# Probability and its Paradoxes for Critical Thinking

Manuscript Submission Deadline 30 April 2023
Manuscript Extension Submission Deadline 30 May 2023

Students of many scientific disciplines often find difficulties in defining concepts, making and proving claims, etc., that affect their education negatively. If they do not enhance their critical, analytical and logical thinking and reasoning abilities then they may come to paradoxical, contradictory and ...

Students of many scientific disciplines often find difficulties in defining concepts, making and proving claims, etc., that affect their education negatively. If they do not enhance their critical, analytical and logical thinking and reasoning abilities then they may come to paradoxical, contradictory and inconsistent conclusions easily. Even though current educational practice has not fully utilized it, study of probability and its paradoxes can enhance students’ logical, analytical and critical thinking abilities substantially. Performing probability calculations in diverse contexts, especially, resolving the probability paradoxes can be a key for improvements. This is because, the probability puzzles can only be resolved through a blend of technical, critical, analytical and logical approaches. Therefore, the students can enhance their abilities in them through resolving these puzzles. A short list of paradoxes to be considered are Simpson’s, Lord’s and exchange paradoxes, and Monty Hall puzzle. Their applications in different contexts enhance students’ understanding of world.

Probability calculations and analyses of related paradoxes are about possibilities and quantifying their chances with appropriate interpretations. When these numbers are interpreted their contexts, constraints and conditions should be identified. Precise definitions of concepts and, critical and logical reasoning are essential. It is useful to differentiate causal reasoning from associational inference. Even though statistical correlation is familiar to many, it is not often understood as a special case of general dependence. These aspects have created controversies among the researchers, teachers, students, etc. of mathematics and related disciplines. Even though there is an extensive literature on probability paradoxes, it is not attractive to the students as far as enhancement of their critical thinking ability is concern. It lacks the required pedagogical quality. However, the state-of-the-art research on probability and statistical puzzles can be useful to enhance critical, analytical, etc. abilities of the students of STEM substantially, if they are presented pedagogically. We aim to achieve it here. Also, we want to show how to bridge the gap between the research and the education through the use of conceptual and philosophical approaches, and empirical studies with new insights. Discussions on inclusion of paradoxes in the mathematics curricular is of interest.

This Research Topic welcomes articles with high pedagogical quality on any probability/statistical paradox or puzzle, ideally providing real world applications. Some of the paradoxes that are of interest are Simpson’s, Monte Hall, exchange, lottery, and alike. Ideally, contributions should discuss the history and, evolution and the state-of-the-art solutions with sufficient critical evaluation and review. An important point to address can be why it is hard to understand these paradoxes. Also, articles should focus on technical, logical, critical and analytical aspects of the solutions. Another important aspect to explore is on bridging the gap between the research and the education through the discussion on how to bring such state-of-the-art research into the probability, statistics and mathematics education. Contribution papers can also be conceptual or philosophical on current and significant issues about the probability and statistics, or/and STEM education. Empirical studies on the topic with new insights are of interest.

Keywords: calculation, interpretation, explanation, logical, reasoning

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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