This study focused on the significant relationship between Creative Thinking Skills and Problem-Solving Skills in Mathematics among Grade 6 pupils. The study's respondents were thirty (30) Grade 6 pupils from one of the elementary schools in the District of Sta. Ana, Pampanga. The respondents were selected using simple random sampling techniques. The study used a survey questionnaire comprising the Creative Thinking Skills Test (Pentang et al., 2022) and a researcher-made word problem-solving written test and rubrics. (...) The researchers found a high level of Creative Thinking Skills among the Grade 6 pupils, while the respondents' problem-solving skills were categorized as competent. The study revealed that the Creative Thinking Skills and Problem-Solving Skills in Mathematics of the Grade 6 pupils were very lowly correlated. Still, creative thinking and problem-solving in the applied subject are recommended to help students acquire the 21st-century skills that empower them to develop holistically and career ready. (shrink)

In the recent years, problem-solving become a central topic that discussed by educators or researchers in mathematics education. it’s not only as the ability or as a method of teaching. but also, it is a little in reviewing about the components of the support to succeed in problem-solving, such as student's belief and attitude towards mathematics, algebraic thinking skills, resources and teaching materials. In this paper, examines the algebraic thinking skills as a foundation for problem-solving, and (...) learning cycle as a breath of continuous learning. In this paper, learning cycle to be used is a modified type of 5E based on beliefs. (shrink)

The paper addresses the methodology used by the teacher-KEYWORDS: facilitator to plan P4C sessions. The classic method consists of identifying the guidelines of the dialogue from a provisional mapping of the text, but this can be supplemented or replaced by other tools‡. GrupIREF and the Filosofía Lúdica movement§ use an approach that focuses on thinking skills. The P4C session is planned from the choice of the thinking skills to be trained - or possibly the attitudes and (...) ethical values that appear in the stimulus used. This article proposes an alternative to the classical planning approach, examining the basis of the model considered and offering a practical example. ITA_Focus dell’articolo è la modalità di pianificazione delle sessioni di Philosophy for Children, P4C, da parte del docente-facilitatore. Il metodo classico consiste nell’individuazione di linee-guida del dialogo a partire da una mappatura orientativa del testo-pretesto, ma ciò può essere integrato, o sostituito da altre modalità*. Il GrupIREF e il movimento della Filosofía Lúdica† utilizzano un approccio che privilegia le abilità di pensiero. La sessione P4C viene pianificata a partire dalla scelta dell’abilità di pensiero da allenare – o eventualmente dell’atteggiamento etico e dei valori legati al pre-testo utilizzato. Il presente lavoro suggerisce un’alternativa alla progettazione classica, attraverso una disamina delle basi del modello considerato, e ne offre un esempio pratico. (shrink)

The urgent need of developing novel teaching methods in education to improve the critical thinking skills has been widely discussed by educational experts. The present study aims to investigate the effectiveness of Fermi problem solving with flipped learning techniques in teaching physics on the improvement of critical thinking skills among Emirati tenth graders. The sample of the study consists of 40 male and female secondary students from two secondary schools belonging to Abu Dhabi Department of Education (...) and Knowledge in United Arab Emirates divided into two groups; the control group consists of 20 students (10 male and 10 female) taught the physics unit by traditional methods, the experimental group consists of 20 students (10 males and 10 females) taught the physics unit by Fermi problem solving with flipped learning techniques. The quasi-experimental design was used, where the modified critical thinking skills test was prepared and administered on the two groups as a pre-test before the students start the treatment and as a post-test once they are finished. The MANCOVA and Two-Way ANCOVA tests were employed to analyze the data. The findings showed that there were statistically significant differences at (α = 0.05) in student’s critical thinking skills test (in favor of experimental group), indicating that the performance of students in treatment group was better than the control group in the post-test. This means that the Fermi problem solving with flipped learning techniques has significant effectiveness on improvement of critical thinking skills among the United Arab Emirates secondary students. Also there were no statistically significant differences between male and female students. (shrink)

Argument-mapping software abounds, and one of the reasons is that using the software has been shown to teach/promote/improve critical thinking skills. These positive results are very encouraging, but they also raise the question of whether the computer tutorial environment is producing these results, or whether learning argument mapping, even with just paper and pencil, is sufficient. Based on the results of two empirical studies, I argue that the basic skill of being able to represent an argument diagrammatically plays (...) an important role in the improvement of critical-thinking skills. While these studies do not offer a direct comparison between the two methods, it is important for anyone wishing to employ argument mapping in the classroom to know that significant results can be obtained even with the most rudimentary of tools. (shrink)

There is substantial evidence from many domains that visual representations aid various forms of cognition. We aimed to determine whether visual representations of argument structure enhanced the acquisition and development of critical thinking skills within the context of an introductory philosophy course. We found a significant effect of the use of argument diagrams, and this effect was stable even when multiple plausible correlates were controlled for. These results suggest that natural⎯and relatively minor⎯modifications to standard critical thinking courses (...) could provide substantial increases in student learning and performance. (shrink)

After determining one set of skills that we hoped our students were learning in the introductory philosophy class at Carnegie Mellon University, we performed an experiment twice over the course of two semesters to test whether they were actually learning these skills. In addition, there were four different lectures of this course in the first semester, and five in the second; in each semester students in some lectures were taught the material using argument diagrams as a tool to (...) aid understanding and critical evaluation, while the other students were taught using more traditional methods. In each lecture, the students were given a pre-test at the beginning of the semester, and a structurally identical post-test at the end. We determined that the students did develop the skills in which we were interested over the course of the semester. We also determined that the students who were taught argument diagramming gained significantly more than the students who were not. We conclude that learning how to construct argument diagrams significantly improves a student’s ability to analyze arguments. (shrink)

