Strategies for Controlling the Work in Mathematics Textbooks for Introductory Calculus

This study analyzes the availability of strategies for (a) deciding whether an action is relevant when solving a problem, (b) determining that an answer has been found, and (c) establishing that the answer is correct in 80 ex- amples 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 a solution is correct or that it makes sense for the given situation. Strategies geared to- ward 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 exam- ples 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 to students that reworking the solution is the only verification alternative. Implications for research and practice are discussed.

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