creating math moments in preschool greg gierhart murray state university dr. nancy lovett regional...
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Creating Math Moments in Preschool
Greg GierhartMurray State University
Dr. Nancy LovettRegional Training Center-Calloway County
This presentation is dedicated to bringing out the inner child within you!
A preschool test
Principles for a Developmental Curriculum
• Each child is an individual and should be treated and respected as such
• The early years are a period of development in their own right, and education of young children should be seen as special with its own valid criteria of appropriate practice.
• The role of the educator of young children is to engage actively with what most concerns the child, and to support learning through these preoccupations
Principles for a Developmental Curriculum
• The educator has a responsibility to foster positive attitudes in children to both self and others, and to counter negative message with children may have received
• Each child’s cultural and linguistic endowment is seen as the fundamental medium of learning
• An anti-discriminatory approach is the basis for all respect-worthy education, and is essential as a criterion for a developmentally appropriate curriculum (DAC)
Principles for a Developmental Curriculum
• All children should be offered equal opportunities to progress and develop and should have equal access to good quality provision. The concepts of multiculturalism and tolerance are intrinsic to this whole educational approach
• Partnership with parents should be given priority as the most effective means of ensuring coherence and continuity in children’s experiences, and in the curriculum offered to them
• A democratic perspective permeates education of good quality and is the basis of transactions between people
Math Wars
• Camp #1-Behavioralists-Math is for knowing– Memorize– Know the basic facts
• Camp #2-Constructivists-math is for understanding
-conceptualize (scaffold learning)
-deeper understanding of mathematics
A Famous Problem
The Horse Problem!
• A man buys a horse for 50 dollars. Decides he wants to sell his horse later and gets 60 dollars. He then decides to buy it back again and paid 70 dollars. However, he could no longer keep it and he sold it for 80 dollars.
• Did he make money? lose money? or break even? Explain why.
Substantial changes in PreK-12 math education are occurring nationwide due to
• New beliefs about how children learn.
• Massive changes in technology-widespread availability of calculators and computers.
• Changing demands on workers made by business and industry
Math: A Natural Principle
• Principle 1-Thinking about the problem, not the answer, this is what is important
• Principle 2- Process is more important than product
• Principle 3- Answers come from a logical certainty, not an authority figure
Summary of changes in Instructional Practice in PreK-4 Mathematics
Increased attention to:• Use of manipulative
materials• Cooperative work• Discussion of mathematics• Questioning• Justification of thinking• Writing about mathematics• Problem-solving approach
to instruction• Content integration• Use of calculators and
computers
Decreased attention to:
• Rote practice• Rote memorization of
rules• One answer and one
method• Use of WORKSHEETS• Written practice• Teaching by telling
Industry Expectations for School Mathematics
• The ability to set up problems with the appropriate operations
• Knowledge of a variety of techniques to approach and work on problems
• Understanding of the underlying mathematical features of a problem
• The ability to work with others on problems
Industry Expectations for School Mathematics (continued)
• The ability to see the applicability of mathematical ideas to common and complex problems
• Preparation for open problem situations since most real problems are not well formulated
• Belief in the utility and value of mathematics
(--Pollack, 1987)
Social and Emotional
Preschoolers with social and emotional problems will need to have those needs addressed before they can successfully develop their mathematical skills
(Sousa)
NCTM
Five Content Strands Process Strands
Number Reasoning
Geometry Communication
Algebra Connections
Prob/Stats Representation
Measurement
Kentucky Early Childhood Standards and Benchmarks
• NCTM Principles and Standards
• NCTM Curriculum Focal Points
• Standards and Benchmarks
NCTM PRINCIPLES
• Equity
• Curriculum
• Teaching
• Learning
• Assessment
• Technology
Goals and Objectives of Mathematics Learning
• Guiding learning• Poster session: creating mathematics-rich
physical environment– Arrival– Large group time– Choice time– Small group time– Snack/meal time– Transitions– Outdoor time– Rest time– Dismissal
Emergent Mathematicians
• Naturally acquire some mathematical concepts without direct teaching
• Follow a generally standard sequence of gradual mathematical development
• Construct mathematical concepts from a very early age
Intentional Teacher
• Understand child development
• Understand each individual needs and interests
• Use this understanding to develop the best curriculum for children
• Take an active role in the development of the curriculum
• Use resources
• Understands that planning involves the objectives,standards, and assessments
Intentional Teacher (Continued)
• Consider student interest
• Consider your standards/benchmarks, objectives, goals, and assessment (not activities)
• Do not rely on pre-made lessons or worksheets (or canned activities)
• Knows the standards/benchmarks of the state
Bridging in Mathematics: How Does a Preschool Teacher Do It?
Observer
Validator
Participant/Converser
Extender
Problem Initiator
Role Model
Instructor
Manager
How Does a Mathematician Solve Problems?
