Dynamic Assessment with AI (Agentic RAG) and Iterative Feedback: A Model for the Digital Transformation of Higher Education in the Global EdTech Ecosystem

1. Introduction

Artificial Intelligence (AI) is rapidly reshaping assessment foundations in higher education. Contemporary systems for automated feedback and intelligent tutoring report positive effects on performance and large-scale personalization; however, the iterative nature of assessment–feedback cycles remains under-theorized from a mathematical and algorithmic standpoint, limiting analyses of convergence, sensitivity, and robustness in learning processes [1,2,3]. Recent syntheses in AI for education summarize advances ranging from automated scoring for writing and programming to learning-analytics dashboards, while emphasizing mixed evidence and the need for reproducible, comparable frameworks across contexts [1,4,5].

In parallel, Retrieval-Augmented Generation (RAG) has emerged as a key mechanism to inject reliable external knowledge into large language models, mitigating hallucinations and improving accuracy on knowledge-intensive tasks. The 2023–2024 survey wave systematizes architectures, training strategies, and applications, providing a technical basis for contextualized and traceable feedback in education [6,7,8]. Closely related prompting/reasoning frameworks (e.g., ReAct) support verifiable, tool-using feedback workflows [9].

Within programming education, systematic reviews and venue reports (e.g., ACM Learning@Scale, EDM) document the expansion of auto-grading and LLM-based formative feedback, alongside open questions about reliability, transfer, and institutional scalability [10,11,12,13,14]. In writing, recent studies and meta-analyses report overall positive but heterogeneous effects of automated feedback, with moderators such as task type, feedback design, and outcome measures—factors that call for models capturing the temporal evolution of learning rather than single-shot performance [3,15]. Meanwhile, the knowledge-tracing literature advances rich sequential models—from classical Bayesian formulations to Transformer-based approaches—often optimized for predictive fit rather than prescribing algorithmic feedback policies with interpretable convergence properties [16,17,18,19,20].

This study frames assessment and feedback as a discrete-time algorithmic process. We formalize two complementary models: (i) a difference equation linking per-iteration gain to the gap-to-target and feedback quality, and (ii) a logistic convergence model describing asymptotic approach to a performance objective. This framing enables analysis of convergence rates, sensitivity to feedback quality, and intra-cohort variance reduction, aligning educational assessment with tools for algorithm design and analysis. Empirically, we validate the approach in a longitudinal study with six feedback iterations in a technical programming course (n = 35), estimating model parameters via nonlinear regression and analyzing individual and group trajectories. Our results show that higher-quality, evidence-grounded feedback predicts larger next-iteration gains and faster convergence to target performance, while cohort dispersion decreases across cycles—patterns consistent with prior findings in intelligent tutoring, automated feedback, and retrieval-augmented LLMs [6,7,8,11].

  Conceptual overview. Figure 1 depicts the student-level loop and its coupling with the formal models used throughout the paper. The process moves the performance state $S_{i,t}$ to $S_{i,t+1}$ via targeted feedback whose quality is summarized by $F_{i,t}\in [0,1]$. The two governing formulations, used later in estimation and diagnostics, are shown in Panel (b): a linear-difference update and a logistic update, both expressed in discrete time and consistent with our Methods.

Scope and contributions. The contribution is twofold: a formal, interpretable algorithmic framing of iterative assessment with explicit update mechanics, and an empirical validation in a real course setting showing sizable gains in means and reductions in dispersion over six iterations (§Section 4). Beyond predictive fit, the models yield actionable parameters (${\eta }_i,{\lambda }_i$) that connect feedback quality to pace and equity of learning, offering a reproducible basis for EdTech deployments at scale.

2. Theoretical Framework

To ground our proposal of a dynamic, AI-supported assessment and feedback system within the broader digital transformation of higher education and the global EdTech landscape, this section reviews the most relevant theoretical and empirical research across educational assessment, feedback for learning, and Artificial Intelligence in Education (AIED), together with implications for pedagogy and evaluation in digitally mediated environments. We also consider a comparative-education perspective to contextualize the phenomenon internationally. Our goal is to provide a conceptual and analytical basis for understanding the design, implementation, and broader implications of the model advanced in this article.

Over the last decade—and especially since the emergence of generative AI—research on assessment in digital environments has accelerated. Multiple syntheses concur that feedback is among the most powerful influences on learning when delivered personally, iteratively, and in context [3,21,22]. In technically demanding domains such as programming, early error identification and precise guidance are critical for effective learning and scalable instruction [10,23,24]. Recent evidence further suggests that AI-supported automated feedback can achieve high student acceptability while raising challenges around factuality, coherence, and alignment with course objectives [4,11,15,25]. These observations motivate hybrid designs that combine generative models with information retrieval and tool use to improve the relevance, traceability, and verifiability of feedback.

2.1. Assessment and Feedback in Technical Disciplines and Digital Settings

Within the digital transformation of higher education, disciplines with high technical complexity and iterative skill formation (e.g., engineering, computational design, and especially programming) require assessment approaches that support rapid, personalized, and precise adjustment of performance as students progress. Digital platforms facilitate content delivery and task management but amplify the need for scalable formative feedback that goes beyond grading to provide concrete, actionable guidance [3,21]. In programming education, research documents expansion in auto-grading, AI-mediated hints, and LLM-based formative feedback, alongside open questions about reliability, transfer, and equity at scale [10,11,12,13,14,24]. Addressing these challenges is essential to ensure that digital transformation translates into improved learning outcomes and readiness for technology-intensive labor markets.

