Prospective teachersunderstanding of proof: What if the truth set of an open sentence is Broader than that covered by the proof?
Stylianides, Andreas J., Stylianides,
Gabriel J. & Philippou, George N.
ABSTRACT. This paper investigates prospective elementary and secondary school
teachers' understanding of proof in a case where the truth set of an open sentence
is broader than the set covered by a valid proof by mathematical induction.
This case breaks the boundaries of students' usual experience with proving tasks.
The most important finding is that a significant number of students from both
groups who recognized correctly the validity of the purported proof thought
that it was not possible for the truth set of the open sentence to include any
number outside its domain of discourse covered by the proof. The discussion
of student difficulties provides insights into the development of instructional
practices in teacher preparation programs aiming to uncover these aspects of
students' knowledge fragility and address them accordingly.