Books by Manfred Borovcnik
Statistics and probability are fascinating fields, tightly interwoven with the context of the pro... more Statistics and probability are fascinating fields, tightly interwoven with the context of the problems which have to be modelled. The authors demonstrate how investigations and experiments provide promising teaching strategies to help high-school students acquire statistical and probabilistic literacy. In the first chapter the authors put into practice the following educational principles, reflecting their views of how these subjects should be taught: a focus on the most relevant ideas and postpone extensions to later stages; illustrating the complementary/dual nature of statistical and probabilistic reasoning; utilising the potential of technology and show its limits; and reflecting on the different levels of formalisation to meet the wide variety of students' previous knowledge, abilities, and learning types. The remaining chapters deal with exploratory data analysis, modelling information by probabilities, exploring and modelling association, and with sampling and inference. Throughout the book, a modelling view of the concepts guides the presentation. In each chapter, the development of a cluster of fundamental ideas is centred around a statistical study or a real-world problem that leads to statistical questions requiring data in order to be answered. The concepts developed are designed to lead to meaningful solutions rather than remain abstract entities. For each cluster of ideas, the authors review the relevant research on misconceptions and synthesise the results of research in order to support teaching of statistics and probability in high school. What makes this book unique is its rich source of worked-through tasks and its focus on the interrelations between teaching and empirical research on understanding statistics and probability.
Papers by Manfred Borovcnik
Revista Sergipana de Matemática e Educação Matemática
We focus on the ways in which we can use a frequentist interpretation of probability to develop s... more We focus on the ways in which we can use a frequentist interpretation of probability to develop suitable methods for statistical inference. The discussion about the controversy in the foundations reveals that a frequentist conception is highly prone to dispute, as a justification of it fails from a rational perspective when the explication of probability integrates statistical inference. We give an overview on the dispute and the crucial examples that highlight the deficiencies of a purely frequentist position towards probability. The concept of probability emerges from a mixture of meanings. A shift in connotation of probability towards a biased frequentist meaning decreases the scope of probability or the quality of applications. Probability is a complementary concept, which falls apart if we reduce it to one view. This gives rise to investigate approaches towards teaching from a wider perspective on the range of meanings of probability apart from frequentist aspects. Empirical st...
Statistics Education and Outreach IASE Satellite Conference
Risk is a major factor in health, with a strong focus on minimising risk wherever possible. The m... more Risk is a major factor in health, with a strong focus on minimising risk wherever possible. The mathematical starting point is probability. Reliable or relevant data is often missing or hard to get. Moreover, the results of studies are all too easily interpreted wrongly – even by medical experts. Usually it is seen as useful to have more information in making decisions. As we show below this is not always true; we will use the exemplar of breast cancer and screening as an illustration throughout this paper to explain circumstances where there is ‘more information and more uncertainty’ following Knight and type 2 errors. We identify the different stakeholders and parts of their internal criteria that form their ‘rationality’, which may well be idiosyncratic. The intention is to pave the way for a ‘shared’ decision which is best for individuals and for society simultaneously. Statistics educators will find an important field of research and teaching.
Statistics Education Research Journal, Nov 30, 2016
Proceedings of the First Scientific Meeting of the IASE Satellite Conference
Statistics Education Research Journal, May 31, 2016
Statistics Education Research Journal, Nov 30, 2018
We address problems that arise in teaching statistics in non-statistical degree courses in statis... more We address problems that arise in teaching statistics in non-statistical degree courses in statistics. The typical student reveals basic difficulties in the understanding of the key concepts. This paper describes experiences with the “project method”, motivating students with real data from the future profession. The project method generated collaborative learning and social interaction between groups by embedding learning statistics in the context of applied problems in the form of projects. Godino’s semiotic ontological framework provides elements of his model of the instructional process and a didactic trajectory in his first exploratory phase of execution, as well as exposing the linguistic, situational, actuative, conceptual, propositional, and argumentative elements that are relevant in understanding a particular topic. Due to its relative success in our classes and a theoretical analysis, we propose the project method for teaching statistics, especially for hybrid courses where face-to-face is combined with virtual parts of knowledge acquisition.
Educação Matemática Pesquisa. Revista do Programa de Estudos Pós-Graduados em Educação Matemática. ISSN 1983-3156, 2016
Avances de investigación en educación matemática, Nov 6, 2012
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Books by Manfred Borovcnik
Papers by Manfred Borovcnik