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

Scaffolding for Geometric
Growth
Math Alliance
November 2, 2010
Beth Schefelker & Melissa Hedges
Learning Intentions and
Success Criteria
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Learning Intentions
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Examine the geometric thinking and reasoning
children exhibit and classify it according to van
Hiele’s level of geometric thought.
Success Criteria
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We will be successful when
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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.
Quick Image
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What do you see? How did you see it?
Thinking about your own
Quick Image Experience
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What did you learn about your students?
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What did you learn about yourself as an
instructor during this activity?
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Is it “good enough” to do this activity just
once?
What’s in the bag? Round #1
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Person 1 selects the shape from the center of
the table.
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Person 2 finds and describes the match in
the bag.
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Person 3 records descriptive language and
questions.
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Person 4 asks clarifying questions.
What’s in the bag? Round #2
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Person 1 selects a shape from the bag and
describes without removing it from the bag.
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Person 2 and Person 3 draw the shape
based on the description. You may ask a total
of 3 clarifying questions.
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Person 4 records descriptive language
questions.
Strategic Instruction
In what ways might the activities of Quick
Images and What’s in the bag be used to
transition students?
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Pre-level 0 → Level 0
Level 0 → Level 1
Level 1 → Level 2
Case #3 Describing Geometric Blocks
pp.15-19
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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?
Strategic Instruction
Characteristics of the van Hiele levels
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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.
Review the Triangle Task Project
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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.
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Patterns of performance, including van Hiele levels of the students.
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Comparisons of the performance of students with disabilities and
without disabilities.
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Instruction implications.
Between now and the beginning of March
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Keep a log identifying the instruction you provide relative to students’
understanding of polygons, specifically triangles, and your reflections
on this instruction.
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
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As a teacher of mathematics
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How is what you are learning supporting your teaching?
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.)
Homework
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Due Nov 18
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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
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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.