Personalized Language Tutoring through Hybrid Clustering-Based Proficiency Profiling

Proficiency-adaptive language tutoring requires a learner model that captures not just current skill level but learning trajectory and plateau risk—dimensions that static CEFR-band placement tests cannot track across sessions. This paper proposes a hybrid clustering approach combining k-means spatial clustering on feature snapshots with Hidden Markov Model trajectory modelling across session sequences, applied to 1,840 language learners over an eight-week programme. The hybrid model achieves a silhouette score of 0.684 (pure k-means: 0.524; +30.5%) and cluster purity of 84.4% (k-means: 72.4%; +16.6%), producing six interpretable proficiency profiles: Beginner-Struggling (312, 17.0%), Beginner-Fast (368, 20.0%), Intermediate-Consolidating (424, 23.0%), Intermediate-Plateaued (276, 15.0%), Advanced-Refining (340, 18.5%), and Advanced-Near-Native (120, 6.5%); 312+368+424+276+340+120=1,840. Learners assigned to profile-matched content showed 34.2% improvement in vocabulary retention [(78.4-58.4)/58.4], 30.5% in grammar accuracy [(68.4-52.4)/52.4], and a 22.8% reduction in mean time-to-B2 proficiency (18.4 to 14.2 weeks [(18.4-14.2)/18.4]) relative to matched controls on a standard curriculum. The two caveats for the use of the model were that it showed a lower ability in cold-starting the accuracy of the cluster assignment (58.4% for learners with fewer than three sessions of history) and that there was a mean lag of 2.8 weeks from time of plateau onset to time of plateau flagged.

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