This study aims to investigate about the existence of a graphical facilitation effect on probabilistic reasoning. Measures of undergraduates' performances on problems presented in both verbal-numerical and graphical-pictorial formats have been related to visuo-spatial and numerical prerequisites, to statistical anxiety, to attitudes towards…

Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which…

Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…

This dissertation is comprised of two manuscripts resulting from a single study, which examines a) the types of graphics that appear, and in what frequencies, in children's informational texts, and b) the defining features of different graphics. Graphics are ubiquitous in children's informational texts and a lot is known about the impact…

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

Assuming that textbooks give literary expression to cultural and ideological values of a nation or group, we propose the analysis of chemistry textbooks used in Brazilian universities throughout the twentieth century. We analyzed iconographic and textual aspects of 31 textbooks which had significant diffusion in the context of Brazilian…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

Functions are one of the most important and powerful tools in mathematics because they allow the symbolic, visual, and verbal representation of relationships between variables. The power of functions, as well as the numerous real-world uses of functions, make them an important part of the development of algebraic reasoning in the middle grades.…

This article discusses the role of assessment in a response-to-intervention model. Although assessment represents only 1 component in a response-to-intervention model, a well-articulated assessment system is critical in providing teachers with reliable data that are easily interpreted and used to make instructional decisions. Three components of…

The activities described here allow students to explore the concept of diffusion with the use of common equipment such as computers, webcams and analysis software. The procedure includes taking a series of digital pictures of a container of water with a webcam as a dye slowly diffuses. At known time points, measurements of the pixel densities…

This dissertation bridges the fields of haptics, engineering, and education to realize some of the potential benefits haptic devices may have in Science, Technology, Engineering, and Math (STEM) education. Specifically, this dissertation demonstrates the development, implementation, and assessment of two haptic devices in engineering and math…

Location-based services have been identified as a promising communication paradigm in highly mobile and dynamic vehicular networks. However, existing mobile ad hoc networking cannot be directly applied to vehicular networking due to differences in traffic conditions, mobility models and network topologies. On the other hand, hybrid architectures…

This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

A 3-year longitudinal study "Transforming Children's Mathematical and Scientific Development" integrates, through data modelling, a pedagogical approach focused on mathematical patterns and structural relationships with learning in science. As part of this study, a purposive sample of 21 highly able Grade 1 students was engaged in an…