It has been over thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but why there is still an officially designated exclusion zone? The Chernobyl Disaster Task combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.…

This Perspectives on Practice manuscript focuses on an innovation associated with "Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task" [EJ1264816] from Volume 7, Issue 2 of "MTE." We built on Aguirre et al.'s (2019) integration of mathematical modeling and social…

The process of diffusion is intimately related to random molecular displacement and is central to many problems in chemistry. Here, we provide an intuitive derivation of the diffusion equation based on the analysis of the random trajectories of particles generated and plotted by simple MATLAB and Python scripts. The codes are very simple and…

This Perspectives on Practice manuscript focuses on an innovation associated with "Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task" from Volume 7, Issue 2 of "MTE". The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

We describe an activity that introduces students to population modelling, enables them to use estimates obtained from a sample to infer back to the population, and understands how the findings are translatable via penguins and their poo!

Inspired by the approach first employed by C.S. Holling in his classic "disc experiment," this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address…

This article provides two activities, exploring genetic drift of small breeding populations, highlighting the black-footed ferret ("Mustela nigripes"). According to the U.S. Fish and Wildlife service, all black-footed ferrets are descended from 18 individuals, making them extremely vulnerable to genetic drift. They were thought to be…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

People use models every day without even realizing it. Models create a structure for predictions (inferences) that can be used or adapted as situations change. A model is a relational system that highlights aspects of a phenomenon that the modeler deems important and diminishes the rest. Statistical models capture variability of data, enabling…

Have you ever noticed trash collecting in streams or waterways? How does trash influence our environment, and what can be done to enact change? These are questions middle school students explored as the authors launched the Great Pacific Garbage Patch (GPGP) task. The Great Pacific Garbage Patch activity involves an urgent environmental issue that…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

The Models and Modeling Working Group at PME-NA has provided a forum for discussing and collaborating on projects fundamental to research on mathematical modeling since the first PME-NA conference in 1978. We propose to convene this Working Group at PME-NA 41 with a dual purpose: (1) to build on a theme begun in Greenville, holding a focused…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…