Tangible programming tools (TPTs) are promising teaching aids in programming courses due to their interactivity and ability to enhance early childhood students' computational thinking, spatial reasoning, and executive function skills. However, it remains unclear whether TPTs support these skills simultaneously. This study examines the impact of…

Developing students' strengths while teaching the content required by national and state standards in science, technology, engineering, and mathematics (STEM) is challenging for classroom teachers. In the Cultivating Diverse Talent in STEM (CDTIS) project, the assessment results found in strength-based reports gave teachers the tools needed to…

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…

Some years back, the author found the following problem in a spatial puzzle book: how many ways can you put four blocks together, face to face (with no vertical rotation symmetry)? He gave each student just four blocks and they collectively tried combinations to eventually agree on the answer of 15. He used to think it was a halfway decent task,…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

Recent studies have shown that strengths in spatial skills are a key to success in STEM (science, technology, engineering, and mathematics) careers. However, these skills are undervalued in our educational system and thus seldom incorporated in classroom teaching. As a first step towards changing the current practices, we worked with a group of…

Teachers of gifted students often are challenged to find ways to stimulate critical thinking and problem-solving skills. School chess clubs are one way of meeting that challenge. This article poses how games such as chess affect learning and gifted students. Two detailed strategies for teaching chess to students beginning in kindergarten are…

External representations (ERs), such as diagrams, animations, and dynamic models are vital tools for communicating and constructing knowledge in biochemistry. To build a meaningful understanding of structure, function, and process, it is essential that students become visually literate by mastering key cognitive skills that are essential for…

Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…

Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…

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.)

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…