Model Comparison and Selection

A comprehensive unit where students act as data scientists to model real-world environmental phenomena using trigonometric functions. They progress from visual estimation to precise algebraic modeling and technological regression to predict future environmental conditions.

This sequence explores real-world applications of rational exponents across biology, astronomy, music, finance, and physics. Students transition from abstract algebraic manipulation to applying fractional powers to model complex natural and human-made systems.

A graduate-level exploration of non-linear bivariate analysis, moving from the limitations of linear correlation to rank-based methods, local regression, and information-theoretic metrics. Students develop the skills to quantify complex dependencies in biological, financial, and environmental systems where standard assumptions fail.

A graduate-level project-based sequence focused on the rigorous comparison and selection of mathematical models. Students progress from strategy definition and candidate generation to statistical benchmarking and stability analysis, culminating in a professional-grade technical defense.

A technical workshop sequence for 11th-grade students focusing on cross-validation techniques, including train-test splits, MSE calculation, and K-Fold validation to assess and select robust mathematical models.

This sequence guides undergraduate students through the transition from descriptive statistics to predictive modeling. It covers hypothesis testing, linear and multiple regression, model evaluation, and logistic classification, emphasizing both mathematical foundations and practical coding implementation.

This sequence moves beyond simple error metrics to explore sophisticated selection criteria that penalize complexity, specifically AIC and BIC. Students learn to balance model fit with parsimony through real-world datasets and comparative analysis.

An advanced 12th-grade mathematics sequence focusing on model evaluation and selection. Students explore the bias-variance trade-off, information criteria (AIC/BIC), and cross-validation to select optimal predictive models.

A project-based exploration of stochastic modeling, focusing on Queueing Theory and Monte Carlo simulations. Students design and build computational models to optimize real-world systems like traffic flow and service lines.

A project-based unit where students apply polynomial calculus concepts to real-world scenarios like business profits, projectile motion, and engineering design. Students transition from abstract solving to modeling data and optimizing outcomes using regression, intercepts, and extrema.

An advanced graduate-level sequence exploring the mathematical foundations of model selection, including bias-variance decomposition, information criteria (AIC/BIC), resampling methods, and high-dimensional diagnostic strategies.

This sequence guides undergraduate students through model comparison and selection, covering the bias-variance tradeoff, cross-validation methods, and information criteria (AIC/BIC). Students will learn to balance model complexity with generalization ability to select the most robust models for prediction and inference.

A targeted Tier 2 intervention lesson focusing on informally assessing function fit using residual plots, designed for small group instruction with scaffolded support and technology integration.

Students will learn to use the R-squared value in GeoGebra to mathematically justify the choice between linear and exponential regression models through a competitive 'Regression Battle' activity.

A lesson introducing students to regression and the 'line of best fit' by moving from manual estimation to computer-aided modeling using real-world messy data.

Students transition from textbook-perfect functions to real-world data analysis using GeoGebra. They will learn to perform linear and exponential regressions, interpret the R-squared value to determine the best fit, and apply these skills to distinguish between population growth and linear accumulation.

A technical, hands-on lesson teaching 11th-grade students how to perform linear and exponential regressions using GeoGebra, transitioning from textbook examples to messy real-world data analysis.

A high school interdisciplinary lesson connecting physics and algebra. Students analyze real-world lab data using linear and exponential regression in GeoGebra, exploring why experimental data rarely fits perfect mathematical models and how R-squared measures the quality of a fit.