2.2. Advanced AI for Personalized Feedback: RAG and Agentic RAG

Recent advances in AI have yielded models with markedly improved capabilities for interactive, context-aware generation. Retrieval-Augmented Generation (RAG) combines the expressive power of foundation models with the precision of targeted retrieval over curated knowledge sources, mitigating hallucinations and improving accuracy on knowledge-intensive tasks [6,7,26]. Agentic variants extend this paradigm with planning, tool use, and self-critique cycles, enabling systems to reason over tasks, fetch evidence, and iteratively refine outputs [8,9]. In educational contexts, connecting agentic RAG to course materials, assignment rubrics, student artifacts, and institutional knowledge bases—via standardized connectors or protocol-based middleware—supports feedback that is course-aligned, evidence-grounded, and level-appropriate. This integration enables detailed explanations, targeted study resources, and adaptation to learner state, making richer, adaptive feedback feasible at scale and illustrating how AI underpins disruptive innovation in core teaching-and-learning processes.

2.3. Mathematical Modeling of Assessment–Feedback Dynamics

Beyond transforming tools and workflows, the digitalization of learning generates rich longitudinal data about how students improve in response to instruction and iterative feedback. Mathematical modeling provides a principled lens to capture these dynamics, shifting the focus from single-shot outcomes to trajectories of performance over time. In systems that allow multiple attempts and continuous feedback, discrete-time updates are natural candidates: they describe how a learner’s performance is updated between evaluation points as a function of the previous state, the gap-to-target, and the quality of feedback. Throughout the paper we consider two complementary formulations at the student level i and iteration t:

$$\begin{array}{cc}\hfill S_{i,t+1}-S_{i,t}& ={\eta }_i{F}_{i,t}\left(1-S_{i,t}\right)+{\epsilon }_{i,t},{\eta }_i\ge 0,F_{i,t}\in [0,1],\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill S_{i,t+1}& =S_{i,t}+{\lambda }_i{F}_{i,t}{S}_{i,t}\left(1-S_{i,t}\right)+{\epsilon }_{i,t},{\lambda }_i\ge 0.\hfill \end{array}$$

(2)

Here $S_{i,t}\in [0,1]$ denotes a normalized performance score (with target $S_{\mathrm{target}}=1$), $F_{i,t}$ summarizes feedback quality (accuracy, relevance, clarity, actionability), ${\eta }_i$ and ${\lambda }_i$ parameterize sensitivity and effectiveness, and ${\epsilon }_{i,t}$ captures unmodeled shocks.

Proposition 1 (Monotonicity, boundedness, and iteration complexity for.

Assume ${\epsilon }_{i,t}\equiv 0$, $S_{i,1}\in [0,1]$, ${\eta }_i\in [0,1]$, and $F_{i,t}\in [0,1]$. Then:

1. 

(Monotonicity & boundedness) $S_{i,t}$ is nondecreasing and remains in $[0,1]$ for all t.

2. 

(Geometric convergence) If there exists $f_{min}>0$ such that $F_{i,t}\ge f_{min}$ for all t, then

$$1-S_{i,t}\le {(1-{\eta }_i{f}_{min})}^{t-1}\left(1-S_{i,1}\right).$$

3. 

(Iteration complexity) To achieve $1-S_{i,t}\le \delta$ with $0<\delta <1$, it suffices that

$$t\ge 1+{\displaystyle \frac{log\left(\delta /(1-S_{i,1})\right)}{log(1-{\eta }_i{f}_{min})}}.$$

Proof. 

Let $g_{i,t}=1-S_{i,t}$. From (1) (without noise), $S_{i,t+1}=S_{i,t}+{\eta }_i{F}_{i,t}{g}_{i,t}$, so $g_{i,t+1}=(1-{\eta }_i{F}_{i,t})g_{i,t}$. Since $0\le {\eta }_i{F}_{i,t}\le 1$, we have $0\le g_{i,t+1}\le g_{i,t}$, implying monotonicity and boundedness. If $F_{i,t}\ge f_{min}$, then $g_{i,t}\le {(1-{\eta }_i{f}_{min})}^{t-1}{g}_{i,1}$, giving geometric convergence. Solving ${(1-{\eta }_i{f}_{min})}^{t-1}{g}_{i,1}\le \delta$ yields the stated bound on t.    □

Proposition 2 (Stability and convergence for (2)).

ProAssume ${\epsilon }_{i,t}\equiv 0$, $S_{i,1}\in (0,1)$, and let $r_{i,t}={\lambda }_i{F}_{i,t}$.

1. 

(Local stability at the target) If $0<{sup}_t{r}_{i,t}<2$, then $S^{★}=1$ is locally asymptotically stable. In particular, if $r_{i,t}\in (0,1]$ for all t, then $S_{i,t}$ increases monotonically to 1.

2. 

(Convergence without oscillations) If $0<{sup}_t{r}_{i,t}\le 1$, then $S_{i,t}$ is nondecreasing and converges to 1 without overshoot.

Proof. 

Define $G\left(S\right)=S+{\lambda }_{i}FS(1-S)$ with $F\in [0,1]$. Fixed points satisfy $G\left(S\right)=S$, giving $S\in \{0,1\}$. The derivative $G^{\prime }\left(S\right)=1+{\lambda }_{i}F(1-2S)$ yields $G^{\prime }\left(1\right)=1-{\lambda }_{i}F$. Local stability requires $|G^{\prime }\left(1\right)|<1$, i.e., $0<{\lambda }_{i}F<2$. If $0<{\lambda }_{i}F\le 1$, then $G^{\prime }\left(S\right)\in (0,1]$ for $S\in [0,1]$, so the map is increasing and contractive near the target, implying monotone convergence.    □

Corollary 1 (Cohort variance contraction (linearized)).

Let ${\overline{S}}_t$ be the cohort mean, ${\sigma }_t^2=\mathrm{Var}\left(S_{i,t}\right)$, and suppose shocks ${\epsilon }_{i,t}$ are independent across students with variance ${\sigma }_{\epsilon }^2$. Linearizing (1) around ${\overline{S}}_t$ and defining ${\overline{F}}_t$ as the cohort-average feedback quality at iteration t,

$${\sigma }_{t+1}^2\approx {\left(1-\overline{\eta }{\overline{F}}_t\right)}^2{\sigma }_t^2+{\sigma }_{\epsilon }^2.$$

Hence, if $0<1-\overline{\eta }{\overline{F}}_t<1$ and ${\sigma }_{\epsilon }^2$ is small, dispersion contracts geometrically toward a low-variance regime, aligning equity improvements with iterative feedback.

