Improving Teacher Knowledge in Geometry and Measurement: A Collaborative Effort Involving Math Educators, STEM Faculty and Teacher Leaders Henry Kepner, Lee Ann Pruske, Mary Mooney, Paige Richards, DeAnn Huinker Milwaukee Mathematics Partnership University of Wisconsin-Milwaukee National Conference of Supervisors of Mathematics 40 th Annual Conference, 2008 Salt Lake City, Utah 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.
Aug Topic Sequence Measurement Personal Benchmarks Sept Error in Measurement Oct Dec Jan Feb Compounding Error in Measurement Characteristics of Triangles van Hiele Levels Geometric Thinking Properties of Quadrilaterals Area (Decomposition, Additive property) Mar Apr Coordinate grid system Transformations Pythagorean Theorem June Volume www.mmp.uwm.edu//_resources/math_content.htm
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.
Always true, Sometimes true Never true Always Sometimes Never Parallelogram is a rectangle Square is a rectangle 24% 67% 9% 65% 11% 24% Trapezoid is a rhombus (Assessment Leaders, n=55) 20% 25% 45%
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
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
MTL Results Mathematical Knowledge for Teaching (MKT) Geometry 2 0-2 Pretest Posttest N= 78
Results MKT Geometry (IRT scores) Group N Pretest (SD) Posttest (SD) Change Sig Preservice Teachers: Foundations Preservice Teachers: Math Minor Assessment Teacher Leaders Math Teacher Leaders 77-0.41-0.08 0.33.000 24-0.03 0.24 0.27.006 62-0.37 0.08 0.45.000 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 Level 1: Analysis (Description) Level 2: Informal Deduction 33 31% 18 17% 41 38%
Thank You! MMP website www.mmp.uwm.edu PD Resources www.mmp.uwm.edu/ _resources/math_content.htm DeAnn Huinker huinker@uwm.edu