This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report here concentrates on investigating the relationship between students' notion of subsets…

What kinds of astronomical lab activities can high school and college astronomy students carry out easily in daytime? The most impressive is the determination of latitude and longitude from observations of the Sun. The "shooting of a noon sight" and its "reduction to a position" grew to become a daily practice at the start of the 19th century…

Maximum marginal likelihood estimation of multidimensional item response theory (IRT) models has been hampered by the calculation of the multidimensional integral over the ability distribution. However, the researcher often has a specific hypothesis about the conditional (in)dependence relations among the latent variables. Exploiting these…

"Clouds, Graphs, and Maps: Distant Reading and Disciplinary Imagination" examines recent efforts by scholars in rhetoric and composition to account for patterns and trends indicative of the discipline's maturation. Many of these "discipliniographic" appraisals resort, on the one hand, to anecdotal, experience-based accounts or, on the other hand,…

A shape grammar is a formalism that has been widely applied, in many different fields, to analyzing designs. Computer implementation of a shape grammar interpreter is vital to both research and application. However, implementing a shape grammar interpreter is hard, especially for parametric shapes defined by open terms. This dissertation…

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

This paper examines the technological affordances of the visualiser, and what teachers actually do with it in the primary (elementary) classroom, followed by an investigation into one example of teaching and learning with this whole-class technology. A visualiser is a digital display device. Connected to a data projector, whatever is in view of…

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 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'…

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

Patients with traumatic brain injury show clear impairments in behavioural flexibility and inhibition that often persist beyond the time of injury, affecting independent living and psychosocial functioning. Functional magnetic resonance imaging studies have shown that patients with traumatic brain injury typically show increased and more broadly…

The aim of this study is to scrutinize the characteristics of conceptual meaning making when students engage with virtual worlds in combination with a spreadsheet with the aim to develop graphs. We study how these tools and the representations they contain or enable students to construct serve to influence their understanding of energy resource…

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

As anyone who has taught or taken a statistics course knows, statistical calculations can be tedious and error-prone, with the details of a calculation sometimes distracting students from understanding the larger concepts. Traditional statistics courses typically use scientific calculators, which can relieve some of the tedium and errors but…

Scholars have argued that imprecise data graphics, specifically those displaying decorative dimensionality of data, may lead to inaccurate interpretations. Empirical tests of decorative dimensionality have produced mixed results. The literature also suggests that the effects of decorative dimensionality may depend on the cognitive demand of a…