2024-05-25T22:48:55Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1572042021-08-27T02:47:01Zoai_pmh:all157204
https://hdl.handle.net/2286/R.I.53628
http://rightsstatements.org/vocab/InC/1.0/
2019
301 pages : illustrations (chiefly color)
Doctoral Dissertation
Academic theses
Text
eng
Weber, Matthew Barrett
Strom, April D
Thompson, Patrick W
Carlson, Marilyn
Middleton, James
Tzur, Ron
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2019
Includes bibliographical references (pages 268-273)
Field of study: Mathematics Education
Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted to quotitive conceptualizations of division, or on symbolic manipulation of variables. Research and curricular activities have largely avoided the study and development of partitive conceptualizations involving fractions, as well as their connection to the invert-and-multiply algorithm. In this dissertation study, I investigated six middle school mathematics teachers’ meanings related to partitive conceptualizations of division over the positive rational numbers. I also investigated the impact of an intervention that I designed with the intent of advancing one of these teachers’ meanings. My findings suggested that the primary cognitive obstacles were difficulties with maintaining multiple levels of units, weak quantitative meanings for fractional multipliers, and an unawareness of (and confusion due to) the two quantitative conceptualizations of division. As a product of this study, I developed a framework for characterizing robust meanings for division, indicated directions for future research, and shared implications for curriculum and instruction.
Mathematics Education
Fractions
Partitive Division
Quotitive Division
Middle school education
Division--Study and teaching.
Division
Fractions--Study and teaching.
Fractions
Investigating the advancement of middle school mathematics teachers' meanings for partitive division by fractional values of quantities