Improving Teacher Knowledge
in Geometry and Measurement:
Sustained Content-Focused Professional Development
Collaboration of Mathematicians, Mathematics Educators,
and Teachers-in-Residence
Lee Ann Pruske, Mary Mooney, & DeAnn Huinker
Milwaukee Mathematics Partnership
University of Wisconsin-Milwaukee
Association of Mathematics Teacher Educators
12th Annual Conference, January 2008
Tulsa, Oklahoma
www.mmp.uwm.edu
This material is based upon work supported by the National Science Foundation under Grant No. 0314898.
Any opinions, findings and conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
Session Goals
 Examine a year-long sequence of
activities used to deepen teachers
knowledge of the big ideas of
geometry and measurement.
 Share impact on teachers’
mathematical knowledge for
teaching.
 Examine assessments that look
more closely at mathematical
knowledge for teaching.
Always true,
Sometimes true
Never true
1. A parallelogram is a rectangle.
2. A square is a rectangle.
3. A trapezoid is a rhombus.
Turn to the person next to you,
share and justify your responses.
Teacher Work
Examine as pairs or small groups…
What are some teacher
understandings and struggles
revealed in this work?
What might be “big ideas” in
geometry for teacher knowledge?
“Some authors choose to define
trapezoid as a quadrilateral with at
least one pair of parallel sides. That
definition is more inclusive and leads to
the conclusion that all parallelograms
are trapezoids.”
“The Navigation books adopt the
classical definition that a trapezoid is a
quadrilateral with exactly one pair of
parallel sides."
Navigating through Geometry in Grades 6 (page 11)
by Pugalee et al. (2002).
Trapezoid Definitions
Everyday Math
Expressions
Quadrilateral
Quadrilateral with
that has exactly at least one pair of
one pair of
parallel sides.(K-1)
parallel sides.
Quadrilateral with
one pair of parallel
sides. (5th)
CMP
Quadrilateral
with at least
one pair of
opposite sides
parallel.
Glencoe
Quadrilateral with
one pair of
opposite sides
parallel. (6th)
Quadrilateral with
one pair of parallel
sides. (7th)
Quadrilateral with
exactly one pair of
parallel opposite
sides. (8th)
Scott Foresman
Quadrilateral
with only one
pair of parallel
sides. (3-4)
Quadrilateral that
has exactly one
pair of parallel
sides. (5th)
Holt
Quadrilateral
with exactly one
pair of parallel
sides.
Some Big Ideas: Geometry
• Two- and three-dimensional objects
with or without curved surfaces can be
described, classified, and analyzed by
their attributes.
• Objects can be oriented in an infinite
number of ways. The orientation does
not change the attributes of the object.
• There is more than one way to classify
most shapes and solids.
• Definitions of shapes and solids are
not universal.
• Attributes of objects are not necessarily
independent—logical relations and
implications exist between them.
Adapted: Charles, R. I. (2005). Big ideas and understandings as the foundation for
elementary and middle school mathematics. Journal of Mathematics Education
Leadership, 7(3), 9-24.
Setting
Pretest: September 2006
MKT 22 items (multiple choice)
School Year: Monthly sessions
~16 hours Math Teacher Leaders
~14 hours Assessment Leaders
About 200 Grades K-8 Teachers
Posttest: June 2007
MKT 22 items
Constructed Response Items
Topic Sequence
Aug
Measurement Personal Benchmarks
Sept
Error in Measurement
Oct
Compounding Error in Measurement
Dec
Characteristics of Triangles
van Hiele Levels Geometric Thinking
Jan
Properties of Quadrilaterals
Feb
Area
(Decomposition, Additive property)
Mar
Coordinate grid system
Transformations
Apr
Pythagorean Theorem
June
Volume
www.mmp.uwm.edu//_resources/math_content.htm
MTL Results
Mathematical Knowledge for
Teaching (MKT) Geometry
22
00
-2
-2
Pretest
IRT_Pre
N= 78
Posttest
IRT_Post
Results MKT Geometry
(IRT scores)
Group
N
Pretest (SD)
Posttest (SD)
Change
Sig
Preservice
Teachers:
77
Foundations
-0.41
-0.08
0.33
.000
Preservice
Teachers:
Math Minor
24
-0.03
0.24
0.27
.006
Assessment
Teacher
62
Leaders
-0.37
0.08
0.45
.000
Math
Teacher
Leaders
-0.10
0.34
0.44
.000
78
van Hiele Test of
Geometric Knowledge
Math Teacher Leaders (n=107)
van Hiele Test
N
Percent
Minimal
15
14%
Level 0:
Visualization
33
31%
Level 1:
Analysis (Description)
18
17%
Level 2:
Informal Deduction
41
38%
Always true,
Sometimes true
Never true
Always Sometimes
Never
Parallelogram
is a rectangle
24%
67%
9%
Square is a
rectangle
65%
11%
24%
Trapezoid is
a rhombus
20%
25%
45%
(Assessment Leaders, n=55)
Find the area of the figure.
What is the name of the figure?
Teacher Work
Examine as pairs or small groups…
What are some teacher
understandings and struggles
revealed in this work?
What might be “big ideas” in
measurement for teacher
knowledge?
Some Big Ideas: Measurement
• Some attributes of objects are
measurable and can be quantified
using unit amounts.
• Area is defined by covering.
• Area is additive.
• The area of a shape does not
depend on its position or orientation.
• Any polygon can be decomposed
into triangles.
Find the area of the figure
in two different ways.
Answer_____________
Thank You!
MMP website
www.mmp.uwm.edu
PD Resources
www.mmp.uwm.edu/
_resources/math_content.htm
DeAnn Huinker
huinker@uwm.edu