Students' informal inference about the binomial distribution of "Bunny hops": A dialogic perspective

This is the final version of the article. Available from IASE / ISI via the DOI in this recordThe study explores the development of 11-year-old students’ informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic ideas. Findings from the study suggest that dialogic talk facilitated students’ reasoning as it was supported by the use of simulation tools available in the software. It appears that the interaction of using simulation tools, talk between students, and teacher prompts helps students develop their understanding of probabilistic ideas in the context of making inferences about the distribution of random bunny hops.This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme. We would also like to acknowledge the generous support of the school, teachers and students who worked with us in this study

Investigation of type-pi 2 geomagnetic pulsations at magnetoconjugate points

Type pi2 geomagnetic pulsations and Alfven wave resonance on night side of magnetospher

The analysis of simultaneous solubility of naphthalene in alcohols and hydrocarbons

The present study considers simultaneous solubility of naphthalene in alcohols and hydrocarbons , together with critically selected literature data. The prediction of simultaneous solubilities of naphthalene in alcohols and hydrocarbons is of great importance in refineries and petrochemical plants in the design, control and optimization of products and processes

The challenges of urban ageing:Making cities age-friendly in Europe

Urban ageing is an emerging domain that deals with the population of older people living in cities. The ageing of society is a positive yet challenging phenomenon, as population ageing and urbanisation are the culmination of successful human development. One could argue whether the city environment is an ideal place for people to grow old and live at an old age compared to rural areas. This viewpoint article explores and describes the challenges that are encountered when making cities age-friendly in Europe. Such challenges include the creation of inclusive neighbourhoods and the implementation of technology for ageing-in-place. Examples from projects in two age-friendly cities in The Netherlands (The Hague) and Poland (Cracow) are shown to illustrate the potential of making cities more tuned to the needs of older people and identify important challenges for the next couple of years. Overall, the global ageing of urban populations calls for more age-friendly approaches to be implemented in our cities. It is a challenge to prepare for these developments in such a way that both current and future generations of older people can benefit from age-friendly strategies

Pre-service mathematics teachers' use of probability models in making informal inferences about a chance game

This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers’ use of probability models for a chance game, where the sum of two dice matters in winning the game. We report on an interview with a group of three pre-service teachers as they engaged in predicting and conducting experiments and computer simulations as an attempt to develop a winning strategy. This paper focuses on how the participants came to use the theoretical model of the sum of two dice as they tried to coordinate the combinatorial analysis and the use of data as evidence in their predictions

Characteristic and Minimal Polynomials In Problems

In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomial p(x) over F of least degree such that p(A)=0. Any other polynomial q with q(A)=0 is a (polynomial) multiple of p. The following three statements are equivalent: ??F is a root of p(x), ? is a root of the characteristic polynomial of A, ? is an eigenvalue of A. The multiplicity of a root ? of p(x) is the geometric multiplicity of ? and is the size of the largest Jordan block corresponding to ? and the dimension of the corresponding Eigen space. The minimal polynomial is not always the same as the characteristic polynomial