The Development of Divergent Thinking in 4- to 6-Year-Old Children

ABSTRACT

This study investigated the development of divergent thinking (DT) in early childhood. We followed 107 4-year-olds for 1.5 years. Children’s DT was assessed with the Alternative Uses Task (AUT) every 6 months, four times in total. Within the AUT, children were asked to generate unusual uses of common objects while explaining how they came up with these uses. Based on the generated uses, two product measures were computed: fluency and originality. We also applied process measures to gain insight into the thinking processes children used to come up with uses. Based on the coded data of children’s verbal explanations of how they generated uses, two process measures were computed: memory retrieval (retrieving uses from episodic and semantic long-term memory) and mental operations (performing mental operations on the object to generate a use). The results revealed substantial growth in fluency and originality with age. The frequencies of occurrence of both memory retrieval and mental operations also increased with age. In line with previous findings, this longitudinal study shows that creativity develops throughout early childhood. Moreover, this study adds to the current knowledge base by providing researchers a first glance at the development of thinking processes underlying DT in this age range.

Nowadays the rapidly changing technologies continuously pose new challenges, leading to increasing demands on inventiveness and creativity. Divergent thinking (DT), as a core component of creativity, thus, has been extensively researched (Runco & Acar, 2012). As first proposed by Guilford (1956), DT can be defined as a thought process characterized by exploring many possible solutions to a problem, in contrast to convergent thinking that usually follows logical (and largely linear) steps of thinking to reach a certain solution. Given this characteristic, DT is essential for activities that require multi-faceted exploration such as innovation and solving open problems (Bijvoet-van & Hoicka, 2014). Therefore, DT has been increasingly recognized as an important competence (Runco & Acar, 2012), and considerable efforts have been devoted to designing intervention programs for fostering children’s levels of DT (e.g., Bai, Duan, Kroesbergen, Leseman, & Hu, 2019). Relatedly, how DT naturally develops in children has also been a subject of research (e.g., Bijvoet-van & Hoicka, 2014; Gralewski, Lebuda, Gajda, Jankowska, & Wiśniewska, 2017; Krampen, 2012). However, previous studies focused mainly on the development of DT in school-age children and adolescents (see for a review Barbot, Lubart, & Besançon, 2016), and there is a lack of research on how DT develops in the preschool years. To fill this gap, the present study aimed to investigate the developmental trajectory of DT in kindergartners from 4 to 6 years of age.

Development of DT in early childhood: A product perspective

In accordance with Rhodes’ (1961; cited from Kupers, Lehmann-Wermser, McPherson, & Van Geert, 2019) influential 4P framework, creativity can be approached on four levels: the Person (creativity as a characteristic of a person), the Product (creativity as a characteristic of a product), the Process (the process of creating), and the Press (focuses on environmental influences). Previous studies that investigated DT development all approached DT from a product perspective (e.g., Bijvoet-van & Hoicka, 2014; Gralewski et al., 2017; Krampen, 2012). This means that children’s DT ability was assessed based on the outcomes of DT tasks and was generally operationalized with “product” measures such as: (1) fluency, i.e., the number of ideas or products generated by children and (2) originality, i.e., the extent to which the generated ideas or products are statistically rare or rated as original (Reiter-Palmon, Forthmann, & Barbot, 2019).

Using product measures, Krampen (2012) revealed a temporary decline in DT when children enter primary school (see also Smith & Carlsson, 1983; Urban, 1991). In contrast, during the kindergarten years, when children do not yet receive formal education, recent work mainly showed an increase in scores on DT product measures with age. Bijvoet-van and Hoicka (2014) tested DT in 40 children aged 2 to 4 years with the Unusual Box Task (UBT). In the UBT, children were guided to play independently with a set of materials, including a novel box and several unconventional objects. By analyzing the actions that children demonstrated during their exploration of the unusual box, Bijvoet-van den Berg and Hoicka found that the number of unique actions displayed by children (i.e., fluency) and the originality of these actions were both positively correlated with age. Krampen (2012) also found that, in samples of 244 Luxembourg and 312 German kindergarten and primary school children, the fluency and flexibility of children measured by six DT tasks increased over the kindergarten years but then decreased upon entering primary schools. In contrast, Daugherty (1993, N = 42) described that children’s DT decreased from the age of 3 to 5 years and then started to increase from the age of 5 to 6 years.

