When she tried to facilitate meaningful mathematical discourse [18] in the control group class, the students were unable to get to the same level of critical thinking as the treatment group discussions.
In particular, when people engage in mathematical discourse, they draw on a variety of personal and material resources to construct, depict, and explain their reasoning in the form of psychological objects and actions that would be intelligible to their interlocutors (Kirsh, 2013; Nemirovsky & Borba, 2004; Nemirovsky & Ferrara, 2009; Nemirovsky, Kelton, & Rhodehamel, 2012; Radford, 2014).
(ii) Yablo (2006) has investigated the possibility that when engaging in mathematical discourse we presuppose that mathematical entities exist.
In an attempt to agree with the truth-value assignments that are usually displayed in mathematical discourse, the mathematical fictionalist introduces a fictional operator: 'According to mathematical theory M…'.
Are the stylistic elements present in mathematical discourse devoid of cognitive value and so only part of the coloring of mathematical discourse or can they be seen as more intimately related to its cognitive content?
The final phase of the task suggests future possibilities for engaging students in mathematical discourse to further support the development of mathematical adaptive expertise.
In her interview at the end of the year, a district math coach highlighted the importance of video-based discussions, noting that they "helped illuminate what mathematical discourse could look like in a classroom," which, she explained, "is new ground for many teachers".
For those who aim to understand mathematical discourse as it is used in the practice of mathematics, and who try to identify suitable features of that practice that prevent commitment to mathematical entities, the proposed translation will make the realization of that goal particularly difficult.
But with fiction operators in place, the syntax of mathematical discourse is changed, and thus the latter cannot be taken literally.
Deflationary nominalism offers an 'easy road' to nominalism, which does not require any form of reformulation of mathematical discourse, while granting the indispensability of mathematics.