Expert skill in music performance involves an apparent paradox. On stage, expert musicians are required accurately to retrieve information that has been encoded over hours of practice. Yet they must also remain open to the demands of the ever-changing situational contingencies with which they are faced during performance. To further explore this apparent paradox and the way in which it is negotiated by expert musicians, this article profiles theories presented by Roger Chaffin, Hubert Dreyfus and Tony and Helga Noice. For (...) Chaffin, expert skill in music performance relies solely upon overarching mental representations, while, for Dreyfus, such representations are needed only by novices, while experts rely on a more embodied form of coping. Between Chaffin and Dreyfus sit the Noices, who argue that both overarching cognitive structures and embodied processes underlie expert skill. We then present the Applying Intelligence to the Reflexes (AIR) approach?a differently nuanced model of expert skill aligned with the integrative spirit of the Noices? research. The AIR approach suggests that musicians negotiate the apparent paradox of expert skill via a mindedness that allows flexibility of attention during music performance. We offer data from recent doctoral research conducted by the first author of this article to demonstrate at a practical level the usefulness of the AIR approach when attempting to understand the complexities of expert skill in music performance. (shrink)

Although expert consensus states that critical thinking (CT) is essential to enquiry, it doesn’t necessarily follow that by practicing enquiry children are developing CT skills. Philosophy with children programmes around the world aim to develop CT dispositions and skills through a community of enquiry, and this study compared the impact of the explicit teaching of CT skills during an enquiry, to The Philosophy Foundation's philosophical enquiry (PhiE) method alone (which had no explicit teaching of CT (...) class='Hi'>skills). Philosophy with children is also said to improve metacognitive (MC) skills but there is little research into this claim. Following observable problems with ensuring genuine metacognition was happening in PhiE sessions - on a reasonably strong understanding of what metacognition is – a method has been developed and trialed in this study to bring together, in mutual support, the development of critical thinking and metacognitive skills. Based on the work of Peter Worley and Ellen Fridland (KCL)The Philosophy Foundation ran an experimental study with King's College London in Autumn 2017 and Autumn 2018 to compare the impact of teaching CT skills and MC skills against classes that just have philosophical enquiry. The approach developed and used for the study employs the explicit teaching of some CT and MC skills within the context of a philosophical enquiry (as opposed to stand-alone teaching of these skills) and yields some positive findings both qualitative and quantitative. Both studies took place over one term (12 weeks) and a control and intervention group were used in each study. This report focuses on the second year of the study, with 220 ten and eleven-year-old children involved in eight classes across three state schools in South East London. Although there were limitations to the study the results indicate that the explicit teaching of these skills during a philosophical enquiry can help children use CT and MC skills more successfully than philosophical enquiry alone. (shrink)

I discuss three features of Matt Stichter’s new book The Skillfulness of Virtue. The thesis of the book is that virtue is best conceptualized as a type of skill, and the chapters of the book explore the implications of this thesis for our understanding of moral development, social psychology and comparisons of virtuous agents with agents who exhibit familiar types of non-moral expertise. The features of the book that I examine are (1) Stichter’s rejection of an ability to articulate reasons (...) for acting as a necessary condition for acting virtuously; (2) his comparison of expertise and virtue with respect to apt motivations and practical wisdom; and (3) whether his thesis invites a comparison of virtue and familiar non-moral expertise that is ultimately unfavourable to the adoption of virtue ethics as a normative ethical theory. I present no devastating objections, for I agree with most of what Stichter presents in the book. Rather, my aim is to raise points of clarification that might further the stimulating discussion of virtues and skills that Stichter’s book already provides. (shrink)

In summaries of “best practices” for pedagogy, one typically encounters enthusiastic advocacy for metacognition. Some researchers assert that the body of evidence supplied by decades of education studies indicates a clear pedagogical imperative: that if one wants their students to learn well, one must implement teaching practices that cultivate students’ metacognitive skills. -/- In this dissertation, I counter that education research does not impose such a mandate upon instructors. We lack sufficient and reliable evidence from studies that use the (...) appropriate research design to validate the efficacy of metacognitive skill-building interventions (not just evaluate their relationship to learning outcomes). I argue that improved academic outcomes following these interventions aren’t necessarily mediated by increased metacognitive skills; rather, enhanced student performance can be accounted for by other factors that accompany metacognitive training, particularly the explicit provision of domain-specific knowledge. -/- On the way to this conclusion, I elaborate some complications and controversies surrounding “metacognition.” This is a sprawling and nebulous construct, which makes generalizations about its pedagogical value dubious from the outset. Moreover, it is unclear the extent to which the end goal of metacognitive skill-building (cognitive self-mastery, involving knowledge of and control over our own minds) is even possible, given our mental architecture; some cognitive scientists allege that we are subject to phenomenological illusions which make this seem more achievable than it actually is. -/- I also attempt to provide an account of how metacognitive skill-building could receive glowing endorsements from educators and education researchers, even though its conceptual and empirical underpinnings are flimsy. The error theory I offer identifies two major factors that may foster belief in the efficacy of metacognitive training: goalpost-shifting around the objective of such efforts, and motivated reasoning in defense of the desirable conclusion that educators can significantly reshape students’ minds and unlock their intellectual potential through simple pedagogical interventions. (shrink)

Mathematical thinking skills are very important in mathematics, both to learn math or as learning goals. Thinking skills can be seen from the description given answers in solving mathematical problems faced. Mathematical thinking skills can be seen from the types, levels, and process. Proportionally questions given to students at universities in Indonesia (semester I, III, V, and VII). These questions are a matter of description that belong to the higher-level thinking. Students choose 5 (...) of 8 given problem. Qualitatively, the answers were analyzed by descriptive to see the tendency to think mathematically used in completing the test. The results show that students tend to choose the issues relating to the calculation. They are more use cases, examples and not an example, to evaluate the conjecture and prove to belong to the numeric argumentation. Used mathematical thinking students are very personal (intelligence, interest, and experience), and the situation (problems encountered). Thus, the level of half of the students are not guaranteed and shows the level of mathematical thinking. (shrink)

This essay investigates, via the concepts of the philosophy of orientation, Annie Duke’s decision-making theory in "Thinking in Bets" and scrutinizes as to what extent one can universalize the 'orientation skill' of decision-making with regard to our everyday and professional life.

