Interactions with Diagrams and the Making of Reasoned Conjectures in Geometry

By Patricio G. Herbst. 2004

70 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/84b21e0bea9350e56d49480237a913197916ec5b

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Citations in the corpus

Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks (2006, background): “…to produce a proof consisting of statements that describe a figure, the tendency to justify every statement made about the figure, and the tendency to refer to objects in the figure by labels (neither conceptually nor by indexical or gestural references; see Herbst, 2004; Herbst & Brach, 2006).”
Research on Practical Rationality: Studying the justification of actions in mathematics teaching (2011, background): “varies according to whether the work is framed as a construction, an exploration, or a proof (Herbst, 2004).”
The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning (2015, background): “…on the diagram by constructing new objects, labeling points, and otherwise using it as a physical model that might suggest possibilities of theoretical properties that could be true about the figure it represents (see Herbst, 2004 for an elaboration of other modes of interacting with diagrams).”
The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning (2013, background): “Students’ interactions with diagrams In his discussion of students’ interactions with diagrams in geometry, Herbst (2004) proposes four modes of interactions between the actor, the diagram and the geometrical object (the figure).”
When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers (2008, background): “... translated from the conceptual register in which theorems are usually stated to the diagrammatic register in which proof exercises are usually posed, and this work is done by the teacher or the book (Weiss & Herbst, 2007) The addition of auxiliary lines to be used in a proof (or the consideratio”