Illuminating NCTM's Principles and Standards for School Mathematics

School Science and Mathematics, Oct 2001 by Keller, Brian A, Martin, W Gary, Hart, Eric W

The National Council of Teachers of Mathematics' Illuminations Project provides electronic resources to illuminate the Principles and Standards for School Mathematics and to improve the teaching and learning of mathematics for all students. This paper describes the types of resources that are available and discusses how the Principles and Standards document has guided work on the project. Organized around the six principles, this paper provides a vehicle for further discussion of the vision put forth in the Principles and Standards.

The National Council of Teachers of Mathematics' (NCTM) Illuminations Project is designed to illuminate the new vision for school mathematics put forth in the NCTM Principles and Standards for School Mathematics (NCTM, 2000). Illuminations is a companion to the e-Standards project in which the Principles and Standards was produced in a web- and CD-based format. Illuminations is also part of the MarcoPolo Internet education partnership (http:// marcopolo.worldcom.com/), a consortium of seven professional organizations, with funding from the WorldCom Foundation. The main goal of Illuminations is to provide online resources to improve the teaching and learning of mathematics for all students. Other goals include providing professional development for teachers and rich classroom materials for students.

The NCTM Illuminations web site is organized into four major sections: i-Math Investigations, which are online, interactive, multimedia mathematics investigations; Reflections on Teaching, which are reflection activities based primarly on video vignettes of learning and teaching mathematics; Selected Web Resources - carefully reviewed and categorized links to other web sites; and Internet-Based Lesson Plans, which show how the Internet can be used in standards-based lessons. Resources from each of these sections will be used to illustrate how the NCTM Illuminations Project illuminates the Principles and Standards.

The Standards for School Mathematics are at the heart of NCTM's recommendations in the Principles and Standards. They describe the mathematical content and processes that should be taught and that students should learn. An important new feature of the Principles and Standards, as compared to previous NCTM standards documents, is the inclusion of principles. The principles describe general features that are essential for highquality mathematics education. This paper is organized around the six principles: technology, teaching, learning, equity, curriculum, and assessment, with emphasis on technology. Our goal is to extend the discussion of the principles by describing how the Illuminations Project strives to illuminate the principles. The following discussion of each principle uses many of the same subsections found in the document itself. The first half of the paper includes in-depth descriptions of some of the Illuminations resources, providing material that will be drawn upon during the discussion of all the principles.

We begin our discussion with the Technology Principle, since the Illuminations Project is an Internetbased resource. We also highlight a central design criterion for the site: to truly understand the vision put forth in the Principles and Standards, an individual must actively engage in mathematics that is reflective of that vision.

"The Technology Principle: Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." (NCTM, 2000, p. 24)

Technology has been an important part ofthe effort to improve the teaching and learning of mathematics over the last two decades. Calculators, computer software, and the Internet are now widely used in mathematics education. This section will focus on how the decision to create a new Internet-based project impacted the manner in which we illuminate the Principles and Standards.

Central to the development of the NCTM Illuminations web site are two key conceptualizations ofthe Internet: (a) a global, online, interactive, multimedia platform on which to build and deliver powerful educational and professional development experiences, and (b) a vast, interconnected database of information and resources.

Related to the first conceptualization ofthe Internet, the Illuminations web site contains online tools for teaching, learning, and professional development in mathematics. The different types of online tools include general purpose tools, such as a spreadsheet and grapher; content-specific tools, such as applets that facilitate exploration of linear regression or fractions; context-specific tools, such as applets that simulate light intensity or a game of pool; and reflection tools, such as online video vignettes of students learning and teachers teaching mathematics. Related to the second conceptualization of the Internet, the Illuminations web site includes a section of Selected Web Resources, which selects a targeted portion of the Internet's global database. We now consider how the Illuminations resources align with the aspects of the Technology Principle. "Technology enhances mathematics learning." (NCTM, 2000, p. 25)