Inverse is a critical topic throughout the K–16 mathematics curriculum where students
encounter the notion of mathematical inverse across many contexts. The literature base on …

In this paper I describe a local instructional theory for supporting the guided reinvention of
the group and isomorphism concepts. This instructional theory takes the form of a sequence …

In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting
students in developing flexible ways of reasoning about matrices as linear transformations in …

In this paper we present an innovative instructional sequence for an introductory linear
algebra course that supports students' reinvention of the concepts of span, linear …

Background Changing mathematics curricula and their emphases, lower numbers of student
enrolments in undergraduate mathematics programmes (Barton and Sheryn 2009; and …

Relatively little is known about how students come to reason coherently about the formal
definition of limit. While some have conjectured how students might think about limits …

In this research report we consider the kinds of knowledge needed by a mathematician as
she implemented an inquiry-oriented abstract algebra curriculum. Specifically, we will …

In this paper, we describe the process of designing and scaling up the TAAFU group theory
curriculum. This work unfolded in three overlapping stages of research and design. The …

Homomorphism is a critical variety of function in undergraduate Abstract Algebra (AA)
courses and function is one of the unifying concepts across many mathematical subject …

Most certification programs in the USA for secondary mathematics require coursework in
abstract algebra. Yet several researchers have shown that most undergraduate students …