The activity of snapping photographs to document all parts of daily life and sharing them with friends is the norm for many students. What if we could make mathematics as natural a part of daily life through "mathematical selfies"? The author's goal is to use students' love of selfies to help them see that mathematics is already part of…

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain…

The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

Mathematics is a form of culture integrated in all aspects of society, wherever there are, including the sundanese ethnic communities. This enables the mathematical concepts embedded in cultural practices and recognizes that all people develop a special way of doing mathematics called ethnomathematics activities. Sundanese ethnomathematics is…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Having a nice mathematical task is one challenge for a teacher--another is making it come alive for students in the classroom. The pathway to the latter is pedagogy--the range of teaching strategies possessed and activated by the teacher. This article presents a delightful mathematical activity known as Spirolaterals, a geometrical figure formed…

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…

In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

As part of the CBAL® learning and assessment initiative in mathematics, we developed a hypothesized learning progression (LP) for geometrical measurement in 1, 2, and 3 dimensions based on a synthesis of empirical literature in this field and through expert review. The geometrical measurement LP is intended to represent a developmental progression…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical…

The aim of this research was to study the effect of activity-based teaching and traditional method of teaching on students' achievement in the subject of Mathematics at elementary stage. The research was experimental based on pre-test, post-test control group design. Two units of geometry were selected from seventh grade Mathematics for this…