Mathematical confidence and critical thinking are essential in preparing preservice teachers. Thus, this study explored the perceived confidence and critical thinking levels in mathematics of elementary and secondary preservice teachers. A descriptive-correlational-comparative research design was employed, with a sample of 107 randomly selected preservice teachers enrolled in the Bachelor in Elementary and Secondary Education programs of a state university in West Philippines. The study used arithmetic mean, standard deviation, Spearman’s rank-order correlation, and independent samples t-test to analyze and (...) draw conclusions from the data. The findings revealed that the preservice teachers have high confidence and critical thinking skills. Their program significantly correlates with their perceived critical thinking and confidence level. Besides, the preservice teachers’ confidence levels and perceived critical thinking skills significantly correlate. Further analysis found significant confidence and critical thinking differences favoring the secondary over the elementary preservice teachers. These findings provide insights that would benefit mathematics educators in providing priority programs to enhance the preparation of future math teachers. (shrink)

In this paper, we propose a framework for fostering argumentative skills in a systematic way in Philosophy and Ethics classes. We start with a review of curricula and teaching materials from the German-speaking world to show that there is an urgent need for standards for the teaching and learning of argumentation. Against this backdrop, we present a framework for such standards that is intended to tackle these difficulties. The spiral-curricular model of argumentative competences we sketch helps teachers introduce the (...) relevant concepts and skills to students early on in their school career. The focus is on secondary schools, but the proposal can also be of use for learning and teaching in universities, especially in introductory classes. (shrink)

The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and achievement (...) test on integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

One important aim of moral philosophy courses is to help students build the skills necessary to make their own well-reasoned decisions about moral issues. This includes the skill of determining when a particular moral reason provides a good answer to a moral question or not. Helping students think critically about religious reasons like “because God says so” and “because scripture explicitly says so” can be challenging because such lessons can be misperceived as coercive or anti-religious. I describe a framework (...) for teaching about religion and moral reasons that I have found overcomes these challenges while also building generalizable skill at analyzing and evaluating moral reasons. (shrink)

The study aimed to identify Design Thinking and its use in NGOs in Gaza Strip. In order to achieve the objectives of the study and to test its hypotheses, the analytical descriptive method was used, relying on the questionnaire as a main tool for data collection. The study society was one of the decision makers in the local NGOs in the Gaza Strip. The study population reached 78 local NGOs in Gaza Strip. The overall inventory of the possible study (...) community was based mainly on the use of the SPSS in processing and analyzing the data obtained through the survey tool. Smart-PLS was also used to construct the structural equation model (SEM) Analyzing the relationship between study variables. The study found that Design Thinking mediates the relationship between the management of process design and decision making with a holistic effect. The study showed the interest of local NGOs in creating a good mental image in the local community. And the ownership of local NGOs to the expertise and technical skills required to implement the projects, and showed the adoption of local NGOs in their activities to meet the needs of the beneficiaries and their wishes, and local NGOs analyze the problem, and causes, through data relevant to the decision, based on reference data for decision-making. The main recommendations of the study are: The need for senior management in the local NGOs in Gaza Strip to adopt the methodology of design thinking because of its impact on the sustainability of the projects, design the technical feasibility study and meet the wishes of the beneficiaries. (shrink)

This book introduces readers to the many arguments and controversies concerning abortion. While it argues for ethical and legal positions on the issues, it focuses on how to think about the issues, not just what to think about them. It is an ideal resource to improve your understanding of what people think, why they think that and whether their (and your) arguments are good or bad, and why. It's ideal for classroom use, discussion groups, organizational learning, and personal reading. -/- (...) From the Preface -/- To many people, abortion is an issue for which discussions and debates are frustrating and fruitless: it seems like no progress will ever be made towards any understanding, much less resolution or even compromise. -/- Judgments like these, however, are premature because some basic techniques from critical thinking, such as carefully defining words and testing definitions, stating the full structure of arguments so each step of the reasoning can be examined, and comparing the strengths and weaknesses of different explanations can help us make progress towards these goals. -/- When emotions run high, we sometimes need to step back and use a passion for calm, cool, critical thinking. This helps us better understand the positions and arguments of people who see things differently from us, as well as our own positions and arguments. And we can use critical thinking skills help to try to figure out which positions are best, in terms of being supported by good arguments: after all, we might have much to learn from other people, sometimes that our own views should change, for the better. -/- Here we use basic critical thinking skills to argue that abortion is typically not morally wrong. We begin with less morally-controversial claims: adults, children and babies are wrong to kill and wrong to kill, fundamentally, because they, we, are conscious, aware and have feelings. We argue that since early fetuses entirely lack these characteristics, they are not inherently wrong to kill and so most abortions are not morally wrong, since most abortions are done early in pregnancy, before consciousness and feeling develop in the fetus. -/- Furthermore, since the right to life is not the right to someone else’s body, fetuses might not have the right to the pregnant woman’s body—which she has the right to—and so she has the right to not allow the fetus use of her body. This further justifies abortion, at least, until technology allows for the removal of fetuses to other wombs. Since morally permissible actions should be legal, abortions should be legal: it is an injustice to criminalizing actions that are not wrong. -/- In the course of arguing for these claims, we: 1. discuss how to best define abortion; 2. dismiss many common “question-begging” arguments that merely assume their conclusions, instead of giving genuine reasons for them; 3. refute some often-heard “everyday arguments” about abortion, on all sides; explain why the most influential philosophical arguments against abortion are unsuccessful; 4. provide some positive arguments that at least early abortions are not wrong; 5. briefly discuss the ethics and legality of later abortions, and more. -/- This essay is not a “how to win an argument” piece or a tract or any kind of apologetics. It is not designed to help anyone “win” debates: everybody “wins” on this issue when we calmly and respectfully engage arguments with care, charity, honesty and humility. This book is merely a reasoned, systematic introduction to the issues that we hope models these skills and virtues. Its discussion should not be taken as absolute “proof” of anything: much more needs to be understood and carefully discussed—always. (shrink)

