The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The current study was conducted with the goal of helping to address the research gap of improving preservice teachers' pedagogical knowledge about probability by investigating how preservice teachers explored concepts of probability during aleatoric music composition, as well as their contemplation process during follow-up reflections focused on…

A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using "induction", "polynomial identities" nor "generating functions", and will give a proof of the "Vandermonde…

Probability education has fast become a contested area, with curriculum authorities in some countries recently suspending its introduction until the post-primary years. In other countries, children as young as 7 years are introduced to informal probability concepts. These recent international shifts in practice have contributed to a paucity of…

While 'flipped' classrooms have been heralded as a valuable tool for student learning, little is known about the process by which students learn from the out-of-class resources. This study investigates 12 undergraduate students' sense-making activities while watching videos about topics in introductory statistics. Analysis of interview data…

This article shows a generalization of Galileo's "passe-dix" game. The game was born following one of Galileo's [G. Galileo, "Sopra le Scoperte dei Dadi" (Galileo, Opere, Firenze, Barbera, Vol. 8). Translated by E.H. Thorne, 1898, pp. 591-594] explanations on a paradox that occurred in the experiment of tossing three fair "six-sided" dice.…

The identification of talented students accurately at an early age and the adaptation of the education provided to the students depending on their abilities are of great importance for the future of the countries. In this regard, this study aims to develop a mathematical ability test for the identification of the mathematical abilities of students…

The purpose of this study is to define teacher views about the difficulties in learning and teaching middle school statistics subjects. To serve this aim, a number of interviews were conducted with 10 middle school maths teachers in 2011-2012 school year in the province of Trabzon. Of the qualitative descriptive research methods, the…

Since 1986, Marilyn Vos Savant, who is listed in the "Guinness Book of World Records Hall of Fame" for the highest IQ, has had a weekly column that is published in "Parade Magazine." In this column, she answers readers' questions on a wide variety of subjects including mathematics and particularly probability. Many of the mathematically oriented…