Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
INDICATORS OF MATHEMATICAL COMPETENCE IN EARLY EDUCATION
From standards to the classroom:
LINDA M. PLATAS
UNIVERSITY OF CALIFORNIA, BERKELEY
JUNE 5, 2013
Outline2
Background
Importance of early childhood education
Importance of early mathematical development
Early Learning Standards
School Readiness Assessments
Zooming in: Mathematics
Zooming out: Use and Misuse
3
Background: Early Childhood Education
Importance of Early Childhood Education4
Preparation for formal education
Family engagement
Identification of special needs
Return on Investment
Heckman 2006
Early Intervention Is Cost Effective:Rates of Return
5
Importance of Early Childhood Education6
Sub-Saharan Africa
The association is positive between preschool enrollment and primary school completion rates (R2 = .39; Garcia et al., 2008)
GDP $ lost (CEECIS)
72008 TransMONEE Data; Engle 2009, p. 22
8
Background: Mathematical Development
Importance of Early Mathematics9
In UK, Canada, US – overall biggest predictor of later academic success (Duncan et al., 2007)
…the mathematical skills that will enhance the preparation of those who aspire to careers in mathematics are the very same skills that will help people become informed and flexible citizens, workers and consumers.” (Shoenfeld2001, 53)
Importance of Mathematics in a Democracy10
A functional democracy requires that citizens make informed decisions, and are able to think for themselves and judge independently. This requires mathematics.
Without a citizenry with the skills to support infrastructure and growth, countries and governments will be dependent on donors, NGOs, and foreign companies. The development of these skills requires mathematics.
11
Early Learning Standards
Early Learning Standards12
First step in aligned systems of:
curriculum
instruction
formative assessment
teacher training
Early Learning Standards13
However, creating these aligned systems based on standards is:
complex (standards may have over 700 indicators)
country-specific
stakeholder-reliant (requires buy-in)
Requires more than just a formulaic insertion of the standards across a system
Early Learning Standards
14
Domains
Physical development
Health and hygiene
Social and emotional development
Language
Literacy
Mathematics
Cognitive development
15
School Readiness Assessments
Purpose of School Readiness Assessment: Formative
16
To support and guide implementation of Early Learning Standards
Monitor children’s development and inform teachers and parents about progress.
Guide the teacher in classroom curriculum choices
Provide differentiated instruction
Provide information to primary school teachers on children’s development prior to school entry to ensure a smoother transition from preschool to primary school and continuity of instruction.
Development of School Readiness Assessments17
Identification of appropriate indicators from the Early Learning Standards
Field-testing of indicators
Each indicator should be understood similarly by all teachers and serve as a reliable measure of skills.
Observable behaviors (not a one-on-one assessment)
18
Issues and Solutions
Which indicators?
How many indicators?
Ratings?
Development of School Readiness Assessments
19
School Readiness Assessments:Mathematics
Which Indicators?:Number Sense20
Uses numbers and simple operations
Uses number sense to solve simple problems
Recognizes numbers and quantities in the everyday environment
Works with teacher and small groups to represent mathematical relations in charts and graphs
Which indicators?: Other Sub-domains21
Compares objects in size and shape
Asks questions and seeks new information
Names two-dimensional shapes
Creates shapes
Shows understanding of positional words
Demonstrates understanding of the pre-number concept of spatial relationships
Creates a pattern
Recognizes how much can be placed within an object
Which indicators?: Solutions22
Measureable
Observable
Predictive
Teachable
Which indicators?: Solutions23
Can count 10 objects
Knows that adding to a group of objects increases the numerosity
Can name two-dimensional shapes (circle, rectangle, triangle, rhombus, square, hexagon, octagon)
Uses positional words (up, down, under, on top of, bottom, inside, beside)
Uses non-standard measurement tools (blocks, hands, feet, etc.) to measure objects (length, height)
How many indicators?24
Issues:
Large class sizes
Low teacher-child ratio
Limited time
Solutions
All indicators (up to 700) is too many
Think about total number of observations of each indicator teachers need to make (20 children @ 30 indicators @ 3 times per year = 1800)
30 seems to be almost tolerable
Math is only 1/5 to 1/7 of total
Ratings25
How do we determine if a child has met a standard?
Is it an all or nothing rating?
Example:
Count 10 objects
If we have a yes/no dichotomous rating, then we can only monitor progress from not knowing how to count 10 objects to knowing how to count 10 objects–nothing in between
Ratings26
Solutions
Gradations:
Meets/Progressing/Limited Skill
Mastered/Progressing/Limited
Can do without any assistance/Can do with a little assistance/Can do with a lot of assistance/Cannot do
Integrating/Building/Developing/Exploring/Discovering
Specifics (up to 7; circle, square, triangle)
Summing Up27
Indicators must be Measureable Observable Predictive Teachable
Number of indicators must be reasonable/implementable
Ratings must accommodate a range of abilities Use must support and guide implementation of Early
Learning Standards Monitor children’s development Inform teachers and parents about progress. Guide the teacher in classroom curriculum choices Provide differentiated instruction Provide information to primary school teachers
28
The Big Picture
School Readiness Assessment and Stakeholders29
Iterative drafts created with stakeholders
Ministry of Education
Local Education Agencies (LEAs)
Principals
Teachers
Parents/Families
Funders
Implementation of School Readiness Assessments
30
Protocol for implementation of School Readiness Assessments Establish confidentiality and access rules and
procedures Establish data use restrictions Create language and cultural adaptations Create teacher training module on:
Use/Misuse and purpose of instrument Observational techniques
Parent involvement
PilotValidation and reliability studies
The School Readiness Assessment is used…31
…for formative assessment
…to assess children’s progress
…to provide for differentiated instruction
…as part of a child’s portfolio
…in conjunction with supportive practices in the Early Learning Standards
…to identify opportunities for teachers and parents to work together
The School Readiness Assessment is not used to…
32
…conduct summative assessments – it is used to document children’s progress, not their achievement of required goals at the end of the year
…prevent children from attending primary school
…externally evaluate teachers
…move or categorize children into special education classes
…compare children or groups of children
L P L A T A S @ B E R K E L E Y . E D U
33
Thank you!
References34
Engel, P. (2009). The Untapped developmental Potential of Early Childhood in the CEE CIS Region. Geneva: UNICEF Regional Office for Central and Eastern Europe and the Commonwealth of Independent States.
Garcia, M. H., Virata, G., & Dunkelberg, E. (2008). The state of young children in Sub-Saharan Africa. In M. H. Garcia, A. Pence & J. L. Evans (Eds.), Africa's future, Africa's challenge: early childhood care and development in Sub-Saharah Africa (pp. 11-28). Herndon, VA: World Bank Publications.
Heckman, J. J. (2006). Skill formation and the economics of investing in disadvantaged children. Science, 312, 1900-1902. doi: 10.1126/science.1128898
Schoenfeld, A. (2001). Reflections on an impoverished educationIn L. A. Steen (Ed.), Mathematics and Democracy: The Case for Quantitative Literacy: National Council on Education and the Disciplines.