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FRHD 2040 (20)

Triciavan Rhijn (20)

Chapter 11

School

University of GuelphDepartment

Family Relations and Human DevelopmentCourse Code

FRHD 2040Professor

Triciavan RhijnChapter

11This

**preview**shows half of the first page. to view the full**3 pages of the document.**Program Design for Children

Chapter 11

Defining Mathematics:

• Children learn math and science from their manipulation of objects and their

discovery of relationships and patterns within their environment

• Hard to separate science and maths in an early child learning environment

• Mathematics for kids is a way of viewing the world and their experiences in it

– solving real problems

Learning Mathematics:

• Piaget describes 3 ways that human beings learn:

1. The Physical World: Concepts such as cold, hot, rough, smooth, etc.

2. The Social World: Socially transmitted info such as language, religion,

superstitions, etc.

3. The Construction of Mental Relationships: Concepts such as counting,

numeration, conservation, etc. (aka logico-mathematical learning)

• Logico-mathematical thinking requires the learner to create categories and

hierarchies of objects without regard to their physical properties

• Simple Abstraction (Empirical Abstraction): Children abstract certain info

from their experiences

• Reflective Abstraction: Learner manipulates objects and then reflects on

the results – leads to re-organizing mental constructs

• Vygotsky’s View: Prompt teachers to think about what kids might be on the

verge of discovering and to provide the materials and assistance that would

help enhance making those discoveries

Teaching Mathematics:

• Teachers should use the same terminology throughout when teaching math,

and it shouldn’t matter the age of the child because they need to learn the

terminology regardless

• Teachers should arrange the environment so that the materials that best

represent a concept are available for manipulation and provide time for

manipulation

Standards for Mathematics Education:

• Content Standards:

o Number and operations

o Geometry and spatial sense

o Measurement

o Patterns, functions and algebra

o Data analysis, stats and probability

• Process Standards:

o Problem solving

o Reasoning and proof

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