Development of probabilistic understanding in fourth grade

We analyzed the development of 4th-grade students’ understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students’ initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computersimulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students’ progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students’ final models indicated increasing levels of probabilistic understanding.

The mesenchymal-to-epithelial reverting transition is enriched in metastatic castration resistant prostate cancer and correlates with poor survival

Despite recent recognition that the epithelial-mesenchymal transition (EMT) program acts in a dynamic manner (termed Epithelial to Mesenchymal Plasticity or EMP) during carcinoma metastasis, it has largely been ignored in the discovery and development of EMT-targeted therapies. In part, this has stemmed from a lack of preclinical models that can mimic the full dynamic nature of EMP and the perception that the EMT-reverting transition [or mesenchymal-epithelial reverting transition; (MErT)] is a mere antithesis of EMT. The objective of this study was to develop the first PCa model capable of recapitulating the dynamic nature of EMP.