This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility…

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

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…

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, photographs of a massive sculpture near the National Mall in Washington, D.C., provide opportunities for counting problems, generalizing from a pattern, and fitting a quadratic to data.

In this study, eight-grade students' estimation achievements in triangles were analysed according to motivation types and knowledge type expectations. Three hundred and thirty-seven students from three different elementary schools attended in this study. In order to determine the students' estimation performances, an estimation test in triangles…

The Isoperimetric Quotient, or IQ, introduced by G. Polya, characterizes the degree of sphericity of a convex solid. This paper obtains closed form expressions for the surface area and volume of any Archimedean polyhedron in terms of the integers specifying the type and number of regular polygons occurring around each vertex. Similar results are…

The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in…

Introduction: For decades, prior to the inception of the Common Core State Standards (CCSS), the National Assessment of Educational Progress (NAEP) was the only vehicle through which states could assess the progress of their students using a common metric. Now, 45 states, 4 U.S. territories, and the District of Columbia have adopted the CCSS to…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…