Education and Learning to Think (1987) / Chapter Skim
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THE NATURE OF THINKING AND LEARNING: GOING BEYOND THE ROUTINE
THE NATURE OF THINKING AND LEARNING: GOING BEYOND THE ROUTINE
Pages 7-14
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From page 7... ...
These abilities go well beyond the routinized skills of the old mass curriculum. In fact, they are much like the abilities demanded for college-bound students in the College Board's book, Academic Preparation for College (College Entrance Examination Board, 1983~.
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From page 8... ...
Cognitive research on the nature of basic skills such as reading and mathematics provides a fundamental challenge to this assumption. Indeed, research suggests that failure to cultivate aspects of thinking such as those listed in our working definition of higher order skills may be the source of major learning difficulties even in elementary school.
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From page 9... ...
Yet our models of skilled comprehension suggest that inferences are being drawn and interpretations are being made throughout. And studies of eye movements during silent reading, of pause patterns as texts are read aloud, and of disruptions in comprehension caused by minor modifications at key points in the text provide convincing evidence of the reader's inferential work even for quite simple texts.
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From page 10... ...
Readers are sensitive to the order in which categories of information are presented. They have difficulty recalling stories when information is given in an order other than that specified in the idealized story schema, and most important as evidence that this story schema plays a key role in understandingpeople tend to recall story information in the order predictecl by the schema even if the version of the story they read or heard uses a nonstandard order.
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From page 11... ...
suggests that as readers develop automatic skills the nature of the process actually changes and certa~n steps drop out. In any case, it is evident that educators ought to aim to produce both kinds of reading comprehension abilities among students: the ability to understand written texts automatically and with little effort, and the capacity to apply deliberate strategies for interpreting and remembering when the need arises.
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From page 12... ...
Nevertheless, a close consideration of recent research on mathematical cognition suggests that in mathematics, as in reading, successful learners understand the task to be one of constructing meaning, of doing interpretive work rather than routine manipulations. In mathematics, the problem of imposing meaning takes a special form: making sense of formal symbols and rules that are often taught as if they were arbitrary conventions rather than expressions of fundamental regularities and relationships among quantities and physical entities.
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From page 13... ...
There is substantial evidence that children's difficulty in learning school mathematics derives in large part from their failure to recognize and apply the relations between formal rules taught in school and their own independently developed mathematical intuitions. Part of the evidence lies in close analysis of the kinds of errors that children typically make in the course of learning arithmetic and, eventually, algebra.
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From page 14... ...
Research on algebra learning shows that when thinking about transformation rules, students rarely refer either to quantitative relationships or to problem situations that could give meaning to algebra expressions. Not surprisingly, students are not very skillful at the process of ~mathematizing," that is, at constructing links between formal algebraic expressions and the actual situations to which they refer (e.g., Clement, 1982~.
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