Abstract
Theory of mind refers to the ability to attribute beliefs to oneself and others. The present study used a dynamic systems approach to assess how environment may affect the development of second-order theory of mind (e.g., “John knows that Mary knows that he went out yesterday”). Theory of mind is divided into two major dimensions: comprehension (i.e., to understand a mental state) and prediction (i.e., to predict someone else’s future behavior or mental state). Two age groups were assessed: 5–6- and 10–11-year-old children. In both age groups, participants were assigned to a condition of “support” (help provided) or “no support” (help not provided). Results show that second-order theory of mind follows a dynamic growth law that depends on support. Support facilitates performance in theory of mind production (i.e., to predict one’s future behavior) for both the 5–6- and 10–11-year-old children. Interestingly, the 5–6-year-olds who received support presented an increase in the second-order prediction performance at the expense of the second-order comprehension, suggesting that a temporary dip in comprehension performance may facilitate the development of mental rules to predict one’s future behavior.
Keywords
Theory of mind (ToM) comprises both cognitive and emotional aspects necessary for the understanding of someone’s thoughts and behavior. More cognate aspects, however, allow the binding of relevant information to render an event (e.g., somebody’s behavior) comprehensible (Frith, 1989), which notably involves the use of executive functions (EFs; see Müller, Liebermann-Finestone, Carpendale, Hammond, & Bibok, 2012).This allows the attribution of mental states (e.g., beliefs, intentions, emotions) to oneself and others, but also involves the use of these mental states to predict and explain one’s own behavior as well as others (see Imuta, Henry, Slaugter, Selcuk, & Ruffman, 2016; Mitchell, 1997).The ability to mentalize is not a unique human ability (Premack & Woodruff, 1978), and even primates such as orangutans and chimpanzees are able to distinguish intentional behavior from accidental actions (see for instance Call & Tomasello, 2008; see also Tomasello, Call, & Hare, 2003).
In humans, ToM normally develops following a certain path (see Wellman, 1990; Wellman, Cross, & Watson, 2001; Liu, Wellman, Tardif, & Sabbagh, 2008): from an implicit and basic theory of others’ desires and intentions to a more explicit belief theory, where a progression of new conceptual insights generalize and modify its structure and functioning. For instance, the ability to understand true beliefs is followed by the understanding of false beliefs, or an understanding of first-order beliefs leads to an understanding of second-order beliefs, and so on (see also Wellman & Liu, 2004).
Although understanding false beliefs is considered to be a strong indicator of ToM development, research has shown that even infants possess a rudimentary ability to understand the mind of others (see for instance Slaughter, 2015). Moreover, older children can understand both lies and deception, which enables more complexity in strategy in late adolescence and early adulthood (Dumontheil, Apperly, & Blakemore, 2010; Peterson & Siegal, 2002; Valle, Massaro, Castelli, & Marchetti, 2015; Vetter, Leipold, Kliegel, Phillips, & Altgassen, 2013). However, a clear change in the understanding of false beliefs can be observed in 3–6-year-olds who are typically developing and become able to distinguish between someone’s beliefs and their own, and to understand the intention and belief of a person (Astington & Gopnik, 1991; Astington, Harris, & Olson, 1988; Gattis, Bekkering, & Wohlschrager, 2002; Gopnik & Wellman, 1994; Mitchell & Riggs, 2000; Onishi & Baillargeon, 2005; Saxe, Carey, & Kanwisher, 2004; Wellman, 1991).
This change in ToM development is reinforced by dynamic systems and physiological studies revealing that changes around 6 years of age coincide with a move from simpler thought processes towards more coordinated ones (Case, 1991; Fischer & Bidell, 2006). One possibility is that in young children ToM is mainly based on an innate biological form of empathy that progresses into a more cognate form of ToM understanding from the age of 3–4 (Low, 2015; Preston & de Waal, 2002).
