Strategies for Controlling the Work in Mathematics Textbooks for Introductory Calculus

This study analyzes the availability of strategies for (1) deciding whether an action is relevant when solving a problem, (2) determining that an answer has been found, and (3) establishing that the answer is correct in 80 examples of Initial Value Problems (IVPs) in twelve calculus textbooks intended for first-year undergraduate calculus. Examples in textbooks provided explicit information about deciding what to do to solve the problem and determining the answer more frequently than they discussed establishing that the solution is correct or that it makes sense for the given situation. Strategies geared toward verification that the answer is correct or makes sense correspond to three aspects of verification: plausibility, correctness, and interpretation. Honors textbooks were more explicit than non-honors textbooks. Presenting examples as a collection of steps to solve problems without consideration of what needs to be done to verify that the answer is correct might obscure the need for verification in solving problems and suggest that reworking the solution is the only verification alternative. Implications for research and practice are