45 Math and Sciencein Early Childhood

Zone of proximal developmentVygotskyskills and understanding children are on the verge of possessing... Number SenseA concept that develops over time as children think about, explore, an

Math and Science

in Early Childhood

CDEC 2307 Nita Thomason Ed.D

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

• 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

a sequence of colors, object, sound, stories, or movements that repeats in the same order over and over again

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

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

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?

• Patterns

• Mathematical Situations and Structure

• Models of quantitative relationships

• Change

• 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

• 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

– What other ways …?

– What kind of pattern …?

– How do you know …?

– What if …?

• Discuss quantitative relationships

• 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 in-depth 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

Process of gathering information about children

from several forms of

evidence, then organizing and interpreting that information

• 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

• Samplings

– Time – Event

• Scales

– Graphic – Numerical

Observation Skill Tips

• Be objective

• Be specific

• Use direct quotes

• Use mood cues

A list of behaviors with

checkmarks, recorded before, during, and after behavior occurs

Concept Activity Observation Checklist

• 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

• 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