• Work for a small amount of time on a problem and will return to it later
• Collaborate with others and study the problem together
• Prove that the solution is correct• Solve complex problems• Take pride in their accomplishments and use
the problem solving process• Never Give Up
Make 10
THE NCTM STANDARDS How and What to teach
How
• Mathematics as Problem Solving
• Mathematics as Communication
• Mathematics as reasoning
• Mathematical Connections
What• Estimation• Number sense and
numeration• Whole number• Geometry and Spatial
Sense (play and proximity)• Measurement (play)• Statistics and Probability
(Graphs)• Patterns and Relationships
(patterns)
Planning Learning Experiences
• Child initiated learning
• Teacher guided instruction
• Large groups
• Small groups
What is the best center?Learning v Interest
Learn concepts, skills and facts independently or in small groups
Planned according to developmental needs
Planned according to the interest of children
Planned to use all of the senses
Dramatic Play
• Prop Boxes http://www.angelfire.com/dc/childsplay/Prop_Box_Ideas.htm
EXAMPLE:
RESTAURANT
Tablecloth napkinsdishes Tablewearmenus (made w/ food pictures) order pads/pencils
Sign for restaurant apronshats Cash registertrays play food
There is Power in REFLECTION
• Students must be given time to reflect
• Reflection reduces math anxiety
How to Best Learn Mathematics?
• Behaviorist Approach
• Montessori Method
• A Visual Approach
• The Constructivist Approach
Concept of Zero
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
Project Approach
• Katz and Helm
• Studies (p. 95-99)
• Introduces children to experiences of mathematics inquiry and explorations at an earlier age (researchers-validation)
• The child’s prior knowledge should be assessed before teachers provide new experiences
Math Backpacks
This provides a link between home and school and the parents get to see
what their child is learning. You will need: 1 backpack, materials required for extension activity, instructions for the parents, and a scribbler for comments. I provide the scribbler so that parents and students may share their thoughts about the activities. I send the backpack home every night with a different student. If by chance they forget the pack, it is not sent home with another student until it returns. When the pack is returned we read and share the comments with the class. Once all of the children have had a chance to take home the pack, I refill it with another activity and we start over again. The children are so eager to take the pack home and share the learning with their parents.
Math Tubs
• Math Tubs are simply plastic tubs containing games and hands on manipulatives for students to use that focus on a particular math concept. The tubs can be used as a directed center, one on one skill practice, or for additional reinforcement during free choice time once introduced. While working with the materials in each tub, students are practicing and developing one to one correspondence, numeral recognition, sorting skills, patterning skills, set recognition, etc.
• The math area also contains manipulatives such as size bears, unifix cubes, pattern blocks, plastic chain links, tiles, colored cubes, plastic animals, tangrams, etc. These are for students to use in conjunction with some of the math tub activities, but also for whole class lessons and free exploration.
Literacy
Math Resources
Cuisenaire Rods
Games
MathematicsHOT TOPICS
• Standards, objectives, assessments, and activities
• Learning trajectories
• Brain Research and Mathematics
• Technology (SMARTBOARDS—HD digital video)
Singers
Websites of interest
Bev Bos: www.turnthepage.com
Lisa Murphy: www.ooeygooey.com
Steve Spangler: www.stevespanglerscience.com
Jim Gill: http://www.jimgill.com/
Greg and Steve: http://www.gregandsteve.com/index.php
Jack Hartmann: http://www.jackhartmann.com/
Hugh Hanley: http://www.hughhanley.com/
Tom Hunter: http://www.tomhunter.com/
Paul “Vincent” Nunes: http://www.lighthouserecords.com/
Math manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.htmlKY math center: http://kentuckymathematics.org/
Math playground: http://www.mathplayground.com/
Math and standards: http://www.mathwire.com/
Math resources:http://www.internet4classrooms.com/early_childhood/math_pre-k.htm
More Websites
• Nick Jr. Activities: http://www.nickjr.com/• Illuminations: http://illuminations.nctm.org/• Games: http://www.prongo.com/games/ages3-6.html• Games galore: http://www.cut-the-knot.org/games.shtml• Math concepts: http://www.internet4classrooms.com/skills-k-mathbuilders.htm• Workjobs: http://www.preschoolfun.com/pages/teacch%20work%20jobs.htm• More Workjobs:
http://www.blaine.k12.wa.us/bes/class/Klemmt/html%20file/workjobs.html• Math tubs: http://www.marcias-lesson-links.com/MathTubs.html• More math tubs: http://www.hubbardscupboard.org/math_tubs.html• More math tubs: http://www.vickymoore2.com/for.cfm?subpage=633403• Math backpack:
http://www2.hcpss.org/res/mathbp/kindergarten/kindergarten.html• Literacy and Mathematics:
http://www.indiana.edu/~reading/ieo/bibs/childmat.html
We thank you!