Studying DT from a process perspective

In addition to studying DT based on product measures, recent studies with adults have increasingly adopted a process approach, shedding light on the dynamic, micro processes of idea generation in order to more fully understand the cognitive mechanisms of creativity. Some studies analyzed the variations of idea originality (Beaty & Silvia, 2012; Hass, 2017b; Wang, Hao, Ku, Grabner, & Fink, 2017) or individuals’ retrieval patterns of episodic and semantic memorial elements (Hass, 2017a) in real time within a DT task to better understand the process of DT. Further, Gilhooly, Fioratou, Anthony, and Wynn (2007) investigated the process of DT by asking university students to think aloud while performing the Alternative Uses Task (AUT). The AUT is a widely applied DT task in which participants are asked to generate alternative uses for common objects (e.g., a brick; Guilford, 1967). Then, Gilhooly et al. analyzed students’ think-aloud reports with a detailed coding scheme. The study revealed that two thinking processes were conducive to DT: (a) the process of retrieving alternative uses from episodic and semantic long-term memory (“memory retrieval” from here on) and (b) the process of performing mental operations on the stimulus object including imagining disassembling the object in parts and recombining these parts in order to come up with new uses (“mental operations” from here on). Specifically, the overall frequency of occurrence of the process memory retrieval during the AUT task was found to predict participants’ fluency and originality, and the overall frequency of occurrence of the process mental operations uniquely predicted participants’ originality.

Extending on Gilhooly et al.’s study, Bai and colleagues examined the thinking processes underlying DT in a cohort of children at the age of 4 years (Bai, Mulder, Moerbeek, Kroesbergen, & Leseman, 2021) and respectively, at the age of 6 years (Bai, Leseman, Moerbeek, Kroesbergen, & Mulder, 2021). In these studies, children were prompted with interactive dialogs to report on their thinking processes while performing the AUT. Analyses of children’s thinking reports revealed that the processes of memory retrieval and mental operations supported the generation of ideas in young children. At the age of 4 years, the frequency of occurrence of memory retrieval predicted fluency but not originality, and the frequency of occurrence of mental operations predicted both fluency and originality (Bai, Mulder, et al., 2021). At the age of 6 years, the frequencies of occurrence of memory retrieval and mental operations were associated with both fluency and originality (Bai, Leseman et al., 2021).

From these three studies, it appears that the two processes – memory retrieval and mental operations – as coded from individuals’ verbalizations underlie the generation of more and especially original ideas in both children and adults (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021; Gilhooly et al., 2007). In this regard, these processes may serve as indicators of individual differences in DT. Compared to the more commonly used product indicators, such process indicators could better inform us on why an individual generates more (or less) original ideas than another individual, and this information could help caregivers or teachers adapt their instructions to the need of individual children. Currently, no study has used process indicators in studying the development of DT in early childhood.

The present study

The present study focused on kindergartners from 4 to 6 years of age before they entered formal education, aiming to investigate the development of DT – a core component of creativity – longitudinally in this period. The significance of studying kindergartners is two-fold. First, currently little research has been done to investigate creativity development in young children. Second, past research has suggested that creativity declines when children enter formal education (Barbot et al., 2016; Krampen, 2012; G. J. W. Smith & Carlsson, 1983; Urban, 1991). Researchers argued that this is most likely due to the predominant focus on the training of academic skills in this period, which comes at the cost of space and time for developing children’s creativity and related competences (Bai et al., 2019; Gralewski et al., 2017).

