The object of this study is to model the level of a question difficulty by a differential equation at a pre-specified domain knowledge, to be used in an educational support system. For this purpose, we have developed an intelligent tutoring system for mathematics education. Intelligent Tutoring Systems are computer systems designed for improvement…

We report on a study of the forced van der Pol equation x + [epsilon](x[superscript 2] - 1)x + x = F cos[omega]t, by solving numerically the differential equation for a variety of values of the parameters [epsilon], F and [omega]. In doing so, many striking and interesting trajectories can be discovered and phenomena such as frequency entrainment,…

This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well…

The Educational Policy Improvement Center (EPIC) conducted an investigation of the Intersegmental Committee for the Academic Senates (ICAS) Statements of Competencies for Mathematics and Academic Literacy. The purpose of this work is to understand how the ICAS competencies relate to college and career readiness, as represented by the augmented…

In this paper, we describe our experience with the creation and utilization of online assignments for several calculus classes at Simon Fraser University (SFU). We present our findings regarding available software by considering the needs and perspectives of the instructors, students, and administrators. We provide a list of questions that guide…

This qualitative case study explored how students learning Maths at an Irish institute of higher education benefited from their instructor's use of self-developed screencasts. The screencasts (47 in total) were posted on the institute's Maths Moodle site for students to access. One hundred and thirty-eight (n = 138) students participated in an…

The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the…

The purpose of this action research was to investigate how the use of technology promotes interaction to foster high school students' mathematical understanding. This mixed method study is guided by social-constructivist theory (Vygotsky, 1978) and framed within Moore's (1989) model of learner-content, learner-instructor, and learner-learner…

Student problem posing has been advocated for mathematics instruction, and it has been suggested that problem posing can be used to develop students' mathematical content knowledge. But, problem posing has rarely been utilized in university-level mathematics courses. The goal of this teacher-as-researcher study was to develop and investigate…

This first draft of the "Comparison of Virginia's 2009 Mathematics Standards of Learning (SOL) with the Common Core State Standards (CCSS) for Mathematics" provides a side-by-side overview demonstrating how the 2009 Mathematics SOL are aligned to the CCSS. The comparison was made using Virginia's complete standards program for supporting…

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the…

Thermodynamic quantities such as the average energy, heat capacity, and entropy are calculated using a Monte Carlo method based on the Metropolis algorithm. This method is illustrated with reference to the harmonic oscillator but is particularly useful when the partition function cannot be evaluated; an example using a one-dimensional spin system…

The purpose of this study was to investigate how the use of TI-Nspire[TM] could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire[TM] for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire[TM], and the learning tasks, and how they lead…

Rate of change is an important concept for students to study, and little is known about the ways in which secondary students make sense of rate of change. In this qualitative study I examined how four high school students who have not taken calculus reasoned about changing quantities when interacting with mathematical tasks involving multiple…