2.3.0.1. Lyapunov and contraction view.

For (1) with ${\epsilon }_{i,t}=0$, the potential $V_{i,t}={(1-S_{i,t})}^2$ satisfies $V_{i,t+1}={(1-{\eta }_i{F}_{i,t})}^2{V}_{i,t}$, a contraction whenever ${\eta }_i{F}_{i,t}>0$. With mean-zero noise, $\mathbb{E}\left[V_{i,t+1}\right]\le \rho \mathbb{E}\left[V_{i,t}\right]+{\sigma }_{\epsilon }^2,$ for $\rho ={sup}_t\mathbb{E}\left[{(1-{\eta }_i{F}_{i,t})}^2\right]<1$, implying bounded steady-state error. These properties justify monitoring both mean trajectories and dispersion (${\sigma }_t$) as first-class outcomes.

2.4. Relation to Knowledge Tracing and Longitudinal Designs

This perspective resonates with—but is distinct from—the knowledge-tracing literature. KT offers powerful sequential predictors (from Bayesian variants to Transformer-based approaches), yet the emphasis is often on predictive fit rather than prescribing feedback policies with interpretable convergence properties and explicit update mechanics [16,17,18,19,20]. Our formulation foregrounds the policy—the mapping from current state and feedback quality to the next state—enabling analysis of stability, rates, and variance dynamics. Methodologically, randomized and longitudinal designs in AIED provide complementary strategies for estimating intervention effects and validating iterative improvement [5]. In our empirical study (§Section 3Section 4), we instantiate this foundation with six iterations and report both mean trajectories and dispersion, together with parameter estimates that connect feedback quality to pace and equity of learning.

2.5. Comparative-Education Perspective

From a comparative-education viewpoint, the algorithmic framing of assessment raises cross-system questions about adoption, policy, and equity: how do institutions with different curricula, languages, and governance structures instrument feedback loops; how is feedback quality $F_{i,t}$ ensured across contexts; and which safeguards (privacy, auditability, accessibility) condition transferability at scale? Because the models here are interpretable and rely on auditable quantities ($S_{i,t}$, $F_{i,t}$, and dispersion ${\sigma }_t$), they are amenable to standardized reporting across institutions and countries—facilitating international comparisons and meta-analyses that move beyond single-shot accuracy to longitudinal, equity-aware outcomes.

Summary. By framing assessment and feedback as a discrete-time algorithm with explicit update mechanics, we connect pedagogical intuition to tools from dynamical systems and stochastic approximation. This yields actionable parameters (${\eta }_i,{\lambda }_i$), interpretable stability conditions (${\lambda }_i{F}_{i,t}<2$), iteration bounds (Proposition 1), and cohort-level predictions (variance contraction; Corollary 1) that inform the design of scalable, equity-aware feedback in digitally transformed higher education.

3. Materials and Methods

3.1. Overview and Study Design

We conducted a longitudinal observational study with six consecutive evaluation iterations ($t=1,\dots ,6$) to capture within-student learning dynamics under AI-supported assessment. The cohort comprised $n=35$ students enrolled in a Concurrent Programming course, selected for its sequential and cumulative competency development. Each iteration involved solving practical programming tasks, assigning a calibrated score, and delivering personalized, AI-assisted feedback. Scores were defined on a fixed scale and rescaled to $[0,1]$ for modeling, with $S_{\mathrm{target}}=1$. Feedback quality was operationalized as $F_{i,t}\in [0,1]$ (Section 3.3).

Participants and inclusion.

All enrolled students who provided informed consent were included. Formal withdrawals followed institutional policy; handling of incomplete records is described under Preprocessing and missing data. Ethical approval was granted by the Research Ethics Committee of Universidad de Jaén (Spain), approval code JUL.23/5-LÍ NEA.

Outcomes and endpoints.

The primary outcome is the per-iteration change in scaled performance, $S_{i,t+1}-S_{i,t}$, and its dependence on feedback quality $F_{i,t}$ (Eqs. (3)–(4)). Secondary outcomes include (i) the relative gain $G_{i,t}$ (Eq. (6)), (ii) cohort dispersion ${\sigma }_t$ (SD of $S_{i,t}$) and tail summaries (Q10/Q90), and (iii) interpretable parameters $({\eta }_i,{\lambda }_i,{\beta }_1)$ linking feedback quality to pace and equity of learning.

3.2. System Architecture for Feedback Generation

The system integrates three components under a discrete-time orchestration loop:

• Agentic RAG feedback engine. A retrieval-augmented generation pipeline with agentic capabilities (planning, tool use, self-critique) that produces course-aligned, evidence-grounded feedback tailored to each submission. Retrieval uses a top-k dense index over course artifacts; evidence citations are embedded in the feedback for auditability.
• Connector/middleware layer (MCP-like). A standardized, read-only access layer brokering secure connections to student code and tests, grading rubrics, curated exemplars, and course documentation. The layer logs evidence references, model/version, and latency for traceability.
• Auto-evaluation module. Static/dynamic analyses plus unit/integration tests yield diagnostics and a preliminary score; salient findings are passed as structured signals to contextualize feedback generation.

All components operate within an auditable controller that records inputs/outputs per iteration and enforces privacy-preserving pseudonymization before analytics.

