Designing a programming-based approach for modelling scientific phenomena

We describe an iteratively designed sequence of activities involving the modelling of 1- dimensional collisions between moving objects based on programming in ToonTalk. Students aged 13-14 in two settings (London and Cyprus) investigated a number of collision situations, classified into six classes based on the relative velocities and masses of the colliding objects. We describe iterations of the system in which students engaged in a repeating cycle of activity for each collision class: prediction of object behaviour from given collision conditions, observation of a relevant video clip, building a model to represent the phenomena, testing, validating and refining their model, and publishing it ? together with comments ? on our web-based collaboration system, WebReports. Students were encouraged to consider the limitations of their current model, with the aim that they would eventually appreciate the benefit of constructing a general model that would work for all collision classes, rather than a different model for each class. We describe how our intention to engage students with the underlying concepts of conservation, closed systems and system states was instantiated in the activity design, and how the modelling activities afforded an alternative representational framework to traditional algebraic description

Environmental policies to cope with novel disturbance regimes–steps to address a world scientists’ warning to humanity

ABL acknowledges postdoctoral funding from the Alexander von Humboldt Foundation and grants RTI2018-096187-J-100 from FEDER/ Ministerio de Ciencia, Innovacion y Universidades and LRB20/1002 from the British Ecological Society.Alexander von Humboldt Foundation RTI2018-096187-J-100FEDER/ Ministerio de Ciencia, Innovacion y Universidades LRB20/1002British Ecological Societ

Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

Invasive Vegetation Affects Amphibian Skin Microbiota and Body Condition

Invasive plants are major drivers of habitat modification and the scale of their impact is increasing globally as anthropogenic activities facilitate their spread. In California, an invasive plant genus of great concern is Eucalyptus. Eucalyptus leaves can alter soil chemistry and negatively affect underground macro- and microbial communities. Amphibians serve as excellent models to evaluate the effect of Eucalyptus invasion on ground-dwelling species as they predate on soil arthropods and incorporate soil microbes into their microbiotas. The skin microbiota is particularly important to amphibian health, suggesting that invasive plant species could ultimately affect amphibian populations. To investigate the potential for invasive vegetation to induce changes in microbial communities, we sampled microbial communities in the soil and on the skin of local amphibians. Specifically, we compared Batrachoseps attenuatus skin microbiomes in both Eucalyptus globulus (Myrtaceae) and native Quercus agriflolia (Fagaceae) dominated forests in the San Francisco Bay Area. We determined whether changes in microbial diversity and composition in both soil and Batrachoseps attenuatus skin were associated with dominant vegetation type. To evaluate animal health across vegetation types, we compared Batrachoseps attenuatus body condition and the presence/absence of the amphibian skin pathogen Batrachochytrium dendrobatidis. We found that Eucalyptus invasion had no measurable effect on soil microbial community diversity and a relatively small effect (compared to the effect of site identity) on community structure in the microhabitats sampled. In contrast, our results show that Batrachoseps attenuatus skin microbiota diversity was greater in Quercus dominated habitats. One amplicon sequence variant identified in the family Chlamydiaceae was observed in higher relative abundance among salamanders sampled in Eucalyptus dominated habitats. We also observed that Batrachoseps attenuatus body condition was higher in Quercus dominated habitats. Incidence of Batrachochytrium dendrobatidis across all individuals was very low (only one Batrachochytrium dendrobatidis positive individual). The effect on body condition demonstrates that although Eucalyptus may not always decrease amphibian abundance or diversity, it can potentially have cryptic negative effects. Our findings prompt further work to determine the mechanisms that lead to changes in the health and microbiome of native species post-plant invasion

Bridging knowing and proving in mathematics An essay from a didactical perspective

Text of a talk at the conference "Explanation and Proof in Mathematics: Philosophical and Educational Perspective" held in Essen in November 2006International audienceThe learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply in significant problem situations, and which is amenable to falsification and argumentation. They can validate what they claim to be true but using means generally not conforming to mathematical standards. Here, I analyze how this situation underlies the epistemological and didactical complexities of teaching mathematical proof. I show that the evolution of the learners' understanding of what counts as proof in mathematics implies an evolution of their knowing of mathematical concepts. The key didactical point is not to persuade learners to accept a new formalism but to have them understand how mathematical proof and statements are tightly related within a common framework; that is, a mathematical theory. I address this aim by modeling the learners' way of knowing in terms of a dynamic, homeostatic system. I discuss the roles of different semiotic systems, of the types of actions the learners perform and of the controls they implement in constructing or validating knowledge. Particularly with modern technological aids, this model provides a basis designing didactical situations to help learners bridge the gap between pragmatics and theory

