A Valid and Reliable Instrument for Cognitive Complexity Rating Assignment of Chemistry Exam Items

The design and use of a valid and reliable instrument for the assignment of cognitive complexity ratings to chemistry exam items is described in this paper. Use of such an instrument provides a simple method to quantify the cognitive demands of chemistry exam items. Instrument validity was established in two different ways: statistically significant correlations between expert-based cognitive complexity ratings and student performance (as measured through statistical difficulty of items), and statistically significant correlations between expert-based cognitive complexity ratings and student mental effort ratings. Key benefits associated with instrument use include an enhanced understanding of the cognitive complexity of chemistry assessment tasks and as a means for characterizing exam content for the measurement of cognitive development

Applying Catastrophe Theory to an Information-Processing Model of Problem Solving in Science Education

In this study, we test an information-processing model (IPM) of problem solving in science education, namely the working memory overload model, by applying catastrophe theory. Changes in students' achievement were modeled as discontinuities within a cusp catastrophe model, where working memory capacity was implemented as asymmetry and the degree of field dependence/independence and logical thinking as bifurcation parameters. Data from achievement scores of high school students in nonalgorithmic problem solving (chemical, organic-synthesis problems) were used and analyzed, using dynamic difference equations and statistical regression techniques. The dependent measure was the score difference in problems of varying demand from M = 3 to M = 8. The cusp catastrophe models proved superior (R2 = .73.84) to the pre-post linear counterpart (R2 =.52-.66). The empirical evidence for the catastrophe effect supports the nonlinear model for the working memory overload hypothesis. The results add to research endeavors that built bridges between concepts of the theory of nonlinear dynamical systems and problem solving in science education, and to IPM as well. Finally, the theoretical and practical implications are discussed. (c) 2012 Wiley Periodicals, Inc. Sci Ed 96:392-410, 2012Science Educatio

Non-linear analysis of the effect of working memory capacity on organic-synthesis problem solving

This work examines the role of working memory capacity in problem solving in chemistry, and in particular it re-examines the validity of the Johnstone-El Banna predictive model, by employing non-linear methods. The study correlates the students"™ information-processing capacity with their performance, by using fractal geometry adapted for treating problem-solving data. The rank order of the subjects"™ achievement scores and their working-memory capacities were treated as dynamic flows and found to possess different geometric characteristics depending on the complexity of the problem and the method of marking. The classification and interpretation of these characteristics were made using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The findings support the hypothesis that long-range correlations exist between the rank order of the subjects"™ achievement scores and their working-memory capacity, and are in agreement with the Johnstone-El Banna model.Chemistry Education Research and Practic

A complexity theory model in science education problem solving: random walks for working memory and mental capacity

The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.Nonlinear Dynamics Psychol Life Sc

Reading Achievement, Mastery, and Performance Goal Structures Among Students With Learning Disabilities: A Nonlinear Perspective

The purpose of the present study was to examine the hypothesis that a nonlinear relationship exists between a performance-classroom climate and the reading achievement of adolescent students with learning disabilities (LD). Participants were 62 students with LD (Grades 5–9) from public elementary schools in northern Greece. Classroom climate was assessed using the Patterns of Adaptive Learning Styles. Achievement in reading was assessed using a normative reading assessment. Data were analyzed by means of catastrophe theory in which the behavior is predicted as a function of two control variables, the asymmetry factor and the bifurcation factor. Reading achievement (word identification) was predicted by students’ ability to decode pseudowords (asymmetry variable) and by a mastery or performance motivational discourse (bifurcation factor). Results indicated that in classrooms with a performance goal structure, the cusp model fit the data and accounted for 54% of the variance in real word identification. In this condition, the association between pseudoword reading and real word reading was nonlinear. When a mastery climate was tested as a bifurcation variable, results indicated that its effect was nonsignificant and that instead the linear model fitted the data more adequately. Thus, increases in a classroom’s performance motivational discourse are associated with sudden, unpredictable, and discontinued changes in students’ reading performance. © 2015, © Hammill Institute on Disabilities 2015