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

Presenters: Steven Jones, Haley Jeppson, and Doug Corey, Brigham Young University
Location: 22nd Annual Conference on Research on Undergraduate Mathematics Education, Oklahoma City, Oklahoma
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.

Variational Reasoning Used by Student While Discussing Differential Equations

Presenters: George Kuster, Christopher Newport University and Steven Jones, Brigham Young University
Location: 22nd Annual Conference on Research on Undergraduate Mathematics Education, Oklahoma City, Oklahoma
Abstract/Description:
In this study we investigated how a small sample of students used variational reasoning while discussing ordinary differential equations. We found that students had flexibility in thinking of rate as an object, while simultaneously unpacking it in the same reasoning instance. We also saw that many elements of covariational reasoning and multivariational reasoning already discussed in the literature were used by the students. However, and importantly, new aspects of variational reasoning were identified in this study, including: (a) a type of variational reasoning not yet reported in the literature that we call “feedback variation” and (b) new types of objects, different from numeric-quantities, that the students covaried.

Influences from Pathways College Algebra on Students’ Initial Understanding and Reasoning about Calculus Limits

Presenters: Brianna Levia, Navy Borrowman, Dawn Teuscher, and Steven Jones, Brigham Young University
Location: 22nd Annual Conference on Research on Undergraduate Mathematics Education, Oklahoma City, Oklahoma
Abstract/Description:
The Pathways to College Algebra curriculum aims to build concepts that cohere with the big ideas in Calculus, and initial results suggest improved readiness for Calculus by students who have taken a Pathways class. However, less is known about how Pathways might influence students’ initial understanding and reasoning about calculus concepts. Our study examines similarities and differences in how Pathways and non-Pathways students initially understand and reason about the calculus concept of the limit. Our findings suggest that Pathways students may engage a little more in quantitative reasoning and in higher covariational reasoning, and have more correct and consistent initial understandings. Further, the Pathways students were explicitly aware of how their Pathways class may have benefited their understanding of limits.

To Pursue or Not to Pursue: Making Decisions about Student Mathematical Thinking

Presenters: Blake E. Peterson, Brigham Young University; Keith R. Leatham, Brigham Young University; and Laura Van Zoest, Western Michigan University
Location: NCTM 2019 in San Diego, California
Abstract/Description:
Incorporating student mathematical thinking into classroom instruction is a best practice, but not all student thinking provides the same leverage for accomplishing mathematical goals. Learn about characteristics of student thinking that can be used to determine which thinking has significant potential to support students’ learning of mathematics.