Enhancing Math Learning in an LMS Using AI-Driven Question Recommendations

Justus R{\aa}munddal

REVIEW 5 major objections 5 minor 20 references

Enhancing Math Learning in an LMS Using AI-Driven Question Recommendations

T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper argues that in a math learning platform, recommending questions with moderate variety—as self-organizing maps do—produces higher user satisfaction than near-identical cosine matches, while Gaussian-mixture recommendations…

desk verdict Honest applied comparison, but the SOM satisfaction claim is statistically unsupported and the conclusion overstates session duration; worth refereeing after adding inference and fixing the overclaim. read the letter →

arxiv 2504.14098 v1 pith:2TVQDNUT submitted 2025-04-18 cs.LG cs.AIcs.CYcs.IR

Justus R{aa}munddal This is my paper · ORCID

classification cs.LGcs.AIcs.CYcs.IR

keywords mathlearningmanagementsystemquestionrecommendationself-organizingmapsGaussianmixturemodelscosinesimilaritydeepembeddingslargelanguage

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tests whether three AI question-recommendation methods behave differently in a real math learning platform, and whether the differences matter for engagement. Questions are converted into 4096-dimensional embeddings using a vision-language model, then similar questions are recommended by cosine similarity, by a self-organizing map, or by a Gaussian mixture model compared with KL divergence. The central finding is that the SOM method, which introduces a controlled degree of variety, earns the highest user ratings and a more balanced pattern of wrong-answer streaks, while cosine similarity returns near-identical questions and GMM underperforms on nearly all metrics. If this holds, system designers should treat moderate variety as a feature of educational recommendations, not a compromise.

What carries the argument

The central objects are three recommendation pipelines over a shared embedding space. Llama-3.2-11B-Vision-Instruct produces a 4096-dimensional mean-pooled vector for each math question, including visual elements. Cosine similarity ranks candidates by direct vector closeness. A self-organizing map (SOM) with a 5×8 grid and 1000 training epochs maps the embedding space onto a two-dimensional lattice; at query time it finds the best-matching unit and then picks the question with smallest Euclidean distance within that neuron's cluster, a mechanism that injects bounded variety. A Gaussian mixture model (GMM), with component counts per subject chosen by BIC (16–31 components), converts each question to a posterior-probability vector, and candidates are ranked by KL divergence between those vectors. The argument runs on the contrast between these similarity notions: exact vector distance, topology-preserving neighborhood, and probability-profile divergence.

What would settle it

Compute rating submission rates per algorithm and run a pre/post math test; if SOM sessions are rated disproportionately often, the satisfaction gap would be a selection artifact, and if learning gains do not follow the engagement ordering, the educational benefit claim would fail.

Watch

Extended reading notes

Core claim

In the author's own terms: for the SweSAT math practice system, cosine similarity retrieves questions that are almost identical to the source, producing confident but repetitive sessions; the SOM-based method clusters embeddings on a 5×8 grid and then selects the nearest question inside the best-matching neuron, delivering recommendations that are still topically close but not carbon copies; the GMM method represents each question by its posterior probabilities over Gaussian components and ranks candidates by KL divergence, which in practice produced recommendations that felt dissimilar to users. Measured across 1,855 sessions, SOM users gave the highest average ratings (4.17 of 5, median 5), GMM gave the lowest (3.96), and cosine sat in between (4.05); session lengths and question counts were similar across methods, but GMM sessions were shortest. The paper interprets this as evidence that moderate novelty supports engagement, while similarity judged on probability profiles can lose touch with perceived pedagogical similarity.

Load-bearing premise

The comparison is only as good as the measures: user ratings and engagement metrics are assumed to reflect recommendation quality, and the users who submit ratings are assumed to represent all users.

Editorial extensions

If this is right

For this LMS, cosine similarity should not be the default recommender: its near-identical matches correlate with the lowest user ratings and longer wrong-answer streaks.
The GMM/KL-divergence configuration underperforms; switching to a cluster-oriented GMM (assigning each question to its top component, then using direct distance) or to Jensen–Shannon divergence is a concrete repair to test.
SOM's balance of similarity and novelty suggests that recommendation algorithms for education should be tuned to a variety sweet spot, not to maximum precision.
Engagement metrics such as ratings, session length, and streak distributions can discriminate between recommenders, but only if the rating subsample is trustworthy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the variety effect is causal, an LMS could deliberately interpolate between cosine and SOM outputs to tune a difficulty/novelty dial per student, a design the paper does not test.
The comparison treats the embedding model as fixed; a weaker or stronger embedding model could change which recommender wins, so the ranking is conditional on Llama-3.2-11B-Vision-Instruct.
A plausible confound is rating self-selection: users who rate may differ systematically across algorithms, so the satisfaction ordering should be re-checked with rating-propensity weights.
Wrong-answer streak distributions may matter more to perceived learning than mean correctness, a hypothesis worth testing with pre/post skill assessments.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The short version: this is an honest applied comparison, but the headline satisfaction claim is not supported by the reported numbers. The SOM-minus-cosine rating difference is 0.12 on a 1–5 scale with standard deviations around 1.2, and there are no significance tests, confidence intervals, or corrections for repeated sessions. The conclusion also says SOM yields longer session durations, which contradicts Table 1, where cosine has the longest mean and median. Those two problems, plus the absence of code and data, are what separate this from a solid empirical paper.

