[250]                           home                           [252]

 

Monday, November 28, 2005

 

 The BCNGroup Beadgames

National Project à 

Challenge Problem  à

 Center of Excellence Proposal à

 

 

 

 

The Taos Institute

(on the possibilities)

 

 

 [bead thread on curriculum reform]

Communication from Gary Berg-Cross

 

 

Paul,

 

Just a quick note on your curriculum project.  As an educational curriculum approach one should consider development/constructionist theories of learning to properly introduce concepts in a manner that student's can assimilate into their cognitive structure.   The usual ones development theories are:

 

·            Piaget's theory of intellectual development;

·            Dewey's theory on the role of experience in learning;

·            Vygotsky's developmental theory emphasizing the importance of the social context in learning; and

·            Bruner's theories concerning categorization and the search for meaning;

 

 

All these provide practical insights into learning mathematics.  Piaget is probably the most often used but even Dewey, for example, offers some ideas on an adequate "context".

John Dewey's Theory on Experience, Reflection, and Learning

John Dewey's  theory emphasizes the experiential aspects of learning, that is,  learning results from our reflections on our experiences, as we strive to make sense of them, We can directly sense "things", and have visceral reactions (e.g., danger at the sight of a tiger), but we also confront situations which leave us challenged, puzzled, or confused (which has "more"?). Through our encounters with the world and our reflections upon these experiences, our current understandings of the world are transformed so that things make more sense. Our understandings become broader and more coordinated, helping us to gain greater meaning from our experiences. And "mathematization" plays a role in that growth of meaning which Dewey believed expands when challenged by problems or dilemmas. But ontology provides a natural bridge to realities that ground knowledge.

So a curriculum should neither to cater completely to a learner's inclinations nor to attempt to force upon a child a preordained curriculum which takes no account of the learner.  As  educators we should structure learning environments that engage children into ontological inquiries which guide them toward broader knowledge.

 

Gary Berg-Cross