Creating Mathematicians and
Scientists within Young Children
Greg Gierhart
Murray State University-College of Education
Dr. Nancy Lovett
Regional Training Center-Calloway
Should Preschoolers Learn
• Born with capabilities to solve simple numerical
• Possess ideas in number and geometry
• Low income and minority have narrowed experiences
and experience math difficulties later in life.
• Brain development within the first year is significant
• Brain is naturally geared to be a powerful pattern
• Preschoolers are intrigued to investigate shapes,
measurement, the meaning of number, and how
numbers work
Math and the Young Child
Naturally Interested in Mathematics
It’s visible in their play and work
Teacher/Parents provide words, math
experiences and resources
• Explore math to scaffold understanding,
Investigate size, quality, categorization,
patterns, space, speed and sequence
Standards Standards Standards
• NCTM Principles and Standards
• NCTM Curriculum Focal Points
• Kentucky Early Childhood Standards and
NCTM Documents
Learning and Teaching Mathematics
Content Strands
• Number
• Geometry and
Spatial relations
• Measurement
• Patterns/Algebra
• Analyzing data
Process Strands
Preschool Teacher’s Role
• Interpret what student is thinking and doing
• Assess the concepts student is learning
• Link concepts to the students’ experiences.
Note: young children do not see the world as
separate subjects—they try to link everything
together—our brains do this.
Is Play and Work Important?
Every person has a developmental need to experience creativity
and self-expression
People skilled at play have more power, influence, and capacity
to create meaningful lives-builds problem-solving,
persistence, and collaboration
Play allows a conduit to new experiences, content, and meaning
Play is integral to curriculum, to allow for engaging for hands-on
problem solving and inspiring projects
Through play, we learn to accept differences of opinion and how
to resolve conflict
Role Play and Model Are Important
Research Alert
Preschoolers with social and emotional
problems will need to have those problems
addressed before they can successfully develop
their mathematical skills.
– (David Sousa, How the Brain Learns Mathematics,
Learning Mathematics Continuum
Promoting Good Beginnings for
• Effective classroom approaches
• Inclusion and equitable experiences for all
• Academically prepared teachers with
knowledge, skills, and dispositions
• Problem solving approach that uses language
and communication
• Using technology
• Lifelong learners
NCTM Stand on Students
Learning Mathematics
• Every child is the most compelling goal!
• All children (no matter race, gender, ability)
should have access to Math experiences
• Provide math experiences for children to be
successful mathematicians
• Promoting live long learners
• Activating the vestibular system---brain is
being told to wake up
• Songs are “hooks to hang a memory on”
• Read read read until you think your lips are
going to fall off, and then read more
NCTM Stand on Students
Learning Mathematics
• Every child is the most compelling goal!
• All children (no matter race, gender, ability)
should have access to Math experiences
• Provide math experiences for children to be
successful mathematicians
• Promoting live long learners
General Guidelines for Preschool
Teacher to Teach Mathematics
• Environment must have opportunity to explore
• Recognize if math is developing or stalled in children
• Plan activities that rely on mathematics (and literacy)
• Use strategies that are meaningful and purposeful and
within context
• Allow students to be active participant in their learning
• Embrace students thinking about mathematics by
modeling and posing higher-order questions
• Know the number in a set of objects without
counting one to one.
• Pre-requisite skill for learning counting
• Strengthen this skill
• Use patterns with dot cards helps
• Avoid using manipulatives at first to teach this
• Leads to understanding of addition and
• Audio Input helps with Subitizing (songs)
Learning to Count
• How many—not based on the arrangement or
• Cardinal principle needs to be reinforced
• By age four-mastered counting and can apply
to new situations
• Once students can count using objects, next
step, counting without objects
Counting in Other Countries
• Language of other cultures logically describes
the counting sequence
• This helps to make sense and a deeper
understanding of the base 10 system
• Counting in other languages does not confuse
Teacher Talk Improves Number
• Used in everyday speech influences
mathematics knowledge over the school year
• Questioning assists in the understanding of
number and mathematics
Sorting and Classifying
• Sorting is different from classifying
• Seriation
• Begins at age three and is used to understand the
real world
• Developmental factors to keep in mind about
sorting and classfying
-Perceptions -Constructing Information
Tactile kinesthetic -Quantity of objects
Mathematical talking
Making it fun and offer choices
Levels of Sorting
• Promotes understandings of relationships
within a group
• Increase difficulty of the sorting tasks by
consideration of attributes
– Level One
– Level Two
– Level Three
– Level Four
Levels of Classifying
Explain their reasons behind the classification
Level One
Level Two
Level Three
Level Four
Sorting and classifying leads to grouping and
regrouping which is helpful to learn math
Number and Operation
Key Concepts
• Counting involves learning the vocabulary of
mathematics, including knowing the names
of the numerals
