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Math

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.

casey-hopkins
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Math

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  1. Math Avoiding Mathphobia

  2. A science of relationships and patternsRelationships: 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

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