ED 661 Understanding Student Thinking in Geometry and Measurement
October 21-22 Agenda
1-1:30 Syllabus for Course Document camera
p.m. Goals for 2 days Handout – goals and agenda
Understanding student misconceptions in Goals Document for Document Camera
elementary is important for laying the Rubric for grading
foundation for future work. For example,
interpreting geometry problems in which you
need to make a sketch, finding areas of
polygons without an understanding of the
attributes of those polygons…
1:30-2:00 Discuss the Van Hiele levels. Big Ideas posted on chart paper as
Discuss the reading in the Van de Walle 3- participants share
5 book. Vandewalle book
Use the “Big Ideas” and questions brought
by the participants as part of their pre-
class assignment. Share at tables first,
then in large group
At tables discuss your big ideas, then we
will do a large group share
Be sure to include:
Difficulties that students have in geometry
1. Build student understanding in Geometry
as a basis for later work in mathematics.
2. Discuss reading in Van De Walle. (What
thoughts and questions did you have?)
a. The van Hiele Levels of Geometric
i. Levels are hierarchal but
you can be this at any
ii. So dependent on spatial
b. Van de Walle defines geometry
and number sense etc. as intuition
and it is up to us as teachers to
give kids experiences to develop
3. Has Geometry been pushed to the back
burner due to national standards etc.
Right now the trend is that if the
mathematical strand supports algebra,
then we should teach it.
4. Should build the attributes in geometry
before giving students the definition.
5. Elementary students are at level 0 and 1.
6. Coverage is a myth that people have been
sold….covering doesn’t necessarily mean
7. Graphic on Pg. 209 will help teachers
understand that you can’t skip steps.
2:00-2:15 Brief Discussion of Triangle activity: Triangles document
Tables share what their students circled and their
definitions of triangles.
Found that all levels of students have
misconceptions of the attributes of a triangle.
We will refocus on this in more depth as we
experience van hiele’s levels during the day.
2:15-3:00 Van de Walle Activity 8.1 or 7.1 Shape Black Line Masters-BLMs 20-26
Note: All BLMs for the book can be Chp. 8 - Pages 212-213 in vandewalle book 3-
downloaded at The ones you need are on 5
Chp. 7 - Pages 194 vandewalle book K-2
the CD, too.
Read through bullets one and two, do
bullet three, read bullet four, and do bullet
Discuss the question under the STOP sign.
Keep track of the language used; read and
discuss the “Assessment Note” on page 214.
3:15-3:45 Activity 8.3(7.3) Geoboard Expansion handouts, “Geoboard Shapes to Copy.”
See also Kathy Richardson, page 50: Geoboards and 5 rubber bands per board
Creating Shapes on the Geoboard. Pg. 215 vdw3-5, pg. 197 vdwK-2
Kathy Richardson Book
3:45-4:15 Activity 8.6 (7.6) Mystery Definition Mystery Definition handout
Provide handout to see if they can Pg. 224 vdw3-5, pg. 207 vdw K-2
figure out the rule
Individual think time
Design your own and have others solve it.
See Figure 8.14(7.14) on page 225 (206) as
See also Kathy Richardson, page 52:
Sorting Shapes on the Geoboard.
4:15-4:45 Activity 8.7 Triangle Sort, page 225 (BLM 29). On web.
Give directions orally; the directions in the
book give too much information.
Your task is to sort the entire collection
into three groups so that no triangle
belongs to two groups. When this is done
and descriptions of the groupings have
been written, students should then find a
second criterion for creating three
Note: the graphic on page 225 is the same
activity we did in “Geometry Camp” (page
4:45-5:00 Closure Handout for Reflection
Exit Question - Comments
Day 2 Response to questions Geom. Camp materials
8-8:30 Activities 8.8, 8.11, and 8.12 correlate to Vandewalle book
activities from “Geometry Camp” (pages 6-
8). Review these pages and relate to the
reading in the Van de Walle book.
Discuss the question under the STOP sign on
8:30-9:30 Read the Introduction to the Casebook on Handouts of intro and case studies 1, 2, 5
pages 1-3. Think about the Van Hiele
Levels as you read.
Chapter 1: Describing 2-D and 3-D
Objects. Read the introduction and Cases
1, 2, and 5.
9:00-9:30 Video clip, “Quick Images”, Chapter 1 in Video from Examining Features and
Examining Features of Shape Shapes
See notes on pages 27-28 F.G. What (BLMs on pages 35-37 F.G.)
different ways do the children describe the Printed Quick Images
images? Think about the Van Hiele levels
that are illustrated.
“Quick Images” math activity:.
Seeing things in different ways. Share the
attributes that you kept in your mind in
order to recreate the images.
Children relied on 3-D, real-world objects
to describe 2-D shapes, but they don’t
necessarily make the distinction between
two and three dimensions.
Some students were not limited by
the orientation of the objects.
9:30- Discuss the Focus Questions: 1, 2, 3, and 4 Focus Questions Handout
10:15 (page 38 F.G.).
Note: Questions 1 and 2 bring up two
topics: the use of technical geometric
vocabulary, and the different ways a 3-D
object can be described by listing its 2-D
components. Throughout this course, we
will explore the difference between a
mathematical definition and a description
of an object, recognizing that correct
vocabulary includes concepts and ideas to
think about before definitions make sense.
Small group discussion: Focus questions
(Compare the language and results you
observed when students completed Circle
the Triangles to the children’s’ language
and thinking in the cases.)
Take turns recording your thoughts on
paper to use during the whole group
Again, keep in mind the Van Hiele Levels.
Whole group discussion
Discussion of the shape as a whole vs. the
parts of the shape
The way you are thinking affects the way
you see an object or what you notice
about it (some may think of the shapes as
Purpose of the activities: develop mental
images of the figures and the means to
communicate about them.
10:30- Math Activity: “What’s in the Envelope?” Envelope and shapes
11:00 (Groups of 3) Page 39 F.G.
Can we put 2-D shapes into the envelope?
Discuss the names of the shapes (briefly).
Sort the shapes into categories of your
Possible extension: Sort as if you were at
a specific Van Hiele level: for example, sort
by Level 0 criteria (or choose a different
11:00- Chapter 2: Developing Meaning for Orange pattern bock and rectangular
11:30 Geometric Terms. Discussion of Cases 9, prism
10, 11. Focus Questions 1, 2, and 3 (page
50 F.G.) go with these cases. Have an
orange square pattern block and a
rectangular prism for the Case 10
Small groups-Discuss the Introduction as it
relates to the Van Hiele Levels.
Whole group (Discuss Focus Question #6,
12:30- View the video, “Angles in a Triangle” Video clips
1:15 See notes on page 46 F.G. Focus Questions 1, 2, 4
Math Activity, “Angles and Angle
Measures”—page 51 F.G. Questions 1, 2,
4, and 5 are activities from Geometry
Camp. Decide how much of each of these
activities you need to do to refresh your
memory. I would actually suggest that you
redo all of the activities. Discuss all the
questions, including #3.
1:15-3:45 Teacher Presentations: 20 minutes each Geometry manipulatives
Break with a bit of time to spare Handouts for each team
inclusive Marnie/Colleen Oct. 22
Cindy/Mary Oct. 22
Rachel/Laurie Oct. 22
Sandy/Annie Oct. 22
Pam/Samra Oct. 22
Sherry/Connie Oct. 22
Samantha/Doreen/Nancy Oct. 22
3:45-4:00 Exit Question Handout
1. Provide a document asking your
students what an angle is through
words and pictures.
2. Hold up 3 lengths of string and ask
them to write their estimated length
and how they came to the decision for
3. Next group presentations.