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1 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN).

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Presentation on theme: "1 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN)."— Presentation transcript:

1 1 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Math Foundations: Geometry ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

2 2 Agenda The relationship between the NCTM Standards, the Preschool Learning Foundations, and the DRDP-R The Research Exceptional Children--Division of Early Childhood Recommended Practices English Learner Strategies Taking It Back to the Classroom

3 3 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Outcomes Become familiar with the mathematics foundations with an emphasis on the Geometry strand. Explain how the DRDP-R and the NCTM Standards relate to the mathematics foundations. Discover the research behind the practice. Explore strategies to make geometry come to life in the classroom. Plan for taking it back to your classroom.

4 4 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Californias Early Learning and Development System

5 5 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Two California Department of Education Resources

6 6 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) California Preschool Learning Foundations Geometry is the study of space and shape (Clements, 1999). Geometry and spatial reasoning offer a way to describe, interpret, and imagine the world. PLF, Vol. 1, p. 164

7 7 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Whats Your Shape?

8 8 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) spherecone prism cylinder cubepyramid cuboid Name Your Shape

9 9 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Peeking Inside the Mathematics Foundations Peeking Inside the Mathematics Foundations ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

10 10 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)Foundations With appropriate support After 1 st or 2 nd year of preschool At 48 and 60 months High-quality program ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

11 11 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) The Sections Introduction The Foundations Bibliographic Notes Glossary References and Source Material

12 12 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Strand Age Domain Mathematics Substrand Examples Foundation Map of the Foundations

13 13 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Domain Foundations Organization Age Strand Substrand Foundation

14 14 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry: Its more than shapes!

15 15 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry: Its more than shapes! Shapes Locations, Directions, and Spatial Orientation Visualization and Spatial Reasoning Transformation and Symmetry NTCM, Showcasing Mathematics for the Young Child, pp

16 16 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Universal Design for Learning Provides for: Multiple means of representationMultiple means of representation Multiple means of engagementMultiple means of engagement Multiple means of expressionMultiple means of expression PCF, Vol. 1, p. 13 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

17 17 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Multiple means of… Credit: CAST:

18 18 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Todays Lesson: The Circle

19 19 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Circle UDL Circle Draw one… Make one … Find one… Show us …

20 20 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) What can we learn from the research about children and shapes? ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

21 21 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Circles Correctness: –92% - 4 year olds –96% - 5 year olds –99% - 6 year olds Few youngest chose ellipse and curved shape Described as round Thus, easily recognized but difficult to describe Matched shapes to visual prototype

22 22 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Squares Only slightly less accurate in identifying squares: 82%, 86%, and 91% Youngest lower on non- square rhombi, but not on tilted squares Minority reasoned about properties. –Was relationship between such responses and correct selections

23 23 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Triangles Task Lower, but not low: about 60% Property responses present, but only 18% Inverse-U pattern: 5s more likely than 4s or 6s accept both non-standard triangles and those with curved sides

24 24 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Rectangles Slightly more than 50% Four-year-olds were more likely to accept the squares All accepted long quads w/ pair of parallel sides (numbers 3, 6, 10, and 14) Properties less frequently

25 25 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Compare to ElementaryRectangles

26 26 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Compare to ElementaryTriangles

27 27 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) What Children See Ring the triangle

28 28 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) What Children See More recent, but not more mathematically precise

29 29 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry Must Move Beyond Basic Shape Naming to: Parts & Properties –Shape attributes –Include analysis and description Mental images and transformations Composing and decomposing

30 30 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Learning Trajectory for Shapes 1.Shape Matcher 2.Shape Prototype Recognizer 3.Shape Recognizer 4.Side Recognizer 5.Angle Recognizer 6.Shape Class Identifier

31 31 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Curriculum Framework Interactions and Strategies Teaching Vignettes Teachable Moments Guiding Principles ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

32 32 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Interaction and Strategy Talk about shapes and discuss their attributes. PCF, Vol. 1, p. 284 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

33 33 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) What it might look like…

34 34 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Application for Dual- Language Learners ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

35 35 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Talk About the Here and Now Gives the child the chance to narrow down what the conversation is aboutGives the child the chance to narrow down what the conversation is about Allows child to focus in on a more restricted number of options to respondAllows child to focus in on a more restricted number of options to respond Share the same physical space and have reference to the same informationShare the same physical space and have reference to the same information Allows the teacher to provide some missing vocabulary informationAllows the teacher to provide some missing vocabulary information Stage 1: Home Language Stage 2: Observational/Listening Stage 3: Telegraphic/Formulaic Stage 4: Fluid Use ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Handout 4

36 36 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)Helpers/Buddies

37 37 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry: Its More than Space Geometric measuring concepts can be motivated through motion. Barrett, J.E., Sarama, J., Clements, D.H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klanderman, D. (2012

38 38 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry and Spatial Sense Get Ready

39 39 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Geometry Snapshots Ready

40 40 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Snapshots with Pattern Blocks Ready GO!

41 41 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Learning Trajectory for Composing Geometric Shapes 1.Pre-composer 2.Picture maker 3.Shape composer 4.Substitution composer

42 42 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Language is a critical element in mathematics. (PCF, Vol. 1, p. 235) Shape Flip Book! The Greedy Triangle Mirror books The Shape of Things Dot and Line What other books do you know about?

43 43 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Children Think About Geometry Pat H.s preschool was studying bees. Children noticed the hexagon. Teacher: Why do you think they chose this shape? Lets see some of the others…

44 44 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Children Talk About Geometry

45 45 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Play It - Chart It - Share It Find your chart. Play your game. Answer the following questions as a group on the chart paper. What was fun about the game? What foundations were addressed in the game? What components of the learning trajectory are emphasized in the game? What might be important to consider for dual-language learners (use the strategies handout)? If a teacher had observed you playing the activity, which measure of the DRDP might he or she have collected data about?

46 46 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) How will it all fit together? ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

47 47 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Teachers Put it all together

48 48 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) What are you packing for home?

49 49 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) Thank you for coming; now go take a rest!


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