More complex forms of ToM emerging at this age can be observed in the dynamic system literature associated to regressions, that is, when an ability (or component of) is temporarily impaired concomitantly with the emergence or refinement of another (see Blijd-Hoogewys, 2008; Blijd-Hoogewy, Van Geert, Serra, & Minderaa, 2008). This reinforces the idea that for an ability to develop, others may temporarily suffer from it for this ability to make its way in the cognitive skillset of an individual.
Furthermore, changes in ToM complexity at this age might not be the result of ToM development per se, and other cognitive components may play a role. Another possibility is that because the switch from an implicit to a more explicit form of ToM may involve conscious thought and action, then EFs might play a role (Carpendale & Lewis, 2006). This implies the use of EFs in synergy with language and working memory (see Apperly, Samson, & Humphreys, 2009; German & Hehman, 2006; Mutter, Alcorn, & Welsh, 2006). Thus, the concomitant development of EFs and language abilities may facilitate the switch from an implicit to an explicit ToM (San Juan & Astington, 2012), though this can be hindered in the presence of an implicit ToM deficit as found in children with autism spectrum disorder (Schuwerk, Vuori, & Sodian, 2015).
This is particularly important for higher levels of ToM recursivity (i.e., second- and third-order nested belief), where an increasingly more complex meta-representational workload is necessary: “I think that you think that s/he thinks [second-order] that another person thinks [third-order].” A typical adult is able to follow only a few levels of recursions, and often loses track at the second or third level (Verbrugge & Mol, 2008; see also Valle et al., 2015; Miller, 2012; and the pioneering study of Perner & Wimmer, 1985).
Our study examined short-term dynamic processes that might lead to long-term changes in the ability of children to master ToM. We assessed the effect of interacting with an expert adult on children’s ToM strategies for the understanding of someone’s beliefs, emotions, or intentions (i.e., “ToM comprehension”), and the ability to actively make a prediction of one’s future behavior or mental state (see Figure 1). This distinction is similar to what has been proposed as implicit and explicit ToM, respectively (see Low & Perner, 2012).

First- and second-order strategic game.
Because conflict inhibition is measured by EFs tasks, then the emergence of false-belief understanding may be the precursor of the children’s ability to predict a conflict between their own and somebody else’s perspective, such as the scenarios faced by children while they are playing PC games (i.e., Strategic Game; see “Methods”). The acquisition of false-belief understanding correlated with substantial changes in EFs around the age of 6, involving inhibition of a dominant response and the subsequent initiation of a subdominant response, which reflects the scenario present in the Strategic Game (see for instance the discussion in Müller et al., 2012).
Dynamic Systems have been used in different domains to study how elements/individuals influence each other on a given time scale, leading to self-organization processes (Thelen & Smith, 1996; Witherington, 2015). One way to address these dynamics is to use coupled equation approaches to model one-to-one dyadic interaction such as parent-child or teacher-child relationships through childhood, but also during adolescence and early adulthood (several implementations can be found in Van Geert, 1994; Steenbeek & Van Geert, 2007, 2008; Hamaker et al., 2009; Steele & Ferrer, 2011; Butner et al., 2007).
In this study the theoretical framework of one of these dyadic interaction models (Steenbeek & Van Geert, 2007, 2008) was used to interpret interactions between the ability to understand and predict mental states. The application of dynamic systems to the development of ToM is not common, and formal modeling of social interaction, which plays a crucial role in ToM development, is scarce (Hayashi, 2007; Hughes, 2011; Hughes & Leekam, 2004; Pavarini, de Holland Souza, & Hawk, 2013).
These systems are driven by two different types of parameters: order parameters, macroscopic/dominant variables that reflect dominant modes of the interactive system as a whole. These parameters emerge from the interaction/coordination of a second type of microscopic parameters, called control parameters: They represent all forms of coordination that the elements of the system can allow (for a discussion see Thelen & Smith, 1996; Steenbeek & Van Geert, 2008).
