DEVELOPMENT OF HUMAN POTENTIAL: INVESTMENT INTO OUR FUTURE

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1 DEVELOPMENT OF HUMAN POTENTIAL: INVESTMENT INTO OUR FUTURE Proceedings of the 8th Conference of the European Council for High Ability (ECHA) Rhodes, October 9-13, 2002 Edited by Franz J. Mönks and Harald Wagner K.H. Bock

2 This book contains a selection of presentations given at the 8th Conference of the European Council for High Ability (ECHA) at the Hilton Rhodes Hotel, Rhodes, Greece, 9-13 October The production of this book was supported by the Stifterverband für die Deutsche Wissenschaft through Bildung und Begabung e.v., Bonn, Germany. Cover design: ORTRA Ltd., Tel Aviv Layout: Menna Jones ISBN 2003 by European Council for High Ability c/o Bildung und Begabung e.v. Godesberger Allee 90, D Bonn, Germany All rights reserved Publisher: Verlag Karl Heinrich Bock, Bad Honnef, Germany

3 Contents Foreword...7 A. PERSONAL TALENT, INTELLIGENCE AND SPECIAL ABILITIES Sidney M. Moon Developing personal talent...11 Daniela Ostatníková, Zdenek Putz, Jolana Laznibatová, Monika Dohnányiová, Janette Okkelová and Karol Pastor Salivary testosterone levels in children: Relation to their IQ scores...22 Heidrun Stöger and Albert Ziegler Living in harmony? Causes of deviation among different indicators of giftedness...30 George Manolitsis Predicting high reading ability from kindergarten: The role of metalinguistic skills...34 Anne McKeough and Randy Genereux Transformations in narrative thought during late childhood and adolescence: A comparison of average and exceptional story writers...38 Kirsi Tirri, Petri Nokelainen and James R. Campbell A cross-cultural study of computer literacy among the academic Olympians...42 Dalia Cohen and Shoshana Rosemarin Analytical aspects of musical and numerical memory...45 Dimitrios Stamovlasis and Georgios Tsaparlis Some psychometric variables contributing to high ability and performance in science problem solving...50 István Czigler, János Horváth, László Balázs and Júlia Weisz Non-verbal abstraction and central executive function: High versus average intelligence...54 Zoltán Kondé and István Czigler Mathematical giftedness and information processing...58 Afonso Galvao Motivation to learn: The case of professional orchestra players...62 B. MORALITY, EMOTION, SOCIAL GIFTEDNESS, VALUES Kirsi Tirri Morality and high ability

4 SOME PSYCHOMETRIC VARIABLES CONTRIBUTING TO HIGH ABILITY AND PERFORMANCE IN SCIENCE PROBLEM SOLVING Dimitrios Stamovlasis and Georgios Tsaparlis Department of Chemistry, University of Ioannina, Ioannina , Greece In this article we report research findings that support the role of a number of psychometric (cognitive) variables and which contribute to high ability and performance in science problem solving. It is shown that variables such as working-memory capacity, mentalspace (M) capacity, disembedding ability (degree of field dependence-independence), developmental level, and the mobility-fixity dimension can be predictive of the student performance. The article presents linear and nonlinear approaches to psychometric research in science problem solving. At the outset, a distinction must be made between problems and exercises, with the latter requiring for their solution only the application of well-known and practiced procedures (algorithms). A predictive model for problem solving. Predictive-explanatory models are very useful for understanding the factors that influence the ability of students to solve problems. The proposal of such models has been facilitated by the consideration of the importance of information processing. Working-memory theory "can account for performance on tasks that involve both processing and storage, and both of these cognitive functions are likely to be required for most forms of scientific problem-solving" (Niaz & Logie, 1993). Each learner has a certain working-memory capacity (X), while each problem has a mental demand (Z). The Johnstone-El-Banna model (Johnstone & El-Banna, 1986) is a predictive model which states that a student is likely to be: (a) successful in solving a problem if the problem has a Z-demand which is less than or equal to the subject's X capacity (Z X), but may fail for lack of information or recall; (b) unsuccessful in solving a problem if Z > X, unless the student has strategies that enable him/her to reduce the value of Z to become less than X. Related to the working-memory capacity X is the mental capacity or M-capacity, which derives from Pascual-Leone's neo-piagetian theory (Pascual-Leone, 1970). A mental power, or M-space, or M-capacity, is attributed to each subject, which is the maximum available M-capacity or structural M-capacity (M s ). However, the actually mobilized M capacity or functional M-capacity (M f ) may be less. Blocking mechanisms in problem solving and necessary conditions for the model. In a number of cases, the solution of a problem may be blocked, despite the satisfaction of the condition Z X. Using non-numerical organic chemical-synthesis problems, Tsaparlis (1998) examined mechanisms that may block the solution, and stated the following necessary conditions that must be observed for the successful operation of the Johnstone- El-Banna model to problem solving in science education: (1) The partial steps must be available in long-term memory, and easily accessible from it. (2) The logical structure of the problem must be simple; the best situation is when only one operative schema exists in the problem. (3) No 'noise' should be present in the problem statement. (4) The degree of 50