3.3. Dynamic Assessment Cycle

Each cycle ($t=1,\dots ,6$) followed five phases:

• Submission. Students solved a syllabus-aligned concurrent-programming task.
• Auto-evaluation. The system executed the test suite and static/dynamic checks to compute $S_{i,t}\in [0,1]$ and extract diagnostics $d_{i,t}$.
• Personalized feedback (Agentic RAG). Detailed, actionable comments grounded on the submission, rubric, and retrieved evidence were generated and delivered together with $S_{i,t}$.
• Feedback Quality Index. Each feedback instance was rated on Accuracy, Relevance, Clarity, and Actionability (5-point scale); the mean was linearly normalized to $[0,1]$ to form $F_{i,t}$. A stratified $20\%$ subsample was double-rated for reliability (Cohen’s $\kappa$) and internal consistency (Cronbach’s $\alpha$).
• Revision. Students incorporated the feedback to prepare the next submission. Operationally, feedback from $t-1$ informs the change observed at t.

3.4. Model Specifications

We formalize three complementary formulations that capture how iterative feedback influences performance trajectories. These definitions appear here for the first time and are referenced throughout using \eqref{}.

(1) Linear difference model.

$$S_{i,t+1}-S_{i,t}={\eta }_i{F}_{i,t}\left(1-S_{i,t}\right)+{\epsilon }_{i,t},$$

(3)

where ${\eta }_i\ge 0$ encodes individual sensitivity to feedback and ${\epsilon }_{i,t}$ captures unexplained variation. Improvement is proportional to the gap-to-target and modulated by feedback quality and learner responsiveness.

(2) Logistic convergence model.

$$S_{i,t+1}=S_{i,t}+{\lambda }_i{F}_{i,t}{S}_{i,t}\left(1-S_{i,t}\right)+{\epsilon }_{i,t},$$

(4)

with ${\lambda }_i\ge 0$ governing how feedback accelerates convergence. In multiplicative-gap form,

$$1-S_{i,t+1}\approx \left(1-S_{i,t}\right)exp\left(-{\lambda }_i{F}_{i,t}\right),$$

(5)

which makes explicit that higher-quality feedback contracts the remaining gap faster. A useful rule-of-thumb is the gap half-life:

$$t_{1/2}\approx {\displaystyle \frac{ln2}{{\lambda }_i{F}_{i,t}}},$$

mapping estimated ${\lambda }_i$ and observed $F_{i,t}$ to expected pacing.

(3) Relative-gain model.

We define the per-iteration fraction of the remaining gap that is closed:

$$G_{i,t}={\displaystyle \frac{S_{i,t+1}-S_{i,t}}{1-S_{i,t}}}\in [0,1](S_{i,t}<1),$$

(6)

and regress

$$G_{i,t}={\beta }_0+{\beta }_1{F}_{i,t}+{\beta }_2{E}_{i,t}+{\mathbf{d}}_t^{\top }\gamma +{\nu }_{i,t},$$

(7)

where $E_{i,t}$ optionally captures effort/time-on-task; ${\mathbf{d}}_t$ are iteration fixed effects (time trends and task difficulty), and ${\nu }_{i,t}$ is an error term. The coefficient ${\beta }_1$ estimates the average marginal effect of feedback quality on progress per iteration, net of temporal and difficulty factors.

3.5. Identification Strategy, Estimation, and Diagnostics

Identification and controls.

Given the observational design, we mitigate confounding via (i) within-student modeling (student random intercepts; cluster-robust inference), (ii) iteration fixed effects ${\mathbf{d}}_t$ to partial out global time trends and task difficulty, and (iii) optional effort covariates $E_{i,t}$ where available. In sensitivity checks, we add lagged outcomes $S_{i,t-1}$ (where appropriate) and verify that inferences on $F_{i,t}$ remain directionally stable.

Estimation.

Equations (3) and (4) are estimated by nonlinear least squares with student-level random intercepts (and random slopes where identifiable), using cluster-robust standard errors at the student level. Equation (7) is fit as a linear mixed model with random intercepts by student and fixed effects ${\mathbf{d}}_t$. Goodness-of-fit is summarized with RMSE/MAE (levels) and $R^2$ (gains); calibration is assessed via observed vs. predicted trajectories. Model comparison uses AIC/BIC and out-of-sample K-fold cross-validation.

Multiple testing and robustness.

We report 95% confidence intervals and adjust p-values using the Benjamini–Hochberg procedure where applicable. Robustness checks include: (i) trimming top/bottom $2.5\%$ changes, (ii) re-estimation with Huber loss, (iii) alternative weighting schemes in $F_{i,t}$ (e.g., upweight Accuracy/Actionability), and (iv) a placebo timing test regressing $S_{i,t}-S_{i,t-1}$ on future$F_{i,t}$ to probe reverse-timing artefacts (expected null).

Preprocessing and missing data.

$S_{i,t}$ and $F_{i,t}$ are normalized to $[0,1]$. Single-iteration missingness in $F_{i,t}$ is handled by last-observation-carried-forward (LOCF), with sensitivity checks using complete cases and within-student mean imputation. Students with $\ge 2$ consecutive missing iterations are excluded from model-based inference and retained in descriptive summaries (final counts reported in Results).

3.6. Threats to Validity and Mitigations

Internal validity. Without randomized assignment of feedback pathways, causal claims are cautious. We partially address confounding via within-student modeling, iteration fixed effects (time/difficulty), and sensitivity analyses (lagged outcomes; trimming; Huber). Practice and ceiling effects are explicitly modeled by the gap-to-target terms in (3)–(4).

Construct validity. The Feedback Quality Index aggregates four criteria; we report inter-rater agreement (Cohen’s $\kappa$) and internal consistency (Cronbach’s $\alpha$) in Section 4. Calibration plots and residual diagnostics ensure score comparability across iterations.

External validity. Results originate from one course and institution with $n=35$. Transferability to other disciplines and contexts requires multi-site replication (see Discussion). Equity-sensitive outcomes (dispersion ${\sigma }_t$, tails) are included to facilitate cross-context comparisons.

3.7. Software, Versioning, and Reproducibility

Analyses were conducted in Python 3.12 (NumPy, SciPy, StatsModels). We record random seeds, dependency versions, and configuration files (YAML) and export an environment lockfile for full reproducibility. Estimation notebooks reproduce all tables/figures and are available upon request; audit logs include model/version identifiers and retrieval evidence IDs.

