This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this…

To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

In this research, quotient strategies and their influence on decision-making in situations that involve the comparison of probabilities are analyzed. In order to achieve this, classical probability situations modeled with urns were designed. In each situation, two urns with simple extraction, involving or not proportional relationships, were…

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

Probabilistic thinking is a structure of thinking characterized by scenarios that allow one to explore reality. Therefore, the characteristic of probabilistic thinking is problem-oriented that will occur in a future full of uncertainty. Nevertheless, few studies examine the students' probabilistic thinking level based on the Stress Tolerance…

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical…

The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

During the last two years, the COVID-19 pandemic had a secondary effect of increased media content loaded with mathematical, often probabilistic information (and misinformation). Our exploratory study investigates the probabilistic intuitions, misconceptions, biases, and fallacies in conditional probability reasoning of mathematics teacher…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

This study focuses on pre-service teachers' experimentation with a game-modding process in a constructionist setting whilst they experimented with randomness embedded in wider socio-scientific issues that call for decision making under uncertainty. In this process, participants created 39 different game mods. Our observations of the participants…

A more motivating way of introducing students to probability theory is through real-world problems. Since heuristics play an important role in our probabilistic judgement, knowing how to avoid incorrect probabilistic reasoning, which leads to several biases, could help students to develop more critical thinking skills. In this paper, we present a…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

This paper reports on a new initiative of collaborative work between the Australian Curriculum, Assessment and Reporting Authority (ACARA) and Cambridge University as part of the 2020-21 review of the Australian Curriculum: Mathematics Foundation -- Year 10. The ACARA mathematics curriculum development team worked with the Cambridge Mathematics…

The St. Petersburg game is a probabilistic thought experiment. It describes a game which seems to have infinite expected value, but which no reasonable person could be expected to pay much to play. Previous empirical work has centered around trying to find the most likely payoff that would result from playing the game n times. In this paper, we…