• Counting involves the ability to understand
one-to-one correspondence
• Counting involves the ability to understand
cardinality; that the last number words said
when counting a group of objects such as
two, represents two things, objects, events,
and so on
Number and Operation
Key Concepts
• Counting involves saying number words in a
consistent, reproducible order
• Counting involves abstraction: any thing can be
collected together for counting
• Counting involves the understanding that things can
be counted in any sequence without changing the
• Counting leads to experiencing the numnber
operations of adding and subtraction
Basic Concepts of Algebra
Key Concepts:
• Patterns exist everywhere in a variety of
shapes, sizes, colors, numbers, and textures
• It is possible to repeat and extend patterns as
in music
• Groups of various items may be sorted,
classified, and ordered by many attributes
Basic Concepts of Algebra
Key Concepts
• The addition and subtraction of whole
numbers may be represented using objects,
pictures, and symbols
• Addition and subtraction sentences may be
constructed. “more” suggests addition, and
“less” suggests subtraction
• A variety of things may change in quality and
in quantity
Basic Concepts of Geometry
Key Concepts:
• Geometric shapes are two- and threedimensional
• Two and three dimensional geometric shapes
have multiple characteristics and properties to
be analyzed
• Spatial reasoning and relationships are
accomplished through geometry and other
representational systems
Basic Concepts of Geometry
Key Concepts
• Children’s spatial sense is their awareness of
themselves in relation to people and objects
around them in space.
• Spatial visualization and reasoning can be
used to solve problems.
• Geometry describes and classifies the physical
world we live in.
Basic Concepts of Measurement
Key Concepts:
• Things may be compared with respect to
length, area, capacity, weight and time.
• Objects may be ordered according to these
• Length concepts involve how long, how high,
how far, and how wide
Basic Concepts of Measurement
Key Concepts:
• Area concepts require that children look at more
than one measurable dimension
• Capacity and volume have many everyday
• Weight can be compared using balance scales or
regular scales
• Time is relative for young children and is best taught
through everyday routines and conversations.
Basic Concepts of Measurement
• Measurement varies with the size of the uit
used to make the measurement
• Accurate measurement depends on proper
use of an appropriate tool
• Estimation is useful in building basic concepts
when things such as a million can be
Basic Concepts in Data
Key Concepts
• The study of statistics involves collecting,
organizing, and sorting data
• Concepts of labeling and scaling are crucial to
data representation
• Data can be described through graphs,
tables, and lists
Basic Concepts of Data
Key Concepts:
• The process of analyzing and interpreting data
involves recognition of patterns or trends, and
gaining information from graphs
• In the process of organizing data, children
make inferences or predictions, and have
initial experiences with probability
Math Problem Solving
Key Concepts:
• Problem solving begins by sensing a problem
and posing thoughtful questions
• All the senses are used to collect information
abut the problem to be solved
• Information or data must be collected and
organized in some representational way
Math Problem Solving
Key Concepts:
• Information collected-the data-is analyzed
• The problem-solving processes are intimately
involved in all areas of mathematics:
knowledge of numbers, counting, measuring,
graphing, beginning algebra, and geometry
Language and Writing in Math
• Language and experiences go together
• Demands listening, speaking, writing, and
• Written language is necessary
• Books are consulted and read
• Math experiences must be continuous
• Reflection is necessary
• Rich environment
• Vocabulary
Activity with Math Standards
What do you need to know?
Literature connection and needed
How to make home connections?
How to assess?
What will children need to do to
demonstrate the concepts?
Websites of Interest (Illuminations) (math their Way)
• Not just for science
Math, Science, and
4 year old Angela
• Knowledge constructed in the mind of
the learner
• Young Children think differently than
older children and adults
• Young children need a specialized
instruction because of their concreteness
and less logical thinking
• Children learn from the environment,
peers, and adults in school and beyond
(culture acquiring)
• Added to Piaget’s theories
• Moving children to higher levels
is because of those interactions
with more accomplished persons
(older children and adults)
• Guide by explaining,
demonstrating, and questioning
to reach higher cognitive thinking
• Zone of Proximal development
Scientific Process
• Formulate questions,
collect data, and develop
• Organize, reflect on,
represent, and document
• Share and discuss ideas
with others
Baby Test Tubes
• This is not finished—what could it be if it
continued down the assembly line?
Carol Seefeldt
• The scientific inquiry
process is observing,
investigating, analyzing,
and reaching
conclusions and
communicating the
results to others
• Give up “show and tell”
in favor of group
National Science
Education Standards
• Teachers should:
– Plan inquiry based science
– Guide and facilitate student
– Engage in on-going assessment
of teaching and learning
– Develop environments that
enable students to learn science
National Science
Education Standards (Cont.)