3.8. Data and Code Availability

The dataset (scores, feedback-quality indices, model-ready covariates) is available from the corresponding author upon reasonable request, subject to institutional policies and anonymization standards. Model scripts and configuration files are shared under an academic/research license upon request.

3.9. Statement on Generative AI Use

During manuscript preparation, ChatGPT (OpenAI, 2025 version) was used exclusively for language editing and stylistic reorganization. All technical content, analyses, and results were produced, verified, and are the sole responsibility of the authors.

3.10. Ethics

Participation took place within a regular course under informed consent and full pseudonymization prior to analysis. The study was approved by the Research Ethics Committee of Universidad de Jaén (Spain), approval code JUL.23/5-LINEA. Formal statements appear in the back matter (Institutional Review Board Statement, Informed Consent Statement).

3.11. Algorithmic Specification and Visual Summary

Algorithm 1:Iterative Dynamic Assessment Cycle with Agentic RAG

Require: Course materials $\mathcal{M}$, rubric $\mathcal{R}$, exemplars $\mathcal{E}$, test suite $\mathcal{T}$; cohort $\mathcal{I}$; $S_{\mathrm{target}}=1$ 1: Initialize connectors (MCP-like), audit logs, and pseudonymization 2: for$t=1$to 6 do▹ Discrete-time learning loop 3:     for each student $i\in \mathcal{I}$ do 4:         Receive submission $x_{i,t}$ 5:         Auto-evaluation: run $\mathcal{T}$ + static/dynamic checks ⇒ diagnostics $d_{i,t}$; compute $S_{i,t}\in [0,1]$ 6:         Build context $C_{i,t}\leftarrow \{x_{i,t},d_{i,t},\mathcal{R},\mathcal{E},\mathcal{M}\}$ 7:         Agentic RAG: retrieve top-k evidence; draft → self-critique → finalize feedback $f_{i,t}$ 8:         Deliver $f_{i,t}$ and $S_{i,t}$ to student i 9:         Feedback Quality Rating: rate {Accuracy, Relevance, Clarity, Actionability} on 1–5 10:         Normalize/aggregate ⇒$F_{i,t}\in [0,1]$; (optional) collect $E_{i,t}$ (effort/time) 11:         (Optional inference) update predictions via (3), (4), (7) 12:         Log $\{S_{i,t},F_{i,t},E_{i,t},d_{i,t}\}$ with pseudonym IDs 13:     end for 14: end for 15: Output: longitudinal dataset $\left\{S_{i,t}\right\}$, $\left\{F_{i,t}\right\}$, optional $\left\{E_{i,t}\right\}$; evidence/audit logs

Algorithm 2:Computation of $F_{i,t}$ and Reliability Metrics ($\kappa$, $\alpha$)

Require: Feedback instances $\left\{f_{i,t}\right\}$ with rubric ratings $r_{i,t}^{\left(c\right)}\in \{1,\dots ,5\}$ for $c\in \{\mathrm{Acc},\mathrm{Rel},\mathrm{Cla},\mathrm{Act}\}$; 20% double-rated subsample $\mathcal{D}$ Ensure:$F_{i,t}\in [0,1]$; Cohen’s $\kappa$ on $\mathcal{D}$; Cronbach’s $\alpha$ across criteria 1: for each feedback instance $(i,t)$ do 2:     Handle missing ratings: if any $r_{i,t}^{\left(c\right)}$ missing, impute with within-iteration criterion mean 3:     for each criterion c do 4:         $s_{i,t}^{\left(c\right)}\leftarrow (r_{i,t}^{\left(c\right)}-1)/4$▹ Normalize to $[0,1]$ 5:     end for 6:     Aggregate: $F_{i,t}\leftarrow {\displaystyle \frac{1}{4}}{\sum }_c{s}_{i,t}^{\left(c\right)}$▹ Equal weights; alternative weights in Sec. Section 3.5 7: end for 8: Inter-rater agreement ($\kappa$): compute linear-weighted Cohen’s $\kappa$ on $\mathcal{D}$ 9: Internal consistency ($\alpha$): with $k=4$ criteria, compute Cronbach’s $\alpha ={\displaystyle \frac{k}{k-1}}\left(1-{\displaystyle \frac{{\sum }_c{v}_c}{v_{\mathrm{total}}}}\right)$ 10: Outputs:$\left\{F_{i,t}\right\}$ for modeling; $\kappa$ and $\alpha$ reported in Results

Figure 2. Discrete -time assessment–feedback workflow and coupling with the modeling layer.

Figure 2. Discrete -time assessment–feedback workflow and coupling with the modeling layer.

Figure 3. Estimation pipeline from longitudinal data to diagnostics and study outputs.

Figure 3. Estimation pipeline from longitudinal data to diagnostics and study outputs.

4. Results

This section reports quantitative evidence on the effectiveness of the AI-supported, dynamic assessment and iterative feedback system. We first present model-based estimates for the three formulations (linear-difference, logistic-convergence, and relative-gain). We then summarize cohort-level dynamics of means and dispersion across six iterations using observed values (baseline ${\overline{S}}_1=58.4$, SD $9.7$; final ${\overline{S}}_6=91.2$, SD $5.8$), followed by simulated individual trajectories and out-of-sample validation, calibration, placebo timing tests, sensitivity to missingness, and robustness. Core artifacts are Table 1 (model parameters), Figure 4 (mean trajectory), Figure 5 (variance dynamics), Table 2 (per-iteration descriptives), Table 3 (RM-ANOVA), the cross-validation summary Table 4, and the individual-level calibration plot Figure 7.

4.1. Model Fitting, Parameter Estimates, and Effect Sizes

Parameter estimates for the linear-difference, logistic-convergence, and relative-gain models are summarized in Table 1.1 Three results stand out: (i) the average learning-rate parameter linked to feedback quality is positive and statistically different from zero in the linear-difference model; (ii) the logistic model indicates accelerated convergence when $F_{i,t}$ is high, with the stability condition $\widehat{\lambda }·F<2$ satisfied across the cohort; and (iii) the relative-gain model yields a positive marginal effect of $F_{i,t}$ on the fraction of the gap closed per iteration.

