Interactive opportunity

Rationale: In recent years, the Internet has been used to allow students to interact directly with mathematical objects, in a variety of ways. The experiences provided are very difficult to provide in other ways and engage the students directly in mathematical activity and a corresponding need to think about what they see on the screen. Most of these require that the browser has particular capabilities (such as having Java enabled or having a plug-in for Flash software). This is a brief introduction: a more extensive collection is available on the companion website.)

Here are some examples:

Interactivate The goals of Project Interactivate are the creation, collection, evaluation, and dissemination of java-based courseware for middle school mathematics explorations. "Interactivated" lessons, discussions, and activities enable the teacher to extend hands-on activities and to teach new content areas with professional competence and confidence, incorporating technology in appropriate ways. The project includes many resources designed specifically for students or teachers, including the java-based activities, sample lesson plans, background materials, and hyperlinked textbook tables of contents. This site contains many interesting Java applets in geometry & measurement, algebra and probability & Statistics. A US project, Project Interactivate is funded, in part, by the Office of Dependent Education of the Department of Defense.	Illuminations This website is intended to help 'illuminate' the new NCTM Principles and Standards for School Mathematics by focusing on Internet-based teaching and learning, including online, interactive, multimedia mathematical investigations. The link above goes directly to various ‘tools’ designed to allow students to engage actively with mathematical ideas. Other parts of the website provide well-structured web links, details of lessons for teachers linked to the Standards and a searchable electronic version of the new standards-based document. The tools provide many examples of interactive mathematical opportunities, graded by (US) school level. The site is intended mostly for teachers, but students can learn a lot by exploring it for themselves, and using the applets provided.
Maths Online This Austrian website contains many interactive resources using Java applets, mostly for secondary school students. A distinctive feature is that they have been carefully designed educationally, so that the Exercises are much more than typical ‘practice’ exercises. Click on the Gallery and try some of the applets to get a feel for the approaches used. The Interactive Tests may also be of interest as well as the substantial collection of online mathematical tools. The authors describe their approach and its educational thinking well in several ways on this superb website, as well as offering substantial classroom advice for using the materials.	Manipula Math with Java This is a Japanese site with a very large number of small, single-purpose Java applets classified by mathematical topic: middle school, trigonometry, vectors, complex numbers, calculus, conics and miscellaneous. A small number can be downloaded for local use, while the site allows commercial purchase of the collection. The ever-expanding collection demonstrates very well a range of nice possibilities for students to manipulate mathematical objects and think about the results. Occasional linguistic problems are not a major concern.
National Library of Virtual Manipulatives A large and impressive collection of applets, with substantial support provided for teachers and parents. Linked to the NCTM Standards. Can be purchased separately as a CD-ROM, avoiding the need for Internet access. These virtual manipulatives are well organised and easily searched to look for good examples in different areas of mathematics across a wide range of ages. Many of the grade-level designations are questionable, so do not rely on them.	NRich The NRich site in the UK contains many interactive resources, each of which is referred to as an interactivity. As well as being used directly by students, many of these lend themselves to whole classroom use, including use on an interactive whiteboard. The link above goes directly to a searchable set of interactivities of various kinds, intended for use in a range of ways. Many of the packages contain interactivities as well, with the advantage that these can be downloaded for use offline.