– Create learning communities
of science learners
– Equity
– Provide a rich learning
environment-you’re the
– Model effective problem
solving techniques
– Have equipment for inquiry
• Develop child’s innate curiosity about
the world
• Broaden procedural and thinking skills
for investigating the world
• Increase the child’s knowledge about
the world
• Emphasis on Inquiry
Themes in Science
Life science and the living environment
Earth science and the physical setting
Science in Personal and social
perspective and the human organism
Physical Science, the physical setting and
the designed world
Life science and the living environment
• Key Concepts:
– Plants require air, water, food, and light to
– There are many kinds of plants, and each
has its own form or structure
– Plants make seeds
– Seeds grown into plants with
roots, stems, leaves, and flowers
– Plants grow and change
Living environment (continued)
• There are many kinds of animals
• Some animals are alike in the way
they look and in the things they do,
and others are very different from
each other.
• Animals need air, water, and food
• Animals can survive only in
environments in which their needs
can be met
Living environment (continued)
• Many animals make shelters to rear
their young
• Stories sometimes give animals
attributes they really do not have.
• Animals have life cycles that include
being born, developing into adults,
reproducing, and dying.
Science in Personal and social perspective and the human
• Observe
• Question
• Hypothesize
• Plan and conduct investigation
• Organize their thinking
• Reach conclusions
Physical Science, the physical setting and the
designed world
Key Concepts:
Moving toys have a source of energy
This source may be the children
themselves, or may stem from
springs or electricity
Wind or air is the source of energy
for other toys
Vibrations cause some toys to make
Human Organism
There are five senses-hearing, smell, taste, touch,
and vision
All of the senses can be used to find out about
people, places, and things
People use their senses to find out about
Used together, the senses can give us more
It is necessary to practice using our senses so
they will help us learn more efficiently
Some persons are not able to use one or more of
their senses
The world
Water can be liquid or solid and move back and
forth between the two
If water is turned into ice and the ice is allowed to
melt, the amount of water is the same as before
Water left in an open container disappears, but
water in a closed container does not.
Water has weight
Water’s weight and up thrust help things float.
Water is a solvent for many materials.
The world (continued)
Chunks of rocks come in many sizes and
shapes, from boulders to grains of sand
and even smaller
Rocks are composed of minerals, but the
amounts of mineral will vary from rock to
Rocks change by wearing away
Plants and animals left prints in rocks a long
time ago
When rocks wear away and are combined
with other materials, they produce soil
Minerals form crystals
Healthy Body
• Each person is unique with a special body type
• Lungs help us to breathe and use the oxygen
in the air
• Bones support our bodies and help them keep
their shape
• Our hearts are a special part of our bodies
• We depend on muscles to move every part of
the human body
• The food pyramid offers many choices of good
foods to keep our bodies healthy
• We must eat foods from each of the major
food groups in order to stay healthy
Project Approach
Katz and Helm
Introduces children to experiences of science inquiry and explorations at an
earlier age
The child’s prior knowledge should be assessed before teachers provide new
Connections to Math
• Young children need many
opportunities to represent,
invent, quantify,
generalize, and refine their
experiential and intuitive
• Health and
• Planning for
• What is beauty?
• Centers
• Bags
• List of Books
• Science through Children’
Using the Outdoors
Sensory experiences
Opportunities to cooperate with others
Teacher’s Role Outside?
Engage children actively
Model displaying what they want for children
(it’s okay to hold worms, mice, etc.)---if
you’ll do it—they will
Work collaboratively with children
Assess children’s attitudes, skills, and
knowledge using varied
Question, Question, Question
Parent Home Connection
• Field trips
• Home
Steve Spangler Science
Top 10 Reasons for Doing Science
• Science responds to children’s need to learn
about the world around them
• Children’s everyday experience is the
foundation for science
• Open-ended science activities involve
children at a wide range of developmental
• Hands-on science activities let teachers
observe and respond to children’s indivdiual
strengths and needs
• The scientific approach of “trial and error”
welcomes error-interprets it as valuable
information not as failure
Top 10 (continued)
• Science strongly supports language and
• Science helps English-language learnes
to participate in the classroom and learn
• Science demonstrations help children
become comfortable in large-group
• Science connecgts easily to other areas,
including center-based play, math,
artistic expression, and social studies
Seelfeldt, C, & Galper, A (2007). Active experiences
for active children: Science.Upper Saddle River:
National Research Council. (1996). National
science education standards. Washington, DC:
National Academy Press.
Epstein, A. (2007). The intentional teacher.
Washington, DC: National Association for the
Education of Young Children.
Helm, J., & Katz, L. (2001). Young investigators:The
proejct approach in the early years.New York,
NY: Teachers College.
Steve Spangler

Creating Mathematicians and Scientists within Young …