Potential Intellectual Needs for Taylor and Power Series within Textbooks, and Ideas for Improving Them

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Abstract/Description:

Unfortunately, students far too often have little or no intellectual need for learning the second semester calculus topic of Taylor and power series. In this study, we examine the “potential intellectual needs” (PINs) provided by commonly used textbooks. While the textbooks used different approaches, they both often lacked problems developing intellectual need, suggesting that instructors must incorporate intellectual need by themselves. To assist in this endeavor, we focus part of the paper on a discussion of including PINs for this content. We found that it may be difficult to incorporate genuine problems for first-year students through an approach based on a “family of series” meaning for Taylor/power series, but that stronger problems could be incorporated through an approach based on an “extension of linear approximation” meaning.


Location: 22nd Annual Conference on Research on Undergraduate Mathematics Education, Oklahoma City, Oklahoma
Presenter:

Steven Jones, Haley Jeppson, and Doug Corey, Brigham Young University