This paper argues that Moore's specifist defence of critical thinking as ‘diverse modes of thought in the disciplines’, which appeared in Higher Education Research & Development, 30(3), 2011, is flawed as it entrenches relativist attitudes toward the important skill of critical thinking. The paper outlines the critical thinking debate, distinguishes between ‘top-down’, ‘bottom-up’ and ‘relativist’ approaches and locates Moore's account therein. It uses examples from one discipline-specific area, namely, the discipline of Literature, to show that the generalist (...) approach to critical thinking does not ‘leave something out’ and outlines why teaching ‘generic’ critical thinking skills is central to tertiary education, teaching and learning, and employment opportunities for students. The paper also defends the assessment of critical thinking skills. (shrink)

Two fundamentally distinct approaches to the teaching of philosophy are contrasted: On the one hand, there is the “information-oriented” approach which has dominated classrooms and which emphasizes the understanding of historically important philosophical works. On the other hand, there is the “cognitive skills” approach. The two approaches may be distinguished under the headings of ‘knowing that’ as opposed to ‘knowing how’. This paper describes and discusses four perspectives relating to the teaching of cognitive skills: (i) the discovery-oriented approach, (...) (ii) Piagetian learning cycles, (iii) protocol analysis, and (iv) conceptual therapy. The latter approach reflects the author’s interest in helping students to develop “therapeutic” skills that enable them to identify and eliminate concepts which they employ in their thinking and which are incompatible with their own presuppositional bases and are therefore self-refuting. ●●●●● -/- 2022 UPDATE: The approach of this paper has been updated and developed further in Appendix II, "Epistemological Intelligence," of the author’s 2021 book _Critique of Impure Reason: Horizons of Possibility and Meaning_. The book is available both in a printed edition (under ISBN 978-0-578-88646-6 from Barnes & Noble, Amazon, and other booksellers) and an Open Access eBook edition (available through Philpapers under the book’s title and other philosophy online archives). (shrink)

This study determined the cognitive skills achievement in mathematics of elementary pre-service teachers as a basis for improving problem-solving and critical thinking which was analyzed using Piaget's seven logical operations namely: classification, seriation, logical multiplication, compensation, ratio and proportional thinking, probability thinking, and correlational thinking. This study utilized an adopted Test on Logical Operations (TLO) and descriptive research design to describe the cognitive skills achievement and to determine the affecting factors. Overall, elementary pre-service teachers (...) performed with sufficient understanding in dealing with the TLO. However, in each logical operation, students were found to have insufficient understanding of probability thinking and correlational thinking. These insufficiencies in other logical operations were attributed to their misconceptions on some mathematical terms, misinterpretation of the problems, poor comprehension skills, poor problem-solving skills, and poor performance in mathematics in general. (shrink)

Practical wisdom is the intellectual virtue that enables a person to make reliably good decisions about how, all-things-considered, to live. As such, it is a lofty and important ideal to strive for. It is precisely this loftiness and importance that gives rise to important questions about wisdom: Can real people develop it? If so, how? What is the nature of wisdom as it manifests itself in real people? I argue that we can make headway answering these questions by modeling wisdom (...) on expert skill. Presenting the main argument for this expert skill model of wisdom is the focus of this paper. More specifically, I’ll argue that wisdom is primarily the same kind of epistemic achievement as expert decision-making skill in areas such as firefighting. Acknowledging this helps us see that, and how, real people can develop wisdom. It also helps to resolve philosophical debates about the nature of wisdom. For example, philosophers, including those who think virtue should be modeled on skills, disagree about the extent to which wise people make decisions using intuitions or principled deliberation and reflection. The expert skill model resolves this debate by showing that wisdom includes substantial intuitive and deliberative and reflective abilities. (shrink)

Effective ethics teaching and training must cultivate both the critical thinking skills and the character traits needed to deliberate effectively about ethical issues in personal and professional life. After highlighting some cognitive and motivational obstacles that stand in the way of this task, the article draws on educational research and the author's experience to demonstrate how cooperative learning techniques can be used to overcome them.

