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…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

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…

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…

This paper contributes to current sociolinguistic research on the rapidly-changing landscape of digitally mediated communication (Androutsopoulos and Staehr 2018) by presenting mediagrams, a new method for research on transnational mediated interaction. Based on an ethnographic study of mediated multilingual communication in four families with…

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…

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…

At first glance it seems easy to attribute cause and effect when it's not applicable, either through mistakenly taking every correlation as a cause and effect relationship, misinterpreting the meaning of independent and dependent variables, or not focusing on direct causes. Sometimes it's easy to help students understand where…

The Tukey mean-difference plot, also called the Bland-Altman plot, is a recognized graphical tool in the exploration of biometrical data. We show that this technique deserves a place on an introductory statistics course by encouraging students to think about the kind of graph they wish to create, rather than just creating the default graph for the…

Admittedly, the notion of generalized integrals in one parameter has a fundamental role. En virtue that, in this paper, we discuss and characterize an approach for to promote the visualization of this scientific mathematical concept. We still indicate the possibilities of graphical interpretation of formal properties related to notion of…

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…