Dynamic Factors Influencing Learning

• Dynamic Factors in Learning are time-varying influences—such as internal states, feedback, and context—that evolve and interact to shape learning trajectories.
• Methodologies like Bayesian dynamic IRT, reinforcement learning updates, and network-based analyses capture nonlinear, history-dependent changes in performance.
• Empirical findings suggest that integrating dynamic measurements yields better insights and interventions than static averages, enhancing adaptive learning and prediction.

Searching arXiv for the cited papers and closely related work on dynamic factors and learning. arXiv search query: "Dynamic Factors Influence Learning learning dynamics education reinforcement learning item response theory" Dynamic factors influence learning when the variables that shape learning are treated as time-varying, interaction-dependent, and often nonlinear rather than as fixed covariates or stable traits. Across educational measurement, adaptive learning, reinforcement learning, optimization, human–robot interaction, network neuroscience, and collective learning, recent work converges on a common premise: learning trajectories depend on changing relations among internal state, feedback, context, memory, social structure, and task dynamics, and these relations often cannot be reduced to static linear effects (Saqr et al., 2024, Ma et al., 14 Jun 2026, Tian et al., 2023).

1. Conceptual scope and theoretical orientation

A complex dynamic systems perspective treats learning as an evolving process shaped by changing interactions among cognitive, motivational, emotional, social, and contextual components over time. In this view, learning phenomena are interaction-dominant rather than component-dominant, time-dependent, context-sensitive, and characterized by emergence, feedback, self-organization, adaptation, and sensitivity to initial conditions. The same framework uses discrete-time and continuous-time expressions such as $x_{t+1}=f(x_t)$ and $\frac{dx}{dt}=f(x)$ to formalize the idea that the current state depends on prior states rather than being generated anew at each observation (Saqr et al., 2024).

A closely related line of work in technology-enhanced learning defines context as “any information that can be used to characterize the situation of an entity,” and, more specifically, as “the current situation of a person related to a learning activity.” In this literature, dynamic factors include current knowledge, goal orientation, motivation, needs, available time, physical environment, device conditions, social relations, instructional strategies, and learning history. These factors matter because they influence what should be recommended, how difficult it should be, how it should be sequenced, what scaffolding is needed, and whether a recommendation is feasible in the learner’s current situation (Abu-Rasheed et al., 2023).

Taken together, these perspectives suggest that “dynamic factors” are not a single variable class. They include temporal exposure, state transitions, nonlinear feedback, contextual constraints, social propagation, and memory-dependent weighting. A plausible implication is that the phrase does not denote one theory of learning, but a family of models that reject the assumption that learning can be understood from static averages alone.

2. State-based and layered formalizations

One influential formalization appears in Bayesian nonparametric dynamic IRT, where learning is modeled as a dynamic latent process rather than a fixed trait. For student $i$, chapter $t$, and item $j$, the measurement model is

$$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$

Ability evolves through a first-order state-space process,

$$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$

so each learner follows a within-person trajectory in which $\delta_{it}$ represents systematic drift due to engagement and $\varepsilon_{it}$ unsystematic fluctuation. The model uses cubic B-spline basis expansions for nonlinear engagement effects and a Mixture-of-Finite-Mixtures prior to estimate the number of latent learner clusters without pre-specification (Ma et al., 14 Jun 2026).

A different but structurally similar formulation appears in human–robot interaction, where the human internal model is itself a nonlinear dynamical system:

$H^{t+1}=f_L(H^0, x^{0:t+1}, H^{0:t}).$

Here the state is the human’s internal model, and the inputs are observation and action histories. The key claim is that robot actions influence what the human observes and therefore influence how the human internal model changes. This moves the locus of learning from static estimation to history-dependent state evolution (Tian et al., 2023).

A more abstract formalization is provided by a five-layer structural coordinate system for learning dynamics. It separates external input $\frac{dx}{dt}=f(x)$0, load generation $\frac{dx}{dt}=f(x)$1, internal understanding transformation $\frac{dx}{dt}=f(x)$2, observation $\frac{dx}{dt}=f(x)$3, and subjective evaluation $\frac{dx}{dt}=f(x)$4. In that framework, cognitive load is a relational quantity generated by decomposing input relative to a contextual basis, internal learning occurs only in the understanding-transformation layer, and evaluation acts as a minimal regulatory interface rather than a utility function (Nakata, 20 Dec 2025).

