Abstract/Details

The relationship between mathematical induction, proposition functions, and implication functions


2010 2010

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Abstract (summary)

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 < 0.001). The general linear model Mathematical Induction = −0.300 + 0.122 ACT Math + 0.222 Function Ability was significant at p < 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.

Indexing (details)


Subject
Mathematics education;
Teaching methods;
Educational tests & measurements
Classification
0280: Mathematics education
Identifier / keyword
Education; APOS; Dubinsky; Harel; Mathematical induction; Mixed methods; Proof
Title
The relationship between mathematical induction, proposition functions, and implication functions
Author
Andrew, Lane
Number of pages
287
Publication year
2010
Degree date
2010
School code
0161
Source
DAI-A 71/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781124103730
Advisor
Soto-Johnson, Hortensia
University/institution
University of Northern Colorado
University location
United States -- Colorado
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3415985
ProQuest document ID
734766639
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/734766639
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