Using geometric vocabulary with meaning Math Alliance November 16, 2010 Beth Schefelker, Judy Winn, & Melissa Hedges.
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Transcript Using geometric vocabulary with meaning Math Alliance November 16, 2010 Beth Schefelker, Judy Winn, & Melissa Hedges.
Using geometric vocabulary
with meaning
Math Alliance
November 16, 2010
Beth Schefelker, Judy Winn, & Melissa Hedges
Learning Intention and
Success Criteria
We are learning to…
Scaffold learning experiences that support
students’ understanding of geometric ideas
while concurrently developing the specialized
vocabulary of geometry.
We will be successful when…
we can identify GKT (Geometry Knowledge
needed for Teaching) and instructional moves
necessary to push student understanding.
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. Person 2 or 3
may ask a total of 3 clarifying questions.
Person 4 records descriptive language
questions.
Round #3 What’s in the bag?
Goal: “Find/Name that shape” in 3 clues or less.
(No questions are permitted.)
Describer silently selects a shape and crafts 3
clues that will help participants identify that
shape.
Describer: Give one clue at time.
Finder: Finds the shape.
Recorder: Keep track of descriptive language in
the clues.
What’s in the bag?
Debrief
Look back on the notes taken by the recorder.
What characteristics “made up” a good
description or helpful clues?
In general, discuss what you chose to tell about
the shapes in your clues. What did you tend to
leave out?
Consider the level of complexity of language
used by your group. (van Hiele level.)
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?
What GKT does Rosemarie need to plan
for subsequent learning experiences?
Strategic Instruction
Characteristics of the van Hiele levels
The levels are sequential.
The levels are not age dependent.
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.
Geometric experience is the greatest single factor
influencing advancement through the levels.
Strategic Instruction
In what ways might the “What’s in the
bag?” be used to transition students
from…
Pre-level 0 to Level 0
Level 0 to Level 1
PreLevel 0 to Level 0
Level 0 to Level 1
Teachers should involve students in lots of naming,
describing, sorting, and classifying of shapes.
Students need numerous opportunities to identify and
express similarities and differences between shapes.
As children surface properties such as symmetry,
numbers of sides and corners, etc. appropriate geometric
terms are introduced by the teacher.
As sorting tasks continue teachers should challenge
students to use features (sides, angles, etc.) to classify
shapes.
Students should be provided numerous, and focused,
opportunities to draw, build, make, put together, and take
apart shapes in both 2-D and 3-D.
Level 0 to Level 1– Geometry Knowledge
for Teaching
Accurate use of Level 0 and Level 1
vocabulary and Level 1 and Level 2
understanding of geometric
properties on behalf of the teacher is
critical!
Strategic Instruction
In what ways might the “What’s in the
bag?” be used to transition students from
Level 1 to Level 2?
Level 1 to Level 2
Focus more on properties of shapes rather than on
simple identification of shapes. As new geometric
concepts are learned, the number of properties that
figures have can be expanded. (Example: sort
quadrilaterals first with “2 pairs of opposite sides are
parallel” then with “2 pairs of opposite sides are
congruent.” What do we notice?)
Apply ideas to all classes of figures (e.g., all
rectangles, all prisms) rather than individual models.
Example: Find ways to sort all possible triangles into
groups. From these groups define types of triangles.
Level 1 to Level 2 -- GKT
Teachers must be comfortable guiding
students through classifying shapes,
identifying and defining properties, and
using geometric vocabulary with
meaning.
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.)
Homework
Work on Part C of the Resource Binder
project. Complete the analysis of the
lessons portion. (Remember, you have
already completed Parts A and B. You
turned them in tonight.)
For November 30, come ready to share
your analysis of the lessons. We will share
your analysis of the differentiation
suggestions on December 7.