Strategies for Controlling the Work in Mathematics Textbooks for Introductory Calculus
Strategies for Controlling the Work in Mathematics Textbooks for Introductory Calculus
复制标题
控制微积分入门数学教科书工作的策略
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
V. Mesa
中科院分区：
文献类型：
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作者：
V. Mesa
本研究分析了策略的可用性，以（a）决定一个行动是否是相关的解决问题时，（B）确定一个答案已经找到，（c）建立答案是正确的80例初值问题（IVP）的12本微积分教科书打算为一年级微积分。教科书中的例子提供了关于决定如何解决问题和确定答案的明确信息，而不是他们讨论确定解决方案是正确的或对给定情况有意义的。为了验证答案是正确的或有意义的策略对应于验证的三个方面：可验证性，正确性和解释。荣誉教材比非荣誉教材更明确。将示例作为解决问题的步骤的集合来呈现-而不考虑需要做什么来验证答案是正确的-可能会掩盖解决问题时验证的必要性，并向学生暗示重新制定解决方案是唯一的验证选择。研究和实践的影响进行了讨论。
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.