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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An illustration of the explanatory and discovery functions of proof
TL;DR: In this article, an illustration of the explanatory and discovery functions of proof with an original geometric conjecture made by a grade 11 student is presented. Butler et al. provide an exemplar for designing learning trajectories to engage students with these functions.
LEVELS OF PROOF IN LOWER SECONDARY SCHOOL MATHEMATICS As Steps from an Inductive Proof to an Algebraic Demonstration
TL;DR: In this article, the authors established levels from an inductive proof to an algebraic demonstration in lower secondary school mathematics, and established six levels of proof in lower-secondary school mathematics.
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Levels of Proof in Lower Secondary School Mathematics
TL;DR: In this paper, the authors established six levels of proof in lower secondary school mathematics as steps from an inductive proof to an algebraic demonstration on the basis of three axes (contents of proof, representation of proof and students' thinking).
Developing Understanding for Different Roles of Proof in Dynamic Geometry
TL;DR: In a recent article submitted to the Philosophae Mathematicae as discussed by the authors, Yehuda Rav poses the interesting hypothetical situation of us having access to an all-powerful computer called PYTHIAGORA with which we can quickly check whether any conceivable mathematical conjecture is true or not.
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Mathematical Explanations that are Not Proofs
TL;DR: In this article, the authors focus on a particular example of an explanatory non-proof: an argument that mathematicians regard as explaining why a given theorem holds regarding the derivative of an infinite sum of differentiable functions.
References
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The Mathematical Experience.
TL;DR: This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about and will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.
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Proving Is Convincing and Explaining.
TL;DR: In mathematical research, the purpose of proof is to convince as discussed by the authors, and the test of whether something is a proof is whether it convinces qualified judges. In the classroom, on the other hand, it is to explain.
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A study of pupils' proof-explanations in mathematical situations
TL;DR: In this paper, the authors analyse pupils' attempts to construct proofs and explanations in simple mathematical situations, to observe in what ways they differ from the mature mathematician's use of proof, and derive guidance about how best to foster pupils' development in this area.