Dragging maintaining symmetry: can it generate the concept of inclusivity as well as a family of shapes?

This article describes a project using Design Based Research methodology to ascertain whether a pedagogical task based on a dynamic figure designed in a Dynamic Geometry Software (DGS) program could be instrumental in developing students’ geometrical reasoning. A dragging strategy which I have named ‘Dragging Maintaining Symmetry’ (DMS) was shown to be important for the making of mathematical meanings in the context of Dynamic Geometry. In particular, it encouraged students’ development of the concept of inclusive relations between shapes generated from the dynamic figure, especially the rhombus as a special case of the kites. This development was not automatic and in addition to their work with the dynamic figure the students were shown an animation of the figure under DMS. Watching the animation allowed the students to attend to the continuous nature of the changing figure and proved to be the catalyst for moving their reasoning towards perceiving inclusive relations between the rhombus and kite

A revised age for the Kawakawa/Oruanui tephra, a key marker for the Last Glacial Maximum in New Zealand

The Kawakawa/Oruanui tephra (KOT) is a key chronostratigraphic marker in terrestrial and marine deposits of the New Zealand (NZ) sector of the southwest Pacific. Erupted early during the Last Glacial Maximum (LGM), the wide distribution of the KOT enables inter-regional alignment of proxy records and facilitates comparison between NZ climatic variations and those from well-dated records elsewhere. We present 22 new radiocarbon ages for the KOT from sites and materials considered optimal for dating, and apply Bayesian statistical methods via OxCal4.1.7 that incorporate stratigraphic information to develop a new age probability model for KOT. The revised calibrated age, ±2 standard deviations, for the eruption of the KOT is 25,360 ± 160 cal yr BP. The age revision provides a basis for refining marine reservoir ages for the LGM in the southwest Pacific. © 2012

The role of neurexins and neuroligins in autism

Autistic spectrum disorder (ASD) is a common, chronic psychiatric disorder for which the current generation of therapeutics are limited in their success at alleviating the neurobehaviors. While it is well established that both genetic and environmental factors contribute to the disorder, there is a lack of understanding about how ASD alters multiple domains of brain function. Identifying genes that are associated with ASD, and then relating how these genetic alterations affect brain structure and function is important to furthering our ability to design treatment and prevention strategies. Recent genome screening using copy number variant (CNV) analysis has identified deletions and duplications within the neurexin and neuroligin genes in patients with ASDs, highlighting their potential importance in ASD research. Neurexins and neuroligins are synaptic cell adhesion molecules and are found at the presynapse and postsynapse, respectively, of both excitatory and inhibitory cells. Neuroligins and leucine-rich repeat transmembranes bind to neurexins and convey a role in synaptic function and maintenance. However, little is known about how alterations within the genes encoding these proteins disrupt biological processes. Here we discuss the functional role of neurexins and neuroligins, the genetic evidence for their involvement in ASD and studies with transgenic mice to elucidate the consequences of these mutations