Creative Mathematics

Objectives

discuss the developmental pattern of learning mathematical ideas

discuss how mathematics learning occurs in learning centers in the ECE classroom

define rote counting and rational counting

Objectives Cont.

discuss classification and sortingdiscuss comparing and orderingdescribe the young child’s understanding

of shape and form

Early Mathematics Experiences

children learn best through hands-on experiences filled with play and exploration

meanings and understandings of mathematical concepts take place in an action-based environment as they use concrete materials

Examples of Math Experiences

counting as you place crackers in each hand of a toddler

discuss shapes (cutting sandwich)sorting stuffed animals (largest to

smallest or vice versa)recognize shapes of signs

Developmental Pattern of Learning Mathematical Ideaschildren are aware of mathematical

concepts before they thoroughly understand themtime, sequence, numbers, weight

pattern of early use of numbers is similar to the general-to-specific pattern of physical growth

Cont.

early stages of mathematical thinking has a general understanding of numbers

National Council of Teachers of Mathematics

proposes mathematical content and processes students should know and be able to use as they progress through school

Mathematics in the Movement Center

children climbing over, under, crawling through climbing equipment

child uses hand-eye coordination, measuring length

cardinal numbers

Mathematics in the Art Center

much math involved in artsequence of steps in collagedifferences and equivalents in number

and sizeone-to-one correspondenceproblem solving

Mathematics in the Water Center

measuring liquid with containerscomparing volume, size and capacity,

fractionsplay reveals a progression of

mathematical thought

Mathematics in the Home Center

dialing a telephone (sequence of numbers)

time sequenceNumbersChildren use play to translate their

understanding of adult activities into their own actions

Mathematics in the Block Center

Real-life examples of geometric shapes and solids

The younger the child, the larger the blocks need to be

Too many blocks too soon may defeat the purpose

Will help to have a waiting list, timer, or a picture stating how many children may be in the block center at a time

Block Experiences related to Math

ClassificationOrderLengthAreaVolumeNumber shape

Clean up in the Block Center

Ask children to put away blocks thatAre curvedHave 3 different lengthsHave the same colorHave a particular shape and/or colorIn groups of twos or threes

Activities in this center afford the child experiences in:

Creating real and imaginary structuresDifferentiating between sizes and shapesClassifying according to size and shapeSelecting according to spaceConceptualizing about space, size, shapeDefining geometric shapesDeveloping perceptive insight, hand-eye

coordination, imagination, and directionality

Definitions and Activities: Numbers

Children learn numbers by roteRote counting -counting in proper orderWords may only be sounds at this timeEach numeral represents the position of

an object in the sequenceRational counting -last number counted

in a sequence of objects represents all the objects

Numbers Cont.

RepetitionTrue counting ability (rational counting) is

not possible until the child understands one-to-one correspondence

As rote counting develops, teachers should also encourage the skills of one-to-one correspondence

Have the child touch one object as she counts

Numbers Cont.

Young children should be asked to count only with number names that are meaningful to them (1, 2, 3…)

Cardinal numbers –number names (1, 2, 3…)

Ordinal numbers –refer to the place of an object in a series of numbers (ex. Second book, third window)

Classification and Sorting

Classification and sorting -putting together things that are alike or belong together

One of the processes necessary for developing the concepts of numbers

Must be able to observe an object for likenesses and differences

Understand concepts like “put together,” “alike,” and “belong together” before they can sort and classify (use sorting trays)

Comparing

Comparing –mathematical skill involving the perception of differences in items (My shoes are bigger than yours.)

May also make comparisons based on volume (different size and shape containers in water play)

Evident in stories and poems

Ordering (Seriation)

Ordering (seriation) – mathematical skill involving the ability to perceive opposite ends of a series (big to little)

Vital part of a complete number concept formation

Ordering activities include length (sticks), height (bottles or bodies), total size (bowls and shoes), weight (stones), color (from light to dark), and others

Shape and Form

Children need many experiences with shapes and making comparisons between shapes before they focus on naming shapes

Include more shapes than the common geometric shapes of a circle, triangle, rectangle, and square

But, familiar shapes need to be taught before uncommon ones

Build on previous knowledge

Math Activity:Title: Button Fun

Materials: buttons, paper, marker

Procedure: Supply an assortment of buttons. Have children separate them according to color, size, or shape. Count them as a group, record the results, then make a graph of the results and display in the classroom.

Guidance Suggestions: have groups of two

Variations: sort according to number of button holes

Suggestions for future use: use different materials, like beads, game pieces, K-Nex pieces, etc