arXiv subjects

Cancan Wang

Publications and source records attributed to Cancan Wang.

2 recordsLinked to original sources

arXiv2026

Sticky Help, Bounded Effects: Session-by-Session Analytics of Teacher Interventions in K-12 Classrooms

Teachers' in-the-moment support is a limited resource in technology-supported classrooms, and teachers must decide whom to help and when during ongoing student work. However, less is known about how students' prior help history (whether they were helped earlier) and their engagement states (e.g., idle, struggle) shape teachers' decisions, and whether observed learning benefits associated with teacher help extend beyond the current class session. To address these questions, we first conducted interviews with nine K-12 mathematics teachers to identify candidate decision factors for teacher help. We then analyzed 1.4 million student-system interactions from 339 students across 14 classes in the MATHia intelligent tutoring system by linking teacher-logged help events with fine-grained engagement states. Mixed-effects models show that students who received help earlier were more likely to receive additional help later, even after accounting for current engagement state. Cross-lagged panel analyses further show that teacher help recurred across sessions, whereas idle behavior did not receive sustained attention over time. Finally, help coincided with immediate learning within sessions, but did not predict skill acquisition in later sessions, as estimated by additive factor modeling. These findings suggest that teacher help is "sticky" in that it recurs for previously supported students, while its measurable learning benefits in our data are largely session-bound. We discuss implications for designing real-time analytics that track attention coverage and highlight under-visited students to support a more equitable and effective allocation of teacher attention.

cs.CY↗

arXiv2024

A New Reduction Method from Multivariate Polynomials to Univariate Polynomials

Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of two multivariate polynomials. Therefore, we consider a new multiplication mechanism that involves a) reversibly reducing multivariate polynomials into univariate polynomials, b) calculating the product of the derived univariate polynomials by the Toom-Cook or FFT algorithm, and c) correctly recovering the product of multivariate polynomials from the product of two univariate polynomials. This work focuses on step a), expecting the degrees of the derived univariate polynomials to be as small as possible. We propose iterative Kronecker substitution, where smaller substitution exponents are selected instead of standard Kronecker substitution. We also apply the Chinese remainder theorem to polynomial reduction and find its advantages in some cases. Afterwards, we provide a hybrid reduction combining the advantages of both reduction methods. Moreover, we compare these reduction methods in terms of lower and upper bounds of the degree of the product of two derived univariate polynomials, and their computational complexities. With randomly generated multivariate polynomials, experiments show that the degree of the product of two univariate polynomials derived from the hybrid reduction can be reduced even to approximately 3% that resulting from the standard Kronecker substitution, implying an efficient subsequent multiplication of two univariate polynomials.

cs.CC↗