Mathematics has been taught throughout history without much more than a straightedge, a compass, and an abacus. So there is little question that all the major concepts of mathematics can be delivered without the aid of modern technology. But clearly, just the time-saving aspect of using technology can greatly enhance the art of teaching. In this…

The Common Core State Standards for Mathematics envisions data analysis as a key component of K-grade 12 mathematics instruction with statistics introduced in the early grades. Nonetheless, deficiencies in statistical learning persist throughout elementary school and beyond. Too often, mathematics teachers lack the statistical knowledge for…

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

Activities for Students appears five times each year in Mathematics Teacher, promoting student-centered activities that teachers can adapt for use in their own classroom. In the course of the activities presented here, students will "look for and make use of structure" by observing algebraic patterns in the power rule and "use…

Students' ability to use appropriate tools strategically is an important skill of mathematically proficient students (SMP 5, CCSSI 2010, p. 7). A parallel practice for teachers is using appropriate tools strategically for mathematics instruction. An important element of this practice is that the use of technology depends on the goals of…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

The Ancient Greeks studied conic sections from a geometric point of view--by cutting a cone with a plane. Later, Apollonius (ca. 262-190 BCE) obtained the conic sections from one right double cone. The modern approach to the study of conics can be considered "analytic geometry," in which conic sections are defined in terms of distance…

Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th…

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…

Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

Many students at all levels--from middle school to graduate programs for in-service teachers--struggle with visualizing three-dimensional shapes. Many also are challenged to locate appropriate centers of rotation, placement of lines of symmetry, and translation vectors for transformations on the plane. Hands-on experience helps with these…

The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…