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.