In this short “exploration” chapter we expand the logic of knowledge developed in the previous chapter to include multiple agents and show how this expanded framework can be applied to gain insight into multi-agent settings, using the three hats puzzle as a running example. We define mutual knowledge and common knowledge and explore the importance and intriguing logical properties of the latter—in particular, how it breaks the link between consistency and satisfiability.

This chapter focusses on how insights from Vygotsky’s work on child and adolescent development can be employed to create a relational pedagogy that nurtures the agency of students as learners, enabling them to be creative makers of their and their communities’ futures. These insights are augmented by more recent contributions to his legacy. Consequently, the role of motive orientation, imagination and agency in taking forward learners’ trajectories is discussed in relation to playworlds in early education settings, makerspaces in schools, the careful use of moral imagining in creating new futures for disengaged adolescents and responsive relational teaching in mainstream schooling. The four approaches all employ pedagogies which aim at the unfolding of student agency and which can be explained by the concepts: relational expertise, common knowledge and relational agency. The need for school systems to create environments where teachers can support student agency is recognised.

The concept of ‘agency’ demands theorization that captures the dynamic (in-motion) and collective nature (motive orientation) of practice. This chapter follows Edwards’ conceptualisation of relational agency and Stetsenko’s critique of grand narratives of agency, viewing agency as central to relational and transformative practice. Methodologically, the chapter argues in favour of researching incomplete practices in their making or formation rather than complete, fossilised, best practice examples. Data from the initial teacher education programme and teacher sharing meetings show how motive orientation for transformative and responsive professional action takes shape among teachers. It is argued that agentic action is historical and located in the collective system of practice. The findings of the study also put more weight behind arguments that understanding agentic action demands more interrogation of the ‘why’ and ‘where to’ questions of practice; that is, unpacking the ‘motion’ and ‘motive orientation’ of the practice.

Chapter 1 introduces the pattern of /str/-retraction and then lays the theoretical groundworkfor the variationist approach to this sound change. The chapter first defines language variation and change and then provides an overview of research paradigms in interspeaker and intraspeaker variation. These approaches are completed with a section on meaning in language.

This chapter serves the purpose of introducing readers both to the paradigms and theoretical expectations in language change research as well as providing the foundation for the types and the nature of language-external variables that will later find their way into the methods and the statistical models developed.

In this concluding chapter, we give a brief overview of the key themes in the book, emphasizing the importance of care in the relational pedagogy we have been discussing. We argue that practitioners should take children seriously by seeking their perspectives and identifying what matters for them while building common knowledge with them and working relationally to help take forward their social situations of development. But our primary purpose here is to look forward and consider the implications of the subtle skilled work we are advocating for practitioners. Care alone is insufficient. Practitioners who work with children and families need knowledge of child and adolescent development; subject matter knowledge in schools, and for other caring professionals their core professional knowledge, such as legal responsibilities for social workers; and knowledge of pedagogy. The professional interactions with children, families and other practitioners in a relational pedagogy are reciprocal, involving ongoing mutual engagement, where power differences are played down, and professional agency is crucial. Much therefore depends on how institutional leaders mediate government policies: Creating and supporting agentic responsive practitioners is a leadership responsibility. Questions of values therefore crucially underpin the ideas shared in this book.

The cultural-historical concepts: relational expertise, common knowledge and relational agency are introduced as central to the work of practitioners who offer a caring (care-full) relational approach to supporting the learning and development of others. Drawing on examples from the field, we examine how the concepts can explain interprofessional collaborations and the prevention of social exclusion, which may frequently include involving parents or carers in focusing on a difficult situation for a child. We consequently discuss and illustrate the concepts in professionals’ work with parents or carers, which aims at mutual support for a child’s social situation of development during transitions. We demonstrate how three concepts can explain how practitioners negotiate their way up a system to find additional support for a child who is in a situation of concern. Our final example is their use in an instrument that assesses the collaborative maturity of teams or networks. The use of the three relational concepts in pedagogy is detailed in Chapter 7.

