Contributions to PME 44

Mathematics Education in the 4th Industrial Revolution: Thinking Skills for the Future
Khon Kaen, Thailand
21-22 July 2020

Antonini, S., Nannini, B. Linking and iteraction signs in proving by mathematical induction, p. 1-10

Cervantes-Barraza, J., Cabañas-Sánchez, G. Teacher promoting student mathematical arguments through questions, p. 81-89

Miyakawa, T, Shinno, Y. Characterizing proof and proving in the classroom from a cultural perspective, p. 403-411

Pearn, C., Stephens, M., Pierce, R. The importance of understanding equivalence for developing algebraic reasoning, p. 448-456

Reid, D., Shinno, Y., Komatsu, K., Tsujiyama, Y. Toulmin analysis of meta-mathematical argumentation in a japanese grade 8 classroom, p. 475-483

Sommerhoff, D., Brunner, E., Ufer, S. How beliefs shape the selection of proofs for classroom instruction, p. 556-565

Sterner, H. Working on graphs in elementary school – a pathway to the generalization of patterns, p. 575-583

To know more, see the Proceedings here.

Contribution to CERME 11

Utrecht University, Utrecht, Netherlands
6-10 February, 2019

Shinno, Y., Miyakawa, T., Mizoguchi, T., Hamanaka, H., Kunimune, S. Some linguistic issues on the teaching of mathematical proof.

There are different meanings of proof-related words and their connotations in different languages. This study aims to reveal issues of the relationship between natural and mathematical language in the teaching of mathematical proof. For this purpose, we examine the grammatical characteristics of language from Japanese and international perspectives, as well as linguistics issues associated with statements with quantifications. A pilot study shows that natural language may influence how statements are formulated by students in mathematical discourse.

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Dissertation: An algebraic opportunity to develop proving ability

Julius Romica Donisan
Columbia University
May 5, 2020

Set-based reasoning and conditional language are two critical components of deductive argumentation and facility with proof. The purpose of this qualitative study was to describe the role of truth value and the solution set in supporting the development of the ability to reason about classes of objects and use conditional language. This study first examined proof schemes – how students convince themselves and persuade others – of Algebra I students when justifying solutions to routine and non-routine equations.

After identifying how participants learned to use set-based reasoning and conditional language in the context of solving equations, the study then determined if participants would employ similar reasoning in a geometrical context. As a whole, the study endeavored to describe a possible trajectory for students to transition from non-deductive justifications in an algebraic context to argumentation that supports proof writing.

First, task-based interviews elicited how participants became absolutely certain about solutions to equations. Next, a teaching experiment was completed to identify how participants who previously accepted empirical arguments as proof shifted to making deductive arguments. Last, additional task-based interviews in which participants reasoned about the relationship between Varignon Parallelograms and Varignon Rectangles were conducted.

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Thesis: Dificultades en la argumentación. Caso: Estudiantes de un curso de Fundamentos de Aritmética de la Licenciatura en Educación Básica con Énfasis en Matemáticas

Ruggeri Antonio Espinoza Castaño
Universidad de Antioquia - 2018

Este trabajo da cuenta de las dificultades en la argumentación que presentan algunos estudiantes de un curso de Fundamentos de Aritmética de la Licenciatura en Educación Básica con énfasis en Matemáticas de la Universidad de Antioquia, al momento de resolver problemas de razonamiento lógico que intencionalmente atienden al aspecto proceso y producto, los cuales son permeados por la argumentación en el marco teórico de la Actividad Demostrativa.

Para ello, se hace un estudio de casos con enfoque cualitativo, permitiendo así dilucidar dichas dificultades en los estudiantes. Finalmente, el trabajo arroja que hay serias dificultades en la argumentación, sobre todo cuando se abordan problemas que requieren de un lenguaje más formal y riguroso, no obstante, algunos ni siquiera logran pasar satisfactoriamente por las acciones de conjeturación y verificación, propias del aspecto proceso de la Actividad Demostrativa.

To know more, PDF.