The demand in the workplace is rapidly changing brought about by the educational reforms and the emergence of disruptive technology. The changes increase the importance of employability skills and literacy that would ensure career success and degree program relevance. On this premise, a study was carried out using a scoping review to examine the existing literature that published information related to employability skills of Teacher Education graduates in the Philippines. The review covered fifteen published articles that qualified in (...) inclusion and exclusion criteria. Results revealed the top employable skills which include communication; information and communication technology; problem-solving and critical thinking; collaboration, cooperation, and teamwork; research; and leadership. This study offers these skills as a framework in the curriculum enhancement of teacher education programs. It was recommended to Teacher Education Institutions to revisit their curriculum and find out if these competencies were given considerable emphasis in instruction. The partially employable skills of graduates from teacher education programs imply the furtherance of the inquiry to confirm if these skills are employable or not. Future tracer studies may take the lens of the framework in evaluating the responsiveness of the curriculum. (shrink)

What occurs in the mind of an expert who is performing at their very best? In this paper, I survey the history of debate concerning this question. I suggest that expertise is neither solely a mastery of the automatic nor solely a mastery of intelligence in skilled action control. Experts are also capable of performing automatic actions intelligently. Following this, I argue that unconscious-thought theory (UTT) is a powerful tool in coming to understand the role of executive, intelligent action control (...) in the fluidly automatic performance of expertise. Relying on a body of empirical evidence concerning the cognitive structures and perceptual strategies employed by experts, I show that the realm of skilled action is an ideal environment within which the powers of unconscious cognitive processing can have positive effects on action. I conclude that experts rely upon unconscious thinking in the production of intelligently automatic skilled actions. (shrink)

Computation and Metacognitive skills are essential sub-skills under the domain of Critical Thinking which is a 21 st Century Skill. Having acquired these skills can greatly help students to have a better performance in the Mathematics course. The purpose of this study was to determine whether computation and metacognitive skills are significant predictors of students' performance in Mathematics. Students from four sections of the course Mathematics in the Modern World which was offered during the first (...) semester of the academic year 2018-2019 were selected as the participants of this study which was conducted at Gov. Alfonso D. Tan College, Tangub City, Misamis Occidental, Philippines. The results of this study showed that students' scores in computation and metacognitive test of skills significantly correlate with the students' performance in Mathematics in terms of Grade Point Average (GPA) and a positive direct relationship has been established. Using the Regression Analysis, the result revealed that both computation and metacognitive skills of the students were significant predictors of their performance in Mathematics. These research outcomes affirm that if students acquire these skills, they tend to perform better in Mathematics. This suggests that teachers are encouraged to be more strategic in training the students to acquire and develop computation and metacognitive skills by administering various mathematical problems that encourage students to think critically. (shrink)

Leave logic at the door and prepare to test your creative thinking skills with these 100 brand new lateral thinking puzzles. Each puzzle describes a situation which at first sounds odd or unlikely, and you have to work your way to the answer using creativity, imagination, and intuition. To cater for all ability levels, the 100 puzzles are arranged into Easy, Moderate, and Difficult categories, and a series of hints is provided for each puzzle to help you (...) along if you get stuck. As lateral thinking puzzles are fun, engaging, and make good icebreakers, they are a perennial favourite at dinner parties, break times, and social evenings. (shrink)

Plagiarism, which Indiana University’s Writing Tutorial Service defines as "using others' ideas and words without clearly acknowledging the source of that information", is often described as a major problem. However, standard definitions such as this one suggest only limited solutions to the problem: acknowledging sources or forbidding reuse. Since all scholarship involves engaging with the ideas of others and academic writing tends to reuse certain expressions, these solutions – though important – are of limited utility. This paper examines a type (...) of plagiarism to which the standard solutions do not apply: the reuse of linguistic models without sufficient attention to the logic or thoughts the texts express. We present two cases of plagiarism, from which we can see that plagiarism shows a gap between the written texts and the thoughts of the author. In order to fill the gap, one needs to know how to integrate not only the texts borrowed from others into one’s writing but also the thoughts expressed by the texts. Thus a satisfactory solution to the plagiarism problem requires not only writing skills but also logical thinking skills. (shrink)

Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional Thinking, (...) Probability Thinking and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions. (shrink)

This paper argues that general skills and the varieties of subject-specific discourse are both important for teaching, learning and practising critical thinking. The former is important because it outlines the principles of good reasoning simpliciter (what constitutes sound reasoning patterns, invalid inferences, and so on). The latter is important because it outlines how the general principles are used and deployed in the service of ‘academic tribes’. Because critical thinking skills are—in part, at least—general skills, they (...) can be applied to all disciplines and subject-matter indiscriminately. General skills can help us assess reasoning independently of the vagaries of the linguistic discourse we express arguments in. The paper looks at the debate between the ‘specifists’—those who stress the importance of critical thinking understood as a subject-specific discourse—and the ‘generalists’—those that stress the importance of critical thinking understood independently of disciplinary context. The paper suggests that the ‘debate’ between the specifists and the generalists amounts to a fallacy of the false alternative, and presents a combinatory-‘infusion’ approach to critical thinking. (shrink)

Math prospective teachers must be able to think creatively and solve problems. The study looked into preservice teachers’ creative thinking and problem-solving abilities in statistics. The investigation was guided by a correlational design in a public university in the Philippines. Stratified random sampling was used to select the 103 study participants from two teacher education programs. Through google forms, data were collected using Torrance et al. (2008)’s tests of creative thinking and researcher-made statistics problem test. The findings revealed (...) that preservice teachers have commendable creative thinking, particularly fluency, flexibility, and elaboration skills. Still, they lack problem-solving skills in statistics, specifically with central tendency, dispersion, and position measures. The correlational analysis revealed no link between creative thinking and problem-solving. Still, creative thinking and problem-solving courses are recommended to help preservice teachers develop their fundamental skills as mathematics educators. (shrink)

“Critical thinking in higher education” is a phrase that means many things to many people. It is a broad church. Does it mean a propensity for finding fault? Does it refer to an analytical method? Does it mean an ethical attitude or a disposition? Does it mean all of the above? Educating to develop critical intellectuals and the Marxist concept of critical consciousness are very different from the logician’s toolkit of finding fallacies in passages of text, or the practice (...) of identifying and distinguishing valid from invalid syllogisms. Critical thinking in higher education can also encompass debates about critical pedagogy, i.e., political critiques of the role and function of education in society, critical feminist approaches to curriculum, issues related to what has become known as critical citizenship, or any other education-related topic that uses the appellation “critical”. Equally, it can, and usually does, refer to the importance and centrality of developing general skills in reasoning—skills that we hope all graduates possess. Yet, despite more than four decades of dedicated scholarly work “critical thinking” remains as elusive as ever. As a concept, it is, as Raymond Williams has noted, a ‘most difficult one’ (Williams, 1976, p. 74). (shrink)

