Teaching Geometric Reasoning: Proof by Pictures?

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Title: Teaching Geometric Reasoning: Proof by Pictures?
Author: Hawkins, Matthew Lee
Advisors: Dr. Lee Stiff, Committee Chair
Dr. Loek Helminck, Committee Member
Dr. Karen Hollebrands, Committee Member
Abstract: The purpose of this study was to investigate students' understanding of proof and proof writing using a new three-column method. The new three-column method consists of the traditional "statements" and "reasons" columns but also contains a "picture" column in which students must draw a picture that corresponds to the "statement." It is believed that this third column will act as a blue print providing students with a visual representation of how the proof is constructed. By examining this blueprint students will understand which steps are needed to complete the proof as well as the proper order of those steps. Thus, students develop a deeper understanding of the proof writing process. The study was conducted in a suburban school in central North Carolina and involved two standard geometry classes. The study lasted for a week and a half and was instituted during a chapter involving different triangle congruencies (i.e. SAS, SSS, etc). The three-column proof was taught to a 3rd period class containing 31 students. Their test and quiz scores were compared to a 2nd period class containing 23 students. After examining the average quiz and average test scores for the chapter it was shown that the 3rd period class did not out score the 2nd period class. Thus, the use of a three-column picture proof is as effective as the traditional approach. An important question pursuant to this outcome is whether there are other teaching/learning benefits from using picture proofs. For example, interviews with the cooperating teacher indicated that the three-column proof was very helpful for several students and also provided good teacher feedback as to students' understanding of theorems and postulates used in proof writing.
Date: 2007-12-18
Degree: MS
Discipline: Mathematics Education
URI: http://www.lib.ncsu.edu/resolver/1840.16/2579

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