Molecular-equilibrium problems: Manipulation of logical structure and of M-demand, and their effect on student performance

Abstract

Molecular‐equilibrium (chemical‐equilibrium) problems are among the most important, and at the same time most complex and difficult general chemistry problems. In this work, we examine the effect on student performance of the manipulation of the logical structure as well as of the M‐demand of these problems. In addition, we study the relationship between student performance on the problems and a number of cognitive variables, viz., developmental level, working memory capacity, functional M‐capacity and disembedding ability of students. In addition, we test the validity of the Johnstone–El‐Banna model. Nine problems of varying number of operative schemata, as well as of varying number of M‐demand, were used. The number of schemata varied from a minimum of two, to a maximum of four, while within each logical schema we had specific mental demand (M‐demand), varying from four to six. As basic molecular‐equilibrium schemata in these problems, we considered the following: (1) the process of establishment of chemical equilibrium; (2) the condition of chemical equilibrium; (3) the case of gaseous systems, with use of partial and total pressures as well as of Kp; and (4) the disturbance of equilibrium and the establishment of a new equilibrium. The correlation between student performance in the schemata and the steps of the problem solutions is low when the number of schemata is low, but high when this number is high. Of the cognitive factors studied, developmental level plays the most important role, especially as the logical structure of the problem increases. The other three cognitive variables also have an effect, with working memory capacity leading. The findings are mainly attributed to the fact that the prob‐lems were rather algorithmic exercises for the students, because of familiarity and training. © 1998 John Wiley & Sons, Inc. Sci Ed 82:437–454, 1998.

Cognitive Variables in Problem Solving: A Nonlinear Approach

“…The present work correlates individual differences, such as cognitive variables, with students' performance in science education, and has mainly explanatory functions. The work supports the findings of previous research (Johnstone et al, 1993;Johnstone & Kellet, 1980;Niaz & Logie, 1993;Tsaparlis & Angelopoulos, 2000;Tsaparlis et al, 1998), and has also important implications for the educational process.…”

A model of problem solving: Its operation, validity, and usefulness in the case of organic-synthesis problems

“…Devices to reduce Z to be less than X, such as familiarity with the problem or subdivision ("chunking") of the problem into familiar chunks, result in a reduction of the Z-demand of the problem. It has been found (Niaz, 1995a;Niaz & Robinson, 1992;Tsaparlis, Kousathana, & Niaz, 1998) that developmental level is the most significant psychometric factor related to performance in familiar problems. Therefore, the model must be valid more in the case of novel problems than in the case of exercises.…”

Animal models for basic and translational research in reconstructive transplantation

“…Both the WM capacity and M ‐capacity variables are operationalized and measured by means of corresponding psychometric tests. With respect to problem solving in science education, research has shown that, in certain cases, the limited human information‐processing capacity (measured as working memory capacity or as M ‐capacity) can predict student performance (Johnstone & Al‐Naeme, 1991; Johnstone & El‐Banna, 1986; Niaz, 1988a, 1988b; Niaz & Logie, 1993; Tsaparlis, 2005; Tsaparlis & Angelopoulos, 2000; Tsaparlis, Kousathana, & Niaz, 1998).…”

“…A sudden decrease in students' performance might occur not only because of the limitation of their channel capacity but also because of the interference of other variables. It has been shown that psychometric variables, such as disembedding ability (degree of field dependence/independence) and/or logical thinking (previously referred to as developmental level), play an essential role in science problem solving (Dempster, 1991; Johnstone, 1984; Johnstone & El‐Banna, 1986; Johnstone, Hogg, & Ziane, 1993; Niaz, 1988a, 1988b; 1989; Niaz & Logie, 1993; Niaz, de Nunez, & de Pineda, 2000; Stamovlasis & Tsaparlis, 2005; Tsaparlis, 2005; Tsaparlis & Angelopoulos, 2000; Tsaparlis et al, 1998). It is worth noting that in the WM model field dependence is seen as a moderator variable: Field‐dependent subjects appear to possess lower WM capacity because they use part of their capacity to process irrelevant information.…”

“…One definition of M ‐demand is “the maximum number of thought steps and processes which have to be activated by the least able, but ultimately successful candidate in the light of what had been taught” (Johnstone & El‐Banna, 1986). The logical structure of a problem is associated with the number of different logical schemata, which the solver has to retrieve from his/her long‐term memory to solve the problem (Niaz & Robinson, 1992; Tsaparlis et al, 1998). Examples of logical schemata in chemistry are: chemical stoichiometry, gas laws, and the state of chemical equilibrium.…”