of the original database. As the recursive process advances, the size of the projected databases generally diminishes, enhancing the efficiency of the algorithm’s execution.

Exploration of directed associativity in student learning patterns

Subsequent to the identification of sequence patterns in student learning behavior, this study employs an advanced ordered funnel analysis algorithm to investigate the degree of directed associativity among learning patterns. This methodology uncovers the dynamic associative pathways and transition rules interlinking various student behaviors. Crucial behavioral transition points and learning bottlenecks are identified, offering targeted data support for educational interventions. Such interventions are instrumental in optimizing the allocation of learning resources, thus facilitating early intervention and personalized teaching approaches, ultimately leading to the enhancement of learning effectiveness and outcomes. Figure 4 delineates the flowchart of the advanced ordered funnel analysis algorithm, providing a visual representation of this analytical procedure.

Figure 4.

Flowchart of the advanced ordered funnel analysis algorithm.

A database comprising student learning behavior data is systematically assembled. The procedure involves documenting students’ interactions on educational platforms, which includes activities such as viewing instructional videos, engaging in discussions, and submitting assignments. These data constitute time-series information, cataloging the sequence and timestamps of the students’ behaviors. The structure of the behavior database thus compiled is represented by the following expression:

M = {t_{1}, t_{2}, \dots, t_{l}}

(7)

Furthermore, specific student learning behaviors that may potentially occur are articulated in the subsequent expression:

t_{u} \in M, \forall u = {1 \dots l}

(8)

Target sequences for learning behaviors are subsequently established. These sequences serve as benchmarks for funnel analysis, representing idealized or anticipated patterns of student learning behaviors. An example could be the progression of steps from the commencement of a course to the final examination, forming a target sequence. This sequence aids in juxtaposing actual student behavior data against it, thereby facilitating the identification of critical conversion points or areas of attrition. The structure of this target sequence is encapsulated in the following expression:

O \subseteq M

(9)

O = {x_{1}, x_{2}, \dots x_{j}}

(10)

A designated time window, referred to as s_WIN, is employed to record the longest sequences of student behaviors that are completed within it, correlating with the predefined target sequence O. This approach involves a comparison of the actual student behavior data against the target sequence. The process incorporates matching and pattern recognition techniques, aimed at identifying patterns within the actual student behavior data that correspond to the target sequence. It is posited that the longest sequence completed by a student within the specified time window is denoted by x₁∼x₄. Consequently, the sequences accomplished by the student are represented by x₁∼x₄, x₁∼x₃, x₁∼x₂, and x₁. The resultant dataset comprises all behavior patterns observed, each aligning with the target sequence to varying extents. This alignment is articulated as follows:

V = {v_{1}, v_{2}, \dots, v_{j}}

(11)

where the quantity of students completing the respective behavior sequence x₁∼x_u within s_WIN is delineated as:

v_{u}, \forall u = {1 \dots j}

(12)

In this component of the methodology, the focus is on determining the conversion rates, defined as the probability of students transitioning from one learning behavior to the next in a predetermined sequence. To ascertain these rates, a discrete analysis of each behavioral node is undertaken, establishing the frequency of student transitions from one node to the subsequent one. The entire student population is denoted by v₀. The collective conversion rate expression is formulated as follows:

E = {z_{1}, z_{2}, \dots z_{j}}

(13)

This collective data on conversion rates provide insights into the fluidity of students’ progression through the learning process, pinpointing stages of high efficiency in conversions and identifying potential areas of concern. The specific conversion rate from behavior x_u-1 to x_u is computed using the expression:

z_{u} = v_{u} / v_{u - 1} \times 100 %, \forall u = {1 \dots j}

(14)

Similarly, the rate of dropout transitioning from behavior x_u-1 to x_u is calculated as:

(1 - z_{u}) \times 100 %, \forall u = {1 \dots j}

(15)

Employing these calculations, a funnel model is constructed, facilitating the exploration of directed associativity in student learning patterns.

Predicting learning outcomes under early intervention in student learning behavior

In the pursuit of accurately predicting students’ future learning outcomes, this research has developed a predictive model that synergizes ICA with the Multi-LSTM network. The Multi-LSTM model is notably effective in processing and forecasting time-series data, while the ICA is instrumental in isolating pivotal features from intricate student learning behavior data. This integration amplifies computational efficiency and refines algorithmic precision. The ICA comprises two primary steps.