We used the AUT to assess children’s DT ability from both a product and a process point of view, in line with the method used by Bai, Mulder, et al. (2021) and Bai, Leseman, et al. (2021). Specifically, we aimed to investigate the development of DT by studying the changes in both the product measures (i.e., fluency and originality) and the process measures (i.e., memory retrieval and mental operations) of the AUT over time. In accordance with previous studies, we expected an increase in fluency and originality with age (Bijvoet-van & Hoicka, 2014; Krampen, 2012). Next, since the DT processes memory retrieval and mental operations were suggested to underly fluency and originality (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021; Gilhooly et al., 2007), we hypothesized that we would also observe an increase in the process measures of memory retrieval and mental operations with age. Given the scarcity of previous research, we did not develop specific hypotheses regarding the growth pattern in both product and process measures (i.e., whether growth would be linear or would accelerate or decelerate with age).

Method

Design and procedures

The present study is part of a longitudinal research project on DT in young children approved by the Ethics Review Board of the Faculty of Social and Behavioral Sciences of Utrecht University in 2016 (reference number: FETC16-066). The project employed a longitudinal design and followed a cohort of children for 1.5 years, from the time that these children entered kindergarten (around 4 years of age) until shortly before they enrolled in formal education (around 6 years of age). Children were measured approximately every 6 months, across four measurement waves. Children were measured on DT and creativity at all waves and additionally on executive functions at the last measurement wave. The present study utilized the DT data, collected using the AUT. Other data are reported in (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021).

To cope with possible testing effects as a consequence of the repeated-measure design, we applied two control procedures. First, to minimize the testing effect, we used two parallel sets of stimuli for the AUT and used them alternately at successive measurement waves. Next, to enable an examination of the testing effect, half of the children, randomly selected, were not tested at the second measurement wave.

At all measurement waves, children were tested individually in a separate room at their schools. Data collection was carried out by trained bachelor’s and master’s students in educational sciences. The training included carefully reading the test manual, watching example test sessions, and reading test transcripts, and practicing the test procedure prior to the actual data collection. In addition, to monitor the quality of test administration, the first author (a) supervised the first two to three test sessions in the field conducted by students and gave feedback when needed and (b) was present at test sessions of all students on a number of occasions across the data collection period.

Participants

Participants were recruited from four typical primary schools in the Netherlands, where kindergarten education is part of the primary school system and comprises the first two of a total of eight grades (see Appendix A for elaborations on the Dutch school system). Two schools were found through the personal network of the last author. Via the principal of one of these schools, two other schools were approached, which subsequently indicated their willingness to participate. All four schools were in middle-class neighborhoods in urban areas, and children in these schools mostly came from middle to high SES families. To recruit participants, schools sent information about the project and the call for participation to parents of all 4-year-olds who were in the first kindergarten grade at the time of the first measurement wave. Based on the available data, about 70% of the parents gave their informed consent in either written form or via e-mail. Eventually, a total of 107 children (49 boys and 58 girls; age ranged from 3.87 to 5.10 years, M = 4.44, SD = 0.26) were enrolled in this project.

Sample size and missing data

Missing data were present at each measurement wave: (1) At the first wave, four children did not finish the DT test and three children’s tests were not recorded due to technical issues. In addition, at this specific wave, 16 children’s data had to be excluded as the experimenter who administered the tests did not prompt children to report on their thinking processes. (2) At the second wave, in addition to the 54 children who were randomly selected to not be tested as explained above, one child did not finish the test and another child was sick on test days. (3) At the third wave, three children were not tested as they moved to other schools, one child refused to attend the test, and another child’s video recording was missing. And (4) at the fourth wave, four children were not tested as they moved to other schools, one child refused to attend the test, and another child was not available on test days. Eventually, the actual sample sizes were 84 (44 girls and 40 boys), 51 (27 girls and 24 boys), 102 (54 girls and 48 boys), and 101 (53 girls and 48 boys) at the first, second, third, and fourth measurement wave respectively.

