Publications 2020

Rø K., Arnesen, K.K. (in press) The opaque nature of generic examples: The structure of student teachers’ arguments in multiplicative reasoning. The Journal of Mathematical Behavior.

Yopp, D. A., Ely, R., Adams, A. E., Nielsen, A. W., Corwine, E.C. (in press) Eliminating counterexamples: A case study intervention for improving adolescents’ ability to critique direct arguments. The Journal of Mathematical Behavior.

Regier, P., Savic, M. (in press) How teaching to foster mathematical creativity may impact student self-efficacy for proving. The Journal of Mathematical Behavior.

Czocher, J.A., Weber, K. (2020) Proof as a Cluster Category. Journal for Research in Mathematics Education, 51/1, 50-74.

Publications 2019

Guerra, F.J.U., Valenzuela, M.L., Almouloud , S.A. (2019) Resolución De Tareas Que Implican Demostración En Geometría Del Espacio Revista Eletrônica de Educação Matemática. REVEMAT,14(2), 1-20, Florianópolis (SC).

Tchonang, P., Njomgang, Y.J., Tieudjo, N.D. & Pedemonte B. (2019) Relationship between drawing and figures on students’ argumentation and proof. African Journal of Educational Studies in Mathematics and Sciences, 15/2, 75-91.

Gyõry, Á., Kónya, E. (2019) Proving skills in geometry of secondary grammar school leavers specialized in mathematics. Annales Mathematicae et Informaticae 50, pp. 217–236.

Gulkilik, H., Kaplan, H.A., Emul, N. (2019) Investigating the Relationship between Argumentation and Proof from a Representational Perspective. International Journal for Teaching and Learning 20/2, 131-148

Waluyo, M., Vidakovich, T., Ishartono, N., Toyib, M. (2019) A Review of Assessing Mathematical Proving Ability. In Proceedings of the 4th Progressive and Fun Education International Conference, Profunedu 2019, 6-8 August 2019, Makassar, Indonesia.

Rubilar, Á.S.B., Badillo, G.Z. (2019) Desarrollo y cambios en las maneras de justificar matemáticamente de estudiantes cuando trabajan en un ambiente sociocultural. Enseñanza de las Ciencias, 37/3, 129-148.

Wathne, U., Brodahl, C. (2019) Engaging Mathematical Reasoning-and- Proving: A Task, a Method, and a Taxonomy. Journal of the International Society for Teacher Education 23(1), 6-17.

Buffarini, F. (2019) El álgebra como herramienta de modelización y validación: las interacciones en el aula como medio para su evolución. Contextos de Educacion, 26.

De la Cruz Mauricio, A., Arriaga G.G., Vázquez, F.J. (2019) Los tipos de prueba en la enseñanza de la geometría. Diferentes niveles de activación en el aula multigrado. In Preliminar-Memorias del Tercer Congreso Nacional de Investigación sobre Educación Normal.

Jankvist, U.F., Misfeldi, M., Aguilar, M. S. (2019) Tschirnhaus' transformation: Mathematical proof, history and cas. In Eighth European Summer University on History and Epistemology in Mathematics Education (ESU-8), Oslo, Norway.

Maarif S., Perbowo, K.S., Noto, M.S., Harisman Y. (2019) Obstacles in Constructing Geometrical Proofs of Mathematics-Teacher- Students Based on Boero’s Proving Model. Journal of Physics: Conferences Series, 1315 - 012043.

Publications 2018

Stuhlmann A.S. (2018) Mathematics students talking past each other: emergence of ambiguities in linear algebra proof constructions involving the uniqueness quantification. ZDM 51 (7). 1083-1095

Articles in: Proof Technology in Mathematics Research and Teaching

Introduction

Hanna, G., Reid, D.A, De Villiers, M. — Proof Technology: Implications for Teaching, pp. 3-9

Ganesalingam, M., Gowers W. T. — A Fully Automatic Theorem Prover with Human-Style Output, pp. 13-57

Bundy, A., Jamnik, M. — A Common Type of Rigorous Proof that Resists Hilbert’s Programme, pp. 59-71

Keller, C. — SMTCoq: Mixing Automatic and Interactive Proof Technologies, pp. 73-90

Arthan, R., Oliva P. — Studying Algebraic Structures Using Prover9 and Mace4, pp. 91-111

Theoretical Perspectives on Computer-Assisted Proving

Durand-Guerrier, V., Meyer, A., Modeste, S. — Didactical Issues at the Interface of Mathematics and Computer Science, pp. 115-138

Richard,P.R., Venant, F., Gagnon, M. — Issues and Challenges in Instrumental Proof, pp. 139-172

Mariotti, M. A. — The Contribution of Information and Communication Technology to the Teaching of Proof, pp. 173-195

Lane, L., Martin, U., Murray-Rust, D., Pease, A., Tanswell, F. — Journeys in Mathematical Landscapes: Genius or Craft? pp. 197-212

Suggestions for the Use of Proof Software in the Classroom

Hohenwarter, M., Kovács, Z., Recio, T. — Using Automated Reasoning Tools to Explore Geometric Statements and Conjectures, pp. 215-236

Quaresma, P., Santos V. — Computer-Generated Geometry Proofs in a Learning Context, pp. 237-253

