The Idea Bank provides tips and techniques for creative teaching, in about 1,000 words. For this article, the authors analyzed 93 educational applications (apps) that have the potential to help students meaningfully engage in the science practices outlined in the Next Generation Science Standards. Some of the ways teachers can use these apps in…

Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., "iPads") in an effort to help students understand mathematics concepts. However, students experience these apps and their affordances in different ways. The purpose of this article is to inform teachers' decisions about app implementation in the…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

The best Science, Technology, Engineering, and Mathematics (STEM) design challenges are student centered, with students themselves making the key decisions. But with young children who are still learning basic academic and social skills, implementing projects where they truly take the lead can be quite challenging. To give students at one…

Having an answer to "When are we ever going to use this in real life?" is important to middle school mathematics teachers. The activity described in this article awakened sixth graders' understanding of how artists use mathematics. By exploring ratio and proportionality in different paintings, students realized the use of proportional…

Describes a number sequence made by counting the occurrence of each digit from 9 to 0, catenating this count with the digit, and joining these numeric strings to form a new term. Presents a computer-aided proof and an analytic proof of the sequence; compares these two methods of proof. (YP)

An environment for investigating vector-valued functions in two- and three-dimensional space using Logo is described. The language is presented, followed by use of the environment. Appended are Logo primitives and procedures. (MNS)

Provided is an overview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics. Describes the impact of numerical computation, graphic computation, symbolic computation, multiple representation of information, programing and information, and artificial…

Notes muMATH is a powerful computer algebra systems assistant for performing symbol manipulation in algebra and calculus. Provides several examples and program listings for calculus tutoring, differentiation drill problems, and integration drill problems. (MVL)

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Provides a program listing in True BASIC which constructs several kinds of matrices: (1) matrices with integral entries that have inverses that have integral entries; (2) matrices with integral entries that have inverses that are rational numbers with reasonable denominators; and (3) matrices with integral entries and prescribed integer…

Presented are some current facts about symbol manipulators and their relation to high school mathematics. The development of computer algebra systems is discussed. Five areas of computer algebra needing investigation (skill proficiency, understanding, curriculum content, student homework, and equity) are identified. (MVL)

Discusses the use of the symbolic manipulator which helps students solve equations one step at a time. Recommends features to look for in algebra tools. Compares 14 programs on general, graphic, numeric, and symbolic manipulation and provides short reviews of each. (MVL)

Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)

Uses a LOGO program and probability to solve systems of equations. Provides a physical model and a LOGO model. Lists programs and explains the methodology used. (MVL)