In our framework, ToM development can be conceived as the result of an interaction between two order parameters (ToM comprehension and prediction of mental states) and three control parameters (i.e., environment, growth rate, and carrying capacity). In dyadic systems, the interplay between these two sets of parameters appears to occur through a causal circular process both in the short- and long-term (i.e., respectively comprehension and prediction), where aspects of daily comprehension of mental state and behavior have a long-term effect on the ability to predict someone’s behavior/mental state. Figure 2 gives an outline of the order and control parameters on both short- and long-term time scales in our model of an interaction framework.

The framework used to present the interaction between the coupled variables “ToM comprehension” and “ToM prediction.”
Long-term changes in ToM prediction influence the interaction with the environment, a control parameter situated on a short-term time scale; interaction with peers and expert figures determine changes in the ToM comprehension level of a child in the short-term, and this in turn influences the ability to predict mental states (ToM prediction), an order parameter that changes on a long-term scale. This order parameter is controlled by control parameters such as the environment, the speed at which the performance grows, and a performance limit depending on the subject’s personal capability (i.e., carrying capacity). In other words, in the long-term subjects’, comprehension of mental states affects their prediction rules to predict future mental states and behaviors. Because ToM has a recursive nature (i.e., mental states can be nested at several levels of recursivity), this framework has the potential to explain the interplay between comprehension and prediction at any ToM order, as well as transitions from one level to another (i.e., first- to second-order ToM).
Although the relationship between support and development of second-order ToM has already been the focus of research (see for instance, Hayashi, 2007), dynamic system research in developmental psychology has not yet addressed the dynamics between different modes of ToM use (i.e., comprehension/prediction) and the effects of the environment. To study environmental influences on comprehension and prediction of second-order mental states, two conditions were designed. Because more complex phenomena (e.g., ToM second-order predictions) can be observed compared to an environment where support is minimal (see, for instance, Fischer & Bidell, 2006), a functional level (i.e., condition with support) can be observed in a given skill domain (e.g., ToM) when a child is given low support and allowed to work on his/her own. This allows us to observe the highest skill level that a child can achieve by his/herself. Conversely, an optimal level (i.e., condition with support) is achieved when high support is provided. These two conditions allow us to measure the two upper limits of the child’s performance, that is, the best performance obtainable without support and the best achievable with support.
Two age groups were assessed: 5–6 and 10–11-year-olds. We predicted that although both age groups may be already capable of taking a second-order perspective (i.e., second-order comprehension acquired), 5–6-year-old children may be poor in predicting someone’s future behavior in a task where second-order ToM prediction is required. Conversely, for the 10–11-year-olds, we would expect minimal second-order ToM differences between the two environmental conditions, because this group of participants is assumed as control group, and should present small differences irrespective of the environmental conditions. Crucially, the help supplied in the condition with support should influence the comprehension–prediction dynamic relation in a way that improves second-order ToM prediction rules to predict another person’s behavior, with larger differences for the 5–6-year-olds than the 10–11-year-olds.
Methods
Stimuli and Procedure
A set of tests assessed the ability to mentalize first- and second-order ToM comprehension and prediction. False-belief stories were used to assess the ability of a child to understand that a character’s action might be based on a wrong belief. Thus, a child will present a correct belief whereas the character has a false belief. Stories were read while at the same time drawings were shown to illustrate the various elements of the story. Children experience this type of assessment as a “being read to” activity, rather than a “being tested” activity (Blijd-Hoogewys & Van Geert, 2017). To assess prediction of mental states, two PC games (Strategic Games) were developed. These were sequential games that are particularly suitable for use with children because of the attractiveness of their audiovisual components.
First- and second-level of recursion were measured for both comprehension and prediction (e.g., “John knows that Mary [first-order] knows that [second-order] he did not go to school yesterday”) by using parallel forms of false-belief stories (Blijd-Hoogewys, 2008; Flobbe, 2006; Flobbe, Verbrugge, Hendriks, & Krämer, 2008) and computer games (Flobbe, 2006; Flobbe et al., 2008; further details are provided in the Supplemental Methods).