What is actually new: the three-way comparison of cosine similarity, SOM, and GMM-with-KL on Llama embeddings for SweSAT math questions. The algorithms are standard, but the deployment is real and the log data look genuine. The paper does several things right. It randomizes algorithm assignment, logs both session-level and question-level interactions, reports wrong-answer streaks, and explicitly says in Section 4.6 that it does not measure long-term learning gains. That last point is honest, even though it means the abstract's phrase 'potential learning outcomes' is speculation. The explanation for GMM's underperformance—KL divergence over posterior vectors being too sensitive to small probability differences—is plausible and consistent with the cited literature.

The soft spots are proportionate. The rating data are optional, with only about 55% of sessions rated per algorithm, and there is no analysis of which users rate. That is a self-selection confound. A 0.12 mean gap with overlapping distributions could easily be noise; I would not walk away from this paper believing SOM is the better recommender. The session-duration overclaim is a factual slip in the conclusion, even though the discussion in Section 4.1 tries to hedge it. Outlier filtering is ad hoc, and the number of tunable choices (SOM grid size, epochs, learning rate, GMM components per subject, outlier thresholds) is large enough to raise a suspicion of overfitting—though the paper at least reports these choices. No code or data are released, which blocks independent verification.

Who should read it: practitioners building educational recommender systems, especially in LMS settings. It is a concrete, readable example of how to evaluate deployed recommenders and where the pitfalls are. It is not a field-changing result and should not be cited as one. A serious referee would have a clear job to do. I would send this to review rather than desk-reject it, expecting the author to add inferential statistics, fix the duration claim, and release anonymized data or at least a reproducibility package.

Referee Report

5 major / 5 minor

Summary. The paper reports a field study in a SweSAT-oriented LMS comparing three question-recommendation methods: cosine similarity on 4096-dimensional embeddings from Llama-3.2-11B-Vision-Instruct, a Self-Organizing Map with intracluster Euclidean ranking, and a Gaussian Mixture Model whose component posteriors are compared via KL divergence. Interaction data from 1855 quiz sessions were analyzed through session durations, question counts, optional user ratings, correctness rates, response times, and wrong-answer streaks. The abstract and §4.1 claim that cosine similarity retrieves nearly identical questions, that SOM yields higher user satisfaction, and that GMM generally underperforms, which is interpreted as evidence that moderate variety may improve engagement.

Significance. If the comparative claims were supported, the study would provide a practically useful data point for educational recommender design: moderate topological variety (SOM) beating strict cosine similarity and probabilistic-profile similarity (GMM) in a live LMS. Strengths include real deployment with randomized assignment to algorithms (as cited in §2.3), detailed logging of session and question-level events, and transparent reporting of tuning hyperparameters in §2.2. The paper is also honest about limitations, acknowledging that engagement metrics do not measure learning gains (§4.6). However, the statistical evidence for the headline claims is currently weak: the rating differences are small relative to their spread, no significance tests or confidence intervals are provided, the rating subsample is self-selected, and at least one statement in the conclusion is contradicted by the paper's own Table 1. The central thesis is plausible but not yet established by the analysis as presented.

major comments (5)

