Abstract
The aim of the book is to provide a deep synthesis of the research field "didactics of mathematics at all levels of tertiary education", as it appears through two INDRUM conferences organised in 2016 and 2018. Chapter 8 deals with Abstract and Linear Algebra. Our goal is to account for “burning issues” within University Mathematics Education research on these mathematical domains, with its related methodological challenges, and to point out current and new avenues for research. We also aim at cross-analysing results and methodologies, thus answering the question: in which respect do these studies complement each other or contrast from each other? What are the main results, open questions, debates among researchers, elements of convergence/divergence within these studies? We thus decided to organize our synthesis according to three groups of papers (merely according to the topic), and for each group of papers to present a cross-analysis of these papers according to main themes that crystallise those burning issues (in terms of epistemological content, methodological issues, results, in fact the main objects of research that seemed to us appropriate for a vivid, illuminating and contrasted account of our data). We end this chapter by summarising what appeared to us as major advances in research on Abstract and Linear Algebra teaching and learning through the work of the INDRUM network as well as the further avenues for research that have been brought to light.