Dynamic Systems methods in the study of development A practice-oriented approach An introduction to the ISED Workshop o

1. Dynamic Systems methods in the study of development A practice-oriented approach An introduction to the ISED Workshop on Dynamic systems methods in development Groningen, May 14-16 2007

2. Dynamics of Development: knowledge map • Dynamic systems • What it is and what it is not not • Development • Basic components • Basic mechanism(s) Development and dynamic systems Theory formation Empirical design Application of dynamic systems to development Model building Statistical methods Dynamic systems of Development

3. 1 Dynamic systems …

4. Dynamics: basic definition and properties • an approach to the description and explanation of change • what it is not: misunderstandings in social science • it is not a model with time as predictor (as in multilevel growth model, for instance) • social science and psychology has focused on static ergodic models • whereas it should have been focusing on dynamic non-ergodic models if it wants to really understand change Dynamic systems of Development

5. Give me a value of x and I will tell you what the next value of x will be The model generates a time series Variable x time Two equations: the static and dynamic models x t+1 = f ( x t ) • Dynamic system: x t+1 = f ( x t ) • The value of a variable x is a function of its preceding state • Static system: x i = f ( y i ) • The value of a variable x • Is a function of the variable y • Or any set of such variables, ya, yb, yc, … Dynamic systems of Development

6. Give me a value of y and I will tell you what the corresponding value of x will be The model generates a population sample Variable x Variable y x i = f ( y i ) Dynamic systems of Development

7. End attractor similarity start Mutual preference Dynamic system and geometric space Example: emergence of friendship in function of mutual preference and similarity; applies to dyad wobbles, humps and sudden jumps - theoretica lreflection

8. Application of Dynamics to Social Sciences • dynamic model • of complexsystems • that are non-ergodic Explain complex system Explain ergodic Dynamic systems of Development

9. ergodicity • An informal definition • Imagine a statistical analysis over the entire ensemble of people at a certain moment in time • and a statistical analysis for one person over a certain period of time • an ensemble is ergodic if the two types of statistics give the same result, and non-ergodic if this is not so • ergodicity hardly ever applies to behavioral data! • Molenaar • considerable consequences for research methodology Dynamic systems of Development

10. What is a complex system? • A complex system is any system featuring a large number of interacting components (agents, processes, etc.) • whose aggregate activity is nonlinear (not derivable from the summations of the activity of individual components) • and typically exhibits … self-organization … • Rocha, 1999 Dynamic systems of Development

11. 2 Development …

12. What does development mean? (1) • meaning unwrapping • like the unwrapping of a bookroll, • notion of an inner logic in the sequence • notion of finality • life span more than just development Dynamic systems of Development

13. What does development mean? (2) • there's also education, learning and teaching • learning: having experiences that make you change • teaching: giving someone experiences that make him change in a particular direction • there is maturation and aging • biologically governed processes of change, including the aspects of rising and falling, deterioration Dynamic systems of Development

14. What does development mean? (3) • developmental viewpoint: development is the overarching term • Encompassing learning, teaching, niche-seeking, maturation, aging, …. Dynamic systems of Development

15. The classical developmentalists’ view • Piaget, Vygotsky, Wallon, Werner. … • all changes of the system occur through information that is "moderated" through the system • “moderated” means that • the system encodes the information and adapts only in function of this encoding (as in Piaget's assimilation and accommodation) • the system selects its own niche, i.e. preferred and adapted environment (also biologically and genetically-Plomin) • the caring environment (educators, parents) adapt the environment to the system's level and possibilities (as in Vygotsky's ZPD) Dynamic systems of Development

16. 3 Developmental mechanisms of change …

17. The basic mechanism (1) • all changes of the system occur through information that is "moderated" through the system • it is a fundamentally recursive notion • next step is a function of the preceding step • and thus a direct expression of a dynamics in the fundamental sense (see basic definition) Dynamic systems of Development

18. The basic mechanism (2) • it is a fundamentally interactional notion • the dynamics occurs through the interaction with an environment or context • this environment is of many kinds: biological, spatial, cultural, ... • a badly missing component: the utility-driven nature of human action and the motor of action and development • biology and economics emphasize the utility-driven nature of action Dynamic systems of Development

19. The drive for developmental change (1) • appears as a factor among many others: motivation for instance • relates to control theory, happiness/pleasure theories; appraisal theory of emotion, self-actualization (Maslow), drives (Freud) …. • but is far from the fundamental dynamic factor that features in biology (fitness-maximization) or economics (utility-drive) • you need to understand the dynamics of the utility function in order to understand the dynamics of the long-term process, e.g. biological evolution, economic processes and trade, ... Dynamic systems of Development

20. The drive for developmental change (2) • the dynamics of the utility function is essential for understanding the short-term dynamics of change • the short-term dynamics of development involves the dynamics of action • see the model of interaction dynamics S and VG Dynamic systems of Development

21. Dynamic systems approach to development (1) • you can define an organism as a manifold, a space of variables • specify its changing position on a developmental ruler • Properties worth studying • discontinuity next to continuity • construction of novelty next to transmission and appropriation • Fuzziness and ambiguity • intra-, inter- and contextual variability Dynamic systems of Development

22. Dynamic systems approach to development (2) • A Dynamic Systems theory of development incorporates • the basic recursive developmental mechanism • Interaction and transaction • Action drives, evaluation and control • Short-term dynamics of action • Long-term dynamics of development • Link between short- and long-term dynamics • Serve as criteria for existing theories Dynamic systems of Development

23. 4 Applying dynamic systems to development ….

