# 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

#### 8 Citations

WHY SOME THEOREMS ARE NOT PROVEN IN GEOMETRY CLASS: DISPOSITIONS AND CONSTRAINTS

- Mathematics
- 2008

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 that… Expand

When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers

- Psychology
- 2008

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? Toward… Expand

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

- Computer Science
- 2014

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

- Sociology
- 2012

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 the… Expand

Using Web 2.0 Interactive Rich-media Technologies in Mathematics Teacher Development

- Computer Science
- 2009

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

- Engineering
- 2011

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 discussion… Expand

ThEMaT’s Virtual Settings: Practicing Math Teaching with Web-based Interactive Rich-Media Technologies

- Computer Science, Mathematics
- 2008

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?

- Psychology
- 2006

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 students… Expand

THE NATURE AND ROLE OF PROOF WHEN INSTALLING THEOREMS : THE PERSPECTIVE OF GEOMETRY TEACHERS

- 2007

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 classroom… Expand

PRODUCING A VIABLE STORY OF GEOMETRY INSTRUCTION: WHAT KIND OF REPRESENTATION CALLS FORTH TEACHERS' PRACTICAL RATIONALITY?

- Psychology
- 2006

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 compelling… Expand

Theory of Didactical Situations in Mathematics: Didactique des Mathématiques, 1970-1990

- Computer Science, Mathematics
- 2014

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

- Mathematics, Psychology
- 1954

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

- Philosophy, Mathematics
- 1991

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 of… Expand

Processus de preuve et situations de validation

- Mathematics
- 1987

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 et… Expand

Knowing about "egual area" while proving a claim about equal areas

- Art
- 2005

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 les… Expand

The Fragility of Knowledge

- Psychology
- 1991

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 mechanisms… Expand

Situated Learning: Legitimate Peripheral Participation

- Psychology, Computer Science
- 1991

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