Pair, J., Strachota, S., Singh, R. (online first) The Academic Community's Perceptions of the Two-Column Proof. Mathematics Enthusiast, 18, Issue 1/2, pp. 210-238.
Mejia-Ramos, J.P., Weber, K. (online first) Using task-based interviews to generate hypotheses about mathematical practice: mathematics education research on mathematicians’ use of examples in proof-related activities. ZDM
Bickerton, R. and Sangwin, C.J. (under revision) Practical Online Assessment of Mathematical Proof.
Buchbinder, O., McCrone, S. (online first) Preservice teachers learning to teach proof through classroom implementation: Successes and challenges. The Journal of Mathematical Behavior, 58
Makowski M. B. (online first) The written and oral justifications of mathematical claims of middle school pre-service teachers.. Research in Mathematics Education.
Doruk, M., Doruk, G. (online first) Students’ ability to determine the truth value of mathematical propositions in the context of operation meanings. International Journal of Mathematical Education in Science and Technology.
Zambak., V.S., Magiera, M.T. (online first) Supporting grades 1–8 pre-service teachers’ argumentation skills: constructing mathematical arguments in situations that facilitate analyzing cases. International Journal of Mathematical Education in Science and Technology.
Tabach, M., Rasmussen, C., Dreyfus, T., Apkarian, N. (2020) Towards an argumentative grammar for networking: a case of coordinating two approaches. Educational studies in Mathematics, 103, 139-155.
Lockwood, E. Caughman, J.S., Weber, K. (2020) An essay on proof, conviction and explanation: multiple representationsystems in combinatorics. Educational studies in Mathematics, 103, 173-189.
Vargas, M.F., Fernandez-Plaza J.A., Ruiz-Hidalgo J.F. (2020) Análisis de los argumentos dados por docentes en formación a una tarea sobre derivadas. PNA, 14(3), 173-203.
Erdogan E., Erdogan, A., Dur Z., Akkurt Denizli, Z. (2020) Exploring, Conjecturing and Proving with Dynamic Geometry Software: a case study. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 14(1), 661-690.
Cuesta W.R. (2020) Competencias de argumentación y modelización en estudiantes de secundaria: la necesidad de un cambio de paradigma en la Educación Matemática del Chocó, Colombia. Pesquisa e Ensino, Barreiras (BA), v.1, e202020, 1-21.
Espinoza, R. M. (2020) Resoluciones de una tarea de cálculo por parte de profesores de matemáticas. ¿cuáles son los argumentos que ellos validan tanto en su trabajo personal como en el aula? Paulo Freire. Revista de Pedagogia Critica Ano 18, 23, 24-46.
Hakim F., Murtafiah M. (2020) Adversity quotient and resilience in mathematical proof problem-solving ability. Mapan Jurnal Matematika & Pembelajaran, 8/1, 87-102.
Faizah S., Nusantara, T. Sudirman, S., Rahardi, R. (2020) Exploring students’ thinking process in mathematical proof of abstract algebra based on Mason’s framework. Journal for Education of Gifted Young Scientists, 8(2), 871-884.
Dogan M.F. (2020) Pre-Service Teachers' Criteria for Evaluating Mathematical Arguments That Include Generic Examples. International Journal of contemporary educational, 7(1), 267-279.
Magiera, M.T. & Zambak, V.S. (2020) Exploring prospective teachers‘ ability to generate and analyze evidence-based explanatory arguments. International Journal of Research in Education and Science (IJRES), 6(2), 327-346.
Cervantes-Barraza J.A. (2020) Concepciones de futuros profesores de matemáticas en el contexto de la argumentación. Revista Academia y Virtualidad, 13(1), 10-22.
Cervantes-Barraza, J.A., Hernandez Moreno A., Rumsey, C. (2020) Promoting mathematicsl proof from collective argumentationin primary school. School Science and Mathematics.
Da Silva Lima, M.L., Dos Santos M.C. (2020) Provas e demonstrações e níveis do pensamento geométrico: conceitos, bases epistemológicas e relações. Revista electrônica de edcaçao matemática, 15(1), 1-21.
Martinez, J.P., Torregrosa Gironés, G. (2020) Razonamiento Configural y Espacio de Trabajo Geométrico en la Resolución de Problemas de Probar. Bolema: Boletim de Educacão Matemática 34, 66.