An increasingly popular solution to the anti-scientific climate rising on social media platforms has been the appeal to more critical thinking from the user's side. In this paper, we zoom in on the ideal of critical thinking and unpack it in order to see, specifically, whether it can provide enough epistemic agency so that users endowed with it can break free from enclosed communities on social media (so called epistemic bubbles). We criticise some assumptions embedded in the ideal (...) of critical thinking online and, instead, we propose that a better way to understand the virtuous behaviour at hand is as critical engagement, namely a mutual cultivation of critical skills among the members of an epistemic bubble. This mutual cultivation allows members within an epistemic bubble (in contrast, as we will show, with the authority-based models of epistemic echo chambers) to become more autonomous critical thinkers by cultivating self-trust. We use the model of relational autonomy as well as resources from work on epistemic self-trust and epistemic interdependence to develop an explanatory framework, which in turn may ground rules for identifying and creating virtuous epistemic bubbles within the environments of social media platforms. (shrink)

This study investigates all available literature related to critical thinking in business education in a survey of publications in the field produced from 1990-2019. It conducts a thematic analysis of 787 articles found in Web of Science and Google Scholar, including a specific focus on 55 highly-cited articles. The aim is to investigate the importance of critical thinking in business education, how it is conceptualised in business education research, the business contexts in which critical thinking is situated, (...) and the key and more marginal themes related to critical thinking outlined in the business and business education literature. The paper outlines six key areas and topics associated with those areas. It suggests future directions for further scholarly work in the area of critical thinking in business education. (shrink)

An editorial / opinion piece on abortion: -/- "I’m a philosophy professor who specializes in medical ethics and I teach and write about the ethics of abortion. So I am very familiar with the medical, legal and – most importantly – ethical or moral issues related to HB 481, the so-called “heartbeat bill” that would effectively ban abortion in Georgia. At least hundreds of other philosophy, ethics and law professors in Georgia teach these ethical debates about abortion: they are also, (...) to varying degrees, experts on the issues. -/- What is taught is the arguments about the ethics of abortion, that is, the reasons to think that abortion is wrong and the reasons to think that it’s not wrong. Evaluating these arguments requires understanding and skill. Much of these skills amount to consistently asking ‘What do you mean?’ and ‘Why think that?’ We need better arguments on these issues, and asking and answering these questions helps with that. . .". (shrink)

Humankind is currently confronted with a critical challenge that determines its very existence, not only on an individual, racial, or national level but as a whole species: the fight against climate change and environmental degradation. To win this battle, humanity needs innovations and non-linear thinking. Nature has long been a substantial information source for unthinkable discoveries that save human lives. The paper suggests that by understanding the nature, emergence, and mechanism of serendipity, the survival skill of humans, humanity can (...) capitalize on it to learn from nature and generate nature-based innovations that can address the climate and environmental degradation crises. In the era of Artificial Intelligence (AI) proliferation, AI will be a vital tool providing navigational and useful information to leverage the power of serendipity in climate and sustainability science. However, an eco-surplus culture that incorporates core values pertaining to nature and sees environmental sustainability as the conscience of the times needs to be built to direct and control the immense power of AI-leveraged serendipity. Insights applied in this paper are drawn from the book titled “A New Theory of Serendipity: Nature, Emergence and Mechanism”. (shrink)

A large body of evidence suggests that the Personalized System of Instruction (PSI) improves learning. In courses that use PSI, the material is divided into units, students must pass a test on each unit before advancing to the next unit, there’s no group-level instruction, and students advance in the course at their own pace. While studies find that PSI improves learning outcomes in a wide range of settings, researchers haven’t studied the effectiveness of PSI in critical thinking classes. In (...) this paper, I argue that teaching critical thinking with PSI can effectively promote critical thinking skills. I describe a course that uses PSI to teach critical thinking and I present evidence from pre- and post-tests that indicates that students substantially improved their reasoning skills in this course. I also discuss the costs and drawbacks of using this method of instruction and consider ways of addressing these problems. (shrink)

The importance of teaching critical thinking skills at the college level cannot be overemphasized. Teaching a subcategory of these skills—argument analysis—we believe is especially important for first-year students with their college careers, as well as their lives, ahead of them. The struggle, however, is how to effectively teach argument analysis skills that will serve students in a broad range of disciplines.

Human language, hominin tool production modes, and multimodal communications systems of primates and other animals are currently well-studied for how they display compositionality or combinatoriality. In all cases, the former is defined as a kind of hierarchical nesting and the latter as a lack thereof. In this article, I extend research on combinatoriality and compositionality further to investigations of everyday primate skills. Daily locomotion modes as well as behaviors associated with subsistence practices, hygiene, or body modification rely on the (...) hierarchical nesting of different behavioral and cognitive actions into complex skills. I introduce a scheme which uses hierarchical organization to differentiate combinatorial from compositional skills. Combinatorial skills are defined either as aggregational or linearly hierarchical depending on whether the skill occurs momentarily in space or unfolds sequentially over time. Compositional skills are defined either as nested or interactionally hierarchical depending on whether the skill results in new constructs or in new interactions between existing constructs. The methodology I propose combines epistemological hierarchy theory with data from primatological field research and experimental and comparative psychological research and provides a means to integrate current constructionist and extended views on cognition and action with older research on behavioral logics in psychology and operational chain thinking in anthropology. The approach furthermore synchronizes with ongoing research on teleonomy, intentionality, and creativity. -/- . (shrink)

