1. Creative Mathematics

2. 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

3. Objectives Cont. discuss classification and sorting
discuss comparing and ordering
describe the young child’s understanding of shape and form

4. 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

5. 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

6. 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

7. 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

8. Mathematics in the Movement Center
children climbing over, under, crawling through climbing equipment
child uses hand-eye coordination, measuring length
cardinal numbers

9. 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

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

11. 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

12. 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

13. Block Experiences related to Math
Classification
Order
Length
Area
Volume
Number
shape

14. 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

15. 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

16. 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

17. 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

18. 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)

22. 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)

23. 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

24. 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

25. 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

27. 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