Critical thinking has been described as an ability to question to acknowledge and test previously held assumptions to recognize ambiguity to examine, interpret, evaluate, reason, and reflect to make informed judgments and decisions and to clarify, articulate, and justify positions (Hullfish & Smith, 1961 Ennis, 1962 Ruggiero, 1975 Scriven, 1976 Hallet, 1984 Kitchener, 1986 Pascarella & Terenzini, 1991 Mines et al., 1990 Halpern, 1996 Paul & Elder, 2001 Petress, 2004 Holyoak & Morrison, 2005 among others).Īfter a careful review of the mountainous body of literature defining critical thinking and its elements, UofL has chosen to adopt the language of Michael Scriven and Richard Paul (2003) as a comprehensive, concise operating definition:Ĭritical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. Readership: Students, graduate students and researchers with an interest in mathematics, mathematicians, scientists, philosophers, psychologists, and readers who use mathematics in their work.The ability to think critically calls for a higher-order thinking than simply the ability to recall information.ĭefinitions of critical thinking, its elements, and its associated activities fill the educational literature of the past forty years. What Mathematics Can Teach Us About the Mind.What the Mind Can Teach Us About Mathematics.Deep Thinking in the Mind and the Brain.Deep Thinking in Mathematics and Science.It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.Ĭhapter 1: What is Deep Thinking? (154 KB)
The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. Deep thinking can be found whenever one conceptual system morphs into another. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”.ĭeep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. It is at the heart of every paradigm shift or reframing of a problematic situation. It results in the discontinuous “aha!” experience, which is the essence of creativity. Deep thinking is a different and more basic way of using the mind. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning.
Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program.
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