Pole vaulting, the aim of which is to jump over a crossbar with the help of a long flexible pole, is considered to be one of the most complicated and technically demanding motions in track and field athletics. Pole vault performance is basically influenced by the energy exchange between the vaulter and pole. It depends on the sprinting, jumping…

Constructing an intuitive theory from data confronts learners with a "chicken-and-egg" problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing…

Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…

We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

To promote and facilitate the teaching of math modeling throughout the K-16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the…

The Corvette Problem is a nonroutine investigation, one that provides an authentic context to explore many interrelated calculus ideas. In our years of sharing this problem with students and colleagues, we have found additional topics from the calculus curriculum to have rich interpretations in this environment. The Corvette Problem contextualizes…

The high school grade point average (GPA) is often adjusted to account for nominal indicators of course rigor, such as "honors" or "advanced placement." Adjusted GPAs--also known as weighted GPAs--are frequently used for computing students' rank in class and in the college admission process. Despite the high stakes attached to…

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

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…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

Based on the unpredictable effect of context familiarity when students solve real-world problems, this work aims to analyse how certain contexts can be used by pre-service mathematics teachers in the representation and real-world verification of a first-order mathematical model in the classroom in the subject of Ordinary Differential Equations.…

The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can…