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College students’ understanding of rational exponents: a teaching experiment

Elstak, Iwan Rene
http://rave.ohiolink.edu/etdc/view?acc_num=osu1186505864

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Teaching and Learning.
The study examines the understanding college students have of the concept of rational and negative exponents and the justifications for their notions of exponents. Pre- interviews with novice and expert mathematics students suggested, that novice students had fragmented notions of exponents. In applications with rational and negative exponents novice students relied on operational procedures and the authority of teachers. Neither novice students nor expert students proposed integrated concept of exponents to explain all types of exponents. A conjecture for transforming the teaching and learning of exponents was proposed, that the teaching and learning of exponents can be improved through the study of the concepts of rate of growth and factors of multiplication, and a thorough study of roots and powers of factors. The conjecture was tested in a teaching experiment with the novice students. The role of the laws of exponents in the formation of rational and negative exponents was examined. The students’ construction of the concept of rational and negative exponents is described through models. The results suggest that students do not base their understanding of rational or negative exponents on patterns of the Laws of Exponents. The Common Definition of Exponents seemed the preferred lens through which the concept of exponents was viewed first, and then replaced by memorized rules, cues from notations, and teachers’ authority. The tendency of students to use linear forms of thinking for multiplicative models of change affected their understanding of factors of multiplication and rates of growth under various conditions. A process for calculating decimal exponents that brings together all the components of the construction of rational exponents was part of the study. The zero exponent was given special attention in the context of rational exponents. Negative exponents were studied as reverse actions of multiplication equivalent to multiplication of inverses. All students showed improvement in their understanding of rational, decimal and negative exponents. Two students presented integrated concept of exponents covering rational, decimal, and negative exponents. The other students continued to focus on the separate operations of different forms of exponents and did not propose integrated concepts.
Douglas Owens (Advisor)
Exponents, decimal exponents; ; Conceptual understanding

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Citations

  • Elstak, I. R. (2007). College students’ understanding of rational exponents: a teaching experiment [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1186505864

    APA Style (7th edition)

  • Elstak, Iwan. College students’ understanding of rational exponents: a teaching experiment. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1186505864.

    MLA Style (8th edition)

  • Elstak, Iwan. "College students’ understanding of rational exponents: a teaching experiment." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1186505864

    Chicago Manual of Style (17th edition)

osu1186505864
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© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.