[§5 and Table 1] The conclusion states that the SOM-based approach results in 'longer session durations' and, in §4.1, that SOM has a 'more consistent engagement profile' partly based on duration. Table 1 contradicts this: cosineSimilarityAlg has a mean session duration of 25.63 minutes and median 13.13, while somSimilarityAlg has mean 22.33 and median 12.32. The claim of longer durations for SOM is not supported by the reported data and must be corrected or re-analyzed; this contradiction is load-bearing for the engagement narrative.
[Table 3 and §4.1] The central claim that 'SOM yields higher user satisfaction' rests on rating means of 4.17 (SOM, n=234), 4.05 (cosine, n=221), and 3.96 (GMM, n=238) with standard deviations between 1.13 and 1.25. No significance tests, confidence intervals, or effect sizes are reported, and the differences are well within the noise implied by the spread. Because ratings are optional (§2.3), the subset with ratings may not be representative, and the paper does not analyze rating propensity or adjust for repeated sessions by the same user. These data do not support the strength of the claim as stated; the authors should add appropriate statistical tests, cluster-robust procedures, and a discussion of selection bias.
[§3.3, Table 4, and §4.2] The discussion of wrong-answer streaks over-interprets descriptive percentages. The paper asserts that cosine similarity has 'wrong-answer streaks distributed higher over streak lengths longer than 1' and that SOM shows a 'balanced distribution', but Table 4 shows mixed patterns: cosine has the highest percentage at length 2 (22.42%), while SOM has the highest at length 4 (3.65% vs 3.77% for cosine? actually cosine 3.77% and SOM 3.65%) and GMM at length 1 (67.01%). These differences are likely within sampling noise, and no formal test is provided. The conclusions drawn from this table should be toned down or supported with inference.
[§2.3 and Tables 1–2] The outlier filtering rules are described as applying to 'some analysis' and differ between tables: Table 1 removes sessions outside the 5th–95th percentiles of duration, while Table 2 removes only sessions shorter than 5 seconds and those without durations. This inconsistency makes the engagement metrics across methods not directly comparable, since the filtering can differentially affect the mean and median for each algorithm. The authors should either apply a consistent, pre-registered filtering rule or report results under multiple definitions to show robustness.
[§2.3 and §3] The analyses treat sessions as independent observations, but the same user can appear in multiple sessions (the data logs include user identification 'when available'). If users contribute multiple sessions, the reported means and any future significance tests would need to account for user-level clustering. The paper should state the number of unique users and either apply cluster-robust standard errors or a mixed-effects model when comparing algorithms.

minor comments (5)

[Abstract] The final clause, 'which our data about the implementations of all three methods demonstrate', is grammatically awkward and obscures the claim; consider rewriting the abstract for clarity.
[Figure 6] The bar chart caption does not specify which bar corresponds to which algorithm; the authors should label each bar or add a legend.
[§2.3] The description of randomization says algorithms were applied 'in a randomized manner', but the session counts differ (367, 415, 444/421, etc.). A brief check that assignment was balanced, or a discussion of why counts differ, would strengthen the claim of unbiased assignment.
[§2.2.3] The SOM hyperparameters (5×8 grid, 1000 epochs, learning rate 0.5) are stated, but no sensitivity analysis is provided for the grid size or epoch count; given that the paper's conclusions depend on SOM's behavior, a small robustness check would be helpful.
[Table 4] The table reports percentages to two decimal places, but for several cells the values appear to be based on small counts; stating raw counts or confidence intervals would avoid over-precision.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the comparison is an external empirical evaluation; no prediction reduces to its own inputs.

full rationale

The paper's central claims are empirical comparisons among three recommendation algorithms evaluated on user interaction data logged in the author's own LMS. No step in the derivation chain equates an output metric to a fitted parameter by construction. Hyperparameters for SOM and GMM are chosen from embeddings via preliminary experiments, BIC/silhouette scores, and manual distribution checks (Sections 2.2.3 and 2.2.4), not from the target evaluation metrics such as user ratings or session duration, so there is no fitted-input-called-prediction pattern. The satisfaction claim compares observed rating distributions (Table 3), and the engagement-profile claim summarizes other observed metrics; these are data descriptions, not quantities defined in terms of each other. The paper explicitly notes limitations (Section 4.6) that session metrics do not measure long-term learning gains, and it acknowledges that ratings are optional (Section 2.3, Table 3 notes); such concerns affect evidential strength and statistical validity, not circularity. No self-citation is load-bearing, no uniqueness theorem is imported, and no known result is merely renamed. The derivation is self-contained with respect to circularity, so the appropriate score is 0; any weaknesses are methodological or statistical, not circular.

Assumptions & free parameters 6 free parameters · 3 assumptions · 0 invented entities

The central claim relies on embeddings from a pretrained model whose math-similarity quality is assumed, and on engagement and rating proxies rather than direct learning outcomes. No new entities are introduced; all listed free parameters are tuning or filtering choices that influence the reported differences.

free parameters (6)

SOM grid size = 5 x 8 (40 neurons)
Chosen by manual evaluation as a trade-off between resolution and overfitting; affects cluster granularity and recommendations.
SOM training epochs = 1000
Set to stabilize the map; authors note acceptable maps at 100 epochs, so this is a tuning choice.
SOM learning rate schedule = 0.5 with linear decay
Initial rate selected from common practice and cited literature.
GMM component counts per subject = XYZ:16, KVA:18, NOG:15, DTK:31
Selected via BIC and silhouette scores on the question embeddings; fitted to the data.
GMM covariance, init, convergence = full covariance, k-means init, tol 1e-3, max 100 iterations
Standard hyperparameters chosen for the mixture model.
Outlier exclusion thresholds = sessions outside 5th to 95th percentile duration; sessions under 5 seconds
Post hoc filtering that changes the duration and count analyses.

