**1. Introduction**

20 Current Topics in Children's Learning and Cognition

York: Guildford Press

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Understanding refers to "the ability to understand", which means "to comprehend, to apprehend the meaning or import of, or to grasp the idea of [something]" (Oxford English Dictionary, 1989). Understanding is a key concept within all fields of study concerning learning and development, such as cognitive psychology, pedagogy, educational sciences, and developmental psychology. Within these fields of study, understanding has been studied for different domains, such as scientific reasoning (e.g., Grotzer, 2004; Inhelder & Piaget, 1958/2001; Rappolt-Schlichtmann, Tenenbaum, Koepke, & Fischer, 2007), social development (e.g., Blijd-Hogeweys, 2008), mathematics (e.g., Dehaene, 1997; Gilmore & Bryant, 2008), and many more. In the field of education, children's understanding is especially important, as understanding involves deep knowledge of concepts, and the active manipulation of this knowledge in the form of explaining, predicting, applying, and generalizing (Perkins & Blythe, 1994). A model of understanding can give guidance to both researchers and educators dealing with children's understanding and the development of their understanding. In this chapter, we will present such a model, based on dynamic Systems and Skill Theory principles. The model is illustrated throughout this chapter with examples of children's understanding of scientific concepts, or more specifically, children's understanding of air flow and air pressure during a syringe task, which is described below. The syringes task is designed to let children explore how air flows through a system, and to introduce them to the relationship between pressure and volume, as well as the way in which pressure can exert forces on objects (see also De Berg, 1995). Although there are some basic questions the researcher asks every child during the administration of the task, most of the interaction between the boy and the researcher emerges in real-time, i.e. during the task itself.

© 2012 Van der Steen et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Between three and seven years of age, important changes in children's conceptual understanding of scientific concepts take place (Van Geert & Steenbeek, 2008), in addition to changes in curiosity and exploration tendencies (Simonton, 1999), which are probably related to important changes in children's lives. That is, they go through a major transition when they enter first grade, and start learning to read, write, and to do arithmetic (Carrière, 2009). During this age period children's learning behavior gets shape, attitudes toward school are formed, and first interactions with peers and teachers in a school setting emerge, which are the building blocks of academic performance at a later age.

Using the Dynamics of a Person-Context System to Describe Children's Understanding of Air Pressure 23

material will explode. Some children say they don't know and others predict that the piston of the other syringe comes out, which is the right answer in this case. After the researcher demonstrates what happens, researcher and child discuss about possible explanations for this phenomenon. Again, multiple answers are given. Some children simply say they don't know. A few mention batteries or electricity as a causal explanation, whereas others say that water flows through the syringes and causes the piston to move upwards. Some children emphasize the tube that connects the syringes, and others understand that air flows through

What accounts for the differences in young children's understanding of scientific concepts, and what is the role of the environment, i.e., the teacher in supporting and promoting this understanding? To answer this question, a model of children's scientific understanding should take the complexity and dynamic nature of this into account, as well as the complex interactions with the environment on which the understanding of children is often based (Fischer & Bidell, 2006). This chapter aims at explaining how children's understanding of scientific concepts can be studied using a model based on properties derived from dynamic systems Theory (e.g. Van Geert, 1994) and Skill Theory (Fischer, 1980; Fischer & Bidell,