Design
A mini version of a cross-sectional microgenetic study was adopted. Models have already been validated with only three repeated observations (see, for example, Van Geert & Steenbeek, 2005a, 2005b; Vleioras, Van Geert, & Bosma, 2008). A mixed design was implemented with one within-subjects factor (session: three weekly testing sessions) and two between-subjects factors (age groups: 5–6, 10–11-year-olds; and environmental condition: support, no support). Environmental effects for the prediction tests were assessed using t-tests with theoretical distribution correction (see Supplemental Methods), whereas for the dynamic system fitting, a dynamic hyperlogistic model used in a wide variety of fields was implemented (see Banks, 1994; Van Geert, 1991; Fischer & Bidell, 2006). The model provides restricted and exponential growth equations as a function of time to explain ToM development (Figure 3): that is, special cases can be derived from its general formula to fit different growth patterns.

Graphical illustration of restricted and exponential restricted growths.
Goodness-of-fit for the dynamic models derived from Equation 1 were assessed using a G2 test statistic.
The study comprised three weekly sessions and tests were administered in the following order: first- and second-order comprehension test; first- and second-order prediction test. The entire session took 50 min and was terminated if the participant exceeded this limit (a zero score was given to the missing items). Because the format of our set of tests was different (i.e., stories and games), two distinctive modes of support were implemented. For false-belief stories, support was provided by repeating crucial details—what has happened and what has not been understood by the child over the stream of events. During prediction tests, support was supplied by providing a further explanation of the strategies used by the opponent when the subject was unable to predict the opponent’s intentions. Conversely, when support was not supplied, subjects were expected to master first- and second-order mental states: Support was not provided and children were assumed to be able to understand false beliefs and to actively produce a prediction of the opponent’s behavior on their own. (Further details for the assessment of the environmental effects and the dynamic system implementation are provided in the Supplemental Methods.)
Participants
Two groups of subjects completed the study: 5–6-year-old children from a primary school (n 1 = 12) and 10–11-year-old children from a middle high school n 2 = 12). Each age group was divided in two subgroups and children were randomly assigned to either the support or non-support condition.
The schools were two well-established public schools (Tuscany, Italy) who welcomed the project and helped to recruit families for the project. Parents signed a written informed consent and all sessions were audio-recorded; consent for the audio-recording was obtained separately. The educational background of the parents was mixed. First-order ToM was used as exclusion criterion and pupils were screened for their ability to use first-order ToM; however, none of the recruited subjects met this exclusion (see Supplemental Methods for further details on screening).
The mean age of the 5–6-year-old group was 6.26 years (median = 6.25; range 5 years and 11 months to 6 years and 9 months) and the mean age of the 10–11-year-old group was 11.24 years (median = 11.25; range = 10 years and 10 months to 12 years and 4 months). An equal number of females and males was allocated in each age group and subgroups (i.e., conditions with and without support).
Result
To assess the main effect of support for ToM comprehension and prediction, t-tests were carried out irrespective of the ToM order (i.e., first- and second-order), and of the weekly session.
The proportion of correct answers (p) was obtained for each subject and converted to its corresponding t-value. These t-values were first used to check for guesswork: both subgroups (i.e., condition with and without support) and age groups answered significantly away from the theoretical distribution (all p-values < 0.001). Next, independent t-test compared the condition with support (supported condition) and without support (non-support condition). To account for the different variance between the groups, Welch’s correction was used.