These formulations differ in ontology, but they share a common architecture: a latent or internal state evolves over time, state change depends on temporally local inputs, and observed performance is a partial or indirect readout of that evolving state.

3. Educational measurement, practice history, and contextual adaptation

In online learning, dynamic IRT has been used to study longitudinal ability trajectories in a 9-chapter introductory statistics course with $\frac{dx}{dt}=f(x)$5 students. The posterior estimated number of clusters was $\frac{dx}{dt}=f(x)$6, yielding the profiles Struggling–Declining ($\frac{dx}{dt}=f(x)$7, 10.6%), Low–Stable ($\frac{dx}{dt}=f(x)$8, 25.8%), Mainstream–Stable ($\frac{dx}{dt}=f(x)$9, 52.0%), and High–Improving ($i$0, 11.6%). The central empirical result was that ability was highly stable over time: $i$1, corresponding to $i$2, and chapter-to-chapter variation within a student was only about 5% of the total between-cluster ability range. In the same dataset, average session duration and session count did not significantly predict ability drift: spline coefficients and cluster-specific scaling coefficients were near zero, 95% HPD intervals spanned zero, and estimated nonlinear drift functions were essentially flat (Ma et al., 14 Jun 2026).

Knowledge tracing work reaches a different but compatible conclusion about temporal specificity: recent practice can matter more than cumulative counts. In MF-DAKT, the recent factor records the most recent success, failure, or non-attempt on each relevant concept and discounts it by a forgetting function,

$i$3

The same model enriches question representations through question relation,

$i$4

and empirical difficulty, then uses a dual-attentional mechanism to weight factor contributions and factor interactions differently across records. On ASSIST2009, Algebra2006, and EdNet, the reported AUC values were 0.851, 0.844, and 0.776, respectively, and ablations showed losses from removing the recent factor, pre-training, difficulty regularization, or the dual-attentional mechanism (Zhang et al., 2021).

Age-dependent heterogeneity appears in AI-augmented programming education. A study of 53 students in authentic extracurricular computer science classrooms reported strong positive correlations across experience, clarity, comfort, and motivation for middle school students, but weak or near-zero correlations between key dimensions for high school students. At the aggregated level, middle school students showed Experience–Clarity $i$5 and Clarity–Motivation $i$6, whereas high school students showed Experience–Clarity $i$7, Experience–Motivation $i$8, and Experience–Comfort $i$9. Only one item-level difference remained significant after Bonferroni correction: Q3 (ease of use), with $t$0 and $t$1; 67.9% of high school students selected the highest ease-of-use option, compared with 24.0% of middle school students (Ebli et al., 24 Dec 2025).

These results support a recurrent distinction between quantity, recency, and structure. Quantity alone may be weakly predictive, as in the CourseKata engagement variables; recent concept-specific practice may be highly predictive, as in knowledge tracing; and the dependency structure among learning factors may itself vary by developmental stage.

4. Algorithmic learning dynamics in reinforcement learning and optimization

In Q-learning, dynamic factors influence not only speed of adaptation but estimation bias. The standard update

$t$2

contains three factors examined directly in stochastic and deep settings: the learning rate $t$3, the discount factor $t$4, and the reward signal $t$5. The reported findings were that large $t$6 propagates noisy optimistic targets more aggressively, high $t$7 compounds overestimation by propagating noisy future values backward, and stochastic rewards can be variance-reduced by replacing $t$8 with an exponential moving average $t$9. In Gridworld, a constant $j$0, $j$1, and averaging parameter $j$2 produced the best estimates in the reported tests; in CartPole, lowering $j$3 from 0.999 to 0.97 significantly improved estimation accuracy without hurting performance (Wagenbach et al., 2022).

For SGD, the central dynamic scaling parameter is the learning-rate-to-batch-size ratio. One general diffusion approximation is

$j$4

which makes the noise magnitude depend on $j$5. The general stationary relation reviewed in that work was

$j$6

so the expected loss depends on learning rate, batch size, Hessian, and gradient covariance rather than on the Hessian alone. Numerically, on ResNet-56 trained on CIFAR-10, keeping BS/LR fixed gave very similar trajectories, while $j$7 was consistently much larger than $j$8, with ratios ranging roughly from about 2.4 up to 11.8 (Luo et al., 2020).

