Instrumental Orchestration of the Use of Programming Technology for Authentic Mathematics Investigation Projects

Abstract

AbstractThis chapter focuses on teaching the use of programming technology for pure or applied mathematics investigation projects to university mathematics students and future mathematics teachers. We investigate how the theoretical frame of instrumental orchestration contributes to our understanding of this teaching. Our case study is situated within the implementation of three undergraduate mathematics courses offered at Brock University (Canada) over the past 20 years, whose main activities include investigation projects. The study examines an instructor’s actions and decision-making in relation to potential students’ schemes that might have been promoted, implicitly or explicitly, by the instructor. The analysis also focuses on two student schemes, namely, the scheme of articulating a mathematics concept within the programming language and the scheme of validating the programmed mathematics. The case study led us to develop an orchestration and genesis alignment (OGA) model that associates different elements of the instructor’s orchestration with the intended student development of specific schemes. Our findings highlight the instructors’ dual role as policy makers and as teachers responsible for orchestrating students’ instrumental geneses (i.e., their web of schemes development). Findings also highlight the integration of projects as a key element of the exploitation mode.KeywordsInstrumental approachInstrumental orchestrationSchemesProgrammingUniversity mathematicsInvestigation projects