Mathematics, mind’s development : Mathematics, mind’s development And powerful learning environment
Demetriou & Panaoura (2006) attempt to propose a theory of cognitive organization and growth that : Demetriou & Panaoura (2006) attempt to propose a theory of cognitive organization and growth that Is experimentally based
Integrates the developmental tradition
And has a differential perspective
Demetriou = an integrative endeavour : Demetriou = an integrative endeavour (1987) The neo-Piagetian theories of cognitive development: toward an integration
(2004) Mind, Intelligence and development: a general cognitive, differential and developmental theory of the mind
Components of a powerful learning environment framework (E De Corte & L. Verschaffel, 2005) and Demetriou’s inputs : Components of a powerful learning environment framework (E De Corte & L. Verschaffel, 2005) and Demetriou’s inputs A theory of competence that analyzes and describes the components of mathematical competence
A theory of learning, that aims at understanding and explaining the processes of learning and development
A theory of intervention, that focusses on principles for the design of powerful learning environments
A theory of assessment that develops forms and methods of assessment for monitoring and improving mathematics learning and teaching Mathematical thought is a largely domain-free enterprise, guided by clear criteria for what is right and wrong
Processing efficiency is the developmental factor in regard to the development of working memory and mathematical thought
Teachers have to decide what is learnable by the pupils and to lead them in the process of reflecting on mathematical objects
…
Two central ideas : Two central ideas Development of processing efficiency and executive control processes in working memory ==> development of mathematical thought “The constructions in mathematics at a particular age reflect at a large extent the available processing and representational resources of the human mind”
Development of self-awareness and self-evaluation ==> development of mathematical thought
The construction of domain-specific concepts and skills depends on the development of general cognitive processes : The construction of domain-specific concepts and skills depends on the development of general cognitive processes
Demetriou and Piaget : Demetriou and Piaget Learning is subordinated to general cognitive growth
Reflective abstraction is a central cognitive mechanism
What is the role of education and mathematical instruction? : What is the role of education and mathematical instruction? Can processing efficiency and executive control in working memory be trained directly or indirectly?
Can self-evaluation and self-representation (= self-regulation?) be educated?
Can the teaching of mathematics concepts and symbol system influence the development of cognitive processing?
About the link between cognitive growth and learning : About the link between cognitive growth and learning What about the concept of ZPD (zone of proximal development)?
Do the teachers have to wait for the readiness of general cognitive processes (processing efficiency and executive control in working memory) before teaching of mathematics concepts and symbol systems?
Can teaching accelerate the growth of cognitive processing and/or the construction in mathematics (especially, for slow learners)?
About mathematical thought, self-awareness and self-representation : About mathematical thought, self-awareness and self-representation The development of self-awareness = a recycling process
« Self-awareness enables the thinker to redescribe the processes and schemes of the present level into a higher level of representation »
Mathematical self-awareness ==> clear attitudes to mathematics
What can be the role of discussion with peers and socio-cognitive conflict?
What can be the role of formal teaching of mathematical procedures and symbols?
What can be the role of beliefs about mathematics transmitted by parents and teachers?
About the way to cope with individual differences : About the way to cope with individual differences Having accurate information on students’ processing efficiency and executive control in working memory, how should teachers plan mathematics activities in order to maximize learning?
Can and should teachers (and if yes, how) intervene when students have negative self-representations concerning their mathematical aptitudes and/or restrictive beliefs in regards to mathematical thought?
Thanks to Demetriou & Panaoura for their excellent conceptual and empirical contribution : Thanks to Demetriou & Panaoura for their excellent conceptual and empirical contribution