What is the place of social theory in mathematics education research, and what is it for? This special issue of "Educational Studies in Mathematics" offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main…

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis…

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of "Educational Studies in Mathematics" on "Semiotic perspectives in mathematics education" (Saenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1-2), 2006). Among these issues are conceptualizations of…

This review synthesizes research on relationships between performance on mathematics learning tasks to determine whether Piagetian tasks make useful readiness measures. Results indicated such tasks do not make useful measures, and suggested success on these is not necessary for many mathematics tasks. (MP)

Different types of hierarchies in the learning of mathematics and criteria by which they might be judged are examined. Current works on mathematical learning hierarchies are illustrated and in particular the work of the mathematics team of the research project "Concepts in Secondary School Mathematics and Science" is examined. (MP)

Varying approaches to mathematics were raised in a Philosophy of Mathematics course. Students were asked which foundational schools they preferred and these preferences were compared with scores on hemispheric tests. The results indicate that preferences may be related to the brain's hemispheres. (MNS)

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

A review of literature provides evidence that certain personality characteristics are associated with a liking or ability in mathematics. More research is recommended to yield a more coherent picture of the situation. (MP)

This study attempts to explain certain difficulties which ninth grade students face in tackling geometrical "problems to prove," by relating them to general and to specific rigidity and cognitive style variables. The results confirm the conceptual analysis of Geometric Rigidity (GR). (MP)

The possible effects and importance of student ability in language use and mathematical reasoning are reviewed. Data from the National University of Lesotho on incoming science students indicated that the relationships between language proficiency and mathematics achievement are quite complex. (MP)

The insufficiency of the standard psychological concepts of instrumental and relational understanding to interpret learning in an educational context is indicated. (MP)

A review of work related to the topological primacy thesis and a critique of some aspects of it are presented. On the basis of the psychological research, it is concluded that topological concepts ought to be taught. (MP)

A test of logic was given to 862 students in their first, second, and fourth years in Lesotho secondary schools. Results supported the contention that while difficulty in understanding English contributes to difficulty with the logical grammar necessary for mathematics, there are factors other than second language interference to consider. (MP)

Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)

Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)