Rigidity in Children's Problem Solving*

Abstract

The growth within the past decade of so-called "discovery" approaches to teaching, particularly in the sciences, has been explosive. These approaches emphasize "inquiry," require a high degree of flexibility in thinking, and stress, more than did traditional curricula, divergent rather than convergent thought processes. This study originated in an attempt to identify some of the variables affecting rigidity in problem-solving behavior in hope that the exclusion or control of such variables might increase flexibility of thought. Of particular concern were the blinding effects of habit, specifically with what happens when, to quote Luchins, a habit "ceases to be a tool discriminately applied but becomes a procrustean bed to which the situation'must conform; when, in a word, instead of the individual mastering the habit, the habit masters the individual" (32).The problem of behavioral rigidity has been of perennial interest to psychologists. Whether the term Einstellung-effect, mental set, disposition, readiness, determining tendency, or other similar term is used, the concept of a predisposition to respond in a given way which can affect perception, reasoning, and memory becomes a very important one. Chown says, "Few major topics in contemporary psychology appear to offer more promise than rigidity, and the amount of work reported on this subject has been increasing year by year" (11).With their concepts of "fixation" and "style of life," Freud and Adier, respectively, described behavior consistently inappropriate or, at least, responsive only to a limited set of cues in a variety of situations (4, 23). These clinical approaches, however, failed to describe clearly the conditions eliciting the behavior except, perhaps, at a high level of generality.While the greatest impetus to research in rigidity in American psychology came with the publication of Luchins5 original work, numerous earlier investigators hinted at its existence (32). Chant, for example, found that many errors in problem solving were caused by an "interpretive" approach, in which old meanings and interpretations determined the response, rather than a fresh approach to the materials at hand (10).

Using Model-Eliciting Activities As a Tool to Identify and Develop Mathematically Creative Students

“…A. Chamberlin, 2010; S. A. Chamberlin & Moon, 2005; Ching & Darussalam, 1997; Cropley, 1992; Cunningham, 1966; D. W. Haylock, 1985, 1997; Prouse, 1967; Stokes, 2001).…”

“…The focus in mathematics classrooms may be on speed and accuracy rather than creativity and problem solving (S. A. Chamberlin, 2010; Cunningham, 1966; Kattou et al, 2012). An extensive focus on such low-level tasks has never been an empirically valid indicator of creativity.…”

“…Cunningham (1966) and others, such as Sir Ken Robinson (http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity.html), postulated that schools and teachers are becoming killers of creativity. They do so by utilizing drill and practice methods and fixed procedures that have a deleterious effect on students’ ability to break from established mind-sets and rigidity of thought (Ching & Darussalam, 1997; Cunningham, 1966; D. W. Haylock, 1985; D.…”

1: Learning Studies in Science Education

“…A theoretical analysis of these two referents was the subject of a dissertation by Grant (1965). Cunningham's (1966a) ex cellent review dealt with rigidity in children's problem solving. More gen eral papers on problem solving are those by Anderson and Weigand (1967), , Mahan (1967), and Aylesworth (1965).…”

On Curiosity and Science Education

“…Although epistemic curiosity would operate most effectively in relieving conceptual conflict if it sought information without bias, this is not always the case. Various factors that contribute to rigidity in thinking are discussed elsewhere [13].…”