{"title":"Kolmogorov, stochastics in Bulgaria, and probabilistic problems with unexpected solutions","authors":"Jordan M. Stoyanov","doi":"10.55630/mem.2024.53.180-197","DOIUrl":"https://doi.org/10.55630/mem.2024.53.180-197","url":null,"abstract":"In this talk, I am going to share with the readers my memories of personal meetings with Andrey Nikolaevich Kolmogorov (1903–1987), the content of our conversations, and the fruitful consequences. The reader is familiar with, or could read, the timely prepared recent comprehensive paper [34], presented by N.M. Yanev at the 52nd Spring Conference of the UBM. Included here are several new details about Andrey Nikolaevich and the great influence of the Moscow Probability School on the development of Stochastics in Bulgaria. I have used MathSciNet and introduced the ‘Kolmogorov number’, a ‘collaboration distance’ between a mathematician and Kolmogorov, with a focus on Bulgarian stochasticians. I am writing about Kolmogorov’s approach to doing mathematics in general and the role of counterexamples. Discussed are two specific probabilistic problems which, according to him, are with most unusual solutions, ‘Skitovich-Darmois theorem’ and ‘Plackett problem’. Several related short stories and not well-known facts are presented.","PeriodicalId":517751,"journal":{"name":"Mathematics and Education in Mathematics","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140391215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simulation study on the offspring mean estimators in discrete time branching processes with migration","authors":"Tsvetomira A. Zlatkova, Vesela Stoimenova","doi":"10.55630/mem.2024.53.099-106","DOIUrl":"https://doi.org/10.55630/mem.2024.53.099-106","url":null,"abstract":"In the present work we consider two widely used definitions of a branching process with migration, related to the controlled branching processes framework, classical and multiple. We simulate the two processes with equal offspring and migration characteristics and estimate the offspring mean via the weighted conditional least squares estimators based on two sampling schemes – on the generation sizes only and the generation sizes and the migration components. We propose a robust modification of the second estimator in the case when several trajectories of the process are observed.","PeriodicalId":517751,"journal":{"name":"Mathematics and Education in Mathematics","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140391218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Embedded assessment throughout the problem-based learning – a path to authentic learning experiences","authors":"Borislava Kirilova","doi":"10.55630/mem.2024.53.109-116","DOIUrl":"https://doi.org/10.55630/mem.2024.53.109-116","url":null,"abstract":"This article examines the benefits and challenges associated with Problem-Based Learning (PBL) as a teaching and assessment tool, a constructivist approach that promotes a more pragmatic and student-centered mode of assessment. A tangible illustration of the proposed assessment tool is presented. The study aims to analyze different aspects of mathematical competence in line with the European Commission Framework for Lifelong Learning, such as critical thinking, practical application in authentic problems, and more effective knowledge acquisition. Data were collected through direct classroom observations, open-ended questionnaires, surveys, and personal interviews. The methodology was applied to a sample of 60 students from American College of Sofia (ACS) who participated in project work instead of conventional testing. The results of the study revealed that assessing students’ progress through problem-based tasks not only enhances the development of students’ mathematical competencies compared to traditional methods, but also fosters lifelong learning skills.However, this approach requires a more significant time commitment compared to tra- ditional testing.","PeriodicalId":517751,"journal":{"name":"Mathematics and Education in Mathematics","volume":" 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140391088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}