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

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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

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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

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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.

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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

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Domains

Physical development

Health and hygiene

Social and emotional development

Language

Literacy

Mathematics

Cognitive development

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School Readiness Assessments

Purpose of School Readiness Assessment: Formative

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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)

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Issues and Solutions

Which indicators?

How many indicators?

Ratings?

Development of School Readiness Assessments

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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

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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

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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…

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…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

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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.