Negotiating textual talk : conversation analysis, pedagogy, and the organisation of online asynchronous discourse

This paper uses Conversation Analysis to investigate the ways in which participants in an online asynchronous postgraduate reading group managed and negotiated their contributions within the discussion. Using the conversation analytic concerns with sequential organisation, adjacency pairs and topicality, this article shows the analytic insights that this perspective can bring to the examination of written asynchronous discourse. The paper shows that in the section of the discussion analysed here, the discourse displayed remarkable similarities to the ways in which face-to-face conversation has been seen to operate in terms of the organisation of conversational turns, the application of specific interactional rights, the lineal development of topics of conversation, and the structural use of question-answer turn pairs. The paper concludes by showing how this form of analysis can relate to the formation of reflexive pedagogy in which course design can be created to take account of such findings. It shows how a detailed understanding of how pedagogy is played out in interaction is fundamental for reflecting on the relationship between pedagogic aims and educational practice

Strolling through Paradise

With each of the usual tree forcings I (e.g., I = Sacks forcing S, Laver forcing L, Miller forcing M, Mathias forcing R, etc.) we associate a sigma--ideal i^0 on the reals as follows: A \in i^0 iff for all T \in I there is S \leq T (i.e. S is stronger than T or, equivalently, S is a subtree of T) such that A \cap [S] = \emptyset, where [S] denotes the set of branches through S. So, s^0 is the ideal of Marczewski null sets, r^0 is the ideal of Ramsey null sets (nowhere Ramsey sets) etc. We show (in ZFC) that whenever i^0, j^0 are two such ideals, then i^0 \sem j^0 \neq \emptyset. E.g., for I=S and J=R this gives a Marczewski null set which is not Ramsey, extending earlier partial results by Aniszczyk, Frankiewicz, Plewik, Brown and Corazza and answering a question of the latter. In case I=M and J=L this gives a Miller null set which is not Laver null; this answers a question addressed by Spinas. We also investigate the question which pairs of the ideals considered are orthogonal and which are not. Furthermore we include Mycielski's ideal P_2 in our discussion

A Special Class of Almost Disjoint Families

The collection of branches (maximal linearly ordered sets of nodes) of the tree ${}^{<\omega}\omega$ (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal -- for example, any level of the tree is almost disjoint from all of the branches. How many sets must be added to the family of branches to make it maximal? This question leads to a series of definitions and results: a set of nodes is {\it off-branch} if it is almost disjoint from every branch in the tree; an {\it off-branch family} is an almost disjoint family of off-branch sets; {\frak o}=\min\{|{\Cal O}|: {\Cal O} is a maximal off-branch family$\}$. Results concerning $\frak o$ include: (in ZFC) ${\frak a}\leq{\frak o}$, and (consistent with ZFC) $\frak o$ is not equal to any of the standard small cardinal invariants $\frak b$, $\frak a$, $\frak d$, or ${\frak c}=2^\omega$. Most of these consistency results use standard forcing notions -- for example, $Con({\frak b}={\frak a}<{\frak o}={\frak d}={\frak c})$ comes from starting with a model of $ZFC+CH$ and adding $\omega_2$-many Cohen reals. Many interesting open questions remain, though -- for example, $Con({\frak o}<{\frak d})$