The transfer dilemma

Abstract In this paper we provide an overview of research on transfer, highlighting its main tenets. Then we look at interviews of two fifth grade students learning about mathematical concepts regarding operations on positive and negative quantities. We attempt to focus on how their learning is influenced by their prior knowledge and experience. We take the position that transfer is a theory of learning and we attempt to show that it cannot provide a solid foundation for explaining such examples of learning

A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end

It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computer-based task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (‘swap’, ‘switch’) and partitional (‘split’, ‘separate’) statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance

Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Sex Pheromone Evolution Is Associated with Differential Regulation of the Same Desaturase Gene in Two Genera of Leafroller Moths

Chemical signals are prevalent in sexual communication systems. Mate recognition has been extensively studied within the Lepidoptera, where the production and recognition of species-specific sex pheromone signals are typically the defining character. While the specific blend of compounds that makes up the sex pheromones of many species has been characterized, the molecular mechanisms underpinning the evolution of pheromone-based mate recognition systems remain largely unknown. We have focused on two sets of sibling species within the leafroller moth genera Ctenopseustis and Planotortrix that have rapidly evolved the use of distinct sex pheromone blends. The compounds within these blends differ almost exclusively in the relative position of double bonds that are introduced by desaturase enzymes. Of the six desaturase orthologs isolated from all four species, functional analyses in yeast and gene expression in pheromone glands implicate three in pheromone biosynthesis, two Δ9-desaturases, and a Δ10-desaturase, while the remaining three desaturases include a Δ6-desaturase, a terminal desaturase, and a non-functional desaturase. Comparative quantitative real-time PCR reveals that the Δ10-desaturase is differentially expressed in the pheromone glands of the two sets of sibling species, consistent with differences in the pheromone blend in both species pairs. In the pheromone glands of species that utilize (Z)-8-tetradecenyl acetate as sex pheromone component (Ctenopseustis obliquana and Planotortrix octo), the expression levels of the Δ10-desaturase are significantly higher than in the pheromone glands of their respective sibling species (C. herana and P. excessana). Our results demonstrate that interspecific sex pheromone differences are associated with differential regulation of the same desaturase gene in two genera of moths. We suggest that differential gene regulation among members of a multigene family may be an important mechanism of molecular innovation in sex pheromone evolution and speciation