The purpose of this study was to obtain data on United States K-5 elementary school teachers' self-reported instructional practices with graphical representations. Via an electronic survey, 388 elementary teachers, from throughout the US, reported about their teaching of the interpretation and the production of graphics within science. The main…

Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…

The purpose of this study was to investigate the effect of technology on one student's solution methods when solving mathematical tasks that included algebra word problems. The student was presented with context tasks in both paper-pencil and computer environments. The results of this study revealed that the student's solution methods differed in…

Tutoring systems are a common tool for delivering educational content and recent advances in this field include the detection of and reaction to learners' motivation. A data set derived from interactions in a tutoring system and its motivationally-aware variant provided opportunities to discover patterns of behavior in connection with motivational…

This article explores the benefits of incorporating student self-graphing into various academic and behavioral tasks to enhance the effects of an intervention and to heighten student motivation. It offers examples to demonstrate how student self-graphing might be observed in a school setting. A list of considerations and tips to ensure successful…

Four experiments examined the roles of extended surfaces and the number of points in the boundary superiority effect in goal localization. Participants learned the locations of 4 objects in the presence of a boundary, landmarks, or both in an immersive virtual environment by reproducing the locations with feedback. Participants then localized the…

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.…