Priyantha Wijayatunga
Prasanta S. Bandyopadhyay
Stephen Woodcock- 1Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University, Umeå, Sweden
- 2Department of History and Philosophy, College of Letters and Science, Montana State University, Bozeman, MT, United States
- 3Faculty of Science, School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, NSW, Australia
Editorial on the Research Topic
Probability and its paradoxes for critical thinking
Critical thinking can be conceptualized as the process of striving for successful solutions to problems presented in their natural context (Bailin et al., 1999; Davies, 2015). Many higher education institutions around the world have included critical thinking among their objectives (Bali, 2015; Zahavi and Friedman, 2019; Cruz et al., 2021). Generally, the tasks that can be used to develop critical thinking skills include defining arguments, evaluating reliability of sources, identifying fallacies and assumptions, using inductive and deductive logic, synthesizing information and making inferences. In this Research Topic, we show that solving probability paradoxes and puzzles can be used for enhancing crictical thinking in science, technology, engineering and mathematics (STEM) fields. It may involve many tasks that can be used for developing critical thinking in one's mind. This Research Topic draws on a variety of perspectives and case studies from higher education institutions around the world.
In their paper “Meta-Critical thinking, paradox, and probabilities”, historian-cum-philosopher of science, Brittan and Taper argue that there is a great need to think critically about critical thinking, which they call “meta critical thinking” mainly due to a lack of clarity and agreement among researchers on what is required or involved in it. They take a close look at act of distinction-making, and concept of evidence in this regard. They show that when it comes to solving paradoxes the main aspect should be to think critically and creatively about inferences/conclusions through making distinctions and reflections. They provide three ways to unravel paradoxes; finding fallacies of premise, fallacies of argument, and making (new) distinctions (in comparison to old ones, if any). Since the third is the most fruitful way, as they argue, a sufficient account on “the discipline of distinction-making” is provided. They emphasize using two statistical inference paradigms of Bayesian and evidential statistics that provide significant perspectives to issues, such as what counts as “evidence,” and how to quantify uncertainty in a given model. The authors provide their analyses for well-known probability/statistical paradoxes of lottery (Kyburg, 1961; Sober, 1993), old evidence (Glymour, 1980), and Humphrey's paradox (Humphreys, 1985, 2004) in their attempt show how critical thinking can be used in solving them.
In the published literature, most papers on paradoxes focus on a single paradox and then explain it, e.g., Bandyoapdhyay et al. (2011) and Wijayatunga (2014). In their paper, “A toolbox to demystify probabilistic and statistical paradoxes,” two mathematicians, Kelter et al., teamed with a philosopher, Susanne Spies to change this status quo regarding the paradox literature by providing a toolbox that can be seen as a guideline for the novice to isolate why a problem which a reader may encounter might appear paradoxical and, if so, how to resolve this. The toolbox contains analyzing tools such as causal reasoning, experimental design, Bayesian analysis and probabilistic modeling and is intended for handling paradoxes with a general framework under which many paradoxes could be brought in for their resolutions. Keeping this goal in mind, they revisit several well-known paradoxes, e.g., Simpson's paradox (Simpson, 1951), Bertrand's paradox (Shackel, 2007), and the two-envelope paradox (McGrew et al., 1997). They do this by identifying the class of scenarios where paradoxes arise and suggest ways on how to make choices in apparently contradictory situations. Though not exhaustive, the toolbox provides a roadmap for teachers to choose appropriate problems and help students to find the right method of addressing them.
In their paper titled “Conceptualizations and instructional strategies on critical thinking in higher education: A systematic review of systematic reviews,” Andreucci-Annunziata et al. present results of a thorough systematic review, selecting quantitative and qualitative empirical studies on the promotion and development of critical thinking in higher education. They aim at answering two points. The first aim is to define what the common definition of critical thinking is. In fact, they conclude that there is no clear agreement among researchers and practitioners (Larsson, 2017), but find that the definition given in Delphi Project (Facione, 1990) is still valid. The second aim of the paper is to examine what the most common teaching strategies of critical thinking are. Again, they find that there is no clear agreement on the best ways, hinting that it can be contextual and discipline-dependent. Their conclusion is that, conceptually, critical thinking is related to both a disposition (a set of basic, predetermining affective propensities toward life in general and toward specific thinking situations) and some skills that are a higher order cognitive process. They emphasize that both dispositions and skills can be trained and enhanced. They have selected five reviews whose characteristics such as number of papers reviewed, type of the study, article selection method, etc. are given.
