The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

Research has identified several students' misinterpretations of the principles of the photoelectric effect (PE). Students cannot interpret the formula using the graph's context despite the linear dependence inherited in it. Many studies pointed out that the graphical representation of kinetic energy of the ejected electrons versus frequency of…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

Large real-world graph (a.k.a network, relational) data are omnipresent, in online media, businesses, science, and the government. Analysis of these massive graphs is crucial, in order to extract descriptive and predictive knowledge with many commercial, medical, and environmental applications. In addition to its general structure, knowing what…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

Estimating the weight of large pumpkins before harvest presents an opportunity for applying several diverse mathematical topics. A model that allows an estimation by easy tape measurement is derived. (MP)

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)

This note describes a large-scale modelling activity involving geometry that can be solved with the help of uni-variable calculus. More specifically, it introduces and proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given…

There are many problems that can be translated into the language of graph theory. Such a problem, discussed in this article is to show that in any group of two or more people, there are at least two people who have the same number of acquaintances in the group. (PK)

Outlines differences between classical statistics and exploratory data analysis. Provides examples in the use of the exploratory techniques. (YP)