1. How Do Systems Change? Behavioral patterns: Variously stable, softly assembled attractor states As system parameters or external boundary conditions change, the old pattern becomes less coherent and stable and the system finds a new pattern –Nonlinear change

2. Ex: Walking –A very stable attractor (behavioral pattern) for human locomotion Can walk across varied surfaces, while doing other things, in different shoes –But when confronted with a steep incline, there is a point at which walking will change to “climbing” (locomotion on all fours) The slope of the incline acts as a “control parameter” that moves the system in a nonlinear way

3. Development is a series of patterns evolving and dissolving over time and, at any point in time, possessing some degree of stability The principles of dynamics systems can be applied to multiple levels and timescales –e.g., can ask questions about development at the neural, physiological, individual, or social level –A framework to guide thinking and research rather than a specific theory of “something”

4. Theory to Research: Dynamic Systems Identify the collective variable of interest –Should be a well-defined and observable variable, not a derived construct Ex: number of words in the lexicon vs. language processing capability Other exs: number of correct object retrievals from transparent vs. opaque containers; number of word retrieval errors; presence or absence of the stepping reflex (and/or relative strength or weakness of the reflex)

5. Characterize the behavioral attractor states –What are the attractor states of the collective variable under different conditions and at different points in time? –Object retrieval errors: Infants reliably search for hidden objects beginning at about 8 months; however, depending on search conditions, they continue to make errors until at least 18-24 months of age –Word retrieval errors: These errors reliably increase in toddlers at some point between about 15-24 months for about 3- to 6 weeks and then decrease again –Stepping reflex: Newborns demonstrate this reflex when held upright so that their soles touch a flat surface; by 2 months it typically “disappears”

7. Describe the dynamic trajectory of the collective variable –Longitudinal designs –When do changes occur? Ex: Object retrieval –At 8 months, can search for hidden objects, but difficulty in retrieving objects if cover is transparent rather than opaque; by about 10-11 months, do not make this error Ex: Word retrieval errors –At around 12 months, infants begin to produce words (comprehension of words precedes production); at some point between 15-24 months, toddlers’ rate of vocabulary acquisition increases rapidly and word retrieval errors for familiar words increases for a brief period (3 to 6 weeks)

8. Ex: stepping reflex –Present at birth and gradually weakens until “disappearance” by about 2 months

9. Identify Points of Transition (to New Forms) –Can be qualitative or quantitative Exs: –Object retrieval: Ability to retrieve objects from transparent containers emerges (qualitative transition) –Word retrieval errors: Decrease some time between 15-24 months, following a brief increase in such errors (quantitative transition) –Stepping reflex: Disappears by about 2 months (qualitative transition) –Often indicated by a lot of variability in the collective variable If looking at a group of children’s behavior with respect to the collective variable, the variance (or standard deviation) will be quite large

10. Identify Potential Control Parameters –What are the factors responsible for changes in the collective variable over time? Ex: Object retrieval from transparent containers –Potential control parameter: Experience with transparent containers to learn that visual and haptic (tactile) cues do not correspond Ex: Word retrieval errors between 15-24 months –Increased rate of acquisition of new vocabulary words and little practice with word retrieval leads to an unstable lexicon and temporary interference with retrieval of familiar words Ex: Stepping reflex –Leg weight and composition (increased fat deposits without corresponding increases in muscle mass) lead to “disappearance” of the reflex

11. Manipulate Potential Control Parameters to Experimentally Generate Transitions –Can generate changes at points of transition because the system is not stable –Practical Implication: Interventions should be timed to coincide with points of transition or “sensitive periods”

12. –Ex: Object retrieval from transparent containers Manipulate experience with transparent containers –Ex: Word retrieval errors between 15-24 months Manipulate experience with word retrieval (i.e., practice) –Ex: Stepping reflex Manipulate weight of legs (by submerging in water and adding weights)

13. Developmental Systems Theories (Recap) What is meant by integrated or fused levels of analysis? –Different theorists seem to mean different things Bronfenbrenner’s model seems to indicate a “traditional” interaction of levels Thelen & Smith state that the levels are “more than just interacting” –Behavior and its development are influenced by changing sets of relationships across levels over time (dynamic rather than static)

14. Distinctions are made between levels for the purposes of analysis –But the appropriate unit of analysis is relational (2 or more levels) Need to examine bidirectional relations between levels over time