Understanding the nature and purpose of models, including mathematical models, is critical to enabling undergraduate chemistry students to use models to predict and explain phenomena. However, students often do not have systematic conceptions about different kinds of models. To gain a sense of how students understand different models in the…

The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

Mathematical modeling has been recognized and highlighted in most standards and reports as an important concept to the teaching and learning of mathematics. The study investigated 208 PK-8 preservice teachers' (PSTs') familiarity and experiences with mathematical modeling. The study adopted a survey-design perspective to collect data from 10…

We present a simple activity based on the liquid-drop model which allows secondary school students to explore the uses of mathematical models and gain an intuitive understanding of the concept of binding energy, and in particular the significance of positive binding energy. Using spreadsheets provided as supplementary material, students can…

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…

Modeling is a major topic of interest in mathematics education. However, the field's definition of models is diverse. Less is known about what teachers identify as mathematical models, even though it is teachers who ultimately enact modeling activities in the classroom. In this study, we asked nine middle school teachers with a variety of academic…

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

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…

Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a…

Metacognitive competencies are of great importance for developing modelling competencies. However, there are assumptions about useful metacognitive knowledge and strategies for individuals working on modelling problems as well as for whole groups, but their coherence as well as their influence on modelling processes is not evaluated…

NP-complete problems such as the traveling salesman problem (TSP) play a prominent role in most advanced undergrad/graduate courses in discrete optimization modeling. Teaching such an important topic from a purely mathematical perspective without discussing specific applications may result in reduced student interest and motivation. The DeLand…

Mathematical modelling is acknowledged to be one of the major dimensions of mathematical competence, and well-designed modelling activities can provide students with the opportunity to use mathematical concepts and procedures in a meaningful way. Additionally, modelling activities are regarded as suitable contexts for enabling students to use…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

To span the great distance from the solar system to the farthest clusters of galaxies in the universe, astronomers break down the distance indicators into steps. The nearest ones are measured geometrically, with what is known as parallax. Among the objects whose distances are thus directly measured are a rare type of star known as a Cepheid…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…