The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

Do young children understand the complex mathematics in the petals of a daisy, the Fibonacci sequence in the spiral of a pinecone, the fractal geometry in the leaves of a fern, or the "golden ratio" in the seed pattern of a sunflower? Probably not, but they certainly can observe and recognize the patterns and compare them to similar…

Mathematics achievement is positively associated with coding in the classroom. By making mathematical relationships visible to students as they code, teachers leverage rich connections between block-based computer programming and mathematical sense making. In this article, the authors describe strategies for adapting a Code.org lesson integrating…

Effective teaching requires enjoyable classroom tasks aimed at promoting students' learning of mathematics meaningfully, and previous research has demonstrated that the use of origami activities in mathematics classrooms can help achieve that goal. In this article, the authors describe their "LOVE MATH" one-straight-cut letter origami…

Exciting examples of physics principles illuminate the power and scope of our discipline. In this paper, we discuss a conservation of energy example for an introductory course. Energy conservation is applied to bird and dinosaur eggs to derive a method to predict the incubation period and the embryonic metabolism solely from the egg geometry. The…

This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

The use of CO[subscript 2] laser cutters/engravers in technology and engineering education "allows even beginning students to produce professional parts in a very short time [and] empowers and motivates students, helping to bring out their creativity" (Flowers, 2000, p. 11). They are fast, accurate, fun to use, and they facilitate…

The cosine theorem is used in solving triangulation problems and in physics when solving problems of addition of unidirectional oscillations. However, this theorem is used only for the analytical calculation of triangles or when solving problems of adding two oscillations. Here we propose a generalization of the cosine theorem for the case of…

Development of three-dimensional (3D) printing technology has started a new chapter for in-classroom modeling of chemical molecules. The technology provides the opportunity to design and produce various types of personalized models. However, using classical 3D printers is time consuming, and it is hard to involve students in the modeling process…

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

This article focuses on the experience of viewing polyhedra in modified kaleidoscopes, highlighting the perceptive acts that take place. It presents aspects of geometry, such as concepts and ideas involved in the visualization of polyhedra in kaleidoscopes, through an analyticalmathematical study of the reflection of images in mirrors and…

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle…

This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of [pi]. The experiment is easy, thrilling, and…

This article discusses the role of the three components of executive functions (EF) in geometric understanding. Discussing several examples of geometry problems, this article shows how EF are actively employed to solve geometry problems. Inhibition as the first component of EF helps the individual to suppress contextually irrelevant information.…

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometly environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a…