000079012 001__ 79012
000079012 005__ 20230914083233.0
000079012 0248_ $$2sideral$$a111508
000079012 0247_ $$2doi$$a10.30722/IJISME.27.02.002
000079012 037__ $$aART-2019-111508
000079012 041__ $$aeng
000079012 100__ $$aGiacomone B.
000079012 245__ $$aCognitive analysis on prospective mathematics teachers' reasoning using area and tree diagrams
000079012 260__ $$c2019
000079012 5060_ $$aAccess copy available to the general public$$fUnrestricted
000079012 5203_ $$aOne of the challenges in mathematics education research is to provide a comprehensive description of mathematical activity carried out by university students. Taking this challenge as an objective, this paper analyses the answers of 30 prospective teachers of primary education to a typical mathematics problem on fractions using area and tree diagrams. Theoretical and methodological tools from the onto-semiotic approach to mathematical knowledge and instruction support the cognitive analysis; hence, the underlying complexity of applying the area diagram to express a multiplicative reasoning should be highlighted. However, the structure of the system of practices that have to be carried out to solve the problem in the tree diagram are better aligned with this kind of reasoning. Furthermore, the use of the natural language in order to communicate the answer has been observed as a necessary register. This result lead to a deeper comprehension of the role played by these two types of diagrams and of the mathematical objects that emerge from such representations. As a conclusion, the type of analysis presented here is revealed as a strategic tool for instructors of primary education students to emphasize the importance of meanings negotiation. © 2019 Institute for Innovation in Science and Mathematics Education.
000079012 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/S36-17D$$9info:eu-repo/grantAgreement/ES/FEDER/EDU2016-74848-P
000079012 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000079012 592__ $$a0.22$$b2019
000079012 593__ $$aEducation$$c2019$$dQ3
000079012 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000079012 700__ $$0(orcid)0000-0002-1275-9976$$aBeltrán-Pellicer P.$$uUniversidad de Zaragoza
000079012 700__ $$aGodino J.D.
000079012 7102_ $$12006$$2200$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Didáctica Matemática
000079012 773__ $$g27, 2 (2019), 18-32$$pInt. j. innov. sci. math. educ.$$tInternational Journal of Innovation in Science and Mathematics Education$$x2200-4270
000079012 85641 $$uhttps://openjournals.library.sydney.edu.au/index.php/CAL/article/view/13065/12003$$zTexto completo de la revista
000079012 8564_ $$s728330$$uhttps://zaguan.unizar.es/record/79012/files/texto_completo.pdf$$yVersión publicada
000079012 8564_ $$s115519$$uhttps://zaguan.unizar.es/record/79012/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000079012 909CO $$ooai:zaguan.unizar.es:79012$$particulos$$pdriver
000079012 951__ $$a2023-09-13-10:44:54
000079012 980__ $$aARTICLE