This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

A classic TV commercial once asked, "How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop?" The narrator claims, "The world may never know" (Tootsie Roll 2012), but an Internet search returns a multitude of answers, some of which include rigorous systematic approaches by academics to address the…

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

Preschoolers' experiences with shapes are important because geometry is foundational to aspects of mathematics and it is now part of the Common Core for school-readiness. Exposure to shapes also provides experiences that are key to developing spatial thinking more broadly. Yet achieving a strong conceptual understanding of geometric categories can…

Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…

The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…

In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Presents an activity in which students investigate geometric probability at a school fair. (YDS)

Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)

Using license plates to generate random number pairs, students can calculate an approximate value for pi. The author views this approach as easier to understand than Buffon's needle. (SD)

Presents an activity on probability and area in which students try to decide which door to buy. (ASK)