Embedding mathematics in a relatable context has changed the way Christie Henderson's elementary students view the subject. In this article, Henderson discusses how presenting mathematics through a relatable context enables students to visualize the math and make a pictorial representation to aid them in solving it. When relevant and relatable…

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

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…

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…

Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…

NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

Presents methods for teaching two mathematical concepts that utilize visualization. The first illustrates a visual approach to developing the formula for the sum of the terms of an arithmetic sequence. The second develops the relationship between the slopes of perpendicular lines by performing a rotation of the coordinate axes and examining the…

Presents three fundamental ideas of calculus and explains using the coordinate plane geometrically. Uses Cabri Geometry II to show how computer geometry systems can facilitate student understanding of general conic objects and its dynamic algebraic equations. (KHR)