Tomas Højgaard Jensen

What’s all the Fuss about Competencies?

This paper deals with applying a description of a set of mathematical competencies with the aim of developing mathematics education in general and in particular the work with mathematical modelling. Hence it offers a presentation of the general idea of working with mathematical competencies as well as an analysis of some potentials of putting this idea into educational practice. Three challenges form the basis of the analysis: The fight against syllabusitis, the dilemma of teaching directed autonomy and the description of progress in mathematical modelling competency.

The influence of the trematode Microphallus claviformis on two congeneric intermediate host species (Corophium): infection characteristics and host survival

In a laboratory experiment the survival of two amphipod species Corophium volutator and C. arenarium was differentially affected by the digenetic trematode Microphallus claviformis, the former suffering from parasite induced mortality. No clear species specific parasite preference was observed, but there was a difference between the two frequency distributions of parasite number per host, indicating a preference for the competitively superior C. volutator. In both species the parasite metapopulation was overdispersed, but to the highest degree in C. volutator. Formation of a penetration cyst on the Corophium cuticle preceeds the penetration of the M. claviformis cercariae, a common feature of microphallid digeneans, but not earlier reported from this species. Dead individuals of both species carried significantly more penetration cysts than the live ones which suggests that massive invasion of cercariae during a short period of time is the cause of death of Corophium, rather than crude parasite intensity. The potential for M. claviformis to act as a structuring agent in communities of Corophium species is discussed.

Parasites on an intertidal Corophium-bed: factors determining the phenology of microphallid trematodes in the intermediate host populations of the mud-snail Hydrobia ulvae and the amphipod Corophium volutator

The phenology of microphallid trematodes within their intermediate host populations has been studied on an intertidal mud flat. The parasites use the mud snail Hydrobia ulvae and the infaunal amphipod Corophium volutator as first and secondary intermediate host, respectively. Migratory shorebirds act as final hosts. Our results show a general trend of decline in the density of infected intermediate hosts during both spring and autumn, which could mainly be ascribed to shorebird predation. During summer the density of both infected snails and infected amphipods increased considerably, with a culmination in June within the snail population (1000 infected m−2) and in August within the amphipod population (40 000 infected m−2). This time lag in parasite occurrence could be related to (1) the development time of larval trematodes within the snails, (2) higher ambient temperatures in late summer increasing parasite transmission between snails and amphipods during this period, and (3) a general increase in the Corophium population during late summer. From samples collected between 1990 and 1995 it is shown that microphallid trematodes occasionally may give rise to mass mortality in the amphipod population. The prerequisites for such an event are a high parasite prevalence within the first intermediate host population and unusually high ambient temperatures, facilitating parasite transmission to the secondary intermediate host, C. volutator.

Assessing Mathematical Modelling Competency

Abstract Focusing on the concept of competence in mathematics education has many analytical implications. Multidimensionality is a necessary, but challenging, approach and in this chapter I address the need to work with at least three dimensions to make a valid assessment of someones possession of competence. This is demonstrated in regard to mathematical modelling competency, before the presentation of two challenges of bringing this multidimensional approach into educational practice. The two challenges are: The conflict with simple ranking as an educational goal and the conflict with the dominant focus on technical levels in mathematics education.

Classroom Activities and the Teacher

In this section we discuss a broad range of classroom activities, and of teaching style, that are required to produce the benefits that modeling can provide to the student learning mathematics. We discuss support for teachers and the shortage of good modeling tasks that need to be developed into effective curriculum materials.

The effect of Sacculina carcini infections on the fouling, burying behaviour and condition of the shore crab, Carcinus maenas

Abstract Crabs infected by rhizocephalans usually do not moult. Because moulting is the ultimate defence against fouling epibionts, infected as opposed to uninfected crabs can be expected to harbour a diversity of hard-bottom organisms on their cuticula. Here we provide unequivocal evidence that this is the case in the Carcinus maenas–Sacculina carcini association. In a Danish sample of shore crabs, 75% of sacculinized individuals harboured macroscopic epibionts, whereas only 29% of the uninfected crabs were colonized. The mean numbers of fouling barnacles and serpulid tubeworms per individual were 7.7 and 47.3 for uninfected and infected crabs, respectively, corresponding to coverage of the cuticula by 0.7 and 5.4%. Infected crabs were 12% lower in tissue dry weight than uninfected individuals, which may be a factor causing the moult of sacculinized crabs to be postponed. Finally, a laboratory experiment suggested that infected crabs are less likely to bury than uninfected specimens. Because burying is an important fouling defence, such a parasite-induced behavioural change will favour the colonization by epibionts. It is argued that rhizocephalans infecting crabs from soft-bottom communities may indirectly affect the structure of the free-living benthic community by adding hard-bottom species that otherwise would be absent.