Exploring students' mathematical discussions in a multi-level hybrid learning environment.

The research described in this paper focused on the issue of describing and understanding how mathematical discussion develops in a hybrid learning environment, and how students participate in it. The experimental plan involved several classes working in parallel, with pupils and teachers interacting both in their real classrooms and in a digital environment with other pupils and teachers. The research was based on a rich set of data collected from the M@t.abel 2020 project, which was developed in Italy during the Covid health crisis. Based on Complementary Accounts Methodology, the data analysis presented in this paper involved specialists from the fields of mathematics education and inclusive education. In the study we considered the complexity of learning and the different elements that have an impact on students' activity and participation, when they are engaged in mathematical discussions within the multilevel-digital environment that emerged due to the pandemic. These parallel analyses showed that 'mathematical discussion in the classroom' is a complex (and sometimes chaotic) phenomenon wherein different factors interweave. A complementary approach assists in developing a global vision for this dynamic phenomenon and in highlighting local episodes that are crucial in this interplay of factors. It is precisely in these episodes that the role of the teacher is fundamental: these episodes appear as catalysts for the different variables, with the teacher acting as mediator.

A method for quantifying focused versus overview behavior in AOI sequences.

We present a new measure for evaluating focused versus overview eye movement behavior in a stimulus divided by areas of interest. The measure can be used for overall data, as well as data over time. Using data from an ongoing project with mathematical problem solving, we describe how to calculate the measure and how to carry out a statistical evaluation of the results.

Semantic processing of mathematical gestures.

OBJECTIVE: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. RESULTS: The N400 effect elicited by words primed with mathematical gestures (e.g. "converging" and "decreasing") was the same in amplitude, latency and topography as that elicited by words primed with action gestures (e.g. drive and lift), and that for terminal words of sentences. SIGNIFICANCE AND CONCLUSION: Findings provide a within-subject demonstration that the topographies of the gesture N400 effect for both action and mathematical words are indistinguishable from that of the standard language N400 effect. This suggests that mathematical function words are processed by the general language semantic system and do not appear to involve areas involved in other mathematical concepts (e.g. numerosity).