Measures

The Alternative Uses Task was used to assess children’s level of DT (Gilhooly et al., 2007; Guilford, 1967). Children were required to generate as many different and unusual uses as possible for common objects while also explaining how they came up with these uses. Two parallel sets of AUT test stimuli, each containing six common objects, were used alternately in successive measurement waves. The first set included pictures of a hand towel, a brick, a fishnet, a basket, a broom, and a spoon as stimuli and were used at the first and third measurement waves; and the second set included pictures of a lunch box, a tire, an umbrella, a pencil, a shovel, and a toothbrush as stimuli and were used at the second and fourth measurement waves.

Test procedures of the Alternative Uses Task

The experimenter first explained to the child that they would be shown pictures of several common objects and that they were required to think of as many different and unusual uses as possible for each object. Next, the experimenter showed the child a real newspaper as an example object to explain the purpose of the task. At this step, the experimenter (a) started the conversation by asking what a newspaper could be used for, then (b) gave three unusual uses of the newspaper (occasionally additional example uses were given when children did not understand the instruction) and explained the thinking processes underlying the generation of these uses, e.g., “if you are going to paint, I have seen once that my mother used a newspaper to keep the table clean” or “you can fold the newspaper, then you have a hat,” and finally (c) asked the child to give unusual uses of the newspaper and explain their thinking processes in a similar way. After this example item, the experimenter presented six formal test stimulus objects, one by one, in a randomized order for each child.

For each stimulus, children were instructed to generate as many different and unusual uses as possible and to report on their thinking processes. During this process, the experimenter gave ample verbal prompts to encourage children (a) to generate more ideas, e.g., “What else can you use a basket for?,” (b) to elaborate on their ideas, e.g., “How do you do that?,” “Can you tell me more about it?,” and (c) to explain their thinking processes, e.g., “How did you come up with this idea?,” “Have you done that before?.” The tests were conducted without a time limit as is common in research with young children to accommodate differences in speech rate and expressive abilities. The whole test took between 15 to 35 minutes, including the instructions and breaks.

All AUT test sessions were video-recorded and subsequently transcribed verbatim for further coding and scoring. Context information related to the test situation but not reflected in the verbalizations (children’s use of signs and gestures, interruptions of the test, et cetera) was additionally noted in the transcripts to facilitate the understanding and correct interpretation of children’s utterances. The transcripts served as the main source for the assessment of children’s DT. However, when doubts or questions arose during coding, video recordings of the test sessions were checked.

Product measures: Scoring based on generated ideas

Two product measures, fluency and originality, were computed based on the uses children generated for the AUT stimuli.

Fluency

Fluency referred to the average number of distinct uses children generated per stimulus object. Two uses were considered to be distinct if either the involved actions or the mentioned objects that afforded the actions were different. For instance, using a brick, the uses of “to build a house” and “to break the house” were distinct from each other as they involved different actions. Meanwhile, the uses of “to build a house” and “to build a bridge” were distinct from each other as, although they involved the same action “to build,” the objects that afforded this action, namely “a house” and “a bridge,” differed from each other. In practice, children’s fluency scores were obtained in two steps: first a fluency score was calculated per stimulus object (i.e., the number of distinct uses), and then, the fluence scores of all stimuli were averaged.

Originality

The calculation of originality scores was based on the action types involved in the generated uses. In practice, children’s originality scores were obtained in three steps. First, all distinct uses generated by all children were categorized based on the involved type of actions, for each stimulus separately. In this regard, using a brick “to build a house” and “to build a bridge” were categorized together as involving the action type of “to build something.” Next, each action type was scored on originality based on how frequently participants mentioned this action type, applying the following equation:

Originality of an action type = 1 – the number of participants who mentioned this action type/the total number of participants

Finally, the originality scores were summed per stimulus, and subsequently, the originality scores of all stimuli were averaged for each child. In Appendix B we presented examples of frequently and infrequently mentioned action types for each stimulus, and further details are given in Appendix C about the reference sample used for computing originality scores to allow comparison across study waves.

