Book ChapterDOI
Proof and Proving
Gila Hanna,Gila Hanna,H. Niels Jahnke,H. Niels Jahnke +3 more
- pp 877-908
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TLDR
In this article, the authors argue that proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. Translating this statement into classroom practice is not a simple matter, however, because there have been and remain differing and constantly developing views on the nature and role of proof and on the norms to which it should adhere.Abstract:
Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. Translating this statement into classroom practice is not a simple matter, however, because there have been and remain differing and constantly developing views on the nature and role of proof and on the norms to which it should adhere.read more
Citations
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Book ChapterDOI
The knowledge complexity of interactive proof-systems
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Journal ArticleDOI
Proof, explanation and exploration: an overview
TL;DR: The role of proof in mathematics education is explored and justification for its importance in the curriculum is provided and three applications of dynamic geometry software are discussed as valuable tools in the teaching of proof and as potential challenges to the importance of proof.
ComponentDOI
Proof and Proving in School Mathematics
TL;DR: In this article, the authors propose a conceptualization of the meaning of proof in school mathematics and use classroom episodes from third grade to elaborate elements of this conceptualization and to illustrate its applicability even in the early elementary grades.
Journal ArticleDOI
Providing a Foundation for Deductive Reasoning: Students' Interpretations When Using Dynamic Geometry Software and Their Evolving Mathematical Explanations
TL;DR: The research suggests that the students' explanations can evolve from imprecise, `everyday' expressions, through reasoning that is isovertly mediated by the software environment, to mathematical explanations of the geometric situation that transcend the particular tool being used.
References
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Book
The culture of education
TL;DR: The Complexity of Educational Aims Teaching the Present, Past, and Possible Understanding and Explaining Other Minds Narratives of Science The Narrative Construal of Reality Knowing as Doing Psychology's Next Chapter Notes Credits Index as mentioned in this paper
MonographDOI
Cognition in practice : mind, mathematics, and culture in everyday life
TL;DR: In this paper, Lave moves the analysis of one particular form of cognitive activity, arithmetic problem-solving, out of the laboratory into the domain of everyday life, and shows how mathematics in the real world, like all thinking, is shaped by the dynamic encounter between the culturally endowed mind and its total context, a subtle interaction that shapes both tile human subject and the world within which it acts.
Journal ArticleDOI
Linguistic Interdependence and the Educational Development of Bilingual Children
TL;DR: In this paper, the authors argue that cognitively and academically beneficial bilingualism can be achieved only on the basis of adequately developed first language (L1) skills and two hypotheses are formulated and combined to arrive at this position.
Book ChapterDOI
The knowledge complexity of interactive proof-systems
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.