TY - JOUR
T1 - The role and use of examples in learning to prove
AU - Knuth, Eric
AU - Zaslavsky, Orit
AU - Ellis, Amy
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2019/3
Y1 - 2019/3
N2 - Proof is central to mathematical practice, yet a perennial concern is that students of all ages struggle in learning to prove. Mathematics education scholars have suggested that overreliance on examples to justify the truth of statements is a contributing factor for students’ difficulties. While example-based reasoning has typically been viewed as a stumbling block to learning to prove, we view example-based reasoning as an important object of study and posit that examples play both a foundational and an essential role in the development, exploration, and understanding of conjectures, as well as in subsequent attempts to develop proofs of those conjectures. In this paper, we provide an overview of our project whose goals were to (a) investigate the nature of middle school and high school students’, undergraduate students’, and mathematicians’ thinking about the examples they use when developing, exploring, and proving conjectures; and (b) investigate ways in which thinking about and analyzing examples may facilitate the development of students’ learning to prove.
AB - Proof is central to mathematical practice, yet a perennial concern is that students of all ages struggle in learning to prove. Mathematics education scholars have suggested that overreliance on examples to justify the truth of statements is a contributing factor for students’ difficulties. While example-based reasoning has typically been viewed as a stumbling block to learning to prove, we view example-based reasoning as an important object of study and posit that examples play both a foundational and an essential role in the development, exploration, and understanding of conjectures, as well as in subsequent attempts to develop proofs of those conjectures. In this paper, we provide an overview of our project whose goals were to (a) investigate the nature of middle school and high school students’, undergraduate students’, and mathematicians’ thinking about the examples they use when developing, exploring, and proving conjectures; and (b) investigate ways in which thinking about and analyzing examples may facilitate the development of students’ learning to prove.
KW - Examples
KW - Justification
KW - Mathematical reasoning
KW - Proof
UR - http://www.scopus.com/inward/record.url?scp=85021951684&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85021951684&partnerID=8YFLogxK
U2 - 10.1016/j.jmathb.2017.06.002
DO - 10.1016/j.jmathb.2017.06.002
M3 - Article
AN - SCOPUS:85021951684
SN - 0732-3123
VL - 53
SP - 256
EP - 262
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
ER -