**4. A model of understanding**

Using the four properties from the dynamic systems paradigm and Skill Theory's ruler, we can construct a model of understanding to guide research and practice in education, but also in other areas that require the evaluation of cognitive growth. The general model of understanding here is that it is an active process, distributed across people involved, and that it is dynamic, i.e., it continuously changes, and self-organizes through iteration. It is important to keep in mind that, even though the four properties describe distinct mechanisms, they all work at the same time while the process of understanding unfolds. Below, we will present the model and briefly highlight its components, after which we discuss these in more detail by using an empirical example.

As Figure 1 shows, children construct levels of understanding during short-term interactions with the environment, such as during a task they are working on together with an adult. Both child and adult are characterized by specific distal factors (e.g. years of schooling) that influence their behaviour. However, those distal factors are not what we focus on, since the figure can be characterized as an action model, that is, it focuses on understandings which are constructed during an interaction by means of a process that is distributed across the child, the adult, and the material context with which they interact or which they manipulate. This means that during an interaction, there is a bidirectional influence between the child's answers and the adult's questions within the material context. This is illustrated in the big square (part A) of figure 1.

Moreover, the process is iterative, meaning that it changes through repeated interactions, instead of being the retrieval of a complete representation that is already there in memory. During a teaching interaction, each previous action of the child has an influence on the subsequent (re-)action. This is illustrated by the big arrows between adult and child (part B of figure 1) and the small arrows on the side of the boxes indicating the child and adult.

Each task-related utterance has two dimensions: a specific content and a complexity level. During interactions, we can observe the complexity level of understanding, as it comes forward in the child's distinct utterances, which are often reactions to what the adult is saying, or are part of the ongoing discussion between an adult and a child. This complexity level, measured by Skill Theory (Fischer, 1980), will vary between different children, and will fluctuate over time within the same child. This is illustrated by part C in figure 1.

Lastly, the long-term development of children's understanding unfolds through several of these short-term interactions. As an example, figure 1 displays the sessions with 3-month intervals we used in our study of young children's understanding of scientific concepts. The link between short- and long-term development is indicated in part D of figure 1.

Using the Dynamics of a Person-Context System to Describe Children's Understanding of Air Pressure 31

30 Current Topics in Children's Learning and Cognition

individual variability into account.

**4. A model of understanding** 

discuss these in more detail by using an empirical example.

This is illustrated in the big square (part A) of figure 1.

adult.

in figure 1.

time scales of development, and takes both the role of context, as well as inter- and intra-

Using the four properties from the dynamic systems paradigm and Skill Theory's ruler, we can construct a model of understanding to guide research and practice in education, but also in other areas that require the evaluation of cognitive growth. The general model of understanding here is that it is an active process, distributed across people involved, and that it is dynamic, i.e., it continuously changes, and self-organizes through iteration. It is important to keep in mind that, even though the four properties describe distinct mechanisms, they all work at the same time while the process of understanding unfolds. Below, we will present the model and briefly highlight its components, after which we

As Figure 1 shows, children construct levels of understanding during short-term interactions with the environment, such as during a task they are working on together with an adult. Both child and adult are characterized by specific distal factors (e.g. years of schooling) that influence their behaviour. However, those distal factors are not what we focus on, since the figure can be characterized as an action model, that is, it focuses on understandings which are constructed during an interaction by means of a process that is distributed across the child, the adult, and the material context with which they interact or which they manipulate. This means that during an interaction, there is a bidirectional influence between the child's answers and the adult's questions within the material context.

Moreover, the process is iterative, meaning that it changes through repeated interactions, instead of being the retrieval of a complete representation that is already there in memory. During a teaching interaction, each previous action of the child has an influence on the subsequent (re-)action. This is illustrated by the big arrows between adult and child (part B of figure 1) and the small arrows on the side of the boxes indicating the child and

Each task-related utterance has two dimensions: a specific content and a complexity level. During interactions, we can observe the complexity level of understanding, as it comes forward in the child's distinct utterances, which are often reactions to what the adult is saying, or are part of the ongoing discussion between an adult and a child. This complexity level, measured by Skill Theory (Fischer, 1980), will vary between different children, and will fluctuate over time within the same child. This is illustrated by part C

Lastly, the long-term development of children's understanding unfolds through several of these short-term interactions. As an example, figure 1 displays the sessions with 3-month intervals we used in our study of young children's understanding of scientific concepts. The

link between short- and long-term development is indicated in part D of figure 1.

**Figure 1.** A conceptual (action) model of understanding based on principles derived from dynamic systems theory and Skill Theory
