Mathematical learning difficulties subtypes classification

In early years schooling it is becoming common to propose activities that involve moving along paths, or programming robots to do so. In order to promote continuity towards the introduction of geometry in primary school, we developed a long-term teaching experiment (with 15 sessions) carried out over 4 months in a first grade classroom in northern Italy. Students were asked to program a robot to move along paths, to pretend to act as robots and to represent the sequence of commands and the resulting paths. In particular, in this teaching experiment, an overarching mathematical aim was to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we intended to foster the students’ transition from a dynamic perception of paths to seeing paths also as static wholes, boundaries of figures with sets of geometric characteristics. The students’ situated productions were collected and analysed together with the specific actions of the adults involved, aimed at fostering processes of semiotic mediation. In this paper we analyse the development of the situated texts produced by the students in relation to the pivot signs that were the beginnings of an inclusive definition of rectangles.

The technology-enhanced development of very young children’s mathematical abilities, apart from some notable exceptions, does not seem to have yet raised a lot of interest within the mathematics education community. This article focuses on the educational potential offered by certain software applications (apps) that exploit affordances of multi-touch devices for fostering preschoolers’ development of number-sense. We introduce theoretical elements derived from recent research in developmental and cognitive psychology, neuroscience, and mathematics education, that concur in defining the aspects of number sense that we will be investigating in relation to specific multi-touch interactions. Our specific research goal is to analyze the multi-touch potential of two apps for fostering preschoolers’ development of those aspects of number sense. The study is based on the analysis of children’s interactions with these apps in the context of a sequence of activities centered on the use of the iPad, carried out in a public preschool in Northern Italy. The specific issue addressed and the perspective adopted position this study at the crossroads between different research fields.

This paper focuses on students’ mathematical discourse emerging from interactions in the digital environment GeoGebra, in which one can construct virtual objects that realize mathematical signifiers and then interact with them. These virtual object realizations can becomedynamic interactive mediators(DIMs) that influence the development of the learners’ mathematical discourse. In this case study, I analyze in fine detail the discourse developed by two dyads of students in response to an unfamiliar interview question. One dyad came from a class in which GeoGebra was not part of classroom practice and included students who, according to the teacher’s evaluation, were standard-to-high achieving. The other dyad was from a generally demotivated and low-achieving class in which GeoGebra had become part of classroom practice. The analyses, focused especially on the low-achieving dyad, are guided by the question of how DIMs shaped these students’ discourse. According to the analysis, these students ended up succeeding where standard-to-high-achieving peers did not. Moreover, the detailed analysis of the ways in which the DIMs supported this dyad’s learning showed mechanisms that may be general rather than specific to this one case. This suggests that appropriate integration of DIMs into the teaching and learning of high school algebra can be beneficial for low-achieving students.