Beyond statistical significance, magnitudes are practically meaningful. Two interpretable counterfactuals:

• Per-step effect at mid-trajectory. At $S_t=0.70$ and $F=0.80$, the linear-difference model implies an expected gain $\Delta S\approx \widehat{\eta }F(1-S_t)=0.32\times 0.80\times 0.30\approx 0.0768$ (i.e., ∼7.7 points on a 0–100 scale). Increasing F by $+0.10$ at the same $S_t$ adds $\approx 0.0096$ (≈1.0 point).
• Gap contraction in the logistic view. Using (5), the multiplicative contraction factor of the residual gap is $exp(-\widehat{\lambda }F)$. For $F=0.70$ and $\widehat{\lambda }=0.95$, the factor is $exp(-0.665)\approx 0.514$, i.e., the remaining gap halves in one iteration under sustained high-quality feedback.

Reliability of the Feedback Quality Index (FQI).

On the stratified 20% double-rated subsample, linear-weighted Cohen’s $\kappa$ indicated substantial inter-rater agreement, and Cronbach’s $\alpha$ indicated high internal consistency: ${\kappa }_{\mathrm{global}}=0.78$ (95% CI $0.71$–$0.84$) and $\alpha =0.89$ (95% CI $0.86$–$0.92$). Per-criterion $\kappa$: Accuracy $0.81$ (0.73–0.88), Relevance $0.77$ (0.69–0.85), Clarity $0.74$ (0.65–0.83), Actionability $0.76$ (0.67–0.84). These results support the construct validity of $F_{i,t}$ as a predictor in Eqs. (3)–(7).

4.2. Cohort Trajectories Across Iterations

Figure 4 displays the average cohort trajectory across the six iterations (0–100 scale). Means increase from $58.4$ at $t=1$ to $91.2$ at $t=6$, a $+32.8$-point absolute gain ($+56.0\%$ relative to baseline). A shifted-logistic fit (dashed) tracks the observed means closely and suggests an asymptote near $97.5$, consistent with diminishing-returns dynamics as the cohort approaches ceiling.2

As a numeric companion to Figure 4, Table 2 reports per-iteration means, standard deviations, and 95% confidence intervals ($n=35$).

4.3. Variance Dynamics, Equity Metrics, and Group Homogeneity

Dispersion shrinks markedly across iterations (Figure 5): the standard deviation decreases from $9.7$ at $t=1$ to $5.8$ at $t=6$ (relative change $-40.2\%$), and the cohort coefficient of variation drops from $0.166$ to $0.064$. A repeated-measures ANOVA on scores across t indicates significant within-student change (sphericity violated; Greenhouse–Geisser corrected), and the exponential-decay fit illustrates the variance contraction over time. Analytically, this pattern is consistent with the variance-contraction prediction in Corollary 1 (Section 2): as $\overline{\eta }{\overline{F}}_t>0$, ${\sigma }_t$ contracts toward a low-variance regime.

To gauge equity effects beyond SD, we report two distributional indicators (approximate normality):

• Inter-decile spread (Q90–Q10). Using $Q90-Q10\approx 2·1.2816·{\mathrm{SD}}_t$, the spread drops from $\approx 24.9$ points at $t=1$ to $\approx 14.9$ at $t=6$ ($-40.2\%$), indicating tighter clustering of outcomes.
• Tail risk. The proportion below an 80-point proficiency threshold moves from $\approx 98.7\%$ at $t=1$ (z$=2.23$) to $\approx 2.7\%$ at $t=6$ (z$=-1.93$), evidencing a substantive collapse of the lower tail as feedback cycles progress.

Pedagogically, these patterns align with equity aims: improving $F_{i,t}$ not only lifts the mean but narrows within-cohort gaps and shrinks the low-performance tail.

4.4. Individual Trajectories: Heterogeneous Responsiveness

To illustrate heterogeneous responsiveness to feedback, Figure 6 simulates three trajectories under the linear-difference mechanism for different sensitivities $\eta \in \{0.15,0.30,0.45\}$ at a moderate feedback level ($F=0.60$) with initial score $S_1=58.4$ (0–100). Higher $\eta$ approaches the target faster, while lower $\eta$ depicts learners who may require improved feedback quality or additional scaffolding. In practice, agentic RAG can be tuned to prioritize actionability/clarity for low-$\eta$ profiles.

4.5. Model Fit, Cross-Validation, Calibration, Placebo Test, Missingness Sensitivity, and Robustness

4.5.0.12. Cross-validation.

Out-of-sample K-fold cross-validation ($K=5$) yields satisfactory predictive performance. For the relative-gain LMM, mean $R^2=0.79$ (SD $0.04$) across folds. For the level models (NLS), the linear-difference specification yields RMSE $0.055$ (SD $0.006$) and MAE $0.042$ (SD $0.005$); the logistic-convergence specification yields RMSE $0.051$ (SD $0.005$) and MAE $0.039$ (SD $0.004$). Full summaries appear in Table 4.

Calibration by individuals (binned).

A calibration-by-bins plot using individual predictions (deciles of the predicted score) appears in Figure 7, showing close alignment to the ${45}^{\circ }$ line with tight 95% CIs. This complements the cohort-level fit in Figure 4 and indicates that predictive layers used within the update models are well calibrated across the score range.

Figure 7. Calibration by individual bins (deciles of predicted score): observed vs. predicted means (0–100) per bin with 95% CIs (bootstrap). Points lie close to the ${45}^{\circ }$ line, indicating good calibration of the predictive layer used in the update models.

Figure 7. Calibration by individual bins (deciles of predicted score): observed vs. predicted means (0–100) per bin with 95% CIs (bootstrap). Points lie close to the ${45}^{\circ }$ line, indicating good calibration of the predictive layer used in the update models.

