Undergraduate mathematics students’ at-home exploration of a prove-or-disprove task

Kristen Lew, Dov Zazkis

Research output: Contribution to journalArticle

Abstract

A common genre of task in proof-centered mathematics courses involves prompting students to evaluate the veracity of a mathematical claim by either proving the claim, or providing a proof that the claim is false (disproving the claim). The way in which students interact with these prove-or-disprove tasks is not well understood. We examine students’ at-home work as a way of learning about their processes of generating disproofs of claims. In particular, we study the interactions between example/counterexample generation activities, attempts to prove the (false) claim, and attempts to prove related results.

Original languageEnglish (US)
JournalJournal of Mathematical Behavior
DOIs
StateAccepted/In press - Jan 1 2018

Fingerprint

Disprove
Mathematics
mathematics
Students
student
genre
Learning
interaction
learning
Counterexample
Evaluate
Interaction

Keywords

  • At-home proving
  • Counterexample
  • Example space
  • Prove-or-disprove
  • Undergraduate

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

Cite this

@article{ba0724548f51482786fd0c3c05ebcb48,
title = "Undergraduate mathematics students’ at-home exploration of a prove-or-disprove task",
abstract = "A common genre of task in proof-centered mathematics courses involves prompting students to evaluate the veracity of a mathematical claim by either proving the claim, or providing a proof that the claim is false (disproving the claim). The way in which students interact with these prove-or-disprove tasks is not well understood. We examine students’ at-home work as a way of learning about their processes of generating disproofs of claims. In particular, we study the interactions between example/counterexample generation activities, attempts to prove the (false) claim, and attempts to prove related results.",
keywords = "At-home proving, Counterexample, Example space, Prove-or-disprove, Undergraduate",
author = "Kristen Lew and Dov Zazkis",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.jmathb.2018.09.003",
language = "English (US)",
journal = "Journal of Mathematical Behavior",
issn = "0732-3123",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Undergraduate mathematics students’ at-home exploration of a prove-or-disprove task

AU - Lew, Kristen

AU - Zazkis, Dov

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A common genre of task in proof-centered mathematics courses involves prompting students to evaluate the veracity of a mathematical claim by either proving the claim, or providing a proof that the claim is false (disproving the claim). The way in which students interact with these prove-or-disprove tasks is not well understood. We examine students’ at-home work as a way of learning about their processes of generating disproofs of claims. In particular, we study the interactions between example/counterexample generation activities, attempts to prove the (false) claim, and attempts to prove related results.

AB - A common genre of task in proof-centered mathematics courses involves prompting students to evaluate the veracity of a mathematical claim by either proving the claim, or providing a proof that the claim is false (disproving the claim). The way in which students interact with these prove-or-disprove tasks is not well understood. We examine students’ at-home work as a way of learning about their processes of generating disproofs of claims. In particular, we study the interactions between example/counterexample generation activities, attempts to prove the (false) claim, and attempts to prove related results.

KW - At-home proving

KW - Counterexample

KW - Example space

KW - Prove-or-disprove

KW - Undergraduate

UR - http://www.scopus.com/inward/record.url?scp=85054438522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054438522&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2018.09.003

DO - 10.1016/j.jmathb.2018.09.003

M3 - Article

AN - SCOPUS:85054438522

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

ER -