Math and Science in Early Childhood CDEC 2307 Nita Thomason Ed.D

(Williams) Tell me mathematics, and I will forget; Show me mathematics and I may remember; Involve me … and I will understand mathematics.

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

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

Geometry 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

Measurement 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 –Beauty –Light –Flexibility Reggio Emilia Montessori

Manipulatives 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?

Manipulatives counters puzzles stacking blocks sewing cards snap blocks magnetic symbols parquetry blocks Legos pegs & boards wooden beads board games lotto dominoes checkers coins buttons shells flannel board pieces

Math Materials balances, weights, scales calendar cans, egg cartons clocks geometric boards magnetic boards measuring cups, spoons, pitchers number strips Objects to count rulers, yard sticks sandpaper numerals shape puzzles table games telephones thermometers timer unit, hollow, shape, and table blocks

Algebra Patterns Mathematical Situations and Structure Models of quantitative relationships Change

Patterns 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

Equality 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

Change 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

Cross-Curricular Connections Science Cooking Art Language, Literacy, and Literature

Assessment documentation of children’s talk collections of children’s work over time appropriate performance assessments checklists anecdotal records