24. 4 areas of discussion • Theory formation • Existing theories • Theories that await application to development • Model building • Empirical design • Statistical methods Dynamic systems of Development

25. Existing theories (1) • qualitative use of complex dynamic systems concepts • Lewis, Fogel, Granic, Dishion, … • theory of embedded-embodied action • Thelen and Smith (Spencer, Schoner, ...) • short-term interactional aspect of development: organism-environment interaction • development as change in the dynamic field (Schoner) • related theories: ecological psychology (Gibson) Dynamic systems of Development

26. Existing theories (2) • Connectionism • Really a DST approach? Or are they supplementary? • Focuses on the organismic-brain component • Dynamic growth theory • Van Geert, Fischer, Case,language development • emphasizes long-term dynamics: growth as an auto-catalytic process under limited resources • related theories: biological theory of ecology Dynamic systems of Development

27. Existing theories (3) • theory of developmental dynamics • Classical developmentalists (Van Geert 1998) • based on the fundamental developmental mechanisms in classical theories • theory of dyadic agents • highly developed in macro-social theory • beginning application to development Dynamic systems of Development

28. theories that await application to development • symbolic dynamics, categorical dynamics • their major advantage: they link categorical with quantitative descriptions and modeling, a link that is badly needed in developmental (and clinical) psychology • fuzzy control system dynamics • control theory and theory of agents Dynamic systems of Development

29. 5 Model building …

30. model building • connectionist modeling • differential and difference models of growth phenomena • Growth models • Interaction models (“The Mathematics of Marriage”, Gottman et al. • agent models • cognitive simulation and AI-models (Anderson, ACT) Dynamic systems of Development

31. 6 Empirical Design …

32. Empirical design (1) • High-frequency, time-serial N=1 studies • samples result as collections of time serial studies • the time-serial study should capture the characteristic dynamics at the time scale at issue (which longitudinal studies nromally not do) • Experiments as perturbations • experimental studies in psychology involve specific perturbations of an ongoing process • the experimental manipulation must be studied time-serially, as a perturbation that is assimilated by the process or to which the process accommodates Dynamic systems of Development

33. Empirical design (2) • mixed time-serial designs • combination of time-serial, longitudinal and cross-sectional Dynamic systems of Development

34. 6 Statistical Methods …

35. Overview of methods • Standard statistical methods • Statistical methods for non-linear time series • Standard optimization techniques for curve-fitting • Analysis of categorical state spaces • State space grids • Karnaugh maps • Finite state diagrams, Markov chains and t-patterns • Monte Carlo tools for statistical simulation • methods that await application to development Dynamic systems of Development

36. standard statistical methods • Why: analysis of sample predictions based on dynamic models • “Who”: standard statistical packages • Example: • dynamic model of dyadic play in children of different sociometric statuses • principal component analysis of dyadic conflict trajectories Dynamic systems of Development

37. statistical methods for non-linear time series • Why: statistical description and analysis of time series • Who: Molenaar, Hamaker, et al. • Example: • non-linear time-serial factor analysis • See Hamaker’s workshop Dynamic systems of Development

38. standard optimization techniques for curve-fitting • Why: fitting dynamic models in the form of differential equations or maps (difference equations) to data • “Who”: standard fitting techniques • Example: • fitting growth models to data, qualitative and quantitative fitting • See Van Geert’s Workshop Dynamic systems of Development

39. categorical analysis of state spaces (1) • State space grids • Why: describe transitions among categorical states and finding categorical attractor states • Who: Lewis, Hollenstein • example: • dyadic interactions among adolescents • See Hollenstein’s workshop Dynamic systems of Development

40. categorical analysis of state spaces (2) • Karnaugh maps • Why: describing transitions through Boolean logic • Who: Dumas et al, Schiepek, Tschacher • example: • mother-child interaction Dynamic systems of Development

41. finite state diagrams, Markov chains and t-patterns • Why: finding patterns in time series • who: Magnusson; Markov chains, • example: • time patterns in teacher-child interactions • See Van Geert’s workshop (if possible) Dynamic systems of Development

42. Monte Carlo tools for statistical simulation • Why: applicable to non-standard data • “Who”: • often used in biology, non-standard problems, small sample problems etc. • Manly; Todman and Dugard • example: • significant peaks in variability of langauge production (time series) • Significance testing of dynamic model of dyadic play Dynamic systems of Development

43. methods that await application to development • fuzzy logic and categorical methods • why: behavioral data are categorical, but fuzzy • Who: Zadeh, Ragin, Smithson, Verkuilen • example: • Emergence of linguistic categories in young children • analysis of computer use in toddlers Dynamic systems of Development