NCTM Standards

The NCTM Principles and Standards for School Mathematics addresses the topic of circles in both the Measurement and the Geometry standards. It states that students should come to the middle grades with informal knowledge of several two-dimensional shapes, with experience in visualizing and drawing them, and "with intuitive notions about shapes built from years of interacting with objects in their daily lives" (NCTM, 2000, p. 233). Likewise, students bring experiences with measurement from prior instruction as well as from everyday use.

Building on this knowledge, middle school students "should explore a variety of geometric shapes and examine their characteristics" (NCTM, 2000, p. 233), learning to precisely define and describe the features of the shapes. Furthermore, at this level students should develop a strong understanding of transformational geometry, including rotational geometry. The NCTM document notes that one important aspect of measurement in the middle grades is "solving problems involving the perimeter and area of two-dimensional shapes" (p. 241). Students need to learn to use appropriate measuring tools and apply appropriate formulas to determine measurements and "whenever possible . . . develop formulas and procedures meaningfully through investigation rather than memorize them"(p. 244).

The resources highlighted in Going Around in Circles! can be used to focus attention on the underlying logic of circle formulas and rotational symmetry. In selecting these resources, our aim has been to invite students to develop intuitive understanding through working with actual materials or interacting with online simulations. Creating their own art with circles, students will come to an appreciation of the use of circles in designs found in many cultures.

Teachers will find resources that support their standards-based instruction. As they investigate the history of circle measurement, experiment with rotating figures, and question the formulas used, teachers will find opportunities to incorporate ideas from the Reasoning and Proof, Problem Solving, and Connections standards. Other valuable resources that feature NCTM Standards-based teaching ideas for geometry and measurement are the series Navigating Through Geometry and Navigating Through Measurement. (Ordering information can be found at the NCTM web site).

Reference

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

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Copyright June 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.