This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense…

The goal the article is to answer the questions: "Why the probability theory and its applications should be studied?" and "What is the attitude of students to the study of probabilistic branches of mathematics?" The values of probabilistic branches of mathematics (stochastics) are revealed on the analysis of scientific…

This article shows how the exciting new field of Machine Learning can be effectively introduced in a standard calculus sequence, once the students have been introduced to functions of several variables. This is an opportunity to engage students in a discussion of an application of calculus to an emerging field that the students encounter in their…

Various solving strategies in probability of events could complicate the students in choosing the best strategy in problem solutions. This research was carried out to identify the favourite solving strategies used by college students to solve probability and event problems. As a preliminary of a case study, only three students were selected as…

Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game "Settlers of Catan" develop a stronger grasp of basic probability concepts…

Statistical education is a very important area of research because it builds knowledge and promotes innovation in the courses of this discipline. Based on the advances in this area, changes in the content and approaches of the courses at all educational levels have been promoted in several countries. In this study, we examine programs of…

Despite the importance of replication, it remains rare in the interactive learning research community. In this paper, we attempt to replicate recent quasi-experimental results suggesting that the ALEKS intelligent tutoring system is effective at improving student course outcomes in higher education (Mojarad et al., 2018). In this paper, we conduct…

The use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate…

Online software systems are extensively used to give students practice on course content, especially in mathematics and physics courses. They offer instant feedback, and several of these systems are open source or very economical compared with hiring graders for traditional paper-and-pencil-based homework (PPH). In this article, the authors…

Everyday encounters with graphical representations include a variety of graphs that superficially appear similar due to their use of bars. This article examines students' conceptions and misconceptions regarding the interpretation of variability in histograms, bar graphs, and value bar charts. A multiple choice assessment with brief written…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

In this article we study the conceptions of an American and a French group of undergraduate pre-service teachers regarding the concept of independent events. Specifically, we study the role that intuition plays in their answers, ascertain the presence of probabilistic biases, and compare the findings with previous results collected on a different…

Finding ways to enhance introductory students' understanding of probability ideas and theory is a goal of many first-year probability courses. In this article, we explore the potential of a prototype tool for Markov processes using dynamic visualizations to develop in students a deeper understanding of the equilibrium and hitting times…