Clockface polygons and the collective joy of making mathematics together

The social and embodied nature at the heart of all knowing, doing, and learning contrasts with the images that pervade our cultural imagination of mathematical work as a solitary, cognitive activity. This article describes a playful experiment by the author group to do collective mathematics, in an extended effort to construct alternative images, instincts, and practices for ourselves. We present a pair of episodes of mathematical exploration that come from our work together and that we have seen as an early success, intimating features of a stabilized collective mathematics that we hope to continue pursuing. Coming from a single investigation of our group, these episodes offer narrative accounts of the parallel inquiries of subgroups, working to define and characterize a mathematical space we had collectively identified, and then to formulate and investigate conjectures about that space. The narratives are followed by a discussion of themes within and across them and reflections on their significance as a step toward self-organized collective mathematics

Relationship Between the Extent of Chromosomal Losses and the Pattern of CpG Methylation in Gastric Carcinomas

The extent of unilateral chromosomal losses and the presence of microsatellite instability (MSI) have been classified into high-risk (high- and baseline-level loss) and low-risk (low-level loss and MSI) stem-line genotypes in gastric carcinomas. A unilateral genome-dosage reduction might stimulate compensation mechanism, which maintains the genomic dosage via CpG hypomethylation. A total of 120 tumor sites from 40 gastric carcinomas were examined by chromosomal loss analysis using 40 microsatellite markers on 8 chromosomes and methylation analysis in the 13 CpG (island/non-island) regions near the 10 genes using the bisulfite-modified DNAs. The high-level-loss tumor (four or more losses) showed a tendency toward unmethylation in the Maspin, CAGE, MAGE-A2 and RABGEF1 genes, and the other microsatellite-genotype (three or fewer losses and MSI) toward methylation in the p16, hMLH1, RASSF1A, and Cyclin D2 genes (p<0.05). The non-island CpGs of the p16 and hMLH1 genes were hypomethylated in the high-level-loss and hypermethylated in the non-high-level-loss sites (p<0.05). Consequently, hypomethylation changes were related to a high-level loss, whereas the hypermethylation changes were accompanied by a baseline-level loss, a low-level loss, or a MSI. This indicates that hypomethylation compensates the chromosomal losses in the process of tumor progression

Classroom Unit: Explorando los impactos de inundaciones en nuestro barrio / Exploring the impacts of flooding in our neighborhood

Slide deck of activities.This unit was designed in the Winter-Spring of 2022 for an after school coding club run by a long-time PiLa-CS partner teacher who taught Science bilingually at a middle school in Upper Manhattan. The club was held weekly, sometimes twice weekly. Student attendance ranged from 2-7 students, they attended intermittently around other after school commitments. Many students had experiences with strong storms from living in New York City and/or the Caribbean. The teacher asked students if they’d want to create Scratch projects about the issue of flooding, and students expressed interest. Students were all bilinguals (Spanish/English), though none who attended were designated “English Language Learners” at the time. The unit unfolded fluidly, in response to student and teacher interests. Essential Questions: How can digital maps and stories help us address problems caused by flooding? How do communities come together in times of need? Goals: Students will create Scratch projects that illustrate / explain the experience of a person in the area during this Summer’s flooding. The project should share some problem caused by flooding and/or a potential solution to flooding.Sponsored by the National Science Foundation under NSF grant CNS-1738645 and DRL-1837446. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation