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

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).

SessionGoals

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 / Scott Foresman
Quadrilateral that has exactly one pair of parallel sides. / Quadrilateral with at least one pair of parallel sides.(K-1)
Quadrilateral with one pair of parallel sides. (5th) / Quadrilateral with only one pair of parallel sides. (3-4)
Quadrilateral that has exactly one pair of parallel sides. (5th)
CMP / Glencoe / Holt
Quadrilateral
with at least one pair of opposite sides parallel. / 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) / 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

MTL Results

Mathematical Knowledge for Teaching (MKT) Geometry

PretestPosttest

N= 78

Results MKT Geometry

(IRT scores)

Group / N / Pretest (SD) / Posttest (SD) / Change / Sig
Preservice Teachers:
Foundations / 77 / -0.41 / -0.08 / 0.33 / .000
Preservice Teachers:
Math Minor / 24 / -0.03 / 0.24 / 0.27 / .006
Assessment
Teacher
Leaders / 62 / -0.37 / 0.08 / 0.45 / .000
Math Teacher
Leaders / 78 / -0.10 / 0.34 / 0.44 / .000

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

PD Resources

_resources/math_content.htm

DeAnn Huinker