A dynamic systems approach describes how one condition changes into another, and how different time scales are interrelated (Van Geert, 1994; Van Geert, 1998; Van Geert & Steenbeek, 2005, 2008; see also the theory of embedded-embodied cognition of Thelen & Smith, 1994). Research in the dynamic systems paradigm investigates real-time processes and captures development as it unfolds through multiple interactions between a child and the environment (Van Geert & Fischer, 2009). Such development can be viewed as a selforganizing process, since the state of the system organizes from the multiple interactions among the elements (e.g. the child and environment). Over time, the system's state may emerge toward certain stable states, or attractors (e.g., Thelen & Smith, 1994). Dynamic systems theory has so far proven to be a valuable framework for studying human development, including reflexes (Smith & Thelen, 2003), parent-child interactions (Fogel & Garvey, 2007), language development (van Dijk & Van Geert, 2007), scaffolding in teachinglearning situations (Van Geert & Steenbeek, 2005), dyadic play interactions (Steenbeek, 2006), identity development (Lichtwarck-Aschoff, Van Geert, Bosma, & Kunnen, 2008), and cognitive development (Fischer, 1980; Fischer & Bidell, 2006). The approach makes use of methods to investigate time-serial processes, and test dynamical relations between these processes (Cheshire, Muldoon, Francis, Lewis, & Ball, 2007; Lichtwarck-Aschoff, et al., 2008; Van Geert & Steenbeek, 2005; 2007; Steenbeek & Van Geert, 2005). For example, Van Geert and Steenbeek (2005; 2007) present mathematical models to predict patterns and variations in combinations of variables over time. Other authors used time series to describe relationships between variables (van Dijk & Van Geert, 2007) or state space grids (Hollenstein, 2007) to investigate interactions between dyads; as opposed to probabilistic

approaches which rely on deviations from the mean and group differences.

the tube and syringes.

**2. Dynamic systems and understanding** 

2006).

Moreover, this is also the age at which important cognitive developmental transitions take place. From the work of Piaget (1947/2001) we know that children between three and seven years old are in the pre-operational stage of development, which is characterized by the forming of concepts, and the use of symbols to think about the world, but also by centrism, i.e., focusing on a single aspect instead of more aspects while children reason or solve problems. More recently, research using Skill Theory, which is inspired by Piaget's theory, illustrated that the highest skill (understanding) level that children first reach between 3 and 7 years of age develops from single representations (understandings that go beyond specific actions on objects) to representational systems (linking several of these representations that define the object or concept at hand – see also section 3) (Fischer & Bidell, 2006). However, this research also showed that children vary enormously in their skills across context, tasks, and within short periods of time. This variation is due to the fact that context dynamically contributes to the deployment of skills in the form of a real-time activity. That is, thinking or understanding takes place in the form of action. How does the process of understanding occur in action, taking into account the real-time interactions that constitute this process in a teaching environment, and taking into account the vast amount of intra-individual variability?

Based on our ongoing longitudinal research project, we will illustrate how short term "building blocks" of understanding give rise to various long-term patterns of understanding. In order to fully understand these short-term building blocks, we have selected one particular problem domain for this chapter, namely air flow and air pressure, because it provides a domain that is both limited and rich enough to study. Zooming in on these short-term interactive processes gives us important information to understand the development and transformations of understanding on the long term (Steenbeek, 2006; Thelen & Smith, 1994).

During the ongoing longitudinal research project, a researcher repeatedly visits 32 young children (3 to 6-years old) as part of an ongoing longitudinal study on children's understanding of scientific concepts, such as the flow of air and air pressure. During one visit, the researcher presents each child with two empty medical syringes without a needle, which are joined together by a small transparent tube. One of the syringes' pistons is pulled out. "What do you think will happen if I push this [piston] in?" is one of the questions the researcher asks. This question triggers a variety of answers from the children. Some children think nothing happens, others say the tube will pop out, whereas others even think the material will explode. Some children say they don't know and others predict that the piston of the other syringe comes out, which is the right answer in this case. After the researcher demonstrates what happens, researcher and child discuss about possible explanations for this phenomenon. Again, multiple answers are given. Some children simply say they don't know. A few mention batteries or electricity as a causal explanation, whereas others say that water flows through the syringes and causes the piston to move upwards. Some children emphasize the tube that connects the syringes, and others understand that air flows through the tube and syringes.

What accounts for the differences in young children's understanding of scientific concepts, and what is the role of the environment, i.e., the teacher in supporting and promoting this understanding? To answer this question, a model of children's scientific understanding should take the complexity and dynamic nature of this into account, as well as the complex interactions with the environment on which the understanding of children is often based (Fischer & Bidell, 2006). This chapter aims at explaining how children's understanding of scientific concepts can be studied using a model based on properties derived from dynamic systems Theory (e.g. Van Geert, 1994) and Skill Theory (Fischer, 1980; Fischer & Bidell, 2006).
