Mathematical reasoning in Elementary School and Higher Education

Authors

  • João Pedro da Ponte Institute of Education, University of Lisbon image/svg+xml
  • Joana Mata-Pereira Institute of Education, University of Lisbon image/svg+xml
  • Ana Henriques Institute of Education, University of Lisbon image/svg+xml

DOI:

https://doi.org/10.5212/PraxEduc.v.7i2.0003

Abstract

This paper analyzes the reasoning processes in mathematical tasks of two students in the 9th year of elementary school and two students in the second year of college. It also focuses the representation and meaningfulness, given their close relation with the mathematical reasoning. Results presented are based on two qualitative and interpretive studies which resort to several data sources. These results show that mastering of the algebraic language by the students in the 9th year is still insufficient to promptly solve the problems proposed, which does not occur with the college students though. All students use inductive initial strategies. However, one of the students in the 9th year and both college students revealed clearly their capability to reason deductively. The signification levels vary considerably, and several students have shown skills to build or mobilize relevant meanings. The model of analysis presented, articulating reasoning, representations and meaningfulness proved itself a promising tool to study the students’ reasoning processes.

 

Keywords: Mathematical reasoning. Representations. Meaningfulness.

Downloads

Issue

Vol. 7 No. 2 (2012): Dossiê: Educação Matemática

Section

Educação Matemática

License

Authors who publish in this journal agree with the following terms:

a) Authors keep the copyrights and concede the right of its first publication to the magazine. The work piece must be simultaneously licensed on the Creative Commons Attribution License which allows the paper sharing, and preserves both the author identity and the right of first publication to this magazine.

b) Authors are authorized to assume additional contracts separately, to not-exclusively distribution of the paper version published in this magazine (e.g.: publish in institutional repository or as a book chapter), with the author identity recognition and its first publication in this magazine.

c) Authors are permitted and stimulated to publish and distribute their papers online (e.g.: in institutional repository or on their personal webpage), considering it can generate productive alterations, as well as increase the impact and the quotations of the published paper.

d) This journal provides public access to all its content, as this allows a greater visibility and reach of published articles and reviews. For more information on this approach, visit the Public Knowledge Project, a project that developed this system to improve the academic and public quality of the research, distributing OJS as well as other software to support the publication system of public access to academic sources.

e) The names and e-mail addresses on this site will be used exclusively for the purposes of the journal and are not available for other purposes.

 

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Mathematical reasoning in Elementary School and Higher Education. Práxis Educativa, [S. l.], v. 7, n. 2, p. 355–377, 2012. DOI: 10.5212/PraxEduc.v.7i2.0003. Disponível em: https://revistas.uepg.br/index.php/praxiseducativa/article/view/4698. Acesso em: 30 apr. 2026.