Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

There is a paucity of information surrounding maths anxiety levels in the British undergraduate student population, and, due to terminological issues, existing measures of maths anxiety may not be appropriate measures to use with this population. The current study, therefore, reports on the development and validation of a new maths anxiety scale.…

Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…

This is a case study of an undergraduate calculus student's nonstandard conceptions of the real number line. Interviews with the student reveal robust conceptions of the real number line that include infinitesimal and infinite quantities and distances. Similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated…

The increasing popularity of R is leading to an increase in its use in undergraduate courses at universities (R Development Core Team 2008). One of the strengths of R is the flexible graphics provided in its "base" package. However, students often run up against its limitations, or they find the amount of effort to create an interesting plot may…

In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In…

Videos have been used in classrooms for decades, but student-produced video has recently become a viable, economical option to enhance learning. Students were asked to create videos to be used for their exam review in two different undergraduate mathematics courses: Differential Equation and Complex Analysis. Students were then surveyed about…

Chemistry students in Israel have two options for studying chemistry: basic or honors (advanced placement). For instruction in high school honors chemistry courses, we developed a module focusing on abstract topics in quantum mechanics: Chemistry--From the Nanoscale to Microelectronics. The module adopts a visual-conceptual approach, which…

This paper proposes a new presentation system integrating a Microsoft PowerPoint presentation in a two-layer method, called the TL system, to promote learning in a physical classroom. With the TL system, teachers can readily control hints or annotations as a way of making them visible or invisible to students so as to reduce information load. In…

Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students' depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an…

This article explores learning opportunities offered by students' written reflections as they learn through writing an action research proposal. From tapping into students' reported struggles, I analysed data using three stages of qualitative data analysis: data reduction, data display, and conclusion drawing (Miles and Huberman 1994). It emerged…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…

Rasch Analysis is a statistical technique that is commonly used to analyse both test data and Likert survey data, to construct and evaluate question item banks, and to evaluate change in longitudinal studies. In this article, we introduce the dichotomous Rasch model, briefly discussing its assumptions. Then, using data collected in an…

The impact of memory and anxiety on math performance was analyzed in a sample of 115 college undergraduates, all of whom had a diagnosed learning disability. The direct effects of memory and anxiety on math performance were first examined, followed by an examination of whether anxiety moderates the relationship between memory and math. Both memory…

This note introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the monotony coefficient for a two-dimensional sample is between /"r"/ and 1, where "r" is the Pearson's…