Teacher professional development and classroom resources across the curriculum

Teacher professional development and classroom resources across the curriculum

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. In grades 3-5, students should be moving from working easily at level 0 through level 1. By fifth grade, they should be starting to work at level 2, thinking in more sophisticated ways.

 Video Segment Watch this clip from Ms. Kurchian's class, 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 14 minutes and 3 seconds after the Annenberg Media logo.

Problem B1

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

 • (Level 1 thinking) Students thinking about classes of shapes rather than the individual shapes in front of them. Do students seem concerned with orientation or size of the figures they use compared with the ones on the board? • (Level 2 thinking) "If-then" reasoning and making geometric arguments

 Problem B2 In Session 9, you worked on the problem of building the five Platonic solids and then arguing from the construction that only five such solids were possible. Recall your own experience in this activity as an adult mathematics learner. During the activity, when did you have to use level 2 thinking? (How did you know when to stop building with triangles and move on to other figures? How did you convince yourself that no other Platonic solids were possible?)

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 students in grades 3-5 and how the Platonic solids 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?