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…

The aim of the research is to describe the profile of problem solving ability of secondary student with high mathematical ability in learning based on realistic mathematics supported by ethnomathematics. The study is a descriptive qualitative research. The subject is a 7th grade student in a public secondary school at Semarang regency, Central…

The study aims to describe the ability of mathematical creative thinking on the aspects of fluency, flexibility, and originality in solving open-ended problem of Linear Equations with One Variable. The subjects are 7th grade students of one private junior high school in Surakarta, Central Java, Indonesia. The data was collected by the test,…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

Collaborative biostatistics is the creative application of statistical tools to biomedical problems. The relatively modest literature about the traits of effective collaborative biostatisticians focuses on four core competencies: (a) technical and analytical; (b) substance-matter knowledge; (c) communication; and (d) problem solving and problem…

Understanding how struggling students approach math is vital to designing effective math lessons. Many low achieving students rely on a weak knowledge of procedures and attempt calculations without adequate consideration of the problem. We investigated how enabling or preventing premature calculations affected learning math. Students were…

In this article we present our arguments in favor of a teaching of mathematics by means of problematization and investigation, one that includes in the classroom multiple ways and meanings for the students to read the world around them. In this respect, we propose a teaching-learning process of mathematics grounded on the relationships between…

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered…

This work presents experiments to teach fundamentals of automation through a sequence of laboratory practices that naturally guide to development of an on/off control system. It focuses on the integration of technological and scientific concepts, based on an educational approach associated with a problem-solving technique.

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somewhat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics…

Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and…

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…