By Paul Ernest
This ebook offers a landscape of complimentary and ahead taking a look views at the studying of arithmetic and epistemology from many of the best participants to the sphere. It explores constructivist and social theories of studying, and discusses the position of the pc within the mild of those theories. It brings analyses from psychoanalysis, Hermeneutics and different views to endure at the problems with arithmetic and studying. It enquires into the character of enquiry itself, and an immense emergent subject is the position of language. ultimately it relates the historical past of arithmetic to its instructing and studying. The e-book either surveys present learn and shows orientations for fruitful paintings sooner or later.
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Additional resources for Constructing Mathematical Knowledge: Epistemology and Mathematics Education
So, the situation was initially not open-ended from the point of view of the children. Protocol IV T: (To Arthur) could you draw a long stick for me? ) T: (To Nathan) mark the stick into thirds before you make a copy. N: (Activates ‘parts’, marks the stick into three parts; makes five copies; upon the teacher’s request, fills 1/3 of the original stick). T: (To Arthur) can you pull that out? 4). LESLIE P. 4 The children had formed no goals that would sustain independent mathematical activity of the nature illustrated in Protocols II and III.
The second is the independence of spontaneous reconstruction. Children contribute the operations and basic structures of a logico-mathematical nature to their interactions in their milieu. But we do not interpret Piaget as having meant that the child is a solo player, a lonely voyager, or a meaning maker in a vacuum even though he viewed mathematics as a contribution of the child. Piaget (1964) made it clear that the mathematical operations and basic structures he identified are reconstructed by children as a product of their interactions within their physical, social, and cultural environments.
In the process of doing so, we learn how we can bring forth the mathematics of children and how we can modify it. The mathematics of children is not independent of our mathematical concepts and operations because it is constructed partially through their interactions with our goals, intentions, language, and actions. Our orientation is compatible but not identical with Vygotsky’s ontogenetic orientation. It is compatible because by seeking to bring forth and to modify the mathematics of children, we are involved in its construction.