We opted for coding originality scores based on action types, and coding fluency scores based on distinct uses, to prevent children’s originality scores being confounded by fluency scores. For instance, a child may say “you can put an apple in the basket, a banana, an orange … ”). If we would have summed the originality scores of all uses (i.e., put an apple in the basket, put a banana in the basket, etc.), the correlation between children’s fluency and originality scores would be very high (Bai, Mulder, et al., 2021).

Process measures: Scoring based on thinking reports

Two processes were coded from children’s explanations regarding how uses were generated, using the coding scheme developed by Bai, Leseman, et al. (2021; see Appendix D): (a) memory retrieval, this process was coded when children referred to retrieval from semantic or episodic memory, for example when referring to past experiences to explain a use, e.g., “I do that (use a toothbrush to brush teeth) everyday”; and (b) mental operations, this process was coded when children referred to performing mental operations on the stimulus while generating a use, e.g., “If you attach a lot of balloons on it (basket), which keeps floating, a lot a lot, then you can sit in there just like a hot air balloon.”

The scores on the process measures referred to how often children explained their thinking of uses in reference to those DT processes. To derive the scores, first, the AUT transcripts were divided into episodes. Each episode contained a use and the related explanations of this use as given by the children. Second, each of these episodes was coded for the occurrence of memory retrieval and mental operations, separately: 1 was coded if children had made one or more references to the process, and 0 was coded if children had not made any reference to this process. Children could refer to none, one, or both DT processes in explaining how they came up with one particular use within one episode. Between 10% to 20% of the transcripts of each measurement wave were double coded, and Cohen’s Kappa’s (see Table 1) showed “moderate” to almost “perfect agreement” (Gwet, 2014) between two coders. Later, only the coding of the main coder (i.e., the first author) was used. Finally, the frequencies of occurrence of each process measure across stimuli were averaged per child and regarded as scores on this process measure.

Table 1. Inter-Coder Reliability of Divergent Thinking (DT) Processes (Cohen’s Kappa’s).

Wave	First wave	Second wave	Third wave	Fourth wave
Memory retrieval	.88	.87	.80	.80
Mental operations	.85	.73	.84	.69

Analysis plan

Multilevel regression analyses were applied to analyze the longitudinal data (level-1: study wave; level-2: child). Note that we included all available data of the AUT across measurement waves in the analyses, also for participants with incomplete data. In accordance with Hox, Moerbeek, and Van de Schoot (2017) and Snijders and Bosker (2012), the possibility to handle incomplete data is a great advantage of multilevel analysis of longitudinal data, as it increases the sample size and, thus, the precision of the estimates and the power of the statistical tests. Children’s age (in years) at each measurement wave was used as a time-varying (level-1) predictor of children’s DT measures, given the wide age range at each measurement wave (Hox et al., 2017, p. 84).

First, we investigated the change in the product measures of fluency and originality over time using data of all measurement waves. Because fluency and originality were two theoretically related measures of DT products, multivariate multilevel regression analyses were applied to analyze these two measures together.¹ In practice, three multivariate models were run: (a) M0, an intercept-only model; (b) M1, a model with linear and quadratic effects of age (level-1), allowing these effects to vary across children; (c) M2, a more parsimonious model of model M1. Detailed explanations regarding which effects were removed from the previous model and the reasons for these removals are given in the Results section; and (d) M3, a model with the effect of stimulus set (level-1) for examining the influence of stimulus set on the product measures of children’s DT when the effect of age was controlled.

