Publication Date

Spring 2011

Degree Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Joanne Rossi Becker

Keywords

college curriculum, learning, mathematical proof, proving methods, study, teaching

Subject Areas

Mathematics; Mathematics Education

Abstract

Mathematical proof, as an essential part of mathematics,

is as difficult to learn as it is to teach. In this thesis, we

provide a short overview of how mathematical proof is understood

by students in K-16. Furthermore, we answer questions about

mistakes students usually make in the transition period from high

school to college in understanding mathematics and mathematical

proof. Through a case study, we learned that deduction mistakes

characteristic for early mathematical education, such as arguing

from an example, can be abandoned very easily as students begin to

understand the inadequacy of one, or finitely many, examples when

arguing about a general mathematical claim. Furthermore, students

accept basic procedures and different methods of proof, but they

experience difficulties when faced with new or complicated

mathematical topics to prove, such as those concerning the floor

function introduced during the proof teaching sessions. Also, we

observe the students' progress during the teaching sessions for a

specific proving method. Finally, we discuss grounds for further

investigation about learning and teaching mathematical proof. For

example, introduced are ideas of how to alter research instruments

and/or modify the group studied to be able to answer more specific

questions about mathematical proof in the college curriculum.

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