Gallo, S. Etchegaray, S.C., Markiewicz, M.E. (2017) Análisis ontosemiótico de un problema que promueve la puesta en funcionamiento del razonamiento conjectural. Revistas Yupana 11, 38-57.
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.
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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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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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.
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Montpellier University
18-21 February, 2020
Branchetti L., Bolondi G. Giberti C. Awakening argumentation processes in geometrical problem solving: does the linguistic variables in the formulation of the task play a role?
The main purpose of this paper is to explore how far the argumentation in a figural-conceptual situation (in the sense of Fischbein) and logical control of the structure are linked to features of the formulation of the task, in particular to the linguistic formulation of a task where both text and figures are essential.
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Faa’a, Polynésie française
April 2020
Ramassamy, M., Delcroix, A., Alì, M. L’apprentissage de la preuve dans l’enseignement supérieur aux Antilles : un état des lieux en début de cursus.
Dans le champ des mathématiques, la preuve – en tant que processus permettant d’établir une proposition à partir d'hypothèses et dans le respect de règles logiques – occupe une place fondamentale. Ses fonctions sont débattues tant dans le domaine de la recherche mathématique, que dans celui de l’épistémologie. Le vocabulaire la concernant (démonstration, justification, explication...) fait aussi l’objet de nombreux débats.
Ainsi, certains lui prêtent une fonction de validation (Balacheff, 1987), d’autres une fonction explicative amenant à une meilleure compréhension des mathématiques (Hanna, 1995). En ce sens, une attention particulière lui est portée dans l’enseignement secondaire français. Les programmes régissant l’enseignement des mathématiques demandent que le début de son apprentissage commence vers l’âge de 12 ans, en classe de cinquième, de façon progressive, en introduisant plusieurs formes de raisonnement (inductif et déductif).
Pour en savoir plus, ici.
Chelsey Lynn Van de Merwe
Department of Mathematics Education, Brigham Young University
June 11, 2020
Proof is an important component of advanced mathematical activity. Nevertheless, undergraduates struggle to write valid proofs. Research identifies many of the struggles students experience with the logical nature and structure of proofs. Little research examines the role mathematical content knowledge plays in proof production.
This study begins to fill this gap in the research by analyzing what role mathematical content knowledge plays in the success of a proof and how undergraduates use mathematical content knowledge during proofs. Four undergraduates participated in a series of task-based interviews wherein they completed several proofs. The interviews were analyzed to determine how the students used mathematical content knowledge and how mathematical content knowledge affected a proof’s validity.
The results show that using mathematical content knowledge during a proof is nontrivial for students. Several of the proofs attempted by the students were unsuccessful due to issues with mathematical content knowledge. The data also show that students use mathematical content knowledge in a variety of ways. Some student use of mathematical content is productive and efficient, while other student practices are less efficient in formal proofs.
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Steven Marta da Silva
Universidad de Lisboa - 2019
This study of an investigative nature was conducted as part of my master program in the teaching of Mathematics as a supervised teaching practice report, during the scholar year of 2018/2019, based on a sequence of five lessons of 90 minute each to a 11th grade mathematics class.
This study is framed on the didactic unit Limits of real functions with real variable according to Heine and aims to understand the mathematic argumentation of the 11th grade students in the learning of concepts and procedures involved in the exploratory study of the limit of functions.
More specifically, this study intends to analyze: (1) What are the characteristics of the students’ argumentative processes when solving exploratory tasks that involved limits of functions? Which difficulties they show in using these processes? (2) Which prior knowledge do students mobilize in their argumentations? (3) Which learnings, related to the limit of functions, the students developed? Which difficulties they reveal in these learnings?
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Editors-in-chief –
Bettina Pedemonte,
Maria-Alessandra Mariotti
Associate Editors –
Orly Buchbinder,
Kirsti Hemmi,
Mara Martinez
Redactor –
Bettina Pedemonte
Scientific Board –
Nicolas Balacheff,
Paolo Boero,
Daniel Chazan,
Raymond Duval,
Gila Hanna,
Guershon Harel,
Patricio Herbst,
Celia Hoyles,
Erica Melis,
Michael Otte,
Philippe Richard,
Yasuhiro Sekiguchi,
Michael de Villiers,
Virginia Warfield