In their paper “How do Chinese undergraduates understand critical thinking? A phenomenographic approach” two educational scientists, Zhao and Liu show that there are limited studies done on critical thinking from the learner's perspective and, argue that better insights into how undergraduates understand critical thinking are important if we are to improve their critical thinking. Therefore, they undertake a study with Chinese undergraduates of different backgrounds with the overarching question of what the conceptions of critical thinking held by Chinese undergraduates are. To answer this, the authors employ a phenomenographic approach on student essays, an empirical research method aiming to study qualitatively different ways in which people perceive, understand, and experience various phenomena. They find that students conceptualize critical thinking as three types of skills and as a disposition that is the extent to which an individual is inclined or willing to perform a given thinking skill. Furthermore, they show that it can be a combination of these main two categories with varying proportions in given practical situation. The three skills in the first category are query and reflection of irrationality of things, objective and comprehensive understanding of things, and independent thinking with innovation while disposition is willingness and attitude.
Author contributions
PW: Conceptualization, Investigation, Methodology, Project administration, Writing – original draft, Writing – review & editing, Validation. PB: Conceptualization, Investigation, Methodology, Writing – original draft, Writing – review & editing. SW: Conceptualization, Investigation, Methodology, Writing – original draft, Writing – review & editing.
Funding
The author(s) declare financial support was received for the research, authorship, and/or publication of this article. PB's research was partially supported by the National Science Foundations under the grant DMR# 1906383.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.
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References
Bailin, S., Case, R., Coombs, J. R., and Daniels, L. B. (1999). Conceptualizing critical thinking. J. Curr. Stud. 31, 285–302. doi: 10.1080/002202799183133
Bali, M. (2015). “Critical thinking through a multicultural lens: Cultural challenges of teaching critical thinking,” in The Palgrave Handbook of Critical Thinking in Higher Education, eds M. Davies and R. Barnett (Berlin: Springer), 317–334.
Bandyoapdhyay, P. S., Nelson, D., Greenwood, M., Brittan, G., and Berwald, J. (2011). The logic of Simpson's paradox. Synthese 181, 185–208. doi: 10.1007/s11229-010-9797-0
Cruz, G., Payan-Carreira, R., Dominguez, C., Silva, H., and Morais, F. (2021). What critical thinking skills and dispositions do new graduates need for professional life? Views from Portuguese employers in different fields. High. Educ. Res. Dev. 40, 721–737. doi: 10.1080/07294360.2020.1785401
Davies, M. (2015). A Model of Critical Thinking in Higher Education. Higher Education: A Handbook of Theory and Research 30. Lausanne: Springer.
Facione, P.A. (1990). Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction. Millibrae, CA: The California Academic Press.
Glymour, C. (1980). Why I am not a Bayesian, in Theory and Evidence. Princeton, NJ: Princeton University Press, 63–93.
Humphreys, P. (1985). Why propensities cannot be probabilities. Philos. Rev. 94, 557–570. doi: 10.2307/2185246
Humphreys, P. (2004). Some considerations on conditional chance. Br. J. Philos. Sci. 55, 667–680. doi: 10.1093/bjps/55.4.667
Kyburg, H. (1961). Probability and the Logic of Rational Belief . Middletown, CT: Wesleyan University Press.
Larsson, K. (2017). Understanding and teaching critical thinking—a new approach. Int. J. Educ. Res. 84, 32–42. doi: 10.1016/j.ijer.2017.05.004
McGrew, T. J., Shier, D., and Silverstein, H. S. (1997). The two-envelope paradox resolved. Analysis 57, 28–33. doi: 10.1093/analys/57.1.28
Shackel, N. (2007). Bertrand's paradox and the principle of indifference. Philos. Sci. 74, 150–175. doi: 10.1086/519028
Simpson, E. H. (1951). The interpretation of interaction in contingency tables. J. Royal Stat. Soc. 13, 238–241. doi: 10.1111/j.2517-6161.1951.tb00088.x
Sober, E. (1993). Epistemology for empiricists. Midwest Stud. Philos. 18, 39–61. doi: 10.1111/j.1475-4975.1993.tb00256.x
Keywords: critical thinking, probability paradoxes and puzzles, STEM students, education, solving
Citation: Wijayatunga P, Bandyopadhyay PS and Woodcock S (2024) Editorial: Probability and its paradoxes for critical thinking. Front. Educ. 9:1474013. doi: 10.3389/feduc.2024.1474013
Received: 31 July 2024; Accepted: 14 August 2024;
Published: 28 August 2024.
Edited and reviewed by: Lianghuo Fan, University of Macau, China
Copyright © 2024 Wijayatunga, Bandyopadhyay and Woodcock. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Priyantha Wijayatunga, priyantha.wijayatunga@umu.se