1. Teaching Young Learners with the Ohio Early Mathematics Standards in Mind Sponsored by the Ohio Department of Jobs & Family Services in collaboration with the Ohio Department of Education Module Three

2. Module 3: Overview of Session How do children develop geometric reasoning through play? How do children develop geometric reasoning through play? What kinds of activities are developmentally appropriate for exploring measurement & data analysis? What kinds of activities are developmentally appropriate for exploring measurement & data analysis?

3. Building Geometric Reasoning What are students learning by interacting with each of these center activities? (Backmapping) How would you adjust the activities for your young learners?

4. Levels of Geometric Thinking Level 0: Visualization Level 0: Visualization Recognizing and naming figures and shapesRecognizing and naming figures and shapes Level 1: Analysis Level 1: Analysis Describing attributes of figures and shapesDescribing attributes of figures and shapes Level 2: Informal deduction Level 2: Informal deduction Level 3: Deduction Level 3: Deduction Level 4: Rigor Level 4: Rigor

5. Van Hiele Model of Geometric Reasoning Students need MANY experiences sorting materials AND explaining to others why they sorted the way they did Students need MANY experiences sorting materials AND explaining to others why they sorted the way they did Experience/play enables students to move through the levels Experience/play enables students to move through the levels

6. Geometry Standards Age 3 Begins to match and name 2D and 3D shapes, first only with same size and orientation, then shapes that differ in size and orientation Begins to match and name 2D and 3D shapes, first only with same size and orientation, then shapes that differ in size and orientation Uses shapes separately to create pictures Uses shapes separately to create pictures Describes object locations with spatial words s.a. under/behind and builds simple “maps” with toys such as houses, cars, and trees Describes object locations with spatial words s.a. under/behind and builds simple “maps” with toys such as houses, cars, and trees Age 6 Recognizes and names a variety of 2D & 3D figures in any orientation Recognizes and names a variety of 2D & 3D figures in any orientation Describes basic features of shapes (e.g., number of sides or angles) Describes basic features of shapes (e.g., number of sides or angles) Makes a picture by combining shapes Makes a picture by combining shapes Builds, draws, or follows simple maps of familiar places such as the classroom or playground Builds, draws, or follows simple maps of familiar places such as the classroom or playground Box

7. Measurement How do children learn about measurement in your classroom? How do children learn about measurement in your classroom? What does measurement mean for a young learner? What does measurement mean for a young learner? How do your preschool children learn about measurement through their spontaneous play and investigation? How do your preschool children learn about measurement through their spontaneous play and investigation? How can you focus on measurement as an intentional teacher? How can you focus on measurement as an intentional teacher?

8. Measurement Activity Estimating and measuring with non-standard (and standard) units of measure

9. Measurement Standards Age 3 Recognizes and labels measurable attributes Recognizes and labels measurable attributes Begins to compare and sort according to attributes Begins to compare and sort according to attributes Age 6 Tries various processes and units for measurement and begins to notice results of different methods Tries various processes and units for measurement and begins to notice results of different methods Uses nonstandard measuring tools Uses nonstandard measuring tools

10. Wrap-up Given all that we have discussed and all that we experienced … Given all that we have discussed and all that we experienced … How would you define “mathematical competence” in your preschool learner?How would you define “mathematical competence” in your preschool learner? How do we help develop these competencies through our interactions with these young learners?How do we help develop these competencies through our interactions with these young learners?

11. Mathematical competence (National Research Council, 2001) 1. Conceptual understanding 2. Procedural fluency 3. Strategic competence 4. Adaptive reasoning 5. Productive dispositions