Cognitive Variables in Problem Solving: A Nonlinear Approach

Abstract

We employ tools of complexity theory to examine the effect of cognitive variables, such as working-memory capacity, degree of field dependence-independence, developmental level and the mobility-fixity dimension. The nonlinear method correlates the subjects' rank-order achievement scores with each cognitive variable. From the achievement scores in organic-synthesis problems of various mental demands, rank-order sequences of the subjects, according to their scores, were generated, and in the place of each subject, his/her score was replaced by the value of the corresponding cognitive variable. Then each sequence was mapped onto a one-dimensional random walk, and when treated as a dynamic flow, was found to possess fractal geometry, with characteristics depending on the complexity of the problem. The findings were interpreted using concepts from complexity theory, such as order, correlation exponents, and entropy. The method provides meaningful results and adds to the understanding of information processing and the role of cognitive variables within the frame of predictive models in problem solving. Although the method is applied to a particular kind of problems (chemical, organic-synthesis problems), it can be generalized to other problems, not only in chemistry, but also in other sciences and in mathematics. Finally, the educational implications are discussed.

A Probabilistic Model for Students’ Errors and Misconceptions on the Structure of Matter in Relation to Three Cognitive Variables

“…In general, field-independent students were more likely to give a 'right' answer, while field-dependent subjects were more likely to give a 'wrong' answer. Although this is a small-scale effect, it is consistent with the fact that field independents have been found to achieve more in science generally (Lawson, 1983;Johnstone & Al-Naeme, 1995;Niaz, 1996;Tinajero & Paramo, 1998;Bahar & Hansell, 2000;Danili & Reid, 2004, 2006Kang et al, 2005;Tsaparlis, 2005;Stamovlasis & Tsaparlis, 2005). This serious advantage of field-independent pupils could be attributed to their ability to separate readily the significant information from its context (Witkin & Goodenough, 1981).…”

“…Research has supported the construct validity of TCO, since CO corresponding to mental resources activated during cognitive tasks can be operationalized by psychometric variables measured at the behavioral level. Thus, variables, such as the information processing capacity (M-capacity), logical thinking (LTh), field dependence/independence (FDI), or convergent/divergent thinking (CD), have been proved to play a significant role in a wide range of tasks, and they affect students' performance in science, such as physics (Johnstone, Hogg & Ziane, 1993), chemistry (BouJaoude, Salloum & Abd-El-Khalick, 2004;Chandran, Treagust & Tobin, 1987), organic synthesis (Stamovlasis & Tsaparlis, 2005), physical chemistry (Tsaparlis, 2005), and earth science (Chiappetta & Russell, 1982), to mention a few. Recently, three of the above-mentioned cognitive variables-LTh, FDI, and CD-were found to affect students' mean achievement score on the topic of the structure of matter and its changes of state (Tsitsipis, Stamovlasis & Papageorgiou, 2010).…”

Animal models for basic and translational research in reconstructive transplantation

“…For the present analysis, an accumulated marking was used, which takes into account the history of achievement in all previous problems, so that the final score is a representative of the overall student problem‐solving ability in the specific domain. More about the study can be found in Tsaparlis and Angelopoulos (2000) (see also Stamovlasis & Tsaparlis, 2001, 2005).…”

La Enseñanza pre-Universitaria en Ciencia y Tecnología Puede Influir en las Funciones Ejecutivas

“…Junto con la capacidad espacial, la resolución de problemas es una habilidad esencial para tener éxito en las asignaturas de ciencia y matemáticas. Esta capacidad incluye la planificación, diseño, construcción, evaluación y rediseño de una solución para un problema dado en cualquier disciplina (Stamovlasis & Tsaparlis, 2005;Lawson, 2004). Estos procesos que permiten la planificación, control y seguimiento de comportamientos complejos dirigidos a una meta se suelen denominar funciones ejecutivas (FE) (Seiferth, Thienel, & Kirchner, 2007).…”