What is mathematics teaching? How do we improve mathematics teaching? Why do we want to improve mathematics teaching? What do we understand by improvement? Brown poses these questions at the beginning of the preface to this, his tenth book. These are big questions which set the tone for the book, without promising any final resolutions. Rather, it invites the reader to consider new ways of looking and offers opportunities to reconsider assumptions that may constrain our thinking. Brown’s main intellectual influence over his career and in this book, are the psychoanalytic theories of Jacques Lacan. We were not familiar with this theoretical approach. In our recent work, we have made use of the work of Michel Foucault (e.g. 2007; 2014) to take a post-structural perspective on issues such as assessment and inclusion in mathematics education, but since Brown identifies his intended audience for the book as the mathematics educators that he has encountered over the years, we feel well positioned to share our thoughts and reflections on his work.