Humans appear to reason using two processing styles: System 1 processes that are quick, intuitive, and effortless and System 2 processes that are slow, analytical, and deliberate that occasionally correct the output of System 1. Four experiments suggest that System 2 processes are activated by metacognitive experiences of difficulty or disfluency…

This research involves an examination of the relationship between education and age on a wide array of neuropsychological test measures among patients diagnosed with Alzheimer's and vascular dementia. The purpose of this study was to investigate the role of education as an attenuating factor to neurocognitive decline in dementia. Although numerous…

Wertsch's clarification of Vygotsky's claims about the role of social interaction in the development of children's thinking made an important contribution to educational research. Revisiting that clarification, I suggest that "talk" instead of "speech" best describes Vygotsky's concern with the functional dynamics of dialogue rather than the…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

Although many students who enter kindergarten are cognitively ready to meet the demands of the kindergarten mathematics curriculum, some students arrive without the early abstract reasoning abilities necessary to benefit from the instruction provided. Those who do not possess key cognitive abilities, including understandings of conservation,…

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. "Psychological Review," 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). "If."…

A scientific definition of the meaning of human creative thought is pursued. (JD)

Article explores some of the key notions of the construct "concept" from the psychological and educational literature in order to demonstrate the need for standardization of definition and a more unified front in future investigations involving this important element in the study of cognition. (Author)

The article reviews six conceptions of genius and offers a seventh. Three types of genius (analytic, synthetic, and integrated) are defined. Common to all three is the sustained ability to use analysis and synthesis (i.e., to be both linear and creative in approaching complex problems). (Author/DB)

Reviews and discusses Piaget's recent work on abstract reasoning. Piaget's distinction between empirical and reflective abstraction is presented; his hypotheses are considered to be metaphorical. (Author/DB)

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

The fundamental relations that underlie cognitive comparisons--''same'' and ''different''--can be defined at multiple levels of abstraction, which vary in relational complexity. We compared response times to decide whether or not two sequentially-presented patterns, each composed of two pairs of colored squares, were the same at three levels of…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

A number of thought experiments are cited, some well-known, some not. These illustrate the power of thought experiments. Other examples are given that show some of the dangers. As well as examples from the science, some examples of visual reasoning from mathematics are also presented, again with an eye to illustrating their promise and perils.…