Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
Follow The Annenberg Learner on LinkedIn Follow The Annenberg Learner on Facebook Follow Annenberg Learner on Twitter
MENU
Learning Math Home
Geometry Session 10: Classroom Case Studies - Grades 6-8
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
Glossary
geometry Site Map
Session 10 Materials:
Notes
Solutions
Video

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 6-8, students should be working comfortably at level 1. Ideally, they will have begun working on drawing logical conclusions and "if-then" thinking characteristic of level 2, but not all students may be comfortable with that kind of task. During middle school, students should be prepared for work at the van Hiele level 3. This means reasoning through more complicated mathematical arguments, leading into some early proofs.



video thumbnail
 

Video Segment
In this clip from Ms. Weber's eighth-grade class, the teacher leads the students as a whole class through a proof of the Pythagorean theorem. Students have already reviewed the statement of the theorem, and they have worked through some numerical examples like the one the teacher works through in general. Note 5

If you are using a VCR, you can find this segment on the session video approximately 16 minutes and 0 seconds after the Annenberg Media logo.

 

 

Problem B1

Solution  

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. Do students seem concerned with orientation or size of the figures?

 

(Level 2 thinking) "If-then" reasoning and making geometric arguments

 

(Level 3 thinking) Students working more abstractly, drawing conclusions based on logic more than on intuition


 

Problem B2

Solution  

Ms. Weber's lesson was based on a lesson from Session 6 of this course. Discuss the ways in which Ms. Weber's lesson was similar to and different from the one in this course. What adaptations did she make and why?


 

Problem B3

Solution  

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?) What about level 3 thinking?


 

Problem B4

Solution  

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 B5

Solution  

Now think about students in grades 6-8 and how this 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?


 
 

Join the discussion! Post your answer to Problem B5 on Channel Talk; then read and respond to answers posted by others.

 
 

Problem B6

Solution  

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?


Next > Part C: Problems That Illustrate Geometric Reasoning

Learning Math Home | Geometry Home | Glossary | Map | ©

Session 10, Grades 6-8: Index | Notes | Solutions | Video

© Annenberg Foundation 2014. All rights reserved. Legal Policy