Large drop towers let you experience a couple of seconds of nearly free fall before stopping gracefully in magnetic brakes or bouncing a number of times on compressed air, as in the Turbo Drop tower considered in this work, where many complementary representations are used. An accelerometer taken along on the ride captured the forces experienced…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

Models are an important tool for geography teaching, as they can be used to represent features of human and/ or physical systems. In addition, they enable the student to identify with the demonstrated reality, since they work with iconic images and symbols specific to each culture, used to represent the elements contained in the models (da Silva…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

Karina Wilkie discusses functional thinking in the primary classroom. She provides a useful learning progression with sample responses to a growing pattern task.

Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

The universities and faculties which educate teachers of mathematics for teaching pupils/students of any age group from pre-school age to higher education carefully monitor and compare valuable results of this research, detect the areas in which the mathematical achievements of pupils should be improved at the national level and propose the ways…

The author recounts experiences introducing a first grade class to the concept of symmetry. The lesson includes activities for developing recognition of objects that have symmetry as well as visualization of both horizontal and vertical lines of symmetry.

Describes seven spatial abilities related to mathematics including eye-motor coordination, figure-ground perception, perceptual constancy, position-in-space perception, perception of spatial relationships, visual discrimination, and visual memory. Discusses the relationship of the spatial abilities to the study of geometry. Lists 19 references.…

Calculus students have great trouble visualizing solids of revolution and their cross sections. Illustrates the use of props in order to help students understand the solid revolution. (ASK)

Describes how to deal with students' structuring of rectangular arrays of squares and other two-dimensional regions. Presents activities that connect spatial structuring to the development of multiplicative thinking. (ASK)

Presents interesting activities to develop mental imagery and the ability to transform these images. Concludes that using images facilitates mathematical thought in numerical and geometric settings. (ASK)

Provided are activities for creating tangrams. Illustrates how to make tangrams and use them. (YP)