We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

The paper discusses the perspectives of teaching geometry based on the study The International Commission on Mathematical Instruction ICMI. Bearing in mind the current needs in geometry teaching, we considered that the topics of space and spatial reasoning should be part of it as key issues, as well as teaching approaches, RME, learning through…

This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some…

These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

This paper presents a way of utilizing interdisciplinary relations between two educational branches, Mathematics and its applications and Information technologies (ICT) in integrated learning by the use of the Scratch programming language. The authors also present how they understand the concept of integrated learning and why they have chosen to…

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…

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

Using the correct materials and manipulatives appropriately allows the richness of geometrical concepts to be fully investigated to enable students to explore and reason about shapes. This article explores some of the key ideas involved in learning about two dimensional shapes and discusses how materials can be used to support learning.

This paper presents an account of a new place-based education initiative using both the mathematical construct of hypothetical learning trajectory and the 3D printing technology or Projection Augmented Landscape Models (PALM), as a tool for learning. The goal of the pilot study is to create bridges between Aboriginal and Western ways of knowing…

This work presents a discussion about the Didactic Training Engineering (EDF) methodology, of French origin, emphasizing the role of the teacher, during his initial or continuous training, through the conception and structuring of a didactic situation, organized by such methodology and based on the Theory of Didactic Situations (TSD). Therefore,…

Findings synthesized across five empirical laboratory- and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single- and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for computer technologies to support…

Most science curricular reform efforts are designed by administrators or science education experts. It is less common for teachers to work collaboratively across disciplines to create, implement, and disseminate an integrated STEM curriculum developed for noncollege-bound students that ended up being popular across student populations at the…