Mathematical versus English meaning in implication and disjunction

As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of ‘if’ and ‘or’ from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students’ mistakes. To fill this gap, this article presents three studies for the classroom that engage students in confronting the differences between mathematical and everyday meaning in statements of implication and statements of disjunction.