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ERIC Number: ED521674
Record Type: Non-Journal
Publication Date: 2010
Pages: 300
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1241-0373-0
ISSN: N/A
The Relationship between Mathematical Induction, Proposition Functions, and Implication Functions
Andrew, Lane
ProQuest LLC, Ph.D. Dissertation, University of Northern Colorado
In this study, I explored the relationship between mathematical induction ability and proposition and implication functions through a mixed methods approach. Students from three universities (N = 78) and 6 classrooms completed a written assessment testing their conceptual and procedural capabilities with induction and functions. In addition, I interviewed a subgroup of 10 participants to add context and meaning to the assessment results. This research study was unique in that it provided numeric correlations among important variables. The correlation between induction ability and function ability was r = 0.47 (p less than 0.001). The general linear model "Mathematical Induction" = -0.300 + 0.122 "ACT Math" + 0.222 "Function Ability" was significant at p less than 0.05 and explained 28.3% of the variation in induction ability. In the written assessment, I asked participants to construct two induction proofs. Out of the 156 attempts, 57 attempts were successful (37%). During the interview analysis, I identified participant subgroups based on mathematical goals, background, and motivation. I argued that the characteristics of these subgroups related directly to their scores on the written assessment. In particular, students who perceived mathematical induction as useful to themselves in their future career put forth the energy required to learn induction, both procedurally and conceptually. Based on the results of this study, I recommended that students learn about proposition functions prior to studying induction. I also recommended that the amount of class time spent on the instruction of induction increase along with a continued focus on the conceptual elements of the proof technique. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A