Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

The aim of this study is to characterise students' understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding…

Visual analysis is the primary method of evaluating data in single-subject research. Few studies have evaluated interventions to teach visual analysis skills. The purpose of this study was to evaluate systematic instruction, delivered using computer-based intervention or a recorded lecture, on identifying changes in slope and level in AB graphs.…

G, G°, [delta][subscript r]G, [delta][subscript r]G°, [delta]G, and [delta]G° are essential quantities to master the chemical equilibrium. Although the number of publications devoted to explaining these items is extremely high, it seems that they do not produce the desired effect because some articles and textbooks are still being written with…

This study explored first-semester calculus students' understanding of tangent lines as well as how students used tangent lines within the context of Newton's method. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and…

There is considerable interest in the cultivation of student graphic literacy among educators and researchers, especially in the sciences. Previous research, however, has shown that many students manifest difficulties in using diagrammatic representations. One explanation that has been proposed to account for these difficulties is that certain…

Current views in the teaching and learning of data handling suggest that learners should create graphs of data they collect themselves and not just use textbook data. It is presumed real-world data creates an ideal environment for learners to tap from their pool of stored knowledge and demonstrate their meta-representational competences. Although…

Contemporary research has suggested that for students to compete globally, pedagogy must shift to emphasize the infusion of mathematics into science instruction to strengthen understanding. Innovative professional development programs are necessary to achieve this goal, particularly with respect to teaching graphing skills in the context of…

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

The Strengthening Career and Technical Education for the 21st Century Act (Perkins V) pushes states to improve the public accessibility of Career Technical Education (CTE) data. According to the law, state agencies, as well as local recipients, must share data on the performance of all CTE students, and subgroups of learners, and make this…

To assist second language learners in becoming effective, aware, and reflective participants in higher education, support can be provided by integrating structured awareness raising approaches in the language curriculum. Drawing on self-regulation principles, such a structured awareness raising curriculum is most notably sustained by reflective…

This study investigates representational code-switching (RCS) by considering three high school students' communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical…

In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

This article presents "concept landscapes"--a novel way of investigating the state and development of knowledge structures in groups of persons using concept maps. Instead of focusing on the assessment and evaluation of single maps, the data of many persons is aggregated and data mining approaches are used in analysis. New insights into…