DIGITAL SUPPORT OF STUDENTS’ JOINT ACTIONS IN INTRODUCTION TO THE CONCEPT’S ORIGIN: THE CASE OF PROPORTIONALITY

Abstract

Our primary school module with the digital support “Inks” was designed following V.V. Davydov’s idea on the assembling sets context as crucial for number concept formation. Making-sets task and the mixture problem scaffold the initial steps towards proportional reasoning, which is known to be diffi cult for students. The learning situation revolves around purposeful transformations of the inks shade towards the one desired, with a variety of tasks’ conditions: restrictions on the available amount of water and inks, some ready-made mixtures provided, etc. The substantial feature of our instruction was the organization of joint work through distribution of the operations on paint components. The necessity of some preliminary coordination between partners is posed by the real-life restrictions: once water and inks have been mixed, they cannot be separated back. The computer simulation adheres to this “rule” and makes students refer to the special modeling space and plan their operations on water and inks beforehand using tokens. The divergence of results, predicted by students through tokens placement, and the real color shade, obtained in computer simulation, sets the learning task and emphasizes the problem of coordination between partners’ actions within the modeling space. As students start to rely on the portion-by-portion counting, they succeed on the fi rst try: the stain of their new paint, prepared with the different amounts of components, merges with the sample mixture.  second-graders from an urban school (– years old) participated in the experimental teaching series, the video-taped classroom discussions, computer logs and written works were analyzed in order to assess students’ conceptual thinking development. Students’ constant success in tasks and the development of their modeling means functionality proved the computer support, which we have designed, to be relevant in several aspects: problematization and feedback, enabling simultaneous partners’ work, providing substantial tasks variations