Dynamic sample importance introduces another level of temporal specificity. DIT defines sample influence over a training window $j$9 through the counterfactual parameter change

$$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$0

and reports four recurring influence patterns: Early Influencers, Late Bloomers, Stable Influencers, and Highly Fluctuating Influencers. The paper also reports weak correlation between early-stage and late-stage influence rankings and argues that convergence-period analysis is more efficient and accurate for detecting corrupted samples than full-training analysis, with up to 0.99 correlation with ground truth and above 98% accuracy in detecting corrupted samples in complex architectures (Xu et al., 15 Feb 2025).

A plausible implication across these studies is that “learning dynamics” in algorithms are governed not only by model architecture or objective choice, but by temporal propagation parameters: step size, discounting, noise geometry, reward smoothing, and phase-specific sample importance.

5. Networked, social, and collective forms of learning

Network neuroscience frames learning as dynamic reconfiguration of modular organization. In a motor-sequence study of 18 right-handed adults across 3 fMRI training sessions over 5 days, whole-brain functional connectivity was measured for 112 cortical and subcortical regions and analyzed over 25 non-overlapping time windows per session. The key dynamic statistic was node flexibility, defined as the number of times a node changes community assignment across adjacent windows, normalized by the number of possible transitions. Flexibility increased from Session 1 to Session 2, then decreased from Session 2 to Session 3, and flexibility in one session predicted the relative amount of learning in the next session: Session 1 flexibility predicted Session 2 learning with $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$1, and Session 2 flexibility predicted Session 3 learning with $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$2 (Bassett et al., 2010).

Collective learning in teams can also be modeled as a coupled system of assignment, appraisal, and influence. In dynamic appraisal-network models, task performance is

$$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$3

with optimal assignment $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$4. In the most complete model, assignments are generated from the appraisal matrix and appraisals are updated both by performance feedback and by DeGroot-style influence. Under the reported conditions, the system converges to

$$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$5

meaning that the team achieves both collective learning and appraisal consensus. The paper also identifies failure modes, including insufficient observation connectivity, wrong assignment rules, and prejudiced opinion dynamics (Mei et al., 2016).

Learning on evolving semantic networks emphasizes temporal exposure and memory error. In textbook semantic graphs, the learner is modeled as a random walker with dilation

$$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$6

where $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$7 is walk time and $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$8 is textbook progression. If $$Y_{ijt}\mid \theta_{it}, b_{jt}\sim \text{Bernoulli}(p_{ijt}), \qquad \text{logit}(p_{ijt})=\theta_{it}-b_{jt}.$$9 is low, node and edge learning remain deeply incomplete before the book ends; the abstract states that learning can be an order of magnitude worse than in the asymptotic limit. The paper then studies three mental errors: forgetting $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$0, shuffling $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$1, and reinforcement $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$2. Forgetting caps usable memory, shuffling lowers precision while permitting limited future-edge prediction, and reinforcement slows exploration via an effective dilation $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$3 and increases path dependence (Klishin et al., 2022).

These accounts share a structural claim: learning depends not only on which units are connected, but on how connectivity changes, how information propagates through the network, and how temporary coalitions or traversals are stabilized or disrupted over time.

6. Steering, weighting, and simulating learning trajectories

Human–robot interaction research treats influence over learning as a planning problem. After inferring a model of human learning dynamics from demonstrations, the robot embeds that model into a joint planning state $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$4 so that its actions can deliberately steer the human’s internal model. Because the full problem is intractable, the paper uses a linear-quadratic approximation together with a transformer-based learning model. In simulation, Active Teach aligned the human internal model with the true robot dynamics faster than Passive Learn or Random, and in a user study with a 7DOF Kinova Jaco arm, active teaching significantly improved human action optimality distance $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$5; trajectories showed that the robot initially exaggerated the dynamics bias to teach the user, then reduced intervention as the user adapted (Tian et al., 2023).