Second, we investigated the change in the process measures of memory retrieval and mental operations over time using data of all measurement waves. Again, because memory retrieval and mental operations were two theoretically related measures of DT processes, multivariate multilevel regression analyses were applied to analyze these two measures together. Three multivariate models, identical to the models described above for the product measures, were run: (a) M0, an intercept-only model; (b) M1, a model with linear and quadratic effects of age (level-1), allowing these effects to vary across children; (c) M2, a more parsimonious model of model M1. Detailed explanations regarding which effects were removed from the previous model and the reasons for these removals are given in the Results section; and (d) M3, a model with the effect of stimulus set (level-1) for examining the influence of stimulus set on the process measures of children’s DT when the effect of age was controlled. In case the variable stimulus set was not a significant predictor of product and process measures in both the M3 models, the stimulus sets were considered to be equivalent.

We also carried out additional analyses to examine whether a testing effect was present due to the repeated-measure design. This was done by investigating whether being repeatedly tested at the second measurement wave influenced the change in children’s DT scores across the other measurement waves. To this end, the change in children’s DT over time was modeled with data of the first, third, and fourth measurement waves. The group variable that defined if children were tested at the second measurement wave (1 = tested at the second wave and 0 = not tested at the second wave) was used as a level-2 predictor. Separately for the product measures and for the process measures, three multivariate multilevel regression models were run: (a) an intercept-only model; (b) a model with the linear effect of age (level-1), allowing this effect to vary across children; and (c) a model with the main effect of group (level-2) and the interaction effect of age by group (cross-level).

All models were fitted in SuperMix version 2.1 (Hedeker, Gibbons, du Toit, & Cheng, 2008) and the maximum likelihood estimation was used. Age was entered in all models grand-mean centered to avoid multicollinearity between the linear and quadratic terms. We used an alpha level of .05 for all statistical tests.

Results

Descriptive statistics

The descriptive statistics as presented in Table 2 showed two patterns. First, the means of all measures increased across measurement waves. On average, children improved from generating 2.67 uses at the first measurement wave (M_age = 4.44 years) to generating 4.21 uses at the fourth measurement wave (M_age = 5.93 years), with an effect size Cohen’s d = 1.00. Moreover, across measurement waves, children referred to memory retrieval more frequently than to mental operations when explaining their thinking of novel uses. Second, the standard deviations of all measures increased across waves, indicating that individual differences on these measures gradually enlarged when children grew older.

Table 2. Descriptive Statistics of Divergent Thinking Measures and Age per Measurement Wave.

Measure	Wave ^a	M	SD	Min.	Max.	Skew.	Kurt.
Fluency	1	2.67	1.25	0.50	8.50	1.58	4.83
	2	3.05	1.20	1.50	7.50	1.37	2.76
	3	4.14	1.65	1.50	11.33	1.11	2.74
	4	4.21	1.79	1.00	11.00	1.58	2.96
Originality	1	0.85	0.46	0.18	2.44	1.14	1.77
	2	1.38	0.87	0.11	4.37	1.50	2.61
	3	1.88	1.03	0.21	4.55	0.62	–0.17
	4	2.20	1.30	0.11	8.00	1.93	5.41
Memory retrieval	1	0.97	0.60	0.00	2.50	0.51	–0.37
	2	0.75	0.54	0.00	2.33	0.83	0.52
	3	1.40	0.74	0.17	3.83	0.87	0.71
	4	1.80	1.05	0.00	6.00	1.35	2.93
Mental operations	1	0.08	0.19	0.00	1.33	4.02	21.76
	2	0.25	0.42	0.00	2.17	2.62	8.63
	3	0.38	0.57	0.00	2.50	2.26	4.89
	4	0.50	0.69	0.00	3.67	2.59	7.49
Age	1	4.44	0.26	4.02	5.10	0.32	–0.92
	2	4.86	0.26	4.35	5.36	0.14	–0.93
	3	5.45	0.26	4.91	5.99	0.20	–0.83
	4	5.93	0.27	5.45	6.53	0.28	–0.80

^aN for wave 1–4 were 84, 51, 102, and 101 respectively.

