Math

Avoiding Mathphobia

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

National consensus on what math is: from preschool to grad school

1. comparing: matching, contrasting, sorting

2. ordering: seriating, sequencing3. quantifying: counting, measuring4. spatial: shapes, spatial relationships5. temporal: time concepts, time

relationships

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

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 NumberStory of DucksStory of Place Setting

CountingA complex process:

1. The one to one principle2. The stable order principle3. The cardinal principle4. The abstraction principle5. The order irrelevance principle

Should be meaningful process in: recipes, attendance, charts, graphing, table setting, settling

disputes

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

Other relevant Piagetian principle

Three types of knowledge

1. Physical knowledge2. Logico-mathematical knowledge3. Social arbitrary knowledge

(Example of cuisenaire rods)

Appropriate preschool math activities1. * Natural integration2. Cuisenaire rods3. Attribute blocks4. Unifix cubes5. Parquetry blocks6. Pegboards and geoboards7. Number scales8. Number boards9. Dice, card and domino games10. Cash register, money, etc.11. Shape sorting box12. Stacking cylinders13. Abacus14. Bingo and lotto games

Natural integration:

5 minutes to clean up or taking turnsMath in cookingMath in blocksMath in dramatic playMath in group time charts and routinesMath in music

Awareness of Patterns

Pattern blocksPatterns on calendarPatterns in manipulativesPatterns in sewing cardsPatterns in clapping

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