Step 1 involves determining the specific features or data dimensions for inclusion in the ICA. These features are typically aligned with aspects of student interactions, engagement levels, and assessment outcomes. It is posited that a l*v student learning behavior time-series matrix is denoted as A = [a₁,a₂,…,a_u…,a_l]^T. In this matrix, the vector representing the uth time series is a_u, where u ranges from 1 to l, and v denotes the length of a_u. A matrix encompassing overlaid learning behavior noise is designated as X_l*l = [x₁,x₂,…,x_u,…x_l]^T, while the matrix representing learning behavior data post-noise separation is ^TT_l*v = [t₁,t₂,…,t_u,…t_l]^T. Utilizing the ICA algorithm, matrix A is articulated as follows:

A = X T = \sum_{u = 1}^{l} x_{u} e_{u}

(16)

In the current research, the application of the ICA algorithm to preprocessed data results in the generation of a set of independent components (ICs). Each IC, being a linear combination of original data, offers insights into potential source signals or influencing factors. The restoration matrix, denoted as Q, facilitates the following computational process:

B = [b_{m}] = Q A

(17)

In the matrix B_l*v, vectors b_u represent the ICs, with B_l*v constituting the matrix of these components. The matrix T_l*v, symbolizing learning behavior data with reduced noise, is reconstructed when Q is set to X⁻¹, based on the formula:

B = Q A = Q • X • T = X X^{- 1} • T = T

(18)

The analysis of the derived ICs is conducted to ascertain the actual learning behaviors or characteristics each component may signify. For example, one component could be related to the distribution of learning time, while another might correlate with assignment submission frequency. The assumption of mutual independence between the components b_u is made when non-Gaussianity is exhibited by an IC b_u. A random Gaussian vector with the same covariance matrix as b, labeled as b_GA, allows for the measurement of b_u’s Gaussian properties through negentropy calculation:

K (b) = G (b_{G A}) - G (b)

(19)

During Step 2 of the methodology, the focus is placed on distinguishing components indicative of noise, such as elements irrelevant or of minimal impact on the prediction target. These components might originate from errors in data collection, random guesses, or activities unrelated to the target behavior. Noise-related components are excluded from the dataset. Subsequently, through the inverse process of ICA and employing the remaining relevant ICs along with the mixing matrix, a dataset with diminished noise is reconstructed. This refined dataset is expected to more precisely reflect those behavioral characteristics that are critical to student learning effectiveness. Assuming the dataset reconstructed with noise reduction is denoted by A^E = [a₁^E,a₂^E,…,A^E_l]^T, and the mixing matrix by X, where X = [x₁, x₂,…,x_l] = Q⁻¹, and considering b_u as the ICs post-noise filtering, the following relationship is established:

A^{E} = \sum_{1 \leq u \leq l}^{u \in T} x_{u} b_{u}, 1 \leq u \leq l

(20)

In the proposed methodology employing the Multi-LSTM predictive model based on ICA, the first step involves a comprehensive preprocessing of student learning behavior data.

Data pertaining to various student activities on learning platforms, such as frequency of logins, duration of study sessions, assignment submissions, and forum participation, are meticulously collected and organized. This process includes the essential tasks of outlier removal and imputation of missing values to maintain the reliability of the dataset. A careful selection of features is then conducted, focusing on those that are deemed most indicative of learning effectiveness. These may encompass time-series data and frequency information, among others. To mitigate any potential bias in the model due to variable scales, all features are normalized to a uniform range. This normalization ensures that no single feature unduly influences the model’s weight adjustments due to its scale. Consequently, five distinct data matrices are generated, each corresponding to a specific aspect of student behavior or performance. These matrices include X_KP, representing behavioral features of l students; X_ZG, depicting students’ grades; X_ZD, detailing social interactions; X_CP, illustrating resource usage; and X_CJ, capturing feedback from interventions. Each row within these matrices correlates to an individual student, while columns represent the time series of the respective input features.

X_{O P} = {[x_{1}, x_{2}, . . ., x_{u}, . . ., x_{l}]}^{S}

(21)

The behavior feature data matrix, denoted as X_OP and of dimensions l*v, encapsulates the behavioral trends of the student cohort. Here, l signifies the total number of students, and v represents the number of days over which learning behaviors are observed. The vector x_u embodies the temporal sequence of each student’s learning behavior features for the uth student (where u ranges from 1 to l), and its length is denoted as v, the days of learning behaviors.

