1. Math
Avoiding Mathphobia

2. A science of relationships and patterns Relationships: bigger/smaller, more than/less than/same as, faster/slower, before/after, first/second/third, over/under, etc. Patterns: counting, odds/evens, times table, shapes, progressions, equations, etc.
Really, any problem solving activity is a math activity

3. National consensus on what math is: from preschool to grad school
1. comparing: matching, contrasting, sorting
2. ordering: seriating, sequencing
3. quantifying: counting, measuring
4. spatial: shapes, spatial relationships
5. temporal: time concepts, time relationships

4. Appropriate activities to develop each
Comparing provides a foundation for numbers
Numbers can plug into graphs, patterns, routines
Should use real measures before abstract ones
Spatial relationships best learned in 3 dimensions
Temporal concepts particularly hard for preschoolers
Start with time sequences, relationships and significance

5. Math usually misrepresented in early childhood
* Arithmetic too abstract
* Counting only meaningful when process-oriented
* Otherwise just memorizing “tricks”
* Not a useful foundation for constructing math knowledge
Illustrations:
Conservation of Number
Story of Ducks
Story of Place Setting

6. Counting A complex process: The one to one principle
The stable order principle
The cardinal principle
The abstraction principle
The order irrelevance principle
Should be meaningful process in:
recipes, attendance, charts, graphing, table setting, settling disputes

7. Process-oriented math
Concrete must precede abstract
Numberness must precede number
Thinking must precede memorizing
Correctness is not goal, but means to an end
Children do not make cognitive mistakes
Must come to cognitive conflict
Correction ineffective; more appropriate to question and discover

8. Other relevant Piagetian principle
Three types of knowledge
Physical knowledge
Logico-mathematical knowledge
Social arbitrary knowledge
(Example of cuisenaire rods)

9. Appropriate preschool math activities
* Natural integration
Cuisenaire rods
Attribute blocks
Unifix cubes
Parquetry blocks
Pegboards and geoboards
Number scales
Number boards
Dice, card and domino games
Cash register, money, etc.
Shape sorting box
Stacking cylinders
Abacus
Bingo and lotto games

10. Natural integration: 5 minutes to clean up or taking turns
Math in cooking
Math in blocks
Math in dramatic play
Math in group time charts and routines
Math in music

11. Awareness of Patterns Pattern blocks Patterns on calendar
Patterns in manipulatives
Patterns in sewing cards
Patterns in clapping

12. Major Problem With Math
Not taught as relevant and useful in life
Not taught as concrete and enjoyable
Not based on problem solving and beauty
If we provide meaningful foundation and context
we can head off math phobia and confusion