JEAN PIAGET
Piaget believed that people go through
definite developmental stages in their lives.
Each stage must be completed before a
person can attain the next stage.
P I AG E T ’ S S TAG E S O F
COGNITIVE DEVELOPMENT
 Sensorimotor (toddler to 2 years old)
 Preoperational (2 to 6 years old)
 Concrete Operational (6 to 12 years old)
 Formal Operational (over 12 years old)
Piaget’s approach of asking questions and building
on the answers of children aligns well with the need
for oral discourse as seen in the NCTM Principles
and Standards of School Mathematics.
PIAG ET’S STAG ES CON TIN UED …
 Sensorimotor
• “Out of sight, out of mind”
• Actions on Objects: Kids will touch, taste, squeeze, etc.
 Preoperational
• Know objects exist, can describe
• Actions on Reality: Children will fill containers from others, may hide containers
within others, etc.
 Concrete Operational
• Can reason with concrete objects: Children will figure out which containers hold the
most, least, equal amounts.
• Actions on Operations
 Formal Operational
• Can reason without concrete objects (with former experience)
• Operations on Operations
LEV VYGOTSKY
People
continually
knowledge.
No
construct
two
people
and
restructure
have
the
same
understanding of concepts. Teacher intervention is
important!
VYGOTSKY’S
CONSTRUCTIVISM
Zone of proximal development
When people can produce & analyze a complex
skill on their own.
Teacher questioning techniques
Children can be guided to better mathematical
understandings as they progressively analyze complex
skills on their own. Children can internalize actions
more quickly with the guidance of good analyzing
questions from his/her teacher.