RUME 26
2024
Omaha, Nebraska
Students’ Treatment of the Negation of Logical Implication
Page: 294
Understanding how students reason about the negation of logical statements is essential in supporting their mathematical development. Prior literature suggests that undergraduate students experience difficulties with the precise negation of logical implications. Many respond with the opposite statement “P implies not Q” when asked for the negation of “P implies Q.” We investigate the challenges that introductory proofs’ students experience when negating implications, and the reasoning they demonstrate in addressing these challenges. Our findings indicate quantification contributes significantly to their difficulties with negation. Further, nuances in students’ quantification may validate an implication’s opposite as its negation.