Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

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…

Teaching about wave structure and function is a critical element of any physical science curriculum and supported by "Next Generation Science Standards (NGSS)" PS4: Waves and Their Applications in Technologies for Information Transfer. To support students' learning of these ideas, teachers often rely on developing graphic models of a…

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…

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…

How many squares can be found on a typical 5 × 5 geoboard? Teachers who are unfamiliar with this question may wish to stop here and reflect a bit. The question can lead to wonderful student discourse: How can someone tell if something is a square? Should squares be counted that are the same size (but in a different location) or just different…

Nondeterminism is a fundamental concept in computer science that appears in various contexts such as automata theory, algorithms and concurrent computation. We present a taxonomy of the different ways that nondeterminism can be defined and used; the categories of the taxonomy are domain, nature, implementation, consistency, execution and…

In this article, the author describes a lesson he observed involving a function machine. This function machine was a box with a slot at the top of one side and a large cut-out hole at the bottom of the opposite side. A card with a number written on it (the input) was pushed into the slot and the teacher put their hand through the hole of the other…

This article presents a case study in which researcher-practitioner collaboration took place to promote effective use of technology in an urban elementary school mathematics classroom. Data were primarily gathered through classroom observations and interviews. The aim of this study was twofold. First, to increase our understanding of the effects…

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

Helping students understand the general nature of scientific models is increasingly regarded as an important goal of the middle and high school science curriculum (e.g., J. K. Gilbert & C. Boutler, 1998. "International Handbook of Science Education"; Kluwer, London; A. G. Harrison & D. F. Treagust, 2000. "Science Education," 352-381). In addition,…

Discusses the nature of misconceptions in science and the role of teachers and students in correcting these misconceptions. Also describes a simulation program that centers on some basic topics in Newtonian mechanics, outlining its structure and examining some of the premises that served as guidelines in its design. (JN)

Uses of Intermedia, computer software designed to help instructors express relationships between concepts in the sciences and humanities, are discussed. The kinds of educational problems Intermedia was intended to address are described, some materials created using it are surveyed, and experiences with Intermedia in various educational contexts…

The computer packages of PLOTALL, SYMAP, SURFACE II, QUSMO, QUSMO2, QUCRS, and QUTAB are commercially available plotting programs that provide aids for visualizing spatial distributed data and concepts. The incremental drum and line printer plots communicate often vast and difficult-to-interpret tabular data with or without geographic coordinates.…