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Keeping in mind that ''everything said is said by an observer'' (Maturana 1987), we would like to preface our observations on the articles in this issue with some background on ourselves as observers. We met by chance in 1994 (at PME 18, the 18th conference of the International Group for the Psychology of Mathematics Education, in Lisbon) and immediately felt that there were points of connection. From 1994 to 2001, we collaborated on Vicki's ongoing research in her classroom, sharing our different perspectives on the children's mathematical activities, developing lessons, and materials together, delving deeper into areas which have puzzled us and piqued our interest, and writing about our work together (Reid 2002a, b; Reid and Zack 2009; Zack 2006; Zack and Reid 2003, 2004). Our collaboration is unusual in that we began our collaboration without having a prior connection as, for example, a professor and a graduate student, or a researcher and a research participant. From 1989 to 2001, Vicki taught full-time at the fifth-grade level (10-11 year olds) and researched the children's work in the areas of mathematics (problem solving) and literature. Her interest in their work in non-routine problem solving led her to be curious about her students' developing algebraic thinking and later to a focus on proof and argumentation, partly as a result of working with David, whose research focuses on proof. David first became involved in teacher education in 1992 while completing his doctorate. He has continued to work primarily with prospective teachers, but also with practising teachers pursuing Master's studies, ever since. His focus gradually shifted from secondary school level to elementary school level, partly as a result of what he learned through working with Vicki. We came to work on this special issue as a result of our own collaboration between an elementary school teacher and a university teacher educator, in which we have had many

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