1. Introduction to Geometry & Measurement
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
July 18, 2016
8:00-9:30
Joe

2. Summer Instructional Staff
Dr. DeAnn Huinker, UWM Curriculum & Instruction
Dr. Michael Steele, UWM Curriculum & Instruction
Dr. Kevin McLeod, UWM Mathematical Sciences
Dr. Henry Kepner, UWM Curriculum & Instruction
Mr. Joe Giera, South Milwaukee School District
Ms. Beth Schefelker, South Milwaukee School District
Ms. Liz Cutter, Whitnall School District

3. School Districts School District of Cudahy
School District of South Milwaukee
Milwaukee Public Schools

4. Project Goals
Goal 1. Deepen mathematical knowledge & understanding of content progressions aligned to the Common Core State Standards for Mathematics. Goal 2. Strengthen instruction through the use of high-leverage teaching practices to increase student success in mathematics. Goal 3. Increase teacher collaboration within and across schools in moving to common practice with the Common Core.

5. Geometry & Measurement
Summer Institute 2016
Geometry & Measurement
Focus on: Operations and Algebraic Thinking Domain
Extensions to Expressions and Equations domain in Grades 6-8
Connections to NBT and NS

6. Learning Intentions & Success Criteria
We are developing:
An understanding of the big ideas of the Geometry and Geometric Measurement as outlined in the CCSSM.
We will know we are successful when we can:
Identify the big ideas of Geometry and Geometric Measurement.
Identify a need to improve instructional practice in the domains of geometry and geometric measurement.

7. Emphasize here that our focus is on geometry and geometric measurement
Emphasize here that our focus is on geometry and geometric measurement. (We will not look at other forms of measurement—weight, time, etc.—and we will not look at Data in the “Measurement and Data” domain.

8. TIMSS Data Grade 4 Whole Numbers Fractions and Proportionality
Measurement Estimation and Number Sense
Geometry
International Mean 67 49 56 64
United States 71 51 53
Grade 8
Fractions / Number Sense
Proportionality
Measurement 58 45 59 42 40 48
The Trends in International Mathematics and Science. The Trends in International Mathematics and Science Study(TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. students compared to that of students in other countries.

9. General conclusions…
As numerous studies have shown, U.S. elementary and middle school students are failing to develop an adequate understanding of geometric concepts, geometric reasoning and geometric problem solving. Furthermore, a majority are unprepared to study the more sophisticated geometric concepts and proof in high school. (Clement and Battista 1992)
Read it, turn and talk- what’s one sentence that stood out for you?
TCM February 1999

10. Additional thoughts…
U.S. students seemed to do better on items that were straightforward but formal in nature and not as well on spatial visualization and problem solving.
The results suggest that U.S. students need more experience with spatial visualization, solving geometric problems and three dimensional geometry.

11. 8th Grade TIMSS 2011
Geometric Shape - Reasoning

12. 8th Grade TIMSS 2011
Geometric Measurement - Applying

13. 4th Grade TIMSS 1995
Geometric Measurement - Applying

14. 4th Grade TIMSS 1995
Geometry

15. 4th Grade TIMSS 1995
Geometry

16. Suggestions
To improve geometry teaching significantly, teachers need tasks that help them better understand the nature of their students’ geometric reasoning, and they need to know what research says about such reasoning.
Where is this quote from??
TCM February 1999

17. As students engage in Geometry and Measurement tasks…
What are you looking for as students work, as
well as, in student work samples?
What are you listening for?
What questions should you be asking to target
the mathematical idea(s)?
How will you use this information to support focused discussions?

18. Starting on the same page

19. Geometry and Geometric Measurement: Easy targets for humor
When you heard this class would be ending with geometry and measurement, what were you thinking?
As you talked, what were some of the ideas brought forward?

20. Thinking back on your own math education…
If you preferred Geometry, go to the left side of the room.
If you preferred Algebra/Number, go to the right side of the room.
If you liked both, go to the back of the room.
If you liked neither, go to the front of the room.
Beth & Liz (preface with connection to when)
Conversation:
What do you notice about the sort?

21. Building Common Ground
Find a partner in your group and have a short conversation about what you have in common with your feelings about Geometry.
Find a partner across the room and share your feelings about Geometry.

22. Building the Landscape of Geometry and Geometric Measurement
Brainstorm concepts and ideas you believe are related to the topic of Geometry and Geometric Measurement.
In trios.. record each original idea on a sticky note.
In table groups…Share and sort into categories; place onto your poster.
Debrief: What are some of the categories you came up with?
Onto poster paper
Use sticky notes and move around

23. Essential Understandings of Geometry
Classification of Shapes
Features or properties of geometric shapes can be analyzed and described to define and refine classification schemes with growing precision.
Spatial Visualization
Spatial relationships and spatial structuring involves developing, attending to, and learning how to work with imagery, as well as to specify locations.
Geometry is the branch of mathematics that addresses spatial sense and geometric reasoning.
Take out and study. What do you notice? Try to make sense in these. Talk in groups. Did any of this come up in your posters?
Transformations
Transformation involves working with geometric phenomena in ways that build on spatial intuition by explaining what does and does not change when moving and altering the objects and the space that they occupy.

24. Essential Understandings of [Geometric] Measurement
How Much
Measurement specifies “how much” by assigning a number that corresponds to a certain unit to attributes such as length, area, volume, and angle.
Comparing
Some attributes can be compared directly, others are measured and compared indirectly, and some are computed from other measurements.
Motion
Motion is useful in coordinating attributes and measures of length, area, volume, and angle.
One way to analyze and describe geometric objects, relationships among them, or the space they occupy is to quantify—measure or count—one or more of their attributes.
Geometric measurement vs measurement
These are my “how”
Composing and Decomposing
Building or breaking apart objects facilitate measuring them; those decompositions and compositions clarify relationships between attributes and units of measure and are the basis to derive formulas.
V = B h

25. Stop & Jot:
As a learner of math, identify your confidence level with Geometry on a scale of 1 to 5. What are you hoping to learn from this study of Geometry?
As a teacher of math, identify your confidence level with Geometry on a scale of 1 to 5. What are you hoping to gain from this study of Geometry?

26. Starting with geometric measurement

27. Progressions Document: K-5 Geometric Measurement
Open your K-5 Geometric Measurement Progressions document to page 2
Read the overview through the bottom of page 3.
Highlight crucial ideas that help define the study of Geometric Measurement.
 Check in with your shoulder partners about the crucial ideas and why you thought they were important.
Chart big ideas they are listing from the progressions doc
Length is continuous, it connects to, but is different from cardinality
Kids have to understand what an attribute is
Indirect vs. direct comparison
Creating personal benchmarks
Overarching concept of a unit
Geometric measurement connects the 2 most critical domains of early math- geometry and number

28. Progressions: Geometry, 7-8, High School
Read the Overview at the top of page 2 and the paragraph on Geometric Measurement at the top of page 4. Turn and Talk… Where does the work we just read about in K-5 grow as students move to the upper grades?

29. Learning Intentions & Success Criteria
We are developing:
An understanding of the big ideas of the Geometry and Geometric Measurement as outlined in the CCSSM.
We will know we are successful when we can:
Identify the big ideas of Geometry and Geometric Measurement.
Identify a need to improve instructional practice in the domains of geometry and geometric measurement.

30. Core Mathematics Partnership Project
Disclaimer
Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.
This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.