Luciana Bazzini

From Grounding Metaphors to Technological Devices: A Call for Legitimacy in School Mathematics.

The mutual relationship between real objects and mathematical constructions is at the very base of studies concerned with making sense in mathematics. In this wider perspective recent research studies have been concerned with the cognitive roots of mathematical concepts. Human perception and movement and, more generally, interaction with space and time are recognized as being of crucial importance for knowledge construction. A new approach to the cognitive science of mathematics, based on the notion of ‘embodied cognition’ assumes that mathematics cannot be considered as mind free. Accordingly, mathematical concepts derive from the cognitive activities of subjects and are highly influenced by the body structure. This article reports some examples of teaching experiments based on body-related metaphors. Some of them are carried out by means of technological devices. A call for legitimacy in school mathematics is made, both for an embodied cognition perspective and for a related use of technology.

Consistencies and inconsistencies in students' solutions to algebraic ‘single-value’ inequalities

This paper describes students’ solutions to a commonly taught and not commonly taught inequality. The findings showed students’ difficulties. Participants implicitly and explicitly exhibited two intuitive beliefs: inequalities must result in inequalities and solving inequalities and equations are the same process. Following the analysis of students’ written solutions, individual interviews were conducted that gave a better insight into their reasoning and provided some ideas for teaching. The concluding section of the paper offers relevant educational implications.

Participation in Mathematics Problem-Solving Through Gestures and Narration

On the one hand, recent results in neuroscience and communication bring the role of multimodal resources in cognitive and communicative processes to the fore. On the other hand, Bruner highlights the different role of narrative and logical thinking in human understanding. Before this background, we investigate the teaching and learning processes when children are introduced to the mathematical meanings by the use of narrative context and multimodality. We focus on a narratively-based problem-solving activity in the first year of primary school. We analyse the teacher-students multimodal interaction and discuss the potential and limits of what we call the “semiotic game” between teacher and students. The importance of the teacher being conscious of the multimodal aspects of teaching and learning mathematics, and of the complexity of narratively-based contexts comes to the fore.