Schumann, H. — Using 3D Geometry Systems to Find Theorems of Billiard Trajectories in Polyhedra, pp. 255-273

Classroom Experience with Proof Software

Avigad, J. — Learning Logic and Proof with an Interactive Theorem Prover, pp. 277-290

Miyazaki, M., Fujita, T., Jones, K. — Web-Based Task Design Supporting Students’ Construction of Alternative Proofs, pp. 291-312

Sangwin, C. — Reasoning by Equivalence: The Potential Contribution of an Automatic Proof Checker, pp. 313-330

Komatsu, K. Jones, K. — Virtual Manipulatives and Students’ Counterexamples During Proving, pp. 331-346

Afterword

Balacheff, N. Boy de la Tour T. — Proof Technology and Learning in Mathematics: Common Issues and Perspectives, pp. 349-365

Contributi a "Conferenze e Seminari dell'Associazione Subalpina Mathesis 2018-2019"

Scegliere, argomentare,comprendere: un laboratorio matematico con la teoria dei giochi
Samuele Antonini

In questo articolo riporto un’attività laboratoriale in teoria dei giochi cooperativi svolta in alcune scuole secondarie di primo e di secondo grado. La metodologia laboratoriale e i problemi proposti, aperti a diverse soluzioni e che necessitano di una riflessione sul significato stesso di soluzione, hanno promosso processi decisionali consapevoli e un’intensa attività argomentativa in cui gli studenti hanno sostenuto e cambiato i propri punti di vista, costruendo infine un modello matematico condiviso. Un breve paragrafo sulla trattazione formale dei giochi cooperativi a utilità trasferibile chiude l’articolo.

Per saperne di più

Un progetto a lungo termine per lo sviluppo delle competenze argomentative
Esther Levenson, Francesca Morselli

In questo contributo si presentano i primi risultati di un progetto di ricerca volto a studiare lo sviluppo a lungo termine delle competenze argomentative in matematica. Il lavoro si avvale di due lenti teoriche opportunamente combinate: le funzioni della spiegazione e le dimensioni della razionalità.

Per saperne di più

Thesis: La Formación didáctico-matemática de los docentes desde el ejercicio de la profesión orientadora a la gestión didáctica de las demostraciones matemáticas

Gladys Raquel Núñez Lazala
Universidad Autónoma de santo Domingo República Dominicana 2018

A través de la utilización de diversos métodos y técnicas de la investigación se han detectado insuficiencias en el tratamiento didáctico de las demostraciones matemáticas que limitan el desempeño didáctico de los docentes en carreras de Educación, mención Matemática; lo cual exige argumentar propuestas trasformadoras que, atendiendo a las características y condiciones del contexto, permitan contribuir a superar dichas insuficiencias.

La presente tesis tiene como objetivo mejorar el desempeño didáctico de los docentes en la carrera de Licenciatura en Educación, mención Matemática de la Universidad Autónoma de Santo Domingo a través de una estrategia metodológica sustentada en un modelo orientado a la gestión didáctica de las demostraciones matemáticas.

Se ofrece como resultado teórico, un modelo que se sustenta desde lo más general, en el enfoque histórico-cultural y en las concepciones de una Didáctica de la Matemática que tiene en cuenta los factores socioculturales que inciden en el desarrollo de las demostraciones matemáticas.

Se ilustran los procedimientos y actividades que conforman la estrategia metodológica y se valoran el modelo y la factibilidad de la implementación de la misma, mediante el criterio de expertos y la aplicación de un pre-experimento pedagógico.

To know more

Special Day in Honor of Viviane Durand-Guerrier

March 26, 2020 - Bizerte, Tunisia

This day is scheduled the day before the INDRUM Conference - Third Conference of the International Network for Didactic Research in University Mathematics, 27-29 March 2020.

INDRUM 2020

Thesis: O desafio de argumentar nas aulas de Matemática: uma investigação com estudantes do 1o ano do Ensino Fundamental

Simone Aparecida dos Anjos Azevedo
Pontifícia Universidade Católica de São Paulo 2019

This research deals with the development of argumentative skills by students of the 1st year of elementary school to solve problems of additive field utterance. National and international studies on the topic of argumentation highlight the difficulties to develop works with this theme and the little attention given to the subject, besides the important role of the teacher in the diffusion of this practice. Thus, using the principles of Didactic Engineering as a research methodology, we draw a research course that involved aspects of the processes of both the teaching and the learning of argumentation in Mathematics.

Through a questionnaire applied to 81 teachers, who work in the first year of Elementary Education, in different regions of the country, we approached their conceptions and performed a praxeological analysis of the didactic book that most of the members of this group adopted in order to verify how the argumentation is treated in this didactic material.

From this perspective, we tried to answer the following research question: does a didactic sequence that articulates the problem solving of additive structures and different moments of discussion in the classroom favor the development of argumentative skills by 1st year students of elementary school? We referred to Brousseau's Theory of Educational Situations (TSD) and Vergnaud's Conceptual Field Theory (TCC) to construct a didactic sequence with six problems of additive structures […].

Keywords: argumentation in Mathematics, moments of discussion in class, problems of the additive field, 1st year of Elementary School.