Dynamic weighting of explanatory factors appears in longitudinal suicide-risk prediction. The model encodes posts with Sentence-BERT, models sequence context with a BiLSTM and temporal attention, predicts risk and protective factors with separate MLP stacks, and then learns whether protective or risk factors are effective for the current transition using $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$6. Protective factors are effective when $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$7 and risk factors when $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$8, and similarity-based scores $$\theta_{it}=\theta_{i,t-1}+\delta_{it}+\varepsilon_{it},$$9 and $\delta_{it}$0 are trained by a dynamic factor integration loss. On the Protective Factor-Aware Dataset built from 12 years of Reddit posts, the model achieved GP 0.8203, GR 0.5545, and FS 0.6617 on PFA, FS=0.8911 on CSSRS-Suicide, and FS=0.6861 on RSD-15K; removing dynamic factor integration dropped FS to 0.6764 in the reported ablation setting (Li et al., 14 Jul 2025).

Longitudinal simulation with LLM-based agents supplies a further distinction between apparent and robust learning. LearnerAgent models a 12-month English grammar learning journey with weekly learning, monthly strategic choices, monthly exams, peer debate, and self-concept evaluation. The reported headline result is that only the Deep Learner achieves sustained cognitive growth. Trap questions diagnose shortcut learning: the Surface Learner performs well on review questions but poorly on trap questions, while the persona-free General Learner behaves like a “diligent but brittle surface learner.” The General Learner also develops surprisingly high self-efficacy despite cognitive limitations (Yuan et al., 7 Aug 2025).

A common feature across these studies is interpretability through dynamic weights or trajectories. In the robot-teaching case, action sequences reveal when intervention is teaching rather than merely assisting. In the suicide-risk model, $\delta_{it}$1 and $\delta_{it}$2 provide interpretable weights for which factor type dominates a transition. In LearnerAgent, longitudinal performance, debate behavior, and self-concept separate short-term test success from deeper transfer.

7. Interpretation, controversies, and design implications

A recurrent misconception is that identifying dynamic factors implies large short-term malleability. The evidence is more differentiated. The dynamic IRT model was explicitly designed to detect within-person ability drift, nonlinear engagement effects, and latent heterogeneity, yet its empirical conclusion for the CourseKata statistics course was that ability looked more like a stable pre-existing characteristic than a rapidly changing within-semester outcome, and engagement quantity did not significantly predict drift (Ma et al., 14 Jun 2026). By contrast, robot teaching, dynamic factor integration, and network flexibility studies report situations in which learning trajectories or future learning capacity are meaningfully shaped by temporally structured intervention or reconfiguration (Tian et al., 2023, Bassett et al., 2010).

A second misconception is that aggregate or static measurements are sufficient. Complex-systems work explicitly argues that averages can be misleading, group-level networks may not represent individual learners well, and temporal methods such as network analysis and recurrence quantification analysis are needed to study stability, transition, and attractor-like behavior (Saqr et al., 2024). DIT makes a parallel point for machine learning: early and late sample influences are only weakly correlated in many settings, indicating distinct learning phases rather than a single homogeneous training process (Xu et al., 15 Feb 2025).

A third misconception is that more activity, more verbosity, or more apparent engagement necessarily implies deeper learning. The online statistics study found that session duration and session count were not meaningful predictors of ability drift (Ma et al., 14 Jun 2026). LearnerAgent found that longer reasoning does not necessarily imply deeper reasoning, and that the General Learner can appear diligent while remaining brittle on trap questions (Yuan et al., 7 Aug 2025). In adaptive learning systems, this suggests that raw usage metrics are insufficient and that richer indicators such as retrieval practice, self-testing, spacing, interleaving, response revision, or context-aware behavioral signals may be needed when the goal is to detect or influence learning trajectories (Abu-Rasheed et al., 2023).

Across the cited work, the most stable synthesis is that dynamic factors influence learning through timing, nonlinear weighting, exposure, propagation, and feedback. What changes across domains is not the relevance of dynamics, but the object whose trajectory is being modeled: latent ability, knowledge state, policy value, sample influence, internal model, modular brain organization, appraisal network, or semantic memory. This suggests that the central research problem is less whether learning is dynamic than which dynamic variables, timescales, and interaction structures are most informative for a given learning system.