Post on 27-Mar-2015
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©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)
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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
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©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.
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
California’s Early Learning and Development System
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©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
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©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
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013) ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
What’s Your What’s Your Shape?Shape?
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
sphere coneprism
cylindercube pyramid cuboid
Name Your Shape
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©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 Peeking Inside the Mathematics FoundationsFoundations
©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
FoundationsFoundations
With appropriate supportWith appropriate support
After 1After 1stst or 2 or 2ndnd year year of preschoolof preschool
At 48 and 60 monthsAt 48 and 60 months
High-quality programHigh-quality program
©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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©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
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
StrandStrand
AgeAge
DomainDomainMathematics
SubstrandSubstrand
ExamplesExamples
FoundationFoundation
FoundationFoundation
Map of the Foundations
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
DomainDomain
Foundations Organization
Age Age
StrandStrand
Substrand Substrand
FoundationFoundation
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Geometry: It’s more than shapes!
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Geometry: It’s more than shapes!
• Shapes
• Locations, Directions, and Spatial Orientation
• Visualization and Spatial Reasoning
• Transformation and Symmetry
NTCM, Showcasing Mathematics for the Young Child, pp. 56-57.
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Universal Design for LearningProvides for:Provides for:• Multiple Multiple
means of means of representationrepresentation
• Multiple Multiple means of means of engagementengagement
• Multiple Multiple means of means of expressionexpression
PCF, Vol. 1, p. 13PCF, 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)
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©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: http://www.cast.org/udl/
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Today’s Lesson: The Circle
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Circle UDLCircleDraw one… Make one…
Find one… Show us…
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
What can we What can we learn from the learn from the
research about research about children and children and
shapes?shapes?
©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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©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
1
2
4
8
6
5
7
12
3
10
13
9
14
15
11
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©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
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2 3 4 5
6 78
9
12
13
1110
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©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: 5’s more likely than4’s or 6’s accept bothnon-standard trianglesand those withcurved sides
1
23
4
5 6
7
8
9
10
11
12
13
14
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©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
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1
2
3
4 5
68
9
10
11
12
13
14
15
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Compare to Elementary—Rectangles
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Compare to Elementary—Triangles
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©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
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©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
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©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
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©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
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©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)
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Interaction and StrategyInteraction 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)
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©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…
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Application for Dual-Application for Dual-Language LearnersLanguage Learners
©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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©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 Gives the child the chance to narrow down
what the conversation is aboutwhat the conversation is about
• Allows child to focus in on a more restricted Allows child to focus in on a more restricted number of options to respondnumber of options to respond
• Share the same physical space and have Share the same physical space and have reference to the same informationreference to the same information
• Allows the teacher to provide some missing Allows the teacher to provide some missing vocabulary informationvocabulary 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
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Helpers/Buddies Helpers/Buddies
©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Geometry: It’s 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
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Geometry Geometry andandSpatial SenseSpatial Sense
Get ReadyGet Ready
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Geometry SnapshotsReady
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©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)
Snapshots with Pattern BlocksReady GO!
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©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
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©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?
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©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?
• Let’s see some of the
others…
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©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
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©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?
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©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)
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©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
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©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?
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©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!