In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infection and death rates. One way of disseminating was through graphs, maps, and diagrams. Such data visualizations communicate numeric data in compact ways, but also require a particular mathematical literacy from readers. We conceptualized this particular…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

In this study, we developed a classification system of programming errors based on the historical data of 680,540 programming records collected on the Online Judge platform. The classification system described six types of programming errors (i.e., syntax, logical, type, writing, misunderstanding, and runtime errors) and their connections with…

Visual displays, such as icon arrays and risk ladders, are often used to communicate numerical health information. Number lines improve reasoning with rational numbers but are seldom used in health contexts. College students solved ratio problems related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly-assigned…

Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with…

Students and professionals from a variety of domains have demonstrated different approaches to problem solving. These two populations have displayed differences when using and perceiving multiple representations of problem-solving tools. In the domain of transportation engineering, this difference has yet to be evaluated in detail. This study…

Successful mathematical problem-solving relies on choices about how best to represent and solve problems. In this article, a range of methods and strategies are presented for solving a single mathematical problem, including novel methods posed by in-service teachers at one Australian university. The variety of problem-solving strategies rely on…

Developing a better understanding of the measurement process and measurement uncertainty is one of the main goals of university physics laboratory courses. This study investigated the influence of graphical representation of data on student understanding and interpreting of measurement results. A sample of 101 undergraduate students (48 first year…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

To succeed within scientific disciplines, using representations, including those based on words, graphs, equations, and diagrams, is important. Research indicates that the use of discipline specific representations (sometimes referred to as expert generated representations), as well as multi-representational use, is critical for problem solving…

The Venn diagram is suggested as a graphical solution to conjunction fallacies and a modification of it is suggested to more fully communicate set relations.

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

The purpose of this article is to identify the order of significance of the variables that affect science and mathematics achievement in middle school students. For this aim, the study deals with the relationship between science and math in terms of different angles using the perspectives of multiple causes-single effect and of multiple…