A reading of the literature on cognitive hierarchies leaves the impression that a subject’s type is predetermined before she comes into the lab so that the distribution of types is exogenous and immutable across games. In this chapter we view the choice of a person’s cognitive level as endogenous and explain it by focusing on subject’s ’expectations about the cognitive levels endogenously chosen by others. We run a set of experiments using the two-thirds guessing game where subjects receive public advice offered by a set of advisors. We discover that certain types of public advice, those that are commonly interpreted as meaningful, are capable of shifting the distribution of observed cognitive types, indicating that the distribution is endogenous.

When new generations arrive in the world, they look around and many times remark about what a lousy job their predecessors (parents) have done. The world we leave our children we hope is better than the one we inherited, but that is many times not the case. The question then arises of how, after we have made a mess of things, we can rectify the situation. The answer is to teach our children to do better. Leave them advice that basically says “don’t do as we did, but do as we say or advise you to do”. This chapter investigates how easy this is to do. The central question is how to break out of unsatisfactory equilibria when they occur. What we find is that intergenerational advice can be beneficial in such situations but only if the advice offered is common knowledge. More precisely, it is hard to act in a risky strategic situation (like the one we place our subjects in) if you know that your opponents have been given advice as to what to do but you do not know what that advice is. In such situations, if a safe action exists, it is probably best to choose it unless you are sure that everyone else has been instructed to act responsibly and you expect them to follow that advice. It is at this juncture that common knowledge of advice matters and this is what we investigate in this chapter.

In this chapter we start by defining an intergenerational game and its equilibria. We then discuss conventions of behavior, their relationship to intergenerational-game equilibria, and what it takes to make such conventions stable. This is followed by describing the relationship between our use of the term “social learning” and what standard economic theory interprets it to mean. At the end of the chapter we discuss two other types of games, dynastic games (Anderlini, Gerardi, and Laguno, 2008) and overlapping generations games (Kandori, 1992), which also have generational structures.

The well-ordered society, according to John Rawls, is one that is regulated by principles of justice and in which everyone accepts these principles. One understanding of publicity takes this latter requirement a step further. According to Rawls, not only must everyone in the well-ordered society accept the same theory of justice, but publicity demands that everyone know that everyone else accepts this theory. Citizens’ beliefs about morality and justice must be transparent to one another. I examine this understanding of publicity in the current chapter. Why insist on such a requirement? I argue that the main reason has to do with social unity. If social unity in a diverse liberal order is to be achieved, then we must know what our fellow citizens believe about justice. The problem is that generating the knowledge required by this understanding of publicity is riddled with difficulties. I propose some mechanisms that might be capable of getting the job done. These mechanisms are, however, deeply imperfect.

The pattern of social role interaction studied in Chapter 3 is an instance of a special kind of norm: a coordination norm. Seeing the pattern as a coordination norm links it to the large body work on such norms in game theory, philosophy, sociology, economics, and political science. The exchange of information in social role interactions is governed by a special kind of coordination norm: an informational norm. Coordination norms – and informational norms in particular – require that the parties to the norm have common knowledge that they will conform to it. When common knowledge collapses (as it may under the onslaught of surveillance), coordination under the norm becomes impossible. People may still coordinate their actions to realized shared goals, but it is significantly more difficult to do so.

People who resist surveillance object to it and try to prevent it. Pervasive surveillance undermines coordination under informational norms. It attacks coordination at a vulnerable point – its reliance on common knowledge. When common knowledge collapses, so does common-knowledge-facilitated coordination. History attests that coordination under informational norms can collapse across the board. The 1950–1990 East German Stasi is a case in point. The Stasi is a convenient reference point that makes current surveillance practices stand out in sharp relief. Resistance is problematic. People generally have a poor understanding of security issues, and even if one mounts a credible defense, a sufficiently skilled adversary can breach it. The rearguard action of preventing surveillance contributes little to the maintenance and creation of informational norms.

Interactions in social roles typically involve the exchange of information. Those exchanges create coordination problems. A coordination problem is a situation in which each person wants to participate in a group action but only if others also participate. The relevant group action in social-role-mediated exchanges of information puts conditions on the flow and use of information. It is easy to solve such coordination problems when it is common knowledge that parties will all conform to the conditions. People’s presentation of themselves in social roles create such common knowledge that they will conform to standards of thought and behavior associated with those roles. We offer six examples of how common knowledge solves the coordination problems that typify social role interaction.