This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…

We introduce a ruler and compass activity designed around Islamic Geometry and provide a detailed description of the various components of the activity along with ideas for students exhibitions in both digital and print form. In our experience, this activity helps students to "buy into" actively doing mathematics, making it an ideal…

Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article…

This paper aims at defining and exploring design principles in a distance technological setting for an educational activity for mathematics undergraduate students, devoted to the construction of basic concepts in general topology, the promotion of problem-solving processes, the development of metacognitive aspects, and, in general, the development…

Practical problem solving is not common in many mathematical classes in Malaysian upper secondary schools. Usually, students receive the mathematical concepts through abstract materials (students cannot see some of them in their daily life). Thus some students believe that 'mathematics is not necessary for human life'. In this article, the…

The paper describes two versions of an inquiry-based activity in geometry, designed as a game between two players. The game is inspired by Hintikka's semantic game, which is a familiar tool in the field of logic to define truth. The activity is designed in a dynamic geometry environment (DGE). The inquiry is initially guided by the game itself and…

In a study about pre-service secondary mathematics teachers' (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments…

This paper explains what drama-based instruction is and offers insights into the phases in drama-based instruction. Further, examples of drama-based lessons in geometry related to ring and circle, and altitude of a triangle together with the teacher and students perceptions related to the strengths and limitations of drama based instruction in…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…

In this article, the author presents one instructional strategy--scribing--tailored to the Tablet PC. He illustrates the role of the scribe during discussion through two classroom examples: (1) generalizing the polygon sum theorem; and (2) proving the third angle theorem. Then he analyzes scribing as an instructional strategy as well as students'…

Although not all children may enjoy eating them, it is fairly safe to assume that most students will at least know what ring doughnuts are, and what they look like. Familiarity with these intriguingly-shaped items of patisserie means that students will not immediately be daunted at the thought of doing some mathematics with the relatively…

Dynamic geometry software (DGS) is often used for development of interactive teaching materials in many subjects, not only mathematics. These interactive materials can contain hundreds of elements in order to represent complex objects, and script programs to control their behavior. We propose an approach for creating, importing and using…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

Discusses research studies which examine why many capable students continue to avoid mathematics in school. The ideal mathematics student, sex differences, teacher behavior, student attitudes, and minority participation are among the areas considered. (JN)

This article describes geometry-oriented problem-solving tasks that can encourage students to develop a positive attitude toward mathematics. The tasks concern working with polyominoes, two-dimensional shapes that consist of squares joined fully at the edges. (Contains 7 figures.)