Creative Mathematics

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