5 field dependence/field independence (disembedding ability) has an effect. Low and, to a lesser extent, intermediate working-capacity subjects who are field dependent may experience a working-memory overload because of a reduction in the available X space. Operation, validation and usefulness of the model. Tsaparlis & Angelopoulos (2000) used chemical organic-synthesis problems, of varying Z-demand from 2 to 8, to test the validity of the model. It was confirmed that as Z increases, there is a general slow fall in performance, but no difference is significant until Z just exceeds X. The fall is significant at the "break" point, but, after that, a gentle slow fall occurs again, in which none of the differences is significant. In each case, the significant fall is when Z = X + 1. Finally, a number of students, notably higher for higher information-processing capacity, can use chunking devices, and this keeps performance from eventually falling to zero. The main conclusion is that it can be predicted that students who have a high working memory capacity (at least of six), and at the same time are not field-dependent, are capable of high information processing, having an advantage in problem solving. The role of the logical structure. The logical structure of a problem is specified by the number of operative schemata entering the problem. Tsaparlis et al. (1998) examined the effect on student performance of the manipulation of the logical structure as well as of the Z-demand of chemical equilibrium problems. It was found that all cognitive variables are quite consistent in correlating with achievement only when the logical structure is fairly complex and even when the Z-demand is relatively low. Developmental level plays the dominant part, which can be accounted for by taking into account that these problems were of an algorithmic nature for the subjects of this study, because of their extended practice (the 'training effect'). On the other hand, working memory maintains some importance too. Finally, training on task could lead to 'chunking', which reduces the Z-demand of a task and thus improves student performance. The "mobility-fixity" dimension. The characteristic of field-dependent subjects to function consistently in a field-dependent fashion (i.e., fixity) and of others to vary more according to circumstances (i.e., mobility) has been referred to as the "mobility-fixity dimension". Stamovlasis et al. (2002) examined the effect of the "mobility-fixity" variable as a function of the type and the complexity of the problem, and found that the mobile subjects demonstrated higher mean achievement than the fixed subjects. Application of complexity theory to problem solving. An important new contribution has been the employment of concepts and tools of complexity theory to re-examine the role of the above variables. The nonlinear approach correlates each psychometric variable with the rank-order achievement. Rank-order sequences of subjects, according to their scores, were generated, and each score was then replaced by the value of the subjects' cognitive variable. The produced symbolic sequences, corresponding to the various problems of different complexity (Z-demand and logical structure), are treated as dynamical flows. When a sequence possesses high entropy (close to surrogate data), there is no preference as to who comes first (there is randomness because everybody solves the problem). On the other hand, a statistically significant decrease of the entropy marks long-range correlations and "memory" (or a "structure") in the sequence. Entropy-change diagrams (or fractaldimension-change diagram) of the rank-order sequences versus the complexity of the problem provide a direct visualization of these correlations. Figure 1 shows such diagram for working memory capacity and for data taken from simple organic-synthesis problems. In the hypothetical one-dimensional space of the rank order achievement scores, we take a 51

6 Decrease of fractal Dimension 0,05-0,05-0,15-0,25-0,35 surrogate Z-demand of the problem Randomness Figure 1: The decrease of fractal dimension versus Z-demand of the problem for the "working memory" random walk 4/5. (Organic-synthesis problems - simple logical structure) random walk among the subjects with working memory capacity 4 and 5 (RW 4/5). It is observed that the fractal dimension, D B, for low values of Z-demand, 2, 3, and 4 has high values close to the surrogate exponent, which corresponds to theoretical randomness. At Z- demand 5, the value of D B decreases, showing long-range correlation, because subjects with working memory capacity 5 outscore subjects with working memory capacity 4. When the Z-demand of the problem becomes 6, the problem becomes difficult for everybody, and the sequence becomes disordered again. A similar pattern is observed for random walk 5/6. Such diagrams provide the medium for exploring the role of various cognitive variables in science problem solving and reveal power law correlations. Recent publications (Stamovlasis & Tsaparlis 2000; 2001; 2002) provide further related information. References Johnstone, A.H. & El-Banna, H. (1986). Capacities, demands, and processes - A predictive model for science education. Education in Chemistry, 23, Niaz, M. & Loggie, R.H. (1993). Working memory, mental capacity and science education: Towards an understanding of the "working memory overload hypothesis". Oxford Review of Education, 19, Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget's developmental stages. Acta Psychologica, 32, Stamovlasis, D., Kousathana, M., Angelopoulos, V., Tsaparlis, G. & Niaz, M. (2002). Achievement in chemistry problem solving as a function of the mobility fixity dimension. Perceptual and Motor Skills. Accepted for publication. Stamovlasis, D. & Tsaparlis, G. (2000). Non-linear analysis of effect of working memory on organic-synthesis problem-solving. Chemistry Education: Research and Practice in Europe (CERAPIE), 1, [ Stamovlasis, D. & Tsaparlis G. (2001). Application of complexity theory to an information-processing model in science education. Nonlinear Dynamics in Psychology and Life Sciences, 5, (3), Stamovlasis, D. & Tsaparlis G. (2002). A complexity theory model for science education problem solving: Random walks for working memory and mental capacity. Nonlinear Dynamics in Psychology and Life Sciences. Accepted for publication. 52

7 Tsaparlis, G. (1998). Dimensional analysis and predictive models in problem solving. International Journal of Science Education, 20, Tsaparlis, G. & Angelopoulos, V. (2000). A model of problem solving: Its operation, validity and usefulness in the case of organic-synthesis problems. Science Education 84, Tsaparlis, G., Kousathana, M. & Niaz, M. (1998). Molecular-equilibrium problems: Manipulation of logical structure and of M-demand, and their effect on student performance. Science Education, 82,

COGNITIVE VARIABLES IN PROBLEM SOLVING: A NONLINEAR APPROACH

DIMITRIOS STAMOVLASIS and GEORGIOS TSAPARLIS COGNITIVE VARIABLES IN PROBLEM SOLVING: A NONLINEAR APPROACH ABSTRACT. We employ tools of complexity theory to examine the effect of cognitive variables, such