The second step encompasses the decomposition of multidimensional feature data into statistically ICs using the ICA algorithm. This decomposition is performed on the preprocessed data, segregating features into components that are statistically independent. Subsequent analysis focuses on discerning which components embody substantial information relevant to learning effectiveness and which represent mere noise. Components identified as noise are meticulously excluded, retaining only those ICs instrumental to predicting learning effectiveness. The IC matrices derived for various aspects of student behavior and performance, including behavior features (Z_OP), grades (Z_ZG), social interactions (Z_ZD), resource usage (Z_SP), and intervention feedback (Z_CJ), are denoted as follows:

Z_{O P} = {[z_{1}, z_{2}, . . ., z_{u}, . . ., z_{m}]}^{S}

(22)

The third step involves inputting the refined ICs into the Multi-LSTM model for training and predictive analysis. The noise-reduced dataset, reconstructed through the mixing matrix, is converted into a format conducive to long short-term memory (LSTM) modeling. This time-series data is then stratified into distinct sets for training, validation, and testing purposes. The Multi-LSTM model undergoes rigorous training, during which parameters are meticulously adjusted to optimize prediction accuracy. The prediction results for the uth time series within the behavior feature IC matrix Z_OP are represented by z_{u_ofs}. The comprehensive prediction results pertaining to each behavior feature IC, denoted as Z_{O_P}, are expressed as:

C_{O_P} = {[z_{1_o f s}, z_{2_o f s}, . . ., z_{u_o f s}, z_{m_o f s}]}^{S}

(23)

In the final phase, the Multi-LSTM model, having undergone rigorous training, is utilized to forecast the future learning behaviors of students. The model operates on the reconstructed dataset, generating predictions for each student’s learning behavior. These predictions are denoted as X_{O_P} = [x_{O_P_1} ,x_{O_P_2} ,…,x_{O_P_u}, ..,x_{O_P_l} ]^S, where x_{O_P_u} represents the predicted learning behavior for an individual student within the reconstructed dataset. The aggregate of these predictions, encompassing the learning behaviors of all students, is expressed as follows:

X_{O_P} = X • Z_{O_P}

(24)

Subsequent analysis of the model’s predictions provides insights into the correlation between specific learning behaviors and overall learning effectiveness. This analysis is instrumental in the formulation of tailored early intervention strategies, aimed at supporting students, particularly those at risk of underperforming, to enhance their learning behaviors proactively. By doing so, the overall effectiveness of the learning process is improved, aligning with the objectives of personalized education and targeted pedagogical interventions.

Once potential learning difficulties are predicted by the model, educators can take a series of practical steps to address them. These steps include communicating with students and parents, developing personalized learning plans, providing additional support and resources, and, when necessary, guiding students to receive professional counseling or therapy. The model is applied in a real school environment, where it analyzes student learning behavior data to help schools identify potential learning issues and provide personalized early intervention measures. By collecting student learning behavior data and applying the model, schools can more accurately understand students’ learning patterns and behavioral trends, thereby intervening timely and enhancing student learning outcomes, ultimately improving educational quality. The interpretability of the model can be achieved by explaining the function and role of each component within the model. For example, it explains how the PrefixSpan algorithm identifies patterns in student learning behaviors, how the ordered funnel analysis algorithm explores the associations between student learning behaviors, and how the Multi-LSTM network integrates this information to predict student learning outcomes. The prediction results are presented in a straightforward and intuitive manner, enabling non-technical educators to understand and apply them.

Experimental results and analysis

In the conducted research, the PrefixSpan sequence pattern mining algorithm was employed to analyze the sequential behavior of students. Additionally, an improved ordered funnel analysis algorithm was introduced for an in-depth examination of learning patterns. The basic characteristics of the dataset may include information, such as the source of data, type of data (e.g., student behavior data), and scale of the data. The preprocessing methods may involve steps, such as data cleaning, removal of outliers, and feature extraction, to ensure the quality and applicability of the data. Figure 5 presents a comparative analysis of the ordered funnel analysis algorithm before and after enhancement. The findings demonstrate a marked increase in time efficiency with the enhanced algorithm, especially in scenarios with constrained time windows. The original algorithm exhibited a notable reduction in performance when the time window was narrowed, whereas the enhanced algorithm’s performance remained largely stable. This disparity is attributed to the early return mechanism incorporated in the enhanced algorithm. It ceases operation as soon as a student completes a predefined length of a learning behavior sequence, thereby curtailing superfluous computational efforts. In extended time windows, such as 7 days, the probability of students completing the entire sequence is higher, frequently activating the early return feature and subsequently reducing the algorithm’s runtime. In contrast, shorter time windows, like a single day, diminish the likelihood of completing the entire sequence, compelling the original algorithm to scan all behaviors and significantly impairing its temporal efficiency. The ability to rapidly analyze learning behaviors is essential, particularly in online learning environments where analysis windows are exceedingly brief, often spanning hours or minutes. In such contexts, the performance of the original ordered funnel analysis algorithm would be substantially compromised. The optimization of the algorithm not only augments efficiency but also guarantees swift and effective analysis of student learning behavior patterns, even within extremely limited time frames.

