Corpus ID: 86437559

Geometry Teachers Perspectives on Convincing and Proving When Installing a Theorem in Class

@inproceedings{Miyakawa2007GeometryTP,
  title={Geometry Teachers Perspectives on Convincing and Proving When Installing a Theorem in Class},
  author={Takeshi Miyakawa and Patricio G. Herbst},
  year={2007}
}
Recent research on mathematics learning has called attention to the nature of the situation that serves as context for that learning (Brousseau, 1997; Lave & Wenger, 1991; Schoenfeld, 1998). In our research, we conceive of classroom life as organized by recurring instructional situations: frames that allow teacher and students to exchange the work they do for claims on the stakes of teaching and learning. Decisions and actions made by teacher or students not only result from individual thinking… Expand

Figures and Topics from this paper

WHY SOME THEOREMS ARE NOT PROVEN IN GEOMETRY CLASS: DISPOSITIONS AND CONSTRAINTS
We research the work of the teacher in the context of proof and proving in secondary school geometry. In this paper we advance understanding of teaching phenomena that result in the fact thatExpand
When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers
While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? TowardExpand
What makes a claim an acceptable mathematical argument in the secondary classroom? A preliminary analysis of teachers' warrants in the context of an Algebra Task
TLDR
The study builds on previous research conducted by Nardi, Biza and colleagues, which examined mathematics teachers’ considerations of what makes a claim an acceptable mathematical argument in the secondary classroom, and proposes a theoretical tool based on Toulmin’s model of argumentation. Expand
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on theExpand
Using Web 2.0 Interactive Rich-media Technologies in Mathematics Teacher Development
TLDR
This roundtable session aims at showing how to exploit interactive rich-media technologies, especially technologies for watching and annotating animated instructional stories, to support teacher learning by developing several virtual settings that can be used to support mathematics teacher learning. Expand
Instructional Alternatives via a Virtual Setting: Rich Media Supports for Teacher Development
In this chapter, we describe the use of an animation of classroom interaction to support conversation with prospective teachers. The animation is used to examine establishing norms for the discussionExpand
ThEMaT’s Virtual Settings: Practicing Math Teaching with Web-based Interactive Rich-Media Technologies
TLDR
This poster shows rich-media applications for teachers to view, comment on, and discuss animated movies of instructional stories, to propose alternatives of those Stories, to compose new stories, and to discuss alternative solutions with peers. Expand

References

SHOWING 1-10 OF 18 REFERENCES
Proving and Doing Proofs in High School Geometry Classes: What Is It That Is Going On for Students?
In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 studentsExpand
THE NATURE AND ROLE OF PROOF WHEN INSTALLING THEOREMS : THE PERSPECTIVE OF GEOMETRY TEACHERS
We report preliminary results of research on the underlying rationality of geometry teaching, especially as regards to the role of proof in teaching theorems. Building on prior work on the classroomExpand
PRODUCING A VIABLE STORY OF GEOMETRY INSTRUCTION: WHAT KIND OF REPRESENTATION CALLS FORTH TEACHERS' PRACTICAL RATIONALITY?
We report on the development of representations of teaching based on sequential-art sketches of classroom stories. We demonstrate with focus group data that these resources can help sketch compellingExpand
Theory of Didactical Situations in Mathematics: Didactique des Mathématiques, 1970-1990
TLDR
Tests have been edited and organised so that they provide a comprehensive presentation of the principles and key concepts of the Theory of Didactical Situations that Guy Brousseau developed in the period from 1970 to 1990. Expand
Mathematics and Plausible Reasoning
This is a guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University,Expand
Structure du raisonnement deductif et apprentissage de la demonstration
Deductive thinking does not work like argumentation. However these two kinds of reasoning use very similar linguistic forms and propositional connectives. This is one of the main reasons why most ofExpand
Processus de preuve et situations de validation
RésuméNous étudions les relations entre preuves et contradictions dans la résolution d'un probleme de mathématiques. Cette étude montre la nécessité d'une approche à la fois situationnelle etExpand
Knowing about "egual area" while proving a claim about equal areas
Quel role peut jouer la preuve dans l'acquisition des connaissances en classe de mathematiques ? Cet article montre comment l'activite qui conduit a fournir une preuve n'amene pas seulement a lesExpand
The Fragility of Knowledge
The social practice of knowledge is conceived of either as the administrative problem of product distribution or as a question of individual access on the consumers’ side. The notions and mechanismsExpand
Situated Learning: Legitimate Peripheral Participation
TLDR
This work has shown that legitimate peripheral participation in communities of practice is not confined to midwives, tailors, quartermasters, butchers, non-drinking alcoholics and the like. Expand
...
1
2
...