Fluency with formal mathematical language is necessary for students in advanced
mathematics. Yet, the language has been documented as being particularly challenging for …

Instructors manage several tensions as they engage students in defining, conjecturing, and
proving, including building on students' contributions while maintaining the integrity of …

Many educators advocate for students to engage in authentic mathematical activity–activity
reflective of the discipline. In our respective design studies, we had a common goal of …

Abstract Mathematics is concerned with the method used in the teaching and learning
process in addition to issues encountered in the cognitive domain. The Philippines' …

Proof-based mathematics courses are often taught in a lecture-based format that deprives
students of the opportunity to engage in authentic mathematical activity. Students are …

Based on analysis with four graduate students' proof productions, this paper characterizes
eight ways of operationalizing quantification for reasoning about and constructing proofs …

Undergraduate students are expected to produce and comprehend constructive existence
proofs; yet, these proofs are notoriously difficult for students. This study investigates students' …

We now have broad consensus in the mathematics education research community that
active, inquiry-based classrooms provide a wealth of learning benefits for students (Freeman …

Instructors manage several tensions as they support students to engage in mathematical
disciplinary practices such as defining, conjecturing, and proving. These tensions include …

The Philippines' education system is still dominated by traditional mathematics teaching,
which frequently overlooks the goal of mathematics education—to prepare students to deal …