Figure 5.

Comparison results of the ordered funnel analysis algorithm before and after improvement. (a) Time window of seven days. (b) Time window of one day.

Results from the ordered funnel analysis, structured within a predefined time window, are delineated in Table 1. This funnel model’s construction, contingent on a time window, is instrumental in capturing and analyzing the sequences of student behaviors. The pivotal role of the time window’s setup, which dictates the analytical breadth and accuracy, is evident. Within this model, the conversion rate for the initial learning stage reflects the percentage of students initiating the first learning activity (Behavior 1) within this period, observed to be 56.32%. This rate suggests that a majority of the cohort embarked on their educational journey. Moreover, the funnel model intricately details the conversion rates across diverse learning behaviors. Among those completing the first learning activity, a mere 28.31% proceeded to the subsequent activity (Behavior 2) within the same time frame. This rate, when calculated against the aggregate student count, translates to 16.38%, indicative of a marked decrease in student engagement from Behavior 1 to Behavior 2.

Table 1.

Results of ordered funnel analysis based on a time window restriction.

	Total number of students	Behavior 1	Behavior 2	Behavior 3	Behavior 4
Number of students	5896	3352	936	768	632
Percentage of students	100%	56.32%	16.38%	12.36%	11.27%
Conversion rate	100%	56.32%	28.31%	82.38%	81.42%

Table 2 exhibits the findings from the ordered funnel analysis employing an interval window. The juxtaposition of these results with those from Table 1 illuminates the interval window-based model’s consideration for the duration students spend within the learning behavior sequence. Notably, certain students allocate additional time to specific learning tasks, leading to their exclusion in the fixed time window setup portrayed in Table 1, thereby skewing conversion rate accuracy. The outcomes in Table 2 underscore the interval window approach’s merit, incorporating students with extended activity durations by broadening the time window. This approach fosters inclusivity of diverse student learning rhythms and precludes overlooking student behaviors due to overly restrictive time windows. It ensures thorough representation of critical insights in the conversion rate assessment of student behavior sequences. Additionally, the interval window methodology augments the precision of subsequent learning behavior conversion rates by accommodating students’ organic progression through the learning behavior sequence, as opposed to constraining them within an artificial, fixed window.

Table 2.

Results of ordered funnel analysis based on an interval window restriction.

	Total number of students	Behavior 1	Behavior 2	Behavior 3	Behavior 4
Number of students	5874	3452	958	823	678
Percentage of students	100%	56.15%	16.23%	12.75%	11.27%
Conversion rate	100%	56.15%	28.71%	83.26%	81.52%

In Table 3, the eigenvalues associated with five distinct ICs (DC1 to DC5) are exhibited, pertaining to various aspects of student behavior such as behavioral features, grades, social interaction, resource usage, and intervention feedback. An analysis of the table reveals that across all matrices, the DC1 eigenvalue notably surpasses the others, signifying its dominance and its substantial impact on student performance. The relative prominence of the DC2 eigenvalue, although considerable, pales in comparison to DC1, implying its lesser influence. Conversely, the eigenvalues for DC3, DC4, and DC5 are lower, indicating their more modest impact on student performance. Particularly noteworthy is the DC1 eigenvalue for intervention feedback, which is exceptionally high. This finding underscores the pivotal role of intervention measures in shaping student performance. The data presented in Table 3 affirm the effectiveness of the combined ICA and Multi-LSTM network architecture proposed in this study. This architecture proficiently identifies the crucial elements affecting student learning effectiveness, especially in the realm of early intervention. The outcomes suggest a promising potential for accurately predicting student learning achievements, thereby facilitating more targeted and effective early interventions.

Table 3.

Eigenvalues corresponding to ICs.