The 5–6-year-olds in the supported group were 12% more accurate in the comprehension tests compared to the non-support group (participants in the supported condition may improve their accuracy up to 24%; the mean proportion difference was 0.94 – 0.82 = 0.12 × 100 = 12%; t(26.51) = 2.25, p < 0.05, CI 95= 0.01, 0.24). Support appears to help subjects improve their ToM skills. The 10–11-year-old subgroup who received support was 4% more accurate than the non-support counter-group (i.e., 1 – 0.96 = 0.4 × 100 = 4%), but this result was nonsignificant: t(17) = 1.37, p = 0.18, CI 95 = −0.01, 0.08; means: SC = 1, UC = 0.96; H0: true difference in means = 0. This is because the second-order ToM comprehension is strongly consolidated in the 10–11-year-olds.
Differences between the condition with and without support were also analyzed for the ToM prediction tests. The 5–6-year-olds benefited when support was received. Those who were assigned to the condition with support scored 28% better than those who did not receive support; i.e., (0.73–0.70) – (0.50–0.25) = 0.28 × 100 = 28%. An independent t-test showed that with 95% confidence level, participants who received support perform up to 13% better than those in the non-support condition: t(28.68) = 5.67, p < 0.001, CI 95 = −0.07, 0.13; means SC = 0.73, UC = 0.70; H0: true difference in means = −0.25. Figure 4 depicts statistical and empirical distributions for the prediction tests.

The theoretical (in black) and empirical probability distribution (e.g., proportion of mean accuracy; in gray for support and no support) for the ToM prediction tests (i.e., number of trial items per game: 36).
A similar trend was found for the 10–11-year-olds who received support, who scored 31% higher than in the non-support condition; i.e., (0.90–0.84) – (0.50–0.25) = 0.31 × 100 = 31%. An independent t-test confirmed that in statistical terms up to 12% of those children who received support performed better than the no-support ones: t(31.11) = 10.52, p < 0.001, CI 95 = 0.00, 0.12; means SC = 0.90, UC = 0.84, H0: true difference in means = −0.25.
Overall, these results show that both age groups performed better in the condition with support, although the support received by the experimenter during the prediction tests appears to have a stronger impact on second-order prediction than comprehension. ToM at 10–11 years of age is robust and allows subjects to complete the tasks, even without support; whereas, for the 5–6-year-old children the second-order ToM is more transient: It shows an enhanced level when support is given but this increase is not observed in the non-support condition.
The dynamic fitting showed that both the restricted and the exponential models provide a good fit for the empirical data in both the conditions with and without support, respectively (all p-values > 0.97; see Figure 5). Table 1 reports the estimates for the growth parameter. Second-order ToM growth shows an accelerated trend in the first sessions in the condition with support at 5–6 years of age. Results shows that both second-order ToM components are fitted well by the restricted model and the exponential restricted model in the conditions with and without support respectively. We noticed an acceleration of the growth, (i.e., performance), in the supported compared to the non-supported condition for both age groups. However, it appears that the 5–6-year-olds receive greater benefit from the support than the 10–11-year-olds. Minor differences—which decreased even further across the weekly sessions—were observed in the 10–11-year-old age group.

Accuracy proportions for empirical and predicted values ranging between 0 and 1 were transformed into t-values before plotting.
Summary of the parameter estimations for the two dynamic models fitted upon the average performance of the groups.
Note. Environmental conditions (i.e., support/non-support), n = 6 per condition, age group (i.e., 5–6/10–11 year-olds), n = 12 per group.
CI 95 = confidence interval at 95%; LL = lower limit; UL = upper limit.
As to the differences between second-order comprehension and prediction, second-order ToM comprehension diminished after initially having accelerated its growth, and generally growth was faster in the 5–6-year-old group who received support. In the condition without support for the same age group, growth was slower and overall reached a lower level. Second-order ToM prediction was higher and faster in the 5–6-year-olds who received support (see Figure 5, top), while performance remained more around chance level (p = 0.5) and is somewhat slower in the same age group who did not receive support.
In the 10–11-year-old group, second-order ToM is robust and allows subjects to complete the tasks irrespective of the second-order ToM dimensions and whether or not they receive support; whereas, for the 5–6-year-old children, the second-order ToM is more transient: It shows an enhanced level when support is given, but this increase is not observed in the non-support condition.
