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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.

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

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

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

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.

5 Practices Session One: Introducing the 5 Practices

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?

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

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

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.

Break Time 1

Representing Relationships Using Venn Diagrams

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?

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.

Lunch

Mosaics of Shapes and How Children Develop an Understanding of Geometry

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

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

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

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

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

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

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

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

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

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

How many triangles do you see?

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.”

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

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

Practice/Assessment Let’s visit a tangrams puzzle online app to practice manipulating shapes and using them to create other shapes: http://www.abcya.com/tangrams.htm

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

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

Break Time 1

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

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

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.

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

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