Change in DT over time and the influence of stimulus set

To investigate the developmental trajectory of DT, the change in children’s DT over time was modeled using data of all measurement waves. In addition, the influence of stimulus set on the development of DT was examined. The results on the product measures are presented in Table 3, and the results on the process measures are presented in Table 4.

Table 3. The Effects of Age and Stimulus Set on the Product Measures of Divergent Thinking (N = 106, with 338 units at the measurement level).

Model	M0: Intercept-only		M1: age		M2: age (A more parsimonious model of M1)		M3: Stimulus set
Measures	Fluency	Originality	Fluency	Originality	Fluency	Originality	Fluency	Originality
Fixed part	Coeff. (s.e.)
Intercept	3.65 (0.11)***	1.65 (0.07)***	3.74 (0.12)***	1.64 (0.08)***	3.64 (0.11)***	1.64 (0.07)***	3.48 (0.14)***	1.66 (0.09)***
Linear age			1.02 (0.14)***	0.86 (0.10)***	1.01 (0.12)***	0.85 (0.08)***	1.13 (0.13)***	0.84 (0.09)***
Quadratic age			–0.28 (0.20)	–0.01 (0.12)
Stimulus set							0.28 (0.16)	–0.02 (0.09)
Random slope
σ^2linear age			0.56 (0.34)	0.37 (0.14)*	0.16 (0.23)	0.15 (0.10)	0.18 (0.23)	0.15 (0.10)
σ^2quadratic age			0.12 (0.58)	0.10 (0.23)
Random effect
σ^2child	0.70 (0.20)***	0.27 (0.09)**	0.55 (0.25)*	0.26 (0.10)*	0.81 (0.19)***	0.36 (.08)***	0.81 (0.18)***	0.36 (0.08)***
σ^2wave	2.14 (0.20)***	0.99 (0.09)***	1.57 (0.20)***	0.55 (0.07)***	1.54 (0.17)***	0.55 (0.06)***	1.51 (0.17)***	0.55 (0.06)***
f ^2			0.34	0.56	0.21	0.38	0.22	0.38
Deviance (df)	1862.67 (8)		1702.97 (30)		1711.85 (17)		1701.08 (19)
Δdeviance (Δdf)			159.7 (22)***, vs. M0		150.82 (9)***, vs. M0		10.77 (2)**, vs. M1

In accordance with Lorah (2018), f ² indicates the proportion of variance explained in an outcome measure by a model with explanatory variables relative to the intercept-only model.

* p < .05. ** p < .01. *** p < .001.

Table 4. The Effects of Age and Stimulus Set on the Process Measures of Divergent Thinking (N = 106, with 338 units at the measurement level).

Model	M0: Intercept-only		M1: age		M2: age (A more parsimonious model of M1)		M3: Stimulus set
Measures	Memory retrieval	Mental operations	Memory retrieval	Mental operations	Memory retrieval	Mental operations	Memory retrieval	Mental operations
Fixed part	Coeff. (s.e.)
Intercept	1.32 (0.06)***	0.32 (0.04)***	1.26 (0.07)***	0.30 (0.05)***	1.26 (0.07)***	0.30 (0.05)***	1.18 (0.09)***	0.31 (0.06)***
Linear age			0.61 (0.08)***	0.28 (0.05)***	0.59 (0.07)***	0.27 (0.05)***	0.64 (0.08)***	0.27 (0.05)***
Quadratic age			0.19 (0.10)	0.04 (0.07)	0.19 (0.10)*	0.04 (0.06)	0.23 (0.10)*	0.03 (0.06)
Stimulus set							0.12 (0.08)	–0.01 (0.05)
Random slope
σ^2linear age			0.23 (0.10)*	0.08 (0.04)	0.15 (0.07)*	0.02 (0.03)	0.16 (0.08)*	0.02 (0.03)
σ^2quadratic age			0.04 (0.16)	0.01 (0.07)
Random effect
σ^2child	0.13 (0.05)**	0.08 (0.02)***	0.17 (0.07)*	0.10 (0.03)	0.23 (0.05)***	0.10 (0.02)***	0.24 (0.05)***	0.10 (0.02)***
σ^2wave	0.64 (0.06)***	0.22 (0.02)***	0.40 (0.05)***	0.18 (0.02)***	0.39 (0.04)***	0.17 (0.02)***	0.39 (0.04)***	0.17 (0.02)***
f ^2			0.34	0.56	0.36	0.08	0.38	0.08
Deviance (df)	1363.54 (8)		1209.45 (30)		1207.94 (19)		1205.51 (21)
Δdeviance (Δdf)			154.09 (22)***, vs. M0		155.60 (11)***, vs. M0		2.43 (2), vs. M1