Interestingly, concomitantly with a decrease in second-order comprehension, an increase of second-order prediction in the supported condition for the 5–6-year-old group (see Figure 6) was observed, which may suggest a temporary regression. This pattern neither is present in the no-support condition for the 5–6-year-olds nor in the supported and no-support conditions for the 10–11 age group. This offers reinforcement to the idea that the 5–6-year-olds in the condition with support benefit from the help supplied, although at the expense of a temporary decrease in second-order comprehension performance.

Cross-comparison between second-order ToM comprehension and prediction for the condition with support in the 5–6-year-old group.
In the condition with support, dynamic systems indicators such an increase in variability from session two to session three (from 0% to 8% for the second-order comprehension; see Figure 5, top-left graph), together with a decrease in growth (i.e., a negative r′ parameter), may be indicative of an increase in cognitive resources consumption (hence the second-order comprehension dip). This may be used to demonstrate transitions in which an increase in the performance of one (developing) component, i.e., second-order prediction, occurs at the expense of another component, i.e., comprehension.
Furthermore, individual performance dynamic fitting was also carried out, showing similar results; however, not all the subjects presented a pattern that resembles the one obtained by averaging across subjects (i.e., not everyone showed a regression in the ability to understand mental states), though dynamic fitting on single individuals showed that learning to use second-order ToM follows dynamic rules for both comprehension and prediction of mental states (see Supplemental Results).
Discussion
Our study used dynamic systems to examine second-order ToM development. Results show that a hyperlogistic model fits the empirical data for second-order ToM comprehension and prediction, suggesting that second-order ToM growth follows a dynamic growth rule. Furthermore, support appears to have a substantial effect for the 5–6-year-olds when they have to predict their opponent’s behavior (i.e., prediction tests), compared to their peers who did not receive it.
In contrast to the Wellman, Cross and Watson’s meta‑-analysis (2001, i.e., having to predict an action that follows from a belief is no more difficult than identifying the belief itself), our study showed that comprehension might be the precursor through which children develop the ability to predict future behaviors or mental states. Thus, a circular mechanism may account for our results (see Figure 2). Our goal was to empirically demonstrate that a dynamic system framework already used in other developmental contexts (see, for instance, Steenbeek & Van Geert, 2008) can be used to explain the dynamics involved in ToM development. Although Steenbeek and Van Geert’s model is not mathematically implemented in the present study (i.e., we used two dynamic models derived from a hyperlogistic dynamic law to fit the two variables separately), it allows us to explain the dynamics involved in a social context where ToM is utilized. As for Figure 2, the environmental condition “with support” (i.e., the experimenter, one of the agents) provides fundamental ToM comprehension strategies to a 5–6-year-old child (the second agent in the dyad); this in turn has a facilitatory effect for the planning of strategies to be actively used to predict one’s thoughts or behavior. Later on, these strategies have a retroactive effect (i.e., ex post facto) on the environmental interaction (i.e., agents adapts to the child’s ToM level); this is implicitly “tuned” to the current child’s ToM level, (e.g., a more complex level of ToM prediction and/or comprehension).
Support provides the necessary scaffoldings for developing a cognitive component that allows for a quicker and better prediction of second-order mental states. However, it is debated whether this might be strictly ToM-based or the result of EFs developing at around the age of 6. A number of accounts have been proposed to explain the relationship between ToM development and EFs, among which proposals discuss that ToM may be the precursor for EFs or vice versa (Moses & Carlson, 2004; Moses & Tahiroglu, 2010; Perner & Lang, 1999; Sabbagh, Xu, Carlson, Moses, & Lee, 2006), as well as suggesting that ToM makes the use of EFs components (Carlson, Moses, & Hix, 1998), particularly when this is necessary for the prediction of mental states. Support plays a crucial role in learning to use second-order ToM prediction, and could be used as a control parameter, along with others reflecting Piagetian processes within the individual (i.e., assimilation and accommodation) and contextual parameters in a Vygotskian perspective (i.e., actual development and zone of proximal development). A future implementation based on the Steenbeek’s and Van Geert’s (2008; see also Van Geert, 1998, 2000) may be used to predict and describe potential performance outcomes under different environmental/contextual conditions and ToM components (i.e., level of recursion, dimension: comprehension/prediction).
