1. Scaffolding for Geometric Growth Math Alliance November 2, 2010 Beth Schefelker & Melissa Hedges

2. Learning Intentions and Success Criteria Learning Intentions  Examine the geometric thinking and reasoning children exhibit and classify it according to van Hiele’s level of geometric thought. Success Criteria  We will be successful when we recognize that “geometry is more than definitions; it is about describing relationships and reasoning.” –PSSM. we can begin to identify “next steps” to move children to more developed levels of geometric thought.

3. Quick Image What do you see? How did you see it?

4. Thinking about your own Quick Image Experience What did you learn about your students? What did you learn about yourself as an instructor during this activity? Is it “good enough” to do this activity just once?

5. What’s in the bag? Round #1 Person 1 selects the shape from the center of the table. Person 2 finds and describes the match in the bag. Person 3 records descriptive language and questions. Person 4 asks clarifying questions.

6. What’s in the bag? Round #2 Person 1 selects a shape from the bag and describes without removing it from the bag. Person 2 and Person 3 draw the shape based on the description. You may ask a total of 3 clarifying questions. Person 4 records descriptive language questions.

7. Strategic Instruction In what ways might the activities of Quick Images and What’s in the bag be used to transition students? Pre-level 0 → Level 0 Level 0 → Level 1 Level 1 → Level 2

8. Case #3 Describing Geometric Blocks pp.15-19 What were the teacher’s mathematical goals of the lesson? What were some instructional moves Rosemarie made to scaffold children’s thinking to reach those goals? What did the teacher learn about her students’ geometric thinking? Next steps?

9. Strategic Instruction Characteristics of the van Hiele levels  The levels are sequential.  The levels are not age dependent.  Geometric experience is the greatest single factor influencing advancement through the levels.  Students required to wrestle with objects of thought that have not been constructed at the earlier level may be forced into rote learning and achieve only temporary and superficial success.

10. Review the Triangle Task Project Now that you know where your students’ thinking lies…  Summarize our discussion from today in a 1.5-2 page paper due November 16. Follow guidelines in syllabus (p. 6). To assist you with this reflect back on Case 2 Falling Triangles. Patterns of performance, including van Hiele levels of the students. Comparisons of the performance of students with disabilities and without disabilities. Instruction implications.  Between now and the beginning of March Keep a log identifying the instruction you provide relative to students’ understanding of polygons, specifically triangles, and your reflections on this instruction.

11. Resource Binder Big Idea #1 Description, Classification, and Analysis of Polygons We will all use the Triangle Task Project for this first Big Idea. Page 5 of the syllabus: As a learner of mathematics  How is what you are learning supporting your teaching? As a teacher of mathematics  Identifying student levels of understanding.  What have we learned from the assessments? Research/Trace how the Big Idea is presented in the textbook program you use. (This is the instructional implications portion of your Triangle Task.)‏

12. Homework Due Nov 18  Triangle Task Project 1.5-2 pages write up.  Develop a one page reflection (typed) for the “As a learner of mathematics” portion of the binder project. (syllabus p. 5). Planning ahead for Resource Binder – Big Idea #1  Develop a one page reflection (typed) for the “As a learner of mathematics” portion of the binder project. (syllabus p. 5).  Find, and become familiar with, the units/lessons in your textbook that support students’ reasoning around polygons.  Bring your textbook materials to class on November 18.