"Doing Proofs" in Geometry Classrooms

Herbst, Patricio; Chen, Chialing; Weiß, Michael; González, Gloriana; Nachlieli, Talli; Hamlin, Maria; Brach, Catherine

doi:10.4324/9780203882009-15

Cited by 15 publications

(13 citation statements)

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“…When he was inferring information from the given or postulates, he still stated them as facts. This observation coheres with observations about the "doing proof" situation in high school geometry classes (Herbst, et al, 2009) in which students know the statement to be true before they do the proof.…”

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confidence: 85%

The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning

Chen

Herbst

2012

Educ Stud Math

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This study identifies forms of interactions with diagrams that are involved in conjecturing; more specifically, how students display their thinking publicly through using multimodal representations. We describe how students interact with diagrams in both gestural and verbal forms, and examine how such multimodal interactions with diagrams reveal their reasoning about diagrams. We hypothesize that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making conjectures. As a byproduct, the study also proposes a set of graphical representations of gestures that have been identified as important for geometrical reasoning. These can be employed to codify the gestural interactions and to depict the practices of teaching and learning in geometry classrooms.

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confidence: 85%

The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning

Chen

Herbst

2012

Educ Stud Math

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“…A partir de nuestras observaciones de situaciones de demostración en la clase de geometría en Estados Unidos (Herbst, Chen, Weiss, & González, 2009), hemos conjeturado que la norma de enunciación de problemas de demostración es que éstos se enuncien en lo que llamamos el registro diagramático (diagramatic register; Herbst, Kosko, & Dimmel, 2013;ver también Boileau, Dimmel, & Herbst, 2016). Esta norma tiene cinco incisos o subnormas, a saber:…”

Section: El Registro Diagramáticounclassified

Teoría y métodos para la investigación de la racionalidad de la práctica en la enseñanza de las matemáticas

Herbst¹

2018

EduMate

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el salón de clases. Se proveen referencias a artículos escritos en inglés durante los pasados 15 años, que dan cuenta de investigaciones en aspectos específicos de aquella racionalidad. Se definen las nociones de transacción de instrucción, situación de instrucción, norma de una situación, y obligación profesional, y luego se describen instrumentos diseñados para medir el grado en el que los maestros reconocen las normas de instrucción y las obligaciones profesionales. Se ilustra cómo funcionan esos constructos mediante el esbozo de algunas preguntas de investigación.

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“…They suggest that although diagrams sit in silence, we need to improve upon hearing what they are telling us. PWWs put diagrams in the foreground instead of relegating them to the background where "marking the diagram" is only a part of the ritualized norm of "doing proof" (Herbst et al 2009). PWWs emphasize that interpreting diagrams and reasoning are at the heart of geometric proof.…”

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confidence: 99%

Proofs without Words in Geometry

Nirode¹

2017

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Pictures and diagrams help high school geometry students develop reasoning and proof-writing skills. P r o o f s w i t h o u t W o r d s S ince the 1970s, the Mathematical Association of America's (MAA) journals Mathematics Magazine and College Mathematics Journal have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one might begin to go about proving it true" (Nelsen 2000, p. i). This article explains how I created and implemented a variation of using diagrams without words to facilitate the development of high school geometry students' reasoning and proof skills. The Common Core (CCSSI 2010) lists approximately twenty geometric theorems for students to prove (e.g., standards G.CO.9, G.CO.10, and G.CO.11) as well as the more general standard of using congruence and similarity criteria for triangles to prove relationships in geometric figures

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"Doing Proofs" in Geometry Classrooms

Cited by 15 publications

References 0 publications

The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning

The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning

Teoría y métodos para la investigación de la racionalidad de la práctica en la enseñanza de las matemáticas

Proofs without Words in Geometry

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