This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

The book "If the World Were a Village," by David J. Smith, is the context for analysing and creating graphs of the world's demographic information. Students examine numerical information regarding the more than six billion world inhabitants by imagining the world's population as 100 people.

This article discusses the role of assessment in a response-to-intervention model. Although assessment represents only 1 component in a response-to-intervention model, a well-articulated assessment system is critical in providing teachers with reliable data that are easily interpreted and used to make instructional decisions. Three components of…

In generative syntax, the theory of asymmetry in syntax has gained much attention due to the influential work of Kayne (1994), who adopts the null hypothesis that syntax is inherently asymmetric. However, such a direction does not seem fully compatible with the general assumptions in Galilean style scientific theories, all of which aspire to…

This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…

Graphs are important for supporting critical thinking and scientific argumentation because students can use them to reason, make judgments and decisions, and solve problems like a scientist (Connery 2007). Yet teaching students how to use math to actually think critically continues to be difficult for teachers. This article describes two…

The activities described here allow students to explore the concept of diffusion with the use of common equipment such as computers, webcams and analysis software. The procedure includes taking a series of digital pictures of a container of water with a webcam as a dye slowly diffuses. At known time points, measurements of the pixel densities…

This dissertation bridges the fields of haptics, engineering, and education to realize some of the potential benefits haptic devices may have in Science, Technology, Engineering, and Math (STEM) education. Specifically, this dissertation demonstrates the development, implementation, and assessment of two haptic devices in engineering and math…

Location-based services have been identified as a promising communication paradigm in highly mobile and dynamic vehicular networks. However, existing mobile ad hoc networking cannot be directly applied to vehicular networking due to differences in traffic conditions, mobility models and network topologies. On the other hand, hybrid architectures…

This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

A 3-year longitudinal study "Transforming Children's Mathematical and Scientific Development" integrates, through data modelling, a pedagogical approach focused on mathematical patterns and structural relationships with learning in science. As part of this study, a purposive sample of 21 highly able Grade 1 students was engaged in an…

Early childhood education and care (ECEC) can help lay the foundations for future skills development, well-being and learning. Having timely, reliable and comparable international information is essential to help countries improve their ECEC services and systems. For over 15 years, the OECD has been conducting policy analysis and gathering new…

Problem Statement: Kinematics is one of the topics in physics where graphs are used broadly. Kinematics includes many abstract formulas, and students usually try to solve problems with those formulas. However, using a kinematics graph instead of formulas might be a better option for problem solving in kinematics. Graphs are abstract…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

This paper seeks to show how self assessment facilitates student-centred learning (SCL) and fills a gap in the literature. Two groups of students were selected from a single class in a tertiary educational institution. The control group of 25 was selected randomly by the tossing of an unbiased coin (heads = control group). They were trained in the…