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 sorting discuss comparing and ordering describe 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 Ideas children are aware of mathematical concepts before they thoroughly understand them time, 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 art sequence of steps in collage differences and equivalents in number and size one-to-one correspondence problem solving

Mathematics in the Water Center measuring liquid with containers comparing volume, size and capacity, fractions play reveals a progression of mathematical thought

Mathematics in the Home Center dialing a telephone (sequence of numbers) time sequence Numbers Children 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 Classification Order Length Area Volume Number shape

Clean up in the Block Center Ask children to put away blocks that Are curved Have 3 different lengths Have the same color Have a particular shape and/or color In groups of twos or threes

Activities in this center afford the child experiences in: Creating real and imaginary structures Differentiating between sizes and shapes Classifying according to size and shape Selecting according to space Conceptualizing about space, size, shape Defining geometric shapes Developing perceptive insight, hand-eye coordination, imagination, and directionality

Definitions and Activities: Numbers Children learn numbers by rote Rote counting -counting in proper order Words may only be sounds at this time Each numeral represents the position of an object in the sequence Rational counting -last number counted in a sequence of objects represents all the objects

Numbers Cont. Repetition True 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