Modeling the Cyclical Effects of Seasonal Teacher Retention on School Performance through Trigonometric Equation Analysis

This study investigates the cyclical effects of seasonal teacher retention on school performance through trigonometric regression modeling. A sinusoidal model was selected to capture periodic, wave-like fluctuations that alternative models fail to represent. Using performance data from 2013–2025 at Warren County High School in Warrenton, North Carolina, the analysis revealed recurring fluctuations that closely align with teacher turnover and reassignment cycles. The derived model, Performance (x) = 6.07 sin (70.67x + 52.32) + 48.13, achieved a goodness of fit of R² = 80.37%, capturing one full performance cycle approximately every five to six academic years. The amplitude (A = 6.07) reflects the extent of performance variation, while the phase shift (C = 52.32) demonstrates the delayed effect of staffing transitions, and the vertical shift (D = 48.13) represents the baseline performance level. This research introduces a novel mathematical framework for educational policy, demonstrating that performance declines coincide with teacher loss while recovery follows instructional stability. To mitigate these cyclical downturns, the study advocates a shift from temporary staffing to long-term residency pathways and stabilized teacher assignments. By linking mathematical modeling with workforce policy design, this research provides an innovative framework for sustaining consistent academic growth.