1. Welcome to …

2. TODAY’S AGENDA SMP Qualities 5 Practices for Mathematical Discourse
Shapes and Relationships
Mosaics of Shapes and How Children Develop an Understanding of Geometry
Lessons and Reflections
PASS OUT NOTE PADS and explain that these pads are to jot down pedagogical and mathematical connections they make…then later they will be given time to reflect on their own connections.

3. Bring your ideas…
As a group of professionals we have made a commitment to helping children attain success in life and a voice in the world.
Many times the best part of these kinds of professional development is simply the chance to share ideas, raise questions, and work with other practitioners to improve our own understandings and practice.
Please bring your stories of children’s learning with you.
Gabriel - Make any agreed upon revisions to the norms

4. Our Socio-mathematical Norms
Listen intently when someone else is talking avoiding distractions
Persevere in problem solving; mathematical and pedagogical
Solve the problem in more than one way
Make your connections explicit - Presentation Ready
Contribute by being active and offering ideas and making sense
Limit cell phone and technology use to the breaks and lunch unless its part of the task.
Be mindful not to steal someone else’s “ice cream”
Respect others ideas and perspectives while offering nurturing challenges to ideas that do not make sense to you or create dissonance.
Limit non-mathematical and non-pedagogical discussions
Gabriel - Make any agreed upon revisions to the norms

5. Presentation Norms
Presenters should find a way to show mathematical thinking, not just say it
Presenters should indicate the end of their explanation by stating something like “Are there any questions, discussion, or comments?”
Others should listen and make sense of presenters’ ideas.
Give feedback to presenters, extend their ideas, connect with other ideas, and ask questions to clarify understandings
Gabriel - Make any agreed upon revisions to the norms

6. The Standards for Mathematical Practice Student Reasoning and Sense Making about Mathematics
Let’s list as many qualities as we can of the kinds of mathematically proficient student behaviors that exemplify the SMP’s.
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Gabriel – Have teachers look at their SMP pages and think about qualities students behaviors should have when engaging in this SMP.

7. 5 Practices
Session One: Introducing the 5 Practices

8. Volume Task
Consider the following question individually then share with your group.
Why does length times width times height (l x w x h) make sense as a way of finding the volume of a rectangular prism?
When would l x w x h NOT work for volume?

9. Solve Volume Task
Solve the ”Volume Task” individually then share your ideas with a partner.
Whole group discussion of task

10. Reading & Reflection Read pages 7 – 12.
Reflect individually then share with a partner.
Use the questions on the handout to guide your discussion.

11. Reading Discussion
Discuss the question(s) assigned to your group and be prepared to present your responses to the group.
Presentation of questions & whole group discussion.

12. Break Time 1

13. Representing Relationships Using Venn Diagrams

14. Constructing a Venn Diagram P = set of parallelograms Rh = set of rhombuses Re = set of rectangles S = set of squares T = set of trapezoids Challenge: Where would you put the set of kites in your Venn diagram?

15. All, Some, or No 1. _______ rectangles are squares.
2. _______ squares are rectangles.
3. _______ rhombuses are squares.
4. _______ squares are rhombuses.
5. _______ squares are parallelograms.
6. _______ parallelograms are squares.
7._______ rhombuses are rectangles.
8._______ trapezoids are parallelograms.

16. Lunch

17. Mosaics of Shapes and How Children Develop an Understanding of Geometry

18. Geometry Mosaic Cut out all of the pieces
Determine the most descriptive name for each of the pieces
Let’s try putting pieces together to form new shapes

19. A Little Psychology …
So, how do children come to know and understand “shapes” and their attributes?

20. Teaching and Learning Geometry
The Van Hiele Model
Teaching and Learning Geometry

22. Pierre Van Hiele (1959)
Why do students struggle so much in geometry?

23. Level 0 – Visualization (whole shapes)
Stages of Development
Level 0 – Visualization (whole shapes)

24. Level 1 – Analysis (characteristics/properties)
Stages of Development
Level 1 – Analysis (characteristics/properties)

25. Level 2 – Informal Deduction (interrelationships)
Stages of Development
Level 2 – Informal Deduction (interrelationships)

26. Level 3 –Deduction (postulates, theorems, proof)
Stages of Development
Level 3 –Deduction (postulates, theorems, proof)

27. Level 4 –Rigor (other geometric systems)
Stages of Development
Level 4 –Rigor (other geometric systems)

28. Properties of the Levels
Development is sequential
Advancement is dependent upon instruction
Linguistics typical of each level
Mismatch between instruction/textbooks and the level at which students function

29. How many triangles do you see?

30. From Focus on Reasoning and Sense Making (NCTM)…
“Thinking, questioning, and justifying should occur whenever students encounter a situation that is new to them, both within and outside of the school setting, and not only when a proof is required in geometry class. We rarely need to line up statements and reasons in our daily life, but we frequently need to provide a rationale … as to why we do or say particular things. Reasoning and sense making should be regular parts of the geometry curriculum, with or without formal proof writing. All students … must be able to reason and make appropriate decisions. Geometry provides an environment that can allow and encourage students to ‘practice’ the process of reasoning and sense making, for the benefit of all.”

31. % of 12th Graders?
International
49%
United States
19%

32. Discussion Question
What are the implications of the Van Hiele’s research on how we plan our lessons?

33. Practice/Assessment
Let’s visit a tangrams puzzle online app to practice manipulating shapes and using them to create other shapes:

34. Ohio’s New Mathematics Standards Geometry
Kindergarten
Identify and describe shapes
Describe, compare, create, and compose shapes
Grades 1, 2, and 3
Reason with shapes and their attributes
Grade 4
Draw and identify lines and angles, and classify shapes by properties of their lines and angles

35. Ohio’s New Mathematics Standards Geometry
Grade 5
Graph points on the coordinate plane to solve real-world and mathematical problems
Classify two-dimensional figures into categories based on their properties

36. Break Time 1

37. Math Content for our Classrooms
Each day we will spend time with grade level teams making lesson plans.
Each of us will make one plan that is part of a unit of plans the grade level team is working on.
Each plan must have the following:
Connected mathematics content focus from Ohio’s Mathematics Learning Standards
A focus SMP
Designed to Orchestrate Productive Mathematics Discussions (The 5 Practices)
Handout Page 15

38. Math Content for our Classrooms
Three checks must be made for the completion of lesson plans:
Check 1) Consult with Sandy and/or Mary about the mathematics content of the lesson and explain to her its mathematical appropriateness. When the lesson is complete Sandy, our resident mathematician, will sign off on its content (SMC’s).
Check 2) Consult with Sherry about the design of the lesson to promote mathematical discourse (5 Practices). Sherry must sign off on the lessons discourse elements.
Check 3) Consult with Dr. Matney about the design of the lesson having a focus Standard for Mathematical Practice. Dr. Matney must sign off on the lessons mathematics proficiency elements (SMP’s)
?Questions about COMP Lesson Plans?
Handout Page 15

39. Air of Appreciation
We want to pass on to each generation a sense of learning how to appreciate life, others, and learning.
Let’s spend some time sharing one thing or experience that we appreciate:
Examples: I appreciated when Ray didn’t give up on solving that hard problem. It encouraged me to keep thinking for myself to make sense of it.

40. On a sticky note tell us one thing you learned today.
Time of Reflection
On a sticky note tell us one thing you learned today.
Tell us one think you liked or one thing you are still struggling with.
Handout Page 15

41. Stay Safe Please help us put the room in proper order.
Please leave your name tents for next time.