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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

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creating mathematicians and scientists within young children

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
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
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
Standards Standards Standards
  • NCTM Principles and Standards
  • NCTM Curriculum Focal Points
  • Kentucky Early Childhood Standards and Benchmarks
nctm documents learning and teaching mathematics
NCTM Documents Learning and Teaching Mathematics

Content Strands

Process Strands







  • Number
  • Geometry and Spatial relations
  • Measurement
  • Patterns/Algebra
  • Analyzing data
  • Equity
  • Curriculum
  • Teaching
  • Learning
  • Assessment
  • Technology
preschool teacher s role
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
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

research alert
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).
promoting good beginnings for mathematics
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
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 mathematics14
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
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
  • 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
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
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
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 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
    • Age -Perceptions -Constructing Information
    • Tactile kinesthetic -Quantity of objects
    • Mathematical talking
    • Making it fun and offer choices
levels of sorting
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
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 operations
number and operation
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 operation24
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
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 algebra26
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
Basic Concepts of Geometry

Key Concepts:

  • Geometric shapes are two- and three-dimensional
  • 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 geometry28
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
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 measurement30
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 measurement31
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
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
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
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 solving35
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 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
Activity with Math Standards
  • 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
Websites of Interest (Illuminations) (math their Way)

sensory tub mathematics
  • Not just for science

Math, Science, and Spanish


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
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
Baby Test Tubes
  • This is not finished—what could it be if it continued down the assembly line?
carol seefeldt
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
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
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
  • 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
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
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
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 continued52
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
Science in Personal and social perspective and the human organism


  • Observe
  • Question
  • Hypothesize
  • Plan and conduct investigation
  • Organize their thinking
  • Reach conclusions
physical science the physical setting and the designed world
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
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 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
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 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
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 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
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
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
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
  • Bags
  • List of Books
  • Science through Children’ Literature
using the outdoors
Using the Outdoors
  • 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


parent home connection
Parent Home Connection
  • Field trips
  • Home
steve spangler science
Steve Spangler Science


top 10 reasons for doing 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 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
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

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.

steve spangler
Steve Spangler