This article examines newly introduced eccentricity topological descriptors that are used to analyze the structures of polycyclic aromatic hydrocarbons. The purpose is to identify structural components that have a significant impact on physicochemical properties. Regression analysis applies to find potential correlation between different drugs…

With recent curricular movements aimed at engaging students in science practices, more work is needed regarding evidence-based approaches for supporting students in developing competency in contexts such as chemistry. In this work, we focus on student engagement in constructing models related to graphical representations of reaction rate. Using…

Quantitative reasoning plays a crucial role in students' and teachers' successful modeling activities. In a semester-long teaching experiment with an undergraduate student, we explore how her conception of a graph plays a role in her ability to quantify and maintain quantitative structures. We characterize here Lydia's conception of a graph as one…

Idaho uses the English Language Arts and Mathematics tests from the Smarter Balanced Assessment Consortium (SBAC) for the Idaho Standard Achievement Tests (ISAT). ISAT results have been have been reported almost exclusively as "percent proficient" statistics (i.e., the percentage of Idaho students who performed at the "A" level…

Social networks are especially applicable in educational and psychological studies involving social interactions. A social network is defined as a specific relationship among a group of individuals. Social networks arise in a variety of situations such as friendships among children, collaboration and advice seeking among teachers, and coauthorship…

This paper aims to contribute to discussions on the multimodal nature of cognition through an elaboration of the ways multimodal aspects of thinking are exploited by learners doing mathematics. Moving beyond the fact "that" multimodality occurs, this paper focuses on "how" it occurs, with particular attention drawn to the…

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a…

This article presents an analysis of a phenomenon that was observed within the dynamic processes of teaching and learning to read and elaborate Cartesian graphs for functions at high-school level. Two questions were considered during this investigation: What types of metaphors does the teacher use to explain the graphic representation of functions…

This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students' solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided…

The authors use a relatively simple diagram accompanied by mathematical analysis to compare two pricing strategies: price-quantity packages and a two-part tariff. This is done both from the monopolist's point of view and from the welfare point of view. The authors show that in the case of two consumer types, the price-quantity packages strategy…

This study examined the fractional graph area (FGA), the proportion of page space used to display statistical graphics, in 11 behavioral journals and places behavior analysis on a continuum with other natural, mathematical, and social science disciplines. The composite FGA of all 11 journals puts behavior analysis within the range of the social…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…