Math and Science
in Early Childhood
CDEC 2307
Nita Thomason Ed.D
(Williams)
Tell me mathematics, and I will
forget;
Show me mathematics and I may
remember;
Involve me … and I will
understand mathematics.
Physical Knowledge
(Piaget)
learning about objects in the
environment and their characteristics,
such as color, weight, and size
Logico-Mathematical Knowledge
(Piaget)
Includes relationships constructed in
order to make sense out of the world
and to organize information, such as
counting and classification
Zone of proximal development
(Vygotsky)
skills and understanding children are
on the verge of possessing
Gardner’s Theory of Multiple Intelligences
Logical-Mathematical Understanding
(Gardner)
form of intelligence in which person
thinks conceptually in logical and
numerical patterns
ECE Math Language
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Numbers and Operations
One-to-One Correspondence
Classifying and Sorting
Patterns, Function, and Algebra
Geometry and Spatial Sense
Measurement
Data Analysis and Probability
Problem Solving
Number Sense
A concept that develops over time as
children think about, explore, and
discuss mathematical ideas
-rote counting
-rational counting
One-to-One Correspondence
the pairing of one object to another
object or one group of objects to
another group of equal number
Classifying and Sorting
grouping objects by a common
characteristic, such as size, shape, or
color
Pattern
a sequence of colors, object, sound,
stories, or movements that repeats in
the same order over and over again
Geometry
the area of mathematics that involves
shape, size, space, position, direction,
and movement
Spatial Sense
comparisons that help children
develop an awareness of themselves
in relation to people and objects in
space
Measurement
finding the length, height, and weight
of an object using units like inches,
feet, and pounds
Data Analysis
Questions that cannot be answered by
direct observation can often be
assessed by gathering data. Data can
be organized, represented, and
summarized in a variety of ways.
Problem Solving
many different ways to solve a
problem and more than one answer is
possible
Environments that Inspire
• Supporting Math Exploration and Learning
– Beauty
– Light
– Flexibility
• Reggio Emilia
• Montessori
Manipulatives
Sensory materials, involving visual
and tactile discrimination; that require
fine motor skill in coordinating the
eyes with what the hands can do
Selecting Manipulatives
• Are they safe?
• Are the ones with small parts used by older
children only?
• Are they durable and long-lasting?
• Are these toys, games, and materials
adaptable to many uses?
• Are they culturally diverse and nonsexist?
Manipulatives
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counters
puzzles
stacking blocks
sewing cards
snap blocks
magnetic symbols
parquetry blocks
Legos
pegs & boards
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wooden beads
board games
lotto
dominoes
checkers
coins
buttons
shells
flannel board pieces
Math Materials
• balances, weights,
scales
• calendar
• cans, egg cartons
• clocks
• geometric boards
• magnetic boards
• measuring cups,
spoons, pitchers
• number strips
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Objects to count
rulers, yard sticks
sandpaper numerals
shape puzzles
table games
telephones
thermometers
timer
unit, hollow, shape,
and table blocks
Algebra
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Patterns
Mathematical Situations and Structure
Models of quantitative relationships
Change
Patterns
• Recognize, describe, extend translate
• Identify relationships, form generalizations
• Increase complexity
– Simplest two part pattern
– Use attributes other than color
– Increasing and decreasing patterns
• In pairs, use manipulatives to design
increasingly complex patterns
Equality
• Recognize, define, create, & maintain
• Use scales
• Discuss concepts
– equal/not equal, same/different, more/less
• Use real object representations
• Concrete object > pictures > symbols
• Make algebraic thinking part of everyday
life
– fairness “She has more than me.”
Quantitative Relationships
• Ask questions
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What other ways …?
What kind of pattern …?
How do you know …?
What if …?
• Discuss quantitative relationships
Change
• Qualitative
– Experiences of a child’s life
– Smaller, taller, fuller
• Quantitative
– Uses more precise numeric language
What types of mathematical learning could be
accomplished using ramps and marbles?
NAEYC & NCTM Position
Provide ample time, materials, and
teacher support for children to engage
in play, a context in which they
explore and manipulate mathematical
ideas with keen interest.
Projects Approach
• Includes both activities designed by the
teacher and project work, which primarily
focuses on questions and ideas the children
generate
• Allows for learning to be applied in
meaningful situations
• Enables children to be self-motivated
learners equipped with the skills to do indepth investigations
Children in Project Work
• Ask thoughtful questions
• Engage in focused investigations
• Use problem-solving skills
effectively
• Discover the power of teamwork
• Take ownership of what they are
learning
Probing for Understanding
• Open-ended questions
– Tell me what you know about…
– How do you think it happened that …
– Why do you think that …
• Ask children to draw or represent what
they know
• Listen, record and reflect
Cross-Curricular Connections
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Science
Cooking
Art
Language, Literacy, and Literature
Assessment
Process of gathering
information about children
from several forms of
evidence, then organizing and
interpreting that information
N.A.E.Y.C
• National Association for the
Education of Young Children
- Guidelines for
Developmentally
Appropriate Assessment
• http://www.naeyc.org
Purposes of Assessment
• Gather information and evidence
about student knowledge, skills, and
attitudes
• Plan Instruction
• Identify children needing special
services
• Evaluate program
Determine “what’s right” with the
child in order to assist growth and
development – strengths and areas
needing strengthening
Assessment Tools
• Child Skills
• Narratives
Checklist
– Anecdotal record
• Assessment tasks
– Running record
• Interviews/informal • Samplings
conversations
– Time
• Play-based
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Event
Assessment
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Scales
• Photographs
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Graphic
• Portfolios
– Numerical
Observation Skill Tips
• Be objective
• Be specific
• Use direct quotes
• Use mood cues
Checklist
A list of behaviors with
checkmarks, recorded before,
during, and after behavior occurs
Concept Activity Observation Checklist
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Selects math center
Selects math concept book
Selects sand or water
Counts spontaneously
Sorts play materials into logical groups
Uses comparison words (i.e., bigger, faster, etc.)
Builds with blocks
Works with part/whole materials
Demonstrates understanding of order & sequence
Points out number symbols in environment
Child Interview
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What were you thinking when you…?
Tell me more about that.
Can you show me another way?
Help me understand.
Why did you …?
How did you know what to do next?
What else do you know about …?
Rating Scales
• Graphic Scale
Always – Often – Sometimes –Seldom - Never
• Numerical Scale
– 1=definitely needs help
– 2=could use help
– 3=adequate
– 4=strength