Complex Argumentation in Elementary School

Abstract

This paper describes a study of mathematical argumentation in primary school. The principal aim is to explore the nature of complex argumentation at a structural level. The context of the study was a teaching experiment involving nine tasks that promoted argumentation among fifth graders. We use the framework and method of reconstructing complex argumentation in the classroom proposed by Knipping (2008). The findings show that complex argumentation at a structural level in the context of refuting conclusions is characterized by a source-like structure with the addition of a new refutation argument element.Handle: http://hdl.handle.net/10481/57623Scopus record and citations

Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories

“…Unlike, TMA has adopted a particular method from philosophical field, Toulmin's (2003) model was designed under informal logic perspective allow researches in adapting this model & analyze mathematical argumentation in classroom (Boero et al, 2010;Conner et al, 2014), also is a methodological tool that allows to reconstruct the meaning of the classroom talk (Krummheuer, 1995(Krummheuer, , 2015, it has been modified in order to reconstruct complex argumentation occurred in mathematics class (Knipping & Reid, 2015;Cervantes-Barraza et al, 2019, 2020. It is for this reason that this research connects theories, but it also analyzes an empirical phenomenon that deals with the mathematical connections that a teacher established when performing the proof of the theorem of the continuity of a function at a point.…”

“…Research studies recognized argumentation as a fundamental part in the process of teaching mathematics (Conner et al, 2014;Erkek & Isiksal-Bostan, 2018;Solar, 2018) and the learning process of mathematics (Cervantes-Barraza et al, 2019Krummheuer, 2015). Curricular proposals encourage teachers to involve their students in the production of arguments, generating opportunities of discussion, validation of mathematical ideas, making connections and convincing others ( 2000).…”

“…Whereas that TMA is on viewing argumentation as a process & a basic ability develop in all education system, it allows students to develop conceptual understanding (Rumsey et al, 2019). Also, argumentation is a means to foster student's learning of mathematics through participation with arguments (Krummheuer, 1995(Krummheuer, , 2015 & promotes development of argumentative skills such us refuting & building counterarguments (Cervantes- Barraza et al, 2019;Rigotti & Greco Morasso, 2009). Also, several plans & programs of mathematics studies in basic education point out relevance of argumentation, they emphasize need to promote construction of arguments by students from first years of schooling, since it helps them gain sufficient confidence to justify conclusions & procedures with arguments oriented towards deductive-inductive reasoning & mathematical proof (CCSSI, 2010;NCTM, 2000;SPE, 2011).…”

“…Another important factor achieved with the articulation of ETC with TMA was that the categories of mathematical connections complemented the types of arguments based on mathematical meanings and properties of the concepts (analyzed in the previous sections), which had not been contemplated in the argument categorization proposed in Cervantes-Barraza et al (2019) and . In fact, the types of arguments proposed in TMA emphasize the characteristics of mathematical objects, but they could be detailed with the connections of feature type and those of different representations (equivalent and alternate).…”

“…2. Researchers focused on specific activities such as the use of semiotic representations (Duval, 2017), problem solving (Liljedahl & Santos-Trigo, 2019;Pólya, 1989), visualization (Presmeg, 2006), mathematical modeling (Borromeo, 2018), mathematical and ethnomathematical connections (Rodríguez-Nieto et al, 2021a;Rodríguez-Nieto & Escobar-Ramírez, 2022) and argumentation (Cervantes-Barraza et al, 2019;Conner et al, 2014;Toulmin, 2003).…”