How Children Learn
Mathematics
Mathematics reform calls for…
 Changes in the way mathematics is taught
 Changes in the mathematics taught
 Changes in the way mathematics is assessed

Learning Theories

The Constructivists
 The Behaviorists
 Cognitive Study
The Constructivists

Constructivists believe that children must be
allowed to experiment physically with the
things around them if they are to learn.
 Piaget (Sensimotor, Preoperational,
Concrete operational, Formal operational)
 Vygotsky
 Bruner
The Behaviorists

Stress the stimulus-response approach to
learning
Learning Styles

Perpetual learning style refers to a person’s
preference for material presented through
one of the fives senses:
– Visual
– Auditory
– Tactile
Gardner’s Four Views of the
Mind

Constructivism
 Multiple Representations
 Individual Differences
 Early Representations
Constructivism

Human mind is active sense-making entity
 The mind receives input and operates on it
 It pays attention to certain kinds of input,
raises questions, reflects on it, sets out
goals, and strives to either achieve or alter
the goals.
Multiple Representations

Three schemes widely acknowledged
– Natural language
– Mathematics
– Spatial Relations
– Additional ones, sometimes called intelligences
are musical, bodily, interpersonal,
intrapersonal, and naturalistic.
Individual Differences

Human beings differ from one another in
personality, appearance and intellect
 Brain studies
 Different populations
 Culture
Early Representations

Representations that we construct in early
childhood are extremely difficult to change
 Jean Piaget has demonstrated this in his
crib-side demonstrations