assumptions (3)

domain assumption Llama-3.2-11B mean-pooled embeddings capture semantic and pedagogical similarity among math questions.
Section 2.1 assumes the embedding space is a valid foundation for all three recommendation methods, without a benchmark against human judgments or known question similarity.
domain assumption User ratings, session duration, question count, and response times are adequate proxies for recommendation quality and potential learning.
Section 4.6 acknowledges these do not measure knowledge gains; the central satisfaction claim relies on these proxies.
domain assumption Random assignment of algorithms to sessions is unbiased and the optional-rating subset is representative.
Section 2.3 cites Kohavi et al. for randomization but gives no balance checks or analysis of who rates; Table 3 shows fewer than 60 percent of sessions have ratings.

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Cite this review

Pith. "Pith review of Enhancing Math Learning in an LMS Using AI-Driven Question Recommendations." pith.science (2026). https://pith.science/paper/2TVQDNUT

@misc{pith2026250414098,
  author       = {Pith},
  title        = {Pith review of: Enhancing Math Learning in an LMS Using AI-Driven Question Recommendations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2TVQDNUT}},
  note         = {Machine review of arXiv:2504.14098}
}

read the original abstract

This paper presents an AI-driven approach to enhance math learning in a modern Learning Management System (LMS) by recommending similar math questions. Deep embeddings for math questions are generated using Meta's Llama-3.2-11B-Vision-Instruct model, and three recommendation methods-cosine similarity, Self-Organizing Maps (SOM), and Gaussian Mixture Models (GMM)-are applied to identify similar questions. User interaction data, including session durations, response times, and correctness, are used to evaluate the methods. Our findings suggest that while cosine similarity produces nearly identical question matches, SOM yields higher user satisfaction whereas GMM generally underperforms, indicating that introducing variety to a certain degree may enhance engagement and thereby potential learning outcomes until variety is no longer balanced reasonably, which our data about the implementations of all three methods demonstrate.

Figures

Figures reproduced from arXiv: 2504.14098 by the authors.

**Figure 2.** A count plot shows that the study includes 1855 quiz sessions distributed among the three algorithms. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Boxplots of quiz durations indicate that the central 90% (5th to 95th percentiles) of session durations range [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: This boxplot shows the distribution of the number of questions per quiz session for each recommendation [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Shows the distribution of user ratings on a provided scale from 1 to 5 where 5 is the best rating. Note: Users [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: A bar chart comparing correctness rates shows that the average quiz session correctness over each respective [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: The figure displays the distribution of question response times for three recommendation algorithms. For [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: A plot illustrating consecutive wrong-answer streaks within sessions. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: A plot illustrating how the GMM as a clustering method determined components (clusters). It might be useful [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

S., Schoenebeck, G., and Dhillon, P

Anwar, M. S., Schoenebeck, G., and Dhillon, P. S. (2024). Filter Bubble or Homogenization ? Disentangling the Long - Term Effects of Recommendations on User Consumption Patterns . Version Number: 2

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[2] [2]

Bhaskaran, S., Marappan, R., and Santhi, B. (2021). Design and Analysis of a Cluster - Based Intelligent Hybrid Recommendation System for E - Learning Applications . Mathematics , 9(2):197

work page 2021

[3] [3]

Bishop, C. M. (2006). Pattern recognition and machine learning . Information science and statistics. Springer, New York

work page 2006

[4] [4]

L., Slodkowski, B

da Silva, F. L., Slodkowski, B. K., da Silva, K. K. A., and Cazella, S. C. (2023). A systematic literature review on educational recommender systems for teaching and learning: research trends, limitations and opportunities. Education and Information Technologies , 28(3):3289--3328

work page 2023

[5] [5]

Guérin, A., Chauvet, P., and Saubion, F. (2025). A Survey on Recent Advances in Self - Organizing Maps . Version Number: 1

work page 2025

[6] [6]

and Gkintoni, E

Halkiopoulos, C. and Gkintoni, E. (2024). Leveraging AI in E - Learning : Personalized Learning and Adaptive Assessment through Cognitive Neuropsychology — A Systematic Analysis . Electronics , 13(18):3762

work page 2024

[7] [7]

Ibrahim, O. A. S., Younis, E. M. G., Mohamed, E. A., and Ismail, W. N. (2025). Revisiting recommender systems: an investigative survey. Neural Computing and Applications , 37(4):2145--2173

work page 2025

[8] [8]

K., Anamisa, D

Khotimah, B. K., Anamisa, D. R., Kustiyahningsih, Y., Fauziah, A. N., and Setiawan, E. (2024). Enhancing Small and Medium Enterprises : A Hybrid Clustering and AHP - TOPSIS Decision Support Framework . Ingénierie des systèmes d information , 29(1):313--321

work page 2024