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Algebra, Symbols, and Translation of Meaning

Algebra, Symbols, and Translation of Meaning,Lillie Crowley,Michael Thomas,David Tall

Algebra, Symbols, and Translation of Meaning   (Citations: 4)
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constructions that may provoke the reversal errors of the "students-professors problem. " MacGregor & Stacey (1993) show that children do not follow a simple word-matching order and postulate the existence of mental models that can be accessed in any order. We hypothesise that the children's responses are a natural consequence of their previous development and show that, as the verbal problems become more complex, children are more likely to revert to a process-orientation with the arithmetic operation on the left, rather than an assignment order with the variable on the left. We place this in a theory of cognitive compression as the children grow in mathematical sophistication.
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    • ...The reference of literal symbols—the numbers literal symbols stand for—is an important source of meaning, which influences performance in various mathematical tasks (Crowley, Thomas, & Tall, 1994; Demby, 1997; Graham & Thomas, 2000; Kaput, 1989; Kieran, 1992; Malara, 1999; Warren & Pierce, 2004)...

    Konstantinos P. Christouet al. What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects o...

    • ...Inspired by the work of Dubinsky (1991), Sfard (1991) and others, Gray & Tall (1991, 1993, 1994) reviewed old research and initiated new studies throughout mathematical development, from young children calculating with symbols in arithmetic, older pupils manipulating symbols in algebra (Crowley et al, 1994) to college students developing conceptualisations of higher order concepts such as limits (Li & Tall, 1993, Monaghan et al, ...
    • ...Crowley et al (1994) found that the more complex the word problem, the more students wrote the process order rather than the assignment order, with those writing the process order making significantly more errors...

    David Tall. THE PSYCHOLOGY OF SYMBOLS & SYMBOL MANIPULATORS: WHAT ARE WE DOING RIG...

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