Home | Chapter 21 |

There is no difficulty identifying the main idea that I want to get across to teachers in this chapter: Geometry can be one of the most fun, exciting, engaging, profitable, and enticing areas of the curriculum if we only let it. (You may want to add your own adjectives to this list.) It is, however, non-trivial to make this point within the limited time allotted by a methods class.
As described on page 408 and briefly listed on Transparency T-118, there are two types of goals that all teachers should be aware of: Growth in geometric thought and growth in understanding of geometric content. The issue of geometric thought is reflective of the van Hiele theory. Geometric content has always been a more difficult concern since there is very little consensus about what content should be taught and at what grade level. To help your teachers with a perspective on content development, I have turned to the *Principles and Standards *document. There the authors describe four goals for geometric content: 1) shapes and properties, 2) location (essentially coordinate geometry), 3) transformation, and 4) visualization.

One aspect of the van Hiele theory that I have come to see as important in terms of daily instruction is the notion that the product of thought at one level becomes the object of thought at the next. To the extent that teachers can grasp that idea, it sends a message about working where students are while simultaneously prodding them forward. Level 0 children need not do trivial activities. Transparency T-117 includes a copy of Figure 21.3 illustrating this progression of objects and products is included here.

Shapes and Properties | Location | Transformations | Visualization | |

Level 0 | ||||

Level 1 | ||||

Level 2 |

This organization allows your teachers to easily find a content area and explore it across the van Hiele levels, or simply look at activities for a level of their interest. You of course can do the same as you make choices for what activities to do in class. [My apologies to those who just got familiar with the fifth edition in which the organization was horizontal across this table. I hope you find this to be an improvement.]

By all means, explain to your students that this rather long chapter is about 80% a resource. I do not require my students to "know" any particular activity found there. I believe they should have some speaking knowledge of the four areas of geometry and probably know at least several representative activities in each. They will have the book as a reference and as a resource for both teaching and learning. Encourage teachers to grow over time with respect to geometry. The organization of the chapter should allow them to select activities that best suit their needs.