IC matrix	DC1 eigenvalue	DC2 eigenvalue	DC3 eigenvalue	DC4 eigenvalue	DC5 eigenvalue
Behavioral features	58.1425863	5.12453658	1.5423157	0.98562415	0.32154789
Behavioral features	7854	8854	7458	123	985
Grades	62.3254852	5.42156851	1.5426586	0.93658425	0.33452586
Grades	7851	254	0621	054	756
Social interaction	53.2645895	4.52368542	1.4526589	0.93521546	0.27851156
Social interaction	3654	578	6235	645	935
Resource usage	58.2345157	5.2315884	1.4756258	0.92356851	0.3258462
Resource usage	2235	124	902	457	256
Intervention feedback	668,542,135	112,458,623	42,254,862	265,845,214	121,452,362
Intervention feedback	043	489	277.3	21.3	88.3

In Table 4, the cumulative variance contribution rates of the ICs are presented, offering insights into the significance of each component in explicating the variance within the original dataset. Higher variance contribution rates are indicative of a greater importance of the respective component within the data group. The analysis of the table reveals that, across all data groups, the cumulative variance contribution rate of the first IC (DC1) markedly exceeds 87%, underscoring its preeminence in explaining the bulk of data variance and suggesting that it encapsulates vital information. While the second IC (DC2) holds the position of second highest variance contribution rate in all groups, its impact is substantially less pronounced compared to DC1. The variance contribution rates of the third (DC3), fourth (DC4), and fifth (DC5) components exhibit a further decline, suggesting their comparatively lesser role in elucidating data variance. Interestingly, the intervention feedback data group exhibits a unique pattern, with a relatively lower cumulative variance contribution rate for DC1, and higher rates for DC2 to DC5. This pattern suggests that, in the context of intervention feedback, additional components beyond DC1 possess significant informative content, likely a result of the increased diversity and complexity introduced by intervention measures. The findings from Table 4 lead to the conclusion that the architecture combining ICA (ICA) and Multi-LSTM (Multi-LSTM) networks, as proposed in this study, proficiently leverages the dominant trends within the data, predominantly represented by DC1, for the prediction of student learning outcomes. This effective utilization of primary data trends underscores the potential of the proposed architecture in enhancing the accuracy and reliability of learning outcome predictions.

Table 4.

Cumulative variance contribution rates of ICs.

Data group	DC1 cumulative variance contribution rate	DC2 cumulative variance contribution rate	DC3 cumulative variance contribution rate	DC4 cumulative variance contribution rate	DC5 cumulative variance contribution rate
Behavioral features	87.25%	7.68%	2.21%	1.42%	0.48%
Grades	87.32%	7.56%	2.15%	1.32%	0.48%
Social interaction	87.34%	7.42%	2.31%	1.52%	0.47%
Resource usage	87.25%	7.56%	2.27%	1.41%	0.47%
Intervention feedback	78.23%	11.26%	5.15%	3.12%	1.23%

In Table 5, the predictive efficacy of the effective ICs (DC1-3) of behavioral features, as assessed by the Multi-LSTM network architecture under varying hyperparameter settings, is presented. The table employs the coefficient of determination R² on the validation set as the metric for predictive performance, with values closer to 1 denoting superior model prediction capabilities. This metric signifies the alignment of the model’s predicted variability with the data’s inherent variability, thereby indicating a robust explanatory capacity. The examination of the table reveals that the learning rate exerts a notable influence on the model’s training efficacy. Specifically, configurations with a learning rate of 0.01 (across learning phases 2, 3, 6, 7, 8, 9, 10) consistently demonstrate enhanced predictive performance. Contrastingly, configurations with either a higher (0.1) or lower (0.001, 0.0001) learning rate exhibit diminished performance. Additionally, batch sizes of 31 (in learning phases 6, 7, 8, 9, 10) generally surpass the predictive performance of those with batch sizes of 62 (in learning phases 1, 2, 3, 4, 5). Moreover, modifications in the quantity of units in both the first and second hidden layers are observed to impact the model’s performance. An increase in the number of units in the first hidden layer from 15 to 31 (as seen when comparing learning phases 2 and 3) correlates with an improvement in model performance. However, a further increment to 62 units in the first layer (observed in learning phase 7) leads to a slight performance decrement. The variations in the number of units in the second hidden layer, particularly when comparing learning phases 6, 8, 9, and 10, appear to predominantly affect the predictive performance for DC3. The configuration in learning phase 9, characterized by a learning rate of 0.01, batch size of 31, 100 training epochs, 31 units in the first hidden layer, and 15 units in the second hidden layer, attains the apex average R² value of 0.9339. This configuration is identified as the most efficacious hyperparameter setting. The findings from Table 5 underscore the criticality of selecting apt learning rates, batch sizes, and hidden layer units to elevate the precision of student learning effectiveness predictions. The Multi-LSTM network architecture proves its capability in effectively predicting the effective ICs of behavioral features, contingent upon optimal hyperparameter configurations. The optimal performance achieved in learning phase 9 accentuates the importance of comprehensive hyperparameter tuning prior to the deployment of deep learning models for early intervention and prediction of student learning outcomes.

