Math empowerment: a multidisciplinary example to engage primary school students in learning mathematics

This paper describes an educational project conducted in a primary school in Italy (Scuola Primaria Alessandro Manzoni at Mulazzano, near to Milan). The school requested our collaboration to help improve upon the results achieved on the National Tests for Mathematics, in which students, aged 7, registered performances lower than the national average the past year. From January to June, 2016, we supported teachers, providing them with information, tools and methods to increase their pupils’ curiosity and passion for mathematics. Mixing our different experiences and competences (instructional design and gamification, information technologies and psychology) we have tried to provide a broader spectrum of parameters, tools and keys to understand how to achieve an inclusive approach that is ‘personalised’ to each student. This collaboration with teachers and students allowed us to draw interesting observations about learning styles, pointing out the negative impact that standardized processes and instruments can have on the self‐esteem and, consequently, on student performance. The goal of this programme was to find the right learning levers to intrigue and excite students in mathematical concepts and their applications. Our hypothesis is that, by considering the learning of mathematics as a continuous process, in which students develop freely through their own experiments, observations, involvement and curiosity, students can achieve improved results on the National Tests (INVALSI). This paper includes results of a survey conducted by children ‐’About Me and Mathematics‘

A symmetry-adapted numerical scheme for SDEs

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the symmetry properties of the equation is introduced. Our algorithmic procedure is applied to the family of general linear SDEs for which two theoretical estimates of the numerical forward error are established.Comment: A numerical example adde

Effect of Lactobacillus rhamnosus HN001 and Bifidobacterium longum BB536 on the healthy gut microbiota composition at phyla and species level: a preliminary study

AIM: To evaluate the ability of Lactobacillus rhamnosus HN001 and Bifidobacterium longum BB536 to colonize the intestinal environment of healthy subjects and modify the gut microbiota composition. METHODS: Twenty healthy Italian volunteers, eight males and twelve females, participated in the study. Ten subjects took a sachet containing 4 × 109 colony-forming units (CFU) of Bifidobacterium longum BB536 and 109 CFU of Lactobacillus rhamnosus HN001, 30 min before breakfast (pre-prandial administration), while ten subjects took a sachet of probiotic product 30 min after breakfast (post-prandial administration). The ability of Lactobacillus rhamnosus HN001 and Bifidobacterium longum BB536 to colonize human gut microbiota was assessed by means of quantitative real-time PCR, while changes in gut microbiota composition were detected by using Ion Torrent Personal Genome Machine. RESULTS: Immediately after 1-mo of probiotic administration, B. longum BB536 and L. rhamnosus HN001 load was increased in the majority of subjects in both pre-prandial and post-prandial groups. This increase was found also 1 mo after the end of probiotic oral intake in both groups, if compared to samples collected before probiotic consumption. At phyla level a significant decrease in Firmicutes abundance was detected immediately after 1-mo of B. longum BB536 and L. rhamnosus HN001 oral intake. This reduction persisted up to 1 mo after the end of probiotic oral intake together with a significant decrease of Proteobacteria abundance if compared to samples collected before probiotic administration. Whereas, at species level, a higher abundance of Blautia producta, Blautia wexlerae and Haemophilus ducrey was observed, together with a reduction of Holdemania filiformis, Escherichia vulneris, Gemmiger formicilis and Streptococcus sinensis abundance. In addition, during follow-up period we observed a further reduction in Escherichia vulneris and Gemmiger formicilis, together with a decrease in Roseburia faecis and Ruminococcus gnavus abundance. Conversely, the abundance of Akkermansia muciniphila was increased if compared to samples collected at the beginning of the experimental time course. CONCLUSION: B. longum BB536 and L. rhamnosus HN001 showed the ability to modulate the gut microbiota composition, leading to a significant reduction of potentially harmful bacteria and an increase of beneficial ones. Further studies are needed to better understand the specific mechanisms involved in gut microbiota modulation