One limitation of our study was not to use third-order tests to assess if the support supplied could be benefited from the 10- to 11-year-olds; this would have allowed a comparison with the 5–6-year-olds had this been observed in the older age group. For instance, further regressions may have been observed in the older age group if more complex tests were used (see, for instance, Perner & Wimmer, 1985). However, this does not affect the relevance of our findings that show a clear change in the ability to use second-order ToM prediction more efficiently when 5–6-year-old children are confronted with an unfamiliar task such as the ability to explicitly predict future mental states.
Development of second-order prediction appears to make use of a more explicit form of ToM, because an individual must be actively engaged in the estimation of a future mental state, rather than understanding a mental state, which may presume a more passive process (i.e., comprehension). It is therefore not surprising that at the age of 6, EFs undergo a remarkable stage of maturation and that this may have important implications for the development of ToM (Brocki & Bohlin, 2004; Carlson, Moses, & Breton, 2002). For instance, some authors have suggested that EFs may also be a prerequisite for the acquisition of explicit ToM (Moses, 2001; see also Devine & Hughes, 2014).
Furthermore, differences found in our results between the ability to understand past mental states (as reported in a story) or to predict future mental states (as emerging through PC games) may suggest that at this age the dip found in the false belief understanding might be explained as a result of the emergence of the ability to use ToM more explicitly. For instance, this may include the ability to use ToM through time, whereby ToM can be used forwards (i.e., to predict), but also backwards (i.e., to comprehend a mental state). This higher mastery of ToM may also contribute to the temporary conflict between competence and performance (Marcus, 2004): The development of second-order prediction of mental states interferes with second-order comprehension.
Because both comprehension and prediction were fitted separately with a dynamic function that comprises a growth factor (r′) and a limit capacity only (K
In summary, the current study demonstrated that second-order ToM can be fitted by a dynamic rule and that when support was provided, this seemed to compensate for the depletion of cognitive resources associated with performing second-order tasks, particularly for the prediction dimension. These results reinforce the idea that environment and interactions among different ToM dimensions can be conceived as control parameters and implemented in a more complex dynamic system.
Supplemental material
JBD824052_supplemental_material - Development of second-order theory of mind: Assessment of environmental influences using a dynamic system approach
JBD824052_supplemental_material for Development of second-order theory of mind: Assessment of environmental influences using a dynamic system approach by Massimiliano Papera, Anne Richards, Paul van Geert and Costanza Valentini in International Journal of Behavioral Development
Footnotes
Authors’ note
M. Papera and P. Van Geert conceptualized the experiment. M. Papera carried out the study and the data analysis. A. Richards and M. Papera wrote this publication. C. Valentini contributed to the programming of the Strategic Games.
Acknowledgements
We thank Dr. Remi Vredeveldt and Mr. Dennis Mulder for helping the authors during the pilot study in the Netherlands, particularly for the translating from Dutch to English, and to Shanti Van Helden for her assistance in finding schools in the Groningen area. We also thank Dr. Blijd-Hoogewys, who kindly agreed to use her storyboard tests, and Dr. Sara Parsi di Landrone and Dr. Carla Finale for their thoughtful reference review and suggestions in this publication.
We thank the schools where the research took place: the primary school “I. Nieri” in Ponte a Moriano (Lucca, Italy) and the middle school of the “A. Manzoni” Institute in Lammari (Capannori, Lucca; Italy).
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
Supplemental material
Supplemental material for this article is available online.
References
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
