The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and…

'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

Black Womxn in Mathematics Education (BWXME) is an international nonprofit organization that creates a brave and safe space for professional Black women in mathematics education. BWXME members are eminent mathematics PK-12 teachers, university and college professors, mathematicians, published authors, mathematics consultants, entrepreneurs,…

The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854-1912), Felix Klein (1849-1925), and Hans Freudenthal (1905-1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears…

The nature of the area of mathematical competitions as a design science is considered, historical roots of mathematical problem-solving competitions are traced, the complementary aspects of mathematics as theory building and as problem solving are touched upon in relation to the practice of competitions. Two historical figures, Euler and Erdos,…

A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

We study the variation of the apparent weight of an object with height above the surface of a planet with a (buoyant) atmosphere. Interestingly, this variation depends on two competing factors--the reduced gravitational acceleration (which acts to reduce the weight with increasing height) and the reduced buoyancy force in the progressively less…

The International Mathematical Olympiad, now 62 years old, has catalyzed the formation of a remarkable international community that meets for 2 weeks each year to celebrate mathematical problem solving. It has influenced and expanded the greater global mathematical culture, and the value of problem-solving in numerous countries. It is time for the…

It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing…

The study of secondary mathematics involves many ideas, but too often high school mathematics curriculum materials and instruction begin by giving students the vocabulary first, along with definitions, before students have been able to explore the ideas. Particularly for students bureaucratically designated as English Learners, preteaching…

This is the third article in the "On the Shoulders of Giants" series that takes an outstanding mathematician, tells something of their life and work, and provides an item or two based on their achievements that can be used in a primary class. This article focuses on the work of Cheryl Praeger, with an activity based upon her work with…

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with…

How can we use math to understand--and solve--challenges in our world? In "What We Do When Fairness Fails Us," Moises, Marissa, and Astrud realize that a specialized high school uses a lottery for admission that prevents many qualified students from attending. As they research how lotteries work, they come across videos by Federico…