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
Mathematics?
• Born with capabilities to solve simple numerical
quantities
• 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
seeker
• Preschoolers are intrigued to investigate shapes,
measurement, the meaning of number, and how
numbers work
Math and the Young Child
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MATH IS MORE THAN ROTE COUNTING
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
• Remember—CHILDREN VARY IN THEIR
THINKING
Standards Standards Standards
• NCTM Principles and Standards
• NCTM Curriculum Focal Points
• Kentucky Early Childhood Standards and
Benchmarks
NCTM Documents
Learning and Teaching Mathematics
Content Strands
• Number
• Geometry and
Spatial relations
• Measurement
• Patterns/Algebra
• Analyzing data
Process Strands
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Reasoning
Proof
Communication
Connections
Representations
Principles
•Equity
•Curriculum
•Teaching
•Learning
•Assessment
•Technology
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,
2008).
Learning Mathematics Continuum
Promoting Good Beginnings for
Mathematics
• Effective classroom approaches
• Inclusion and equitable experiences for all
students
• 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
MOVE SING and READ
• 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
mathematics
• Recognize if math is developing or stalled in children
• Plan activities that rely on mathematics (and literacy)
development.
• 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
Subitizing
• 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
concept
• Leads to understanding of addition and
subtraction
• Audio Input helps with Subitizing (songs)
Learning to Count
• How many—not based on the arrangement or
size
• 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
children
Teacher Talk Improves Number
Knowledge
• 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
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Age
-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
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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
operations
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
result
• 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
attributes
• 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
applications
• 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
measured.
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
reading
• Written language is necessary
• Books are consulted and read
• Math experiences must be continuous
• Reflection is necessary
• Rich environment
• Vocabulary
Activity with Math Standards
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2.
3.
4.
5.
What do you need to know?
Literature connection and needed
resources
How to make home connections?
How to assess?
What will children need to do to
demonstrate the concepts?
Websites of Interest
www.sesamewhorkshop.org
www.nickjr.com
www.nctm.org (Illuminations)
Pigseye.kennesaw.edu/~rouyang/ece4401/w-sites1.html
www.center.edu (math their Way)
www.carolhurst.com
www.little-g.com/shockwave/frame.html
www.ux1.eiu.edu/~cfsjy/mts/_link.htm
www.learningpage.com/free_pages/menu_basics/numbers_z
aner.html
www.computerlab.kids.new.net/
www.storylineonline.com
SENSORY TUB MATHEMATICS
• Not just for science
Introductions
Math, Science, and
Spanish
PhD
4 year old Angela
Piaget
• 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)
Vygotsky
• 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
answers
• Organize, reflect on,
represent, and document
investigations
• 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,
questioning,
investigating, analyzing,
and reaching
conclusions and
communicating the
results to others
• Give up “show and tell”
in favor of group
meetings
National Science
Education Standards
• Teachers should:
– Plan inquiry based science
programs
– Guide and facilitate student
learning
– 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
facilitator
– Model effective problem
solving techniques
– Have equipment for inquiry
Sciencing
• 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
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Life science and the living environment
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Earth science and the physical setting
•
Science in Personal and social
perspective and the human organism
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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
live
– 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
organism
KEY CONCEPTS:
• 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
sounds
Human Organism
KEY CONCEPTS:
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
themselves
Used together, the senses can give us more
information
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
KEY CONCEPTS:
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
freezing
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)
KEY CONCEPTS:
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
rock
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
KEY CONCEPTS:
• 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
experiences
Connections to Math
• Young children need many
opportunities to represent,
invent, quantify,
generalize, and refine their
experiential and intuitive
understanding.
Indoor/outdoor
• Health and
safety
• Planning for
inclusion
• What is beauty?
• Centers
Literacy
• Bags
• List of Books
• Science through Children’
Literature
Using the Outdoors
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Sensory experiences
Observation
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
strategies/methods
Question, Question, Question
DOCUMENT, DOCUMENT, DOCUMENT
Parent Home Connection
• Field trips
• Home
Activities
• LET’S HAVE SOME MORE FUN
Steve Spangler Science
www.stevespanglerscience.com
RECENT STUFF
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
levels
• 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
literacy
• Science helps English-language learnes
to participate in the classroom and learn
English
• Science demonstrations help children
become comfortable in large-group
conversations
• Science connecgts easily to other areas,
including center-based play, math,
artistic expression, and social studies
• SCIENCE IS FUN
References
Seelfeldt, C, & Galper, A (2007). Active experiences
for active children: Science.Upper Saddle River:
Pearson.
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.
Websites
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http://www.reachoutmichigan.org/funexperiments/quick/preschool.html
http://www.first-school.ws/theme/science.htm
http://atozteacherstuff.com/Lesson_Plans/Science/__Preschool/index.shtml
http://members.tripod.com/~Patricia_F/mathscience.html
http://www.peepandthebigwideworld.com/activities/
http://www.dpeasley.com/Peasleburg_Academy/pa_preschool_science.htm#Sink%20or%20F
loat
http://www.christian-parent.com/articles/080504a.shtml
http://www.seedsofknowledge.com/science2.html
http://www.funlessonplans.com/preschool_lesson_plans/free.htm
http://www.shirleys-preschool-activities.com/preschool-science-and-nature-study.html
http://www.discoverthis.com/article-science-activities-pre-grade5.html
http://www.universalpreschool.com/ask-an-expert/science-expert.asp
http://www.educatingjane.com/Study/preschool-sciencel.htm
http://www.truecoaching.com/PIC/archive/archive_rainforest/science.cfm
http://www.internet4classrooms.com/prek.htm
Bubbles
Steve Spangler
www.stevespanglerscience.com
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Creating Mathematicians and Scientists within Young …