Placebo timing test (lead).

To probe reverse timing, we regressed $S_{i,t}-S_{i,t-1}$ on future$F_{i,t}$ (same controls as Eq. (7)). The lead coefficient was null as expected: ${\widehat{\beta }}_{\mathrm{lead}}=0.004$ (95% CI $-0.018$ to $0.026$), $p=0.71$—consistent with temporal precedence of feedback quality.

Sensitivity to missingness and influence.

Results are stable across missing-data strategies: replacing LOCF with complete-case analysis changes ${\widehat{\beta }}_1$ by $+0.01$ (absolute), and within-student mean imputation changes it by $-0.01$. Leave-one-student-out influence checks vary ${\widehat{\beta }}_1$ within $\pm 0.03$, and vary $\widehat{\eta }$ and $\widehat{\lambda }$ means within reported CIs, indicating no single-student leverage.

Robustness.

Residual diagnostics are compatible with modeling assumptions (no marked heteroskedasticity; approximate normality). Robustness checks—2.5% trimming, Huber loss, and alternative rubric weights in $F_{i,t}$ (e.g., upweighting Accuracy/Actionability)—produce substantively similar estimates. As anticipated, the linear-difference specification is more sensitive to fluctuations in $F_{i,t}$ than the logistic and gain models.

Equity and design implications.

The joint pattern of (i) higher means, (ii) lower dispersion, (iii) inter-decile spread reduction, and (iv) a significant positive ${\widehat{\beta }}_1$ suggests that improving feedback quality at scale directly translates into faster progress per iteration and more homogeneous trajectories—relevant for platform and course design in large cohorts. Empirically, estimated $\widehat{\lambda }$ and observed $F_{i,t}$ satisfy the stability condition $\lambda F<2$ (Proposition 2), and the reduction in ${\sigma }_t$ matches the variance-contraction mechanism of Corollary 1.

5. Discussion: Implications for Assessment in the AI Era

5.1. Principal Findings and Their Meaning

The evidence supports an algorithmic view of learning under iterative, AI-assisted feedback. At the cohort level, the mean score increased from $58.4$ to $91.2$ across six iterations while dispersion decreased from $9.7$ to $5.8$ points (0–100 scale), as shown in Figure 4 and Figure 5 with descriptives in Table 2. Model estimates in Table 1 indicate that (i) higher feedback quality is associated with larger next-step gains (linear-difference: $\widehat{\eta }>0$), (ii) convergence accelerates when feedback quality is high and remains in the stable regime (logistic: $\widehat{\lambda }>0$ with $\widehat{\lambda }F<2$), and (iii) the fraction of the remaining gap closed per iteration increases with feedback quality (relative-gain: ${\widehat{\beta }}_1>0$). These patterns are robust: the lead-placebo is null (${\widehat{\beta }}_{\mathrm{lead}}=0.004$, 95% CI $[-0.018,0.026]$, $p=0.71$), cross-validated $R^2$ for the gain model averages $0.79\pm 0.04$ and level-model errors are low (Table 4), and the Feedback Quality Index (FQI) shows substantial inter-rater agreement and high internal consistency (${\kappa }_{\mathrm{global}}=0.78[0.71,0.84]$, $\alpha =0.89[0.86,0.92]$). Taken together, the joint pattern—higher means, lower dispersion, and a positive marginal effect of $F_{i,t}$—suggests that dynamic, evidence-grounded feedback simultaneously raises average performance and promotes more homogeneous progress.

5.2. Algorithmic Interpretation and Links to Optimization

The three formulations articulate complementary facets of the assessment–feedback loop. The linear-difference update (Eq. (3)) behaves like a gradient step with data-driven step size ${\eta }_i{F}_{i,t}$ scaled by the gap-to-target; early iterations (larger gaps) yield larger absolute gains for a given feedback quality. The logistic model (Eqs. (4)–(5)) captures diminishing returns near the ceiling and makes explicit how feedback multiplicatively contracts the residual gap; the cohort fit in Figure 4 is consistent with an asymptote near $97.5/100$. The relative-gain regression (Eq. (7)) quantifies the marginal effect of feedback quality on progress as a share of the remaining gap, which is useful for targeting: for mid-trajectory states ($S_t\approx 0.70$), improving F by $+0.10$ increases the expected one-step gain by $\approx 1$ point on the 0–100 scale.

These correspondences align with iterative optimization and adaptive control. Proposition 1 provides monotonicity and geometric contraction under positive feedback quality via a Lyapunov-like gap functional, yielding an iteration-complexity bound to reach a target error. Proposition 2 ensures local stability around the target for $\lambda F<2$, a condition met empirically. Corollary 1 predicts cohort-level variance contraction when average feedback quality is positive; this mirrors the observed decline in ${\sigma }_t$ and the reduction in inter-decile spread. In short, the update rules are not only predictive but prescriptive: they specify how changes in $F_{i,t}$ translate into pace (convergence rate) and equity (dispersion).

5.3. Relation to Prior Work and the Digital-Transformation Context

Prior research shows that high-quality, timely, contextualized feedback improves performance in digital learning, especially in technical disciplines. Our contribution is to make that process formal and auditable. First, we instantiate explicit update rules with interpretable parameters $({\eta }_i,{\lambda }_i,{\beta }_1)$ rather than black-box predictors. Second, we operationalize a measurable FQI with demonstrated reliability, closing the loop between feedback quality and learning quantity. Third, we evaluate convergence and variance dynamics with longitudinal criteria and calibration tests (individual binned calibration in Figure 7), which are rarely reported in educational deployments. Within intelligent tutoring, learning analytics, and retrieval-augmented generation, the proposed framework bridges descriptive dashboards and end-to-end LLM systems by exposing the mechanics that matter for scale and reproducibility.

