Analysis of errors and improvements in numerical approximations and methods in secondary mathematics curriculum

This report discusses three topics relating to errors of numerical methods and to improvements of numerical approximations. The introduction connects these topics to the secondary mathematics curriculum. The three chapters which follow develop the three selected topics: improving approximations of irrational numbers, error analysis of numerical integration methods, and discretization versus rounding error in Euler’s Method for solving ordinary differential equations. The conclusion describes specific national secondary mathematical standards and classroom activities relevant to numerical approximations and error analysis.