By Raffaella Borasi
As dissatisfaction with the present prestige of faculty arithmetic grows world wide, educators and pros alike are calling for reforms and tutorial alterations. but, major adjustments can in basic terms be accomplished if each one educator of faculty arithmetic in my view rethinks numerous elements of arithmetic guide, and identifies concrete ways that their present perform can be transformed. ahead of such visions might be meaningfully carried out in school rooms, it is vital that arithmetic academics and educators research seriously either the assumptions and implications of the imaginative and prescient for faculty arithmetic that the experiences suggest. This e-book is meant to help educators in the sort of tough firm by means of focusing consciousness on "errors" and their use in arithmetic guide. in the course of the ebook, an method of mistakes as possibilities for studying and inquiry might be constructed and hired either as a way to create the types of educational studies recommended for faculty arithmetic reform, and as a heuristic to ask reflections approximately tuition arithmetic in addition to arithmetic as a self-discipline. stories: "...Raffaella Borasi's most modern booklet bargains vital contributions to the present debate on university arithmetic reform." - magazine for learn in arithmetic schooling "There are a few nice bits of philosophy during this book..." - arithmetic educating
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Extra info for Reconceiving Mathematics Instruction: A Focus on Errors (Issues in Curriculum Theory, Policy, and Research)
Sample text
In sum, the philosophical contributions summarized here suggest that errors have the potential to raise constructive doubt and questions that can, in turn, lead to worthwhile mathematical inquiries. Furthermore, such inquiries do not always need to be reduced to a search for the causes of the error, with the ul- timate goal of eliminating it. "-then the analysis of an error might lead to a reformulation of the problem under study, a deeper understanding of the context in which the problem was generated, and even to some unexpected and novel results.
Constructive Uses of Errors Made in Instructional Contexts Other Than the Mathematics Classroom The value of engaging the students themselves in a constructive use of their er- rors has already been explicitly recognized in some academic subject areas other than mathematics. In what follows, I briefly review a few examples that can help us rethink the potential role of errors in mathematics instruction. An academic area where in the last few decades the approach to errors has been radically reconceived is that of writing instruction.
5). In addition, it would expect students to gain some initiative and ownership in their mathematical activity, by learning to pose problems and questions for exploration on their own as well as to monitor their own mathematical work. Mathematics students would also be expected to gain a better understanding of mathematics as a discipline by coming to appreciate the roots and the forces behind its historical development, the tentative and socially constructed nature of its results, the power and limitations of its application to solve problems in other domains, and the positive role played by ambiguity.