In accordance with Lorah (2018), f ² indicates the proportion of variance explained in an outcome measure by a model with explanatory variables relative to the intercept-only model.

* p < .05. ** p < .01. *** p < .001.

Results on the product measures

The results of the intercept-only model (M0) revealed that the ICCs for fluency and originality were .25 and .21 respectively, meaning that 25% of the variance of the fluency scores and 21% of the variance of the originality scores was at the child level (level 2).

Changes in fluency and originality over time

Compared to the multivariate intercept-only model (M0), adding the linear and quadratic effects of age to the model and allowing these effects to vary across children (M1) significantly improved the model fit. Given that, in this model, the quadratic effects were not significant, nor were the variances as estimated for these quadratic effects, we ran a more parsimonious model without these effects (M2). The parsimonious model was favored because the deviance of the model was only slightly higher while the number of parameters decreased substantially.

The results of the parsimonious model (M2) showed that the linear effect of age was significant on both fluency and originality. The standardized coefficient of the linear effect of age was larger for originality (=0.48) than for fluency (=0.38). Thus, one standard deviation increase in age was related to 0.48 expected standard deviations increase in originality and 0.38 expected standard deviations increase in fluency. Next, the results of the M2 model also showed that the linear effects of age on fluency and originality did not vary across children.

The influence of stimulus set on fluency and originality

Next, adding stimulus set as a predictor again improved the model fit (M3). However, when the linear effect of age was taken into account, the effect of stimulus set was not significant on both fluency and originality. These results indicated that stimulus set had no or only a very limited influence on the product measures of children’s DT.

Results on the process measures

The results of the intercept-only model (M0) revealed that the ICCs for memory retrieval and mental operations were .17 and .27 respectively, meaning that 17% of the variance of the memory retrieval scores and 27% of the variance of the mental operations scores was at the child level (level 2).

Changes in memory retrieval and mental operations over time

Compared to the multivariate intercept-only model (M0), adding the linear and quadratic effects of age and allowing these effects to vary across children (M1) significantly improved the model fit. In this model, the quadratic effect of age showed borderline significance (p = .06) on memory retrieval and no significance on mental operations, and the variances of both quadratic effects were not significant. Therefore, we ran a more parsimonious model without the random terms of the quadratic effects of age (M2). The more parsimonious model was favored given that the deviance of the model was smaller with less parameters.

The results of the parsimonious model (M2) showed that, first, the linear effect of age was significant on both memory retrieval and mental operations. In addition, the standardized coefficient of the linear effect of age was larger for memory retrieval (=0.43) than for mental operations (=0.31). Second, the quadratic effect of age became significant on memory retrieval in this model, with a standardized coefficient of 0.09, but not on mental operations for which the standardized coefficient was 0.03. Taken together, these results indicated that, with increasing age, children increasingly referred to both memory retrieval and mental operations in explaining how they came up with their ideas. In particular, the growth rate of referring to the process of memory retrieval in children accelerated with age.

Finally, it is worth noting that the variance of the linear effect of age was significant on memory retrieval (but not on mental operations), indicating that the growth rate of referring to the process of memory retrieval varied across children. Based on the estimated linear slope of