Guiding Math Experiences

1. Guiding Math Experiences

2. Early Math Experiences • Should focus on exploration, discovery, and understanding • Concepts are developed by hands-on materials, 3-D objects and the discovery of their relationships • Almost every activity area promotes math exploration

3. Teacher’s Role • Offer opportunities for kids to develop mathematical thinking • Ex. Classroom games can teach the concepts of first and last, high and low numbers • Ask questions: Are there enough chairs? Is everybody here today? Is there a cookie for each child

4. Goals of Early Experiences • Recognizing colors, patterns, attributes, and shapes • Classifying sets of objects • Comparing objects and using terms that describe quantity • Copying patterns • Recognizing and writing numerals • Estimating quantity and measurement • Developing problem-solving skills

5. Assessing Math Experiences • Assessment by observation – helps you determine child’s needs • Ex. If you notice a child cannot sort objects, you will need to provide sorting activities • Specific task assessment – involves giving children set activities to determine skills or needs • Ex. Show a child four different-sized ball. Ask child which is the smallest ball? Which is the largest?

6. Math Equipment • Provide a variety of 3-D objects • Collections of items for counting, observing, creating, sorting and discussing, construction and comparing

7. Color Concept • Color is considered a math concept since it helps children learn to discriminate among objects • Generally easier to understand because it is used in everyday conversation • Activities: classify eye colors, sort objects by color, match shapes, play I Spy

8. Shape • Roundness is the first, shape-related concept that children learn • Most often name shapes before they can draw them • Activities: trace around a shape, match cut of a shape to ones drawn on paper **Don’t teach shape and color concepts at the same time; wait until color concepts are well-understood

9. Classification • It is the process of mentally sorting and grouping objects or ideas by a common attribute • Attribute examples: size, color, shape, pattern, or function • Children learn classification within the first few weeks of life; i.e. classify experiences as pleasant or unpleasant

10. Types of Classification • Matching: involves putting like objects together • Sorting: process of physically separating objects based on unique features • Sequencing: process of ordering real-life objects from shortest to tallest or tallest to shortest

11. Sets • A set is a group of objects that are alike in some way and therefore belong together • Objects belonging to a set are its members • A set can have a few or many members • A set with no members is called an empty set

12. Sets, cont’d • Ex. Introduce one set of objects at a time. Say “What are these? These are all blocks. We call them a set of blocks.” Ask “What are some other sets in the room?” (cards, crayons, buttons, . . . )

13. 1 1 2 2 3 4 3 5 4 5 Counting • Kids develop oral counting skill as early as two • Kids are first exposed to counting by listening to adults • After learning names of numbers, they can identify written words (two) and numerals (2)

14. One-to-one correspondence • It is understanding that one group has the same as another • Ex. Put 7 pennies in a pile and spread out 7 pennies next to it. Ask child to identify which has more

15. Cardinality • It is the concept that the last number in a counting sequence tells how many objects exist in a set • The number will not change regardless of the order in which objects are counted

16. One-to-One Principle • Children count each object once and only once, saying one number word for each object they count

17. Stages of Counting • Rote counting: recitation of numbers in order • Involves memory, not order • Rational counting: involves attaching a number to a series of objects • Test understanding by sending a child to get four crayons, two pieces of paper, etc.

18. Identifying Numerals • Numerals: symbols that represent numbers • Children gain recognition skills when they are continually exposed to numerals at home, school, store, etc.

19. Space Concepts • Describing positions of objects in space is an important part of early math experience • Have kids move physically to learn • Space concepts: * before, after * high, low * up, down * here, there * far, near * above, below * inside, outside * top, center, bottom * first, middle, last * in front of, in back of

20. Size and Volume Concepts • Size Concepts: * big, little * large, small * long/tall, short * wide, thin * big, bigger, biggest * small, smaller smallest * inches, feet, pounds * smaller than, bigger than * high, low * large, larger • longer, taller, shorter • Volume Concepts: * full, little, much, a lot, some

21. Time Concepts • Hard for kids to understand because it can stand for so many things • Past, present, future • Hours, days, tomorrow, yesterday, today • Morning, afternoon, evening • Spring, summer, autumn, winter • Use routines to teach time • Examples: • “After lunch we take naps.” • “ Your mother will come pick you up after outdoor playtime.”

22. Temperature Concepts • Cooking and outdoor activities help introduce temperature concepts • Include words such as thermometer, hot, cold, warm, and cool

23. Questions to Encourage Mathematical Thinking • How could you figure that out? • Is there another way to do it? • How do you know? • If you wanted to show Amy how to do that, what would you say? • I wonder what would happen if you tried a different way? • What can I do to help you?