This book delves into the embodied ground of thinking, illuminating the transition from theorising about the embodied mind to actively practising embodied thinking in research, teaching, and learning. The authors speak from immersing themselves in novel methods that engage the felt, experiential dimensions of cognition in inquiry. -/- The turn to embodiment has sparked the development of new methodologies within phenomenology, pragmatism, and cognitive science. Drawing on Eugene Gendlin’s philosophical work on felt understanding, and Francesco Varela’s enactivist approach, (...) contributors explore innovative embodied thinking methods such as Focusing, Thinking at the Edge, micro-phenomenology, and mindfulness practices. They demonstrate the practical applications of these methods in research, teaching, and learning, highlighting their liberating and empowering potential for researchers and students. In an age marked by information overload and societal polarisation, methods of embodied thinking provide an innovative edge to critique, complementing more traditional approaches to critical thinking with listening skills and reflexive care. -/- This book shows how heeding the essential, yet often overlooked, embodied grounds of critical and creative thinking can deepen and strengthen each of research, teaching, and learning. It will interest philosophers of education and educators in higher education in particular, as well as researchers and postgraduate students from philosophy, and the cognitive and social sciences, who are curious about how embodied thinking can enrich research, teaching, and learning. (shrink)

For the past few years in the United States, almost daily there’s a headline about new proposed abortions restrictions. Conservatives cheer, liberals despair. But who is right here? Should abortion be generally legal or should it be banned? Is it usually immoral or is it usually not wrong at all? These same questions, of course, are asked in other countries. To many people, answers to these questions seem obvious, and people with different or contrary answers are, well, just wrong. But (...) how can we know? In particular, could anyone know that abortion is not wrong and should be legal? If so, how? And how would anyone effectively, persuasively, communicate that knowledge? One important set of answers depends on this idea: critical thinking. Critical thinking can help people know, not merely believe or feel, that their perspectives on issues are true or correct, and it can help them persuade others to understand and accept that knowledge. We are philosophy professors who teach courses in critical thinking and its applications to ethical, political, scientific, and legal issues. In our 2019 open-access book, Thinking Critically About Abortion: Why Most Abortions Aren’t Wrong & Why All Abortions Should be Legal, we apply well-confirmed methods of critical thinking to the most discussed arguments about abortion. Critical thinking can be operationalized as skills. Three key critical thinking skills involve defining words, identifying the structures of arguments, and evaluating explanations. Understanding these and other critical thinking skills can only help improve conversations and advocacy about abortion. Let’s see them in action. (shrink)

Good Thinking is a collection of papers about abilities, skills, and know-how and the distinctive but often overlooked—or explained away—role that these phenomena play in various foundational issues in epistemology and action theory. Each chapter, taken on its own, represents a fairly specific intervention into debates in (i) epistemic responsibility, (ii) the nature of inferential justification, and (iii) connections between inference and action. But taken collectively, these chapters constitute fragments of a larger mosaic of commitments about the explanatory (...) priority of abilities in normative theories. One distinctive argumentative strategy employed throughout Good Thinking is its placing special emphasis on what might be called “bad thinking”: defective judgments borne out of cognitive short-circuiting, incoherence or self-doubt, depression, or anxiety. The underlying motivation for this is that much of what we can learn about good thinking is only revealed at the margins, where thinking has in some respects gone bad without being entirely spoiled. (shrink)

John Carvalho’s Thinking with Images, an Enactivist Aesthetics argues that puzzling artworks can draw us into a special activity – thinking when we don’t know what to think – which is valuable because it takes us beyond our skills and understanding. Enactivism is the theory of mind that best explains such thinking. The book illustrates this proposal with four chapters that detail Carvalho’s highly personal or individual encounters with enigmatic works of art. I raise two concerns. (...) First, the four illustrative chapters say that they are enactivist, but they do not show this. The illustrative chapters detail considerations about the works that are not distinguished by a particular theory of mind and might fit with any number of approaches to works of art. The suggestion that the thinking presented in each chapter is skillful is not explained. Second, the book does not just focus on thinking when we don’t know what to think, it also claims that such thinking frees us from mere looking. But enactivism does not require us to deny that our engagement with particular works in their ‘concrete singularity,’ to use Carvalho’s term, is perceptual. If perception is richly integrated or even continuous with what we understand skillfully or cognitively – and enacted in one’s circumstances – this does not erase differences between perception and thought or between their functions. When we ‘think with’ an individual so that we are engaged with it in its concrete singularity, perception is involved either in the present or the past. There is no need to shunt perception or looking aside as life activities that are just rule-bound, just part of knowing what to think rather than part of our response when we don’t know what to think. (shrink)

This textbook is not a textbook in the traditional sense. Here, what we have attempted is compile a set of assignments and exercise that may be used in critical thinking courses. To that end, we have tried to make these assignments as diverse as possible while leaving flexibility in their application within the classroom. Of course these assignments and exercises could certainly be used in other classes as well. Our view is that critical thinking courses work best when (...) they are presented as skills based learning opportunities. We hope that these assignments speak to that desire and can foster the kinds of critical thinking skills that are both engaging and fun Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version. Rebeka Ferreira and Anthony Ferrucci. (shrink)

