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. 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) 1 2 3 4 5

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?