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