The chapter presents the prototyping of a thinking routine designed to foster good inference habits in children ages 6 to 11. The prototyping was developed at Ninho, an educational project for children from underprivileged households in Brazil. The thinking routines by Ritchhart and colleagues (2006) served as our starting point. Following a Virtue Education (VE) approach, we supposed that the repeated application would conduce to habituation. In addition, to increase peer-to-peer interactions, the teacher applying the routines worked as (...) a facilitator in a Community of Inquiry (CI). After six months of application, the results were partially successful. We identified that the repeated exposition to the magic question “What makes you say that?” made children more aware of the evidence supporting their assumptions. Furthermore, the interactions between peers made them recognize different perspectives. However, we also identified some shortcomings. Most of them seemed to arise from cognitive biases. At the individual level, belief perseverance kept children too attached to their first assumptions. They preferred self-serving rationalizations instead of accepting a counter-argument. At the group level, we identified problems of social contagion such as information cascades. The effects of a first opinion rhetorically voiced were hard to efface. Since none of the steps on the previous routines addressed these biases, we prototyped a routine to start filling this gap. Following Critical Thinking (CT) theorists, we added a step of structured instruction concerning one specific reasoning technique - the inference to the best explanation. Moreover, the recommendation of cognitive psychologists motivated the inclusion of some extra features to avoid groupthink biases. For instance, a visual table that juxtaposes contrasting arguments should facilitate comparative evaluations. Also, a star-based evaluation scale should help different individuals to discuss their assessments based on a common ground. As described in the end, the prototype with elements from VE, CI and CT presented promising results. (shrink)

Proprioception is usually used in reference to body movement and the self-perception of body movement. Proprius in Latin means “one’s own,” or “self.” It refers to the physical knowledge acquired, say, in the process of doing a particular activity, such as riding a bicycle, for instance. You can be told how to ride a bicycle, and this may be of some help. But in the end, it’s the physical knowledge and not the mere theoretical knowledge that enables you to ride (...) your bike. David Bohm, a world-renowned theoretical physicist, applied this notion of proprioception to the movement of thought, the process of thought. In On Dialogue, he contends that thinking can become aware of its own movement and aware of itself in action: -/- “Proprioception” is a technical term – you could also say “self-perception of thought,” “self-awareness of thought,” or “thought is aware of itself in action.” Whatever terms we use, I am saying: thought should be able to perceive its own movement, be aware of its own movement. In the process of thought there should be the awareness of that movement, of the intention to think, and of the result which the thinking produces. -/- This opens the door to an understanding of thinking as a process like any other physical process, such as riding a bicycle. We usually think of thinking as an abstract process – one of learning abstract knowledge and how to apply that knowledge. And this is what we are primarily taught in school. Unfortunately, some methods used in doing philosophy with children focus too much on strictly developing abstract critical thinking skills. -/- In doing philosophy with children, I am interested in focusing on the process of thinking in the process of thinking. In this way, it is also different from metacognition, which tends to focus on the ability to self-correct in response to the self-assessment toward the completion of a task. (shrink)

The 21st academic curriculum worldwide has emphasized Critical Thinking as one of the paramount thinking skills. However, the fact that whether EFL teachers- as direct guides in the classroom- have thoroughly grasped the concept, have been exposed to the concept or equipped with adequate methods and approaches to teach critical thinking in daily lessons remains questionable. This paper aims to present the Vietnamese EFL teachers’ perceptions of critical thinking and provide an overview of their current (...) practices of critical thinking skills. The paper emphasized the extent of understanding of critical thinking that Vietnamese EFL teachers show in comparison with definitions in the literature, and how they apply what they understand in the EFL classroom. Participants of the study are 5 teachers who have teaching experience of more than 3 years, and the researchers collected data through in-depth interviews. The findings revealed a lack of information and training from the participants as well as some challenges in practicing the skills due to time-constraints or inadequate general knowledge and limited language level of students. This paper gives EFL managers and practitioners’ assessment criteria for whether to include or exclude critical thinking in their classes and sheds light on how Vietnamese EFL teachers can structure their lessons to critical thinking in the classroom. (shrink)

This article attempts to think of thinking as the essence of critical education. While contemporary education tends to stress the conveying of knowledge and skills needed to succeed in present-day information society, the present article turns to the work of Theodor W. Adorno to develop alternative thinking about education, thinking, and the political significance of education for thinking. Adorno touched upon educational questions throughout his writings, with growing interest in the last ten years of his (...) life. Education, he argues following Kant, must enable students to think for themselves and to break free of the authority of teachers, parents and other adults. Nevertheless, in his discussions of education Adorno says little about the nature of thinking, and the secondary literature on his educational theory addresses this question only cursorily. Important claims on the nature of thinking do appear elsewhere in Adorno's work. From his early writings up to Negative Dialectics, Adorno is preoccupied with thinking, sketching the outlines of critical-dialectical thought. Still, these reflections rarely touch upon educational questions, and the Adorno scholarship has yet to establish this link. Unlike studies which read Adorno's educational thought against the backdrop of the history of education and the German Bildung tradition, or in relation to art and aesthetics, the present article brings together Adorno's ideas on education and thinking in an attempt to contribute both to the Adorno scholarship and to the growing field of education for thinking. (shrink)

Among the many commonalities between memory and imagination is the fact that they can both be understood as skills. In this chapter, I aim to draw out some connections between the skill of memory and the skill of imagination in an effort to learn something about the nature of these activities and the connection between them. I start by considering the ways that one might work to cultivate these skills in the hope that we could learn something about (...) imagination training by reflection on memory training and vice versa. Interestingly, however, an initial look at the empirical research on the respective training regimens does not show much potential for this kind of crossover. Though there are some commonalities that can be found across the training regimens, these commonalities are nothing special over and above the kinds of commonalities one might find in training regimens for skills of any sort. Fortunately, however, the matter does not end there. When we think more deeply about the details of some of the training regimens for memory, we discover some important connections between the skill of memory and the skill of imagination. In particular, I argue that the two skills turn out to be interestingly intertwined. (shrink)