Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Genome sequence of Xanthomonas fuscans subsp. fuscans strain 4834-R reveals that flagellar motility is not a general feature of xanthomonads

Abstract Background Xanthomonads are plant-associated bacteria responsible for diseases on economically important crops. Xanthomonas fuscans subsp. fuscans (Xff) is one of the causal agents of common bacterial blight of bean. In this study, the complete genome sequence of strain Xff 4834-R was determined and compared to other Xanthomonas genome sequences. Results Comparative genomics analyses revealed core characteristics shared between Xff 4834-R and other xanthomonads including chemotaxis elements, two-component systems, TonB-dependent transporters, secretion systems (from T1SS to T6SS) and multiple effectors. For instance a repertoire of 29 Type 3 Effectors (T3Es) with two Transcription Activator-Like Effectors was predicted. Mobile elements were associated with major modifications in the genome structure and gene content in comparison to other Xanthomonas genomes. Notably, a deletion of 33 kbp affects flagellum biosynthesis in Xff 4834-R. The presence of a complete flagellar cluster was assessed in a collection of more than 300 strains representing different species and pathovars of Xanthomonas. Five percent of the tested strains presented a deletion in the flagellar cluster and were non-motile. Moreover, half of the Xff strains isolated from the same epidemic than 4834-R was non-motile and this ratio was conserved in the strains colonizing the next bean seed generations. Conclusions This work describes the first genome of a Xanthomonas strain pathogenic on bean and reports the existence of non-motile xanthomonads belonging to different species and pathovars. Isolation of such Xff variants from a natural epidemic may suggest that flagellar motility is not a key function for in planta fitness.