Prioritization of fish communities with a view to conservation and restoration on a large scale European basin, the Loire (France)

The hierarchical organization of important sites for the conservation or the restoration of fish communities is a great challenge for managers, especially because of financial or time constraints. In this perspective, we developed a methodology, which is easy to implement in different locations. Based on the fish assemblage characteristics of the Loire basin (France), we created a synthetic conservation value index including the rarity, the conservation status and the species origin. The relationship between this new synthetic index and the Fish-Based Index allowed us to establish a classification protocol of the sites along the Loire including fish assemblages to be restored or conserved. Sites presenting disturbed fish assemblages, a low rarity index, few threatened species, and a high proportion of non-native species were considered as important for the restoration of fish biodiversity. These sites were found mainly in areas where the assemblages are typical of the bream zone, e.g. with a higher number of eurytopic and limnophilic species. On the contrary, important sites for conservation were defined as having an important conservation potential (high RI, a lot of threatened species, and few nonnatives fish species) and an undisturbed fish assemblage similar to the expected community if habitats are undisturbed. Important sites for conservation were found in the Loire basin’s medium reaches which host assemblages typical for the grayling and the barbell zones, e.g. with a higher number of rheophilic species. The synthetic conservation value index could be adapted and completed with other criteria according to management priorities and capacities

Optimizing Reserve Expansion For Disjunct Populations Of San Joaquin Kit Fox

Expanding habitat protection is a common strategy for species conservation. We present a model to optimize the expansion of reserves for disjunct populations of an endangered species. The objective is to maximize the expected number of surviving populations subject to budget and habitat constraints. The model accounts for benefits of reserve expansion in terms of likelihood of persistence of each population and monetary cost. Solving the model with incrementally higher budgets helps prioritize sites for expansion and produces a cost curve showing funds required for incremental increases in the objective. We applied the model to the problem of allocating funds among eight reserves for the endangered San Joaquin kit fox (Vulpes macrotis mutica) in California, USA. The priorities for reserve expansion were related to land cost and amount of already-protected habitat at each site. Western Kern and Ciervo-Panoche sites received highest priority because land costs were low and moderate amounts of already-protected habitat resulted in large reductions in extinction risk for small increments of habitat protection. The sensitivity analysis focused on the impacts of kit fox reproductive success and home range in non-native grassland sites. If grassland habitat is lower quality than brushland habitat resulting in higher annual variation in reproductive success or larger home ranges, then protecting habitat at the best grassland site (Ciervo-Panoche) is not cost–efficient relative to shrubland sites (Western Kern, Antelope Plain, Carrizo Plain). Finally, results suggested that lowest priority should be given to three relatively high-cost grassland sites (Camp Roberts, Contra Costa, and Western Madera) because protecting habitat at those sites would be expensive and have little effect on the expected number of surviving kit fox populations

Mathematical images in advertising: constructing difference and shaping identity, in global consumer culture

Mathematics educators have long emphasised the importance of attitudes and feelings towards mathematics, as crucial in motivating (or not) its learning and use, and as influenced in turn by its social images. This paper is about images of mathematics. Our search for advertisements containing such images of in UK daily newspapers, during 2006-2008, found that 4.7% of editions included a ‘mathematical’ advert, compared with 1.7% in pilot work for 1994-2003. The incidence varied across type of newspaper, being correlated with class and gender profiles of the readership. Three-quarters of advertisements were classified as containing only very simple mathematics. ‘Semiotic-discursive’ analysis of selected advertisements suggests that they draw on mathematics not to inform, but to connote qualities like precision, certainty and authority. We discuss the discourse on mathematics in advertising as ‘quasi-pedagogic’ discourse, and argue that its oversimplified forms, being empty of mathematical content, become powerful means for regulating and ‘pedagogising’ today’s global consumers