5.4. Design and Policy Implications for EdTech at Scale

Treating assessment as a discrete-time process with explicit update mechanics unlocks concrete levers for platform and course design. Instrument the loop so each iteration records inputs and outputs (submissions, diagnostics, feedback text, evidence citations, $F_{i,t}$, optional effort $E_{i,t}$, model/versioning, latency), enabling auditability and A/B testing over feedback templates. Ground feedback in evidence via agentic RAG that consistently cites course materials, rubrics, and exemplars; empirically, raising $F_{i,t}$ increases both convergence rate ($\lambda F$) and relative gain (${\beta }_1$). Monitor equity alongside means: dispersion ${\sigma }_t$ and tail shares (e.g., below proficiency) should be first-class outcomes; in our data, the SD fell $-40.2\%$ and the estimated proficiency tail collapsed across cycles. Finally, use predicted gains (Eq. (7)) to pace intensity (e.g., more granular hints, additional exemplars) for low-responsiveness profiles (small ${\eta }_i$) or persistent gaps, while respecting latency and cost constraints in production.

5.5. Threats to Validity and Limitations

External validity is bounded by a single course (Concurrent Programming) and $n=35$ students; multi-site replication is warranted. Construct validity hinges on the FQI; while inter-rater agreement and internal consistency are strong ($\kappa \approx 0.78$, $\alpha \approx 0.89$), future work should triangulate with student-perceived usefulness and effort mediation. Causal identification remains cautious given an observational design; the strong longitudinal signal (RM-ANOVA), cross-validation, calibration, and placebo timing tests help, but randomized or stepped-wedge designs are needed to isolate counterfactuals. Model assumptions (linear/logistic updates) capture central tendencies; richer random-effect structures and task-level effects could accommodate effort shocks, prior knowledge, and prompt-template heterogeneity.

5.6. Future Work

Three immediate avenues follow. Experimental designs: randomized or stepped-wedge trials varying grounding (citations), scaffolding depth, and timing to estimate causal effects on $({\eta }_i,{\lambda }_i,{\beta }_1)$ and to test fairness-aware objectives. Personalization policies: bandit/Bayesian optimization over prompts and exemplars with relative-gain predictions as rewards, plus risk-aware constraints on dispersion and tail mass. Cross-domain generalization: replications in writing, design, and data analysis across institutions to characterize how discipline and context modulate convergence and variance dynamics, together with cost–latency trade-off analyses for production deployments.

5.7. Concluding Remark and Implementation Note

Framing assessment and feedback as an explicit, measurable algorithm in discrete time offers a rigorous yet practical foundation for AI-enabled evaluation in higher education. In our setting, this perspective explains the joint rise in means and fall in dispersion, clarifies why feedback quality matters for both pace and equity, and yields deployable levers for improving outcomes at scale.

Implementation note for Algorithms readers (text-only guidance). Treat the pipeline as auditable: log every update with full provenance (submission inputs, diagnostics, feedback text, evidence citations, $F_{i,t}$, model/versioning, latency); report cohort dispersion ${\sigma }_t$ and tail shares alongside means with reliability ($\kappa$, $\alpha$) and calibration; and publish reproducibility assets—prompt templates, the test suite $\mathcal{T}$, and configuration files with seeds and versions—under an institutional or research license with appropriate anonymization.

Figure 8. Implementation roadmap for deploying the discrete-time assessment–feedback system: instrumentation and logging, measurement with equity metrics, and release of reproducibility assets.

Figure 8. Implementation roadmap for deploying the discrete-time assessment–feedback system: instrumentation and logging, measurement with equity metrics, and release of reproducibility assets.

6. Conclusions

This study formalized AI-assisted dynamic assessment as an explicit, discrete-time algorithm and validated it in higher education. Across six assessment iterations in a Concurrent Programming course ($n=35$), cohort performance rose from $58.4$ to $91.2$ points while dispersion fell from $9.7$ to $5.8$ points (0–100 scale), evidencing simultaneous gains in central tendency and equity (Section 4; Figure 4, Figure 5, Table 2). These empirical patterns are consistent with an algorithmic feedback loop in which higher feedback quality contracts the gap to target at each iteration and progressively narrows within-cohort differences.

Methodologically, three complementary formulations—the linear-difference update, the logistic convergence model, and the relative-gain regression—yielded interpretable parameters that link feedback quality to the pace and magnitude of improvement. Estimates in Table 1 indicate that higher-quality, evidence-grounded feedback is associated with larger next-step gains (positive $\widehat{\eta }$), faster multiplicative contraction of the residual gap (positive $\widehat{\lambda }$ within the stable regime), and a greater fraction of the gap closed per iteration (positive ${\widehat{\beta }}_1$). Together with repeated-measures ANOVA (Table 3), these findings support an algorithmic account of learning where feedback operates as a measurable accelerator under realistic classroom conditions.

Practically, the framework shows how agentic RAG—backed by standardized connectors to course artifacts, rubrics, and exemplars—can deliver scalable, auditable feedback that both improves outcomes and reduces dispersion. Treating assessment as an instrumented, discrete-time pipeline enables reproducible measurement of progress (means, convergence) and equity (dispersion, tails), and exposes actionable levers for platform designers: modulating feedback intensity, timing, and evidence grounding based on predicted gains and observed responsiveness.

The work has limitations typical of a single-course longitudinal study: one domain and one institution with a moderate sample. Generalization to other disciplines and institutional contexts requires multi-site replications with larger cohorts. Stronger causal identification would benefit from randomized or stepped-wedge designs comparing feedback pathways or grounding strategies, and production deployments should incorporate fairness-aware objectives and cost–latency analysis to ensure sustainable scaling.

In sum, framing assessment and feedback as an explicit, data-driven algorithm clarifies why and how feedback quality matters for both the speed (convergence rate) and the equity (variance contraction) of learning. The models and evidence presented here provide a reproducible basis for designing, monitoring, and improving AI-enabled assessment loops in large EdTech settings, with direct implications for scalable personalization and outcome equity in digital higher education.