Talk moves simulations were used in tutorials for a mathematics education unit. Pre-service teachers (PSTs) and tutors were surveyed about their perceptions of the purposes, benefits, and drawbacks of the simulations. There was strong support from both groups for the benefits of talk moves in developing PSTs' ability to manage discussions, ask…

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation…

This paper reports research on student produced screencasts to support learning. Participants in a Mathematics for Teachers course were asked to create and peer critique screencasts to explain concepts (year 4 to 9 level). They were also asked about their experience with screencasting and its impact on their own teaching and learning. This paper…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

For online mathematics instructors, synchronous communication can be a challenge due to the need for specialized symbols, graphics, or notations to explain key concepts. While software tools exist to support such communication, they can often be cumbersome and time-consuming for users to adopt in online exchanges. As one way of addressing this…

In the fall of 2005 the Maui Educational Consortium began a project that was funded through the Math Science Partnership program to implement the "Cognitive Tutor[R]" (CT) program, published by Carnegie Learning, in some of the Algebra 1 classes in the Maui School District and at the Maui Community College. At that time, Empirical…