Open Access
Pupils' needs for conviction and explanation within the context of dynamic geometry.
TLDR
The research attempted to determine whether pupils were convinced about explored geometric statements and their level of conviction, and established whether pupils exhibited an independent desire for why the result, they obtained, is true, within the context of dynamic geometry.Abstract:
Recent literature on mathematics education, and more especially on the teaching and learning of geometry, indicates a need for further investigations into the possibility of devising new strategies, or even developing present methods, in order to avert what might seem to be a "problem" in mathematics education. Most educators hIld textbooks, it would seem, do not address the need (function and meaning) of proof at all, or those that do, only address it from the limited perspective that the only function of proof is verification. The theoretical part of this study, therefore, analyzed the various functions of proof: in order to identify possible alternate ways of presenting proof meaningfully to pupils. This work further attempted to build on existing research and tested these ideas in a teaching environment. This was done in order to evaluate the feasibility of introducing "proof' as a means of explanation rather than only verification, within the context of dynamic geometry. Pupils, who had not been exposed to proof as yet, were interviewed and their responses were analyzed. The research focused on a few aspects. It attempted to determine whether pupils were convinced about explored geometric statements and their level of conviction. It also attempted to establish whether pupils exhibited an independent desire for why the result, they obtained, is true and if they did, could they construct an explanation, albeit a guided one, on their own. Several useful implications have evolved from this work and may be able to influence, both the teaching and learning, of geometry in school. Perhaps the suggestions may be useful to pre-service and in-service educators.read more
Citations
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Journal ArticleDOI
Proofs produced by secondary school students learning geometry in a dynamic computer environment
Ramón Marrades,Ángel Gutiérrez +1 more
TL;DR: In this article, the authors present an analytic framework to describe and analyze students' answers to proof problems and verify the usefulness of learning in dynamic geometry computer environments to improve students' proof skills.
Journal ArticleDOI
Using Dynamic Geometry to Expand Mathematics Teachers' Understanding of Proof.
TL;DR: In this article, a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers' understanding of other functions of proof than just the traditional function of "verification" is given.
Journal ArticleDOI
Students’ encounter with proof: the condition of transparency
TL;DR: In this paper, the condition of transparency refers to the intricate dilemma in the teaching of mathematics about how and how much to focus on various aspects of proof and how to work with proof without a focus on it.
Journal ArticleDOI
Aspects of Mathematical Explanation: Symmetry, Unity, and Salience
TL;DR: For example, the authors argues that mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds can be seen as explanations.
Book
Approaching Proof in a Community of Mathematical Practice
TL;DR: The authors describe how students encounter proof in a community of mathematical practice at a mathematics department and how they are drawn to share mathematicians' views and knowledge of knowledge of the mathematical community.
References
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Journal ArticleDOI
Van Hiele Levels and Achievement in Writing Geometry Proofs
TL;DR: This article investigated relations between van Hiele levels, achievement in writing geometry proofs, and achievement in standard geometry content, and found that proof-writing achievement correlated significantly with van-hiele level when either entering knowledge of geometry or geometry achievement in the spring.
Journal ArticleDOI
The Ongoing Value of Proof
TL;DR: The authors argues that none of these factors justifies such a move, and that proof continues to have value in the classroom, both as a reflection of its central role in mathematical practice and as an important tool for the promotion of understanding.
An alternative approach to proof in dynamic geometry
TL;DR: The issue then, is not, what is the best way to teach proof, but what are the different roles and functions of proof in mathematics?
Journal ArticleDOI
Proof and Application.
Gila Hanna,Hans Niels Jahnke +1 more
TL;DR: In this article, an epistemological conception of mathematical proof is presented, which attempts to relate formal aspects of mathematical proofs to their pragmatic dimensions, and makes use of several concepts from the domain of analytical philosophy, to present a view of proof that might best be categorized as a dialectical one.
Book
Mathematics : the new golden age
TL;DR: In this paper, the class number problem beauty from chaos simple groups Hilbert's tenth problem the four-colour problem hard problems about complex numbers knots, topology and the universe Fermat's last theorem the efficiency of algorithms.