Epistemological Framework and Mathematical Learning

Epistemological Framework and Mathematical Learning

Cesare Fregola (Roma Tre University, Italy)
DOI: 10.4018/978-1-60566-930-4.ch001
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Abstract

The aim of this chapter is to provide some indications on the background of our research regarding the use of simulation games for learning geometry and arithmetic. We reinterpret certain educational goals from the perspective of the anthropology of the virtual. Within this context, a number of important international commissions on math teaching are analyzed with particular reference to the difficulties involved in finding the right balance between the need for a formal mathematical language and teaching solutions to guide learning.
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Determine a reality that is within the child’s grasp, describe the relations that the mind builds, the structure and the underlying models, and reconstruct linguistic codes for mathematics that form a communicative link between reality, thought, emotions, behaviour and the joy of discovery.

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Learning Needs Reviewed From The Perspective Of Virtual Anthropology

Up until the advent of the virtual world in every day reality every child arrived in class with learning needs clearly defined by organizational and social contexts. At school the children found a learning environment organized to respond, in a fairly predictable predetermined way, to their learning requirements; the roles (teachers, heads, admin staff, the organization itself) were clearly defined as were the tools and methods employed to teach certain facts and encourage certain behavior in the right way, often, vis-à-vis the knowledge to be communicated and the attitudes to be encouraged.

Up until the advent of the virtual world in every day reality every teacher brought to the classroom a metaphorical toolbox of materials and techniques, even if one may sometimes doubt the methodological value and motivational effectiveness of some of the contents.

It is a complex business finding causal connections or other forms of correlation between the natural inclination and motivation to learn mathematics- variables known to influence the learning process- and strategies that organise and shape the process of learning of mathematics in the reality in which both parties-children and teachers- find themselves, i.e., the classroom.

We can say that teaching provision that should facilitate math learning is only partly able to respond adequately to the changing needs of virtual anthropology1 (Levy P., 1994). The environments children grow up in are already vibrant and sometimes conflicting mixtures of the real and the virtual. As ever the case when innovations upset the established paradigms, it becomes necessary to reanalyze the underlying structures and harness the potential of change (Fregola, 2003). Or society is based on paradigms that are linear, certain, deterministic, where everything is reduced to the smallest detail, and these can only partly help us understand the changes in progress. It is, therefore, essential to search for more suitable models of analysis and interpretation of daily life and this implies recourse to paradigms involving simultaneity and uncertainty, situational paradigms, and the ability to reconstruct an overall vision, starting from the need to manage processes of communication, production and development that characterize complex systems to be determined or defined (Gandolfi A., 1999).

In order to deal with the consequences of this profound paradigm shift, primary school math, besides counting and measuring, should also develop competences that contribute to personal growth and supply pupils with the tools to deal with complexity2.

What is clear is that the theme of prospective methodologies has been left open and there is little trace of references to learning and teaching models that take into account the consequences of recent changes that have involved children, adults, the interrelationships and their respective roles3 in different contexts of life.

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