Table 5.

Comparison of predictive performance of effective ICs of behavioral features under different hyperparameter settings.

Learning phase	Learning rate	Batch size	Training epochs	Number of units in first hidden layer	Number of units in second hidden layer	Coefficient of determination R² for validation set
Learning phase	Learning rate	Batch size	Training epochs	Number of units in first hidden layer	Number of units in second hidden layer	DC1	DC2	DC3	Average
1	0.1	62	100	15	11	0.435	0.7652	0.8124	0.6708
2	0.01	62	100	15	11	0.7895	0.8784	0.9235	0.8638
3	0.01	62	100	31	11	0.8754	0.8879	0.9254	0.9862
4	0.001	62	100	31	11	0.8651	0.8962	0.9237	0.895
5	0.0001	62	100	31	11	0.8125	0.8125	0.8315	0.8188
6	0.01	31	100	31	11	0.9236	0.9352	0.8457	0.9015
7	0.01	31	100	62	11	0.8451	0.8451	0.8896	0.8599
8	0.01	31	100	31	23	0.8453	0.8875	0.9432	0.892
9	0.01	31	100	31	15	0.9236	0.9326	0.9456	0.9339
10	0.01	31	100	31	13	0.8147	0.8895	0.9365	0.8802

Compared to other prediction methods, the proposed model excels in its comprehensiveness and precision. By integrating the PrefixSpan algorithm, the ordered funnel analysis algorithm, and the Multi-LSTM network architecture, the model is able to capture patterns and trends in student learning behavior more accurately, providing more reliable prediction results and offering more effective decision support for educators.

Conclusion

In this research, technology based on the PrefixSpan algorithm was initially utilized, leading to the effective identification of sequential patterns in student learning behaviors and the capturing of their temporal evolution. This initial phase laid the groundwork for a comprehensive understanding of student behavior. Subsequently, the study advanced this understanding by employing an enhanced ordered funnel analysis algorithm, which delved into the directed associativity among learning patterns, thereby uncovering intrinsic connections among various student behaviors. This exploration was instrumental in delineating the progression pathways and potential causal links in student behavior. Furthermore, the study incorporated ICA to leverage a Multi-LSTM network architecture, aimed at predicting student learning outcomes. This phase, emphasizing deep learning application, focused on extracting salient features from time-series data to enable accurate predictions.

The paper presented a comparative analysis of the ordered funnel analysis algorithm, both before and after its enhancement, highlighting the augmented efficiency of the refined algorithm in extracting behavioral patterns. This comparison extended to the ordered funnel analysis based on varying time and interval window constraints, thus revealing the adaptability of behavior patterns under different conditions. Additionally, the study provided insights into the eigenvalues and cumulative variance contribution rates of ICs, elucidating the significance of each component within the dataset. Experimental comparisons of the predictive performance of effective ICs of behavioral features under diverse hyperparameter configurations were conducted, affirming the model’s accuracy and stability across various scenarios.

In conclusion, the model proposed in this paper, synthesizing state-of-the-art data mining technologies with deep learning approaches, has proven effective in predicting student learning outcomes and facilitating early intervention. The results of the experiments underscore the importance of selecting suitable algorithms and fine-tuning hyperparameters for enhancing prediction accuracy. The research has not only refined the precision in analyzing student learning behavior but has also laid the foundation for predictive models, thereby opening avenues for tailored educational interventions. This advancement contributes significantly to the progression of personalized and precise education. The limitations of the model include its dependency on data quality and scale, as well as insufficient prediction accuracy in certain scenarios. Future research directions involve improving data collection and processing methods, exploring the applicability of the model in different educational settings and subject areas, and further enhancing the predictive performance and interpretability of the model.

Statements and declarations

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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