Chapter 5Math

Mathematics

• Is everywhere• Daily living provides a math-rich

environment• Math must be hands-on and DAP• Relationships and repetition are key to

math learning

Concept Development

• Concepts are the building blocks of knowledge

• Concepts are acquired through children’s active involvement with their environment

• Concepts are fostered by solving problems

Names Associated with Mathematical Concepts

• Piaget– Two types of knowledge

• Physical• Logico-Mathematical

• Vygotsky– Skills learned from those who have more skills– Zone of proximal development

• Gardner– Logical-Mathematical intelligence

Math Language Development

• Math language development occurs as children develop number sense and logical ways of thinking about time, space, and other mathematical ideas

• Language based on recommendations from NCTM’s Principles and Standards

Math Concepts

• One-to-one correspondence– Each object has the value of one

• Classifying and sorting– Grouping objects by a common characteristic—size,

shape, or color• Patterns, functions, and algebra

– Sequence of numbers, colors, objects, sounds, shapes, or movements that repeat, in the same order, over and over

• Seriation

Math Concepts (continued)

• Geometry and spatial sense– Children’s awareness of themselves in

relation to the people and objects around them

• Measurement• Data analysis and probability• Problem solving

Math Experiences• Games

– Folder games– Lotto games

• Bingo• Matching outdoor activities

– Counting– Climbing– Finding shapes– Comparing

Math across the Curriculum• Science

– Sorting collections– Graphing– Charting– Counting

• Cooking– Measuring– Counting

• Art– Outlining

• Language, literacy, and literature– Speaking– Reading

Manipulatives

• Create a manipulative center• Think about the purpose and objectives• The teacher’s role

– Criteria for selecting materials, including multicultural and needs of identified children

• Manipulative toys, games, and materials– Self-correcting, structured toys– Open-ended toys

Materials for Developing Math Concepts

• Children will naturally explore their environments• Role of teacher to provide words, materials, and

resources to scaffold learning• Materials could include

– Balances– Bingo cards– Calculators– Geoboards– Magnetic boards– Objects to count, sort, classify, make patterns– Table games– Table blocks

Technology and Mathematics

• Calculators should be available for use by young children

• Teachers should review software carefully– Open-ended software preferred

Observation, Assessment, and Evaluation

• Assessment is crucial to effective teaching• Careful assessment can help you when

planning for culturally and linguistically diverse children

• Anecdotal assessment form helpful– Keep anecdotal records on all children

Encouraging Family Support

• Inform them about opportunities for math at home– Sorting laundry

• By color• By shape• By family members

– Setting the table

Tips for Teachers

• Encourage exploration by children• Focus on process, not “correct” answer• Discover together• Use

– Number songs and books– Rhymes and rhythm

• Plan appropriate activities