Session 10, Part B:
Developing Geometric Reasoning

In This Part: Introducing van Hiele Levels | Analyzing with van Hiele Levels

In this course, we have primarily worked across levels 2-4. You may feel that the activities we've done are not appropriate for the level of your students, and you're probably right. The goal for this session is for you to think about problems and activities that are at your students' level, and how to help them prepare for the next level of thinking.

Students in pre-K-2 generally fall at level 0 (visualization). This level describes students who reason about shapes primarily on the basis of visual considerations of the whole without explicit regard to the properties of the components (Burger and Shaughnessy, 1986). One goal of the schooling of these students is to move them to level 1 (analysis), where they can informally analyze component parts and attributes. In the primary grades, students build the foundation for understanding shapes, both two- and three-dimensional. They learn what shapes look like, the features that distinguish shapes from one another, and ways to describe shapes.

 Navigating through Geometry in Prekindergarten - Grade 2, p. 9 Reston, VA: National Council of Teachers of Mathematics, 2001

 Video Segment Watch this clip from Ms. Christiansen's class again, and think about how both the lesson and the teacher are encouraging students to move to that next level of geometric reasoning. Note 5 If you are using a VCR, you can find this segment on the session video approximately 22 minutes and 32 seconds after the Annenberg Media logo.

Problem B1

Where in the video do you see evidence of the following?

 • (Level 0 thinking) Students thinking about particular shapes and not their properties • (Level 1 thinking) Students thinking about classes of shapes rather than the individual shapes. Do students seem concerned with orientation or size of the figures?

 Problem B2 In Session 3, you worked on the problem of finding hidden polygons. Recall your own experience in this activity as an adult mathematics learner. During the activity, when did you have to use level 1 thinking? (How did you think about properties of figures to help you find them?)

Problem B3

 a. What do you think were the key pieces of geometry content in this activity? What knowledge did you learn, solidify, or connect with better? b. What do you think were the key thinking and reasoning skills in this activity? How did the reasoning and geometric content tie together?

 Problem B4 Now think about K-2 students and how this hidden polygon activity might work with them. What must students know and be comfortable with to get the most out of this activity? What are potential stumbling blocks for them?

 Join the discussion! Post your answer to Problem B4 on Channel Talk; then read and respond to answers posted by others.

 Problem B5 What might students misunderstand or find confusing in the lesson? How could you alter the lesson or prepare them beforehand to help avoid these misunderstandings?

 Findell, Carol R.; Small, Marian; Cavanagh, Mary; Dacey, Linda; Greenes, Carole E.; and Sheffield, Linda Jensen. Navigating through Geometry in Prekindergarten-Grade 2. (Reston, VA: National Council of Teachers of Mathematics, 2001), 9. Reproduced with permission from the publisher. Copyright © 2001 by the National Council of Teachers of Mathematics. All rights reserved.
 Session 10, Grades k-2: Index | Notes | Solutions | Video