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, sequencing 3. quantifying: counting, measuring 4. spatial: shapes, spatial relationships 5. 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 Number Story of Ducks Story of Place Setting

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

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 Physical knowledge Logico-mathematical knowledge Social arbitrary knowledge (Example of cuisenaire rods)

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

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

Awareness of Patterns Pattern blocks Patterns on calendar Patterns in manipulatives Patterns in sewing cards Patterns 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