This study compares the relative influence of syntax, semantics, and pragmatics in university students' interpretation of multiply quantified statements in mathematics, both before and after instruction. Like previous studies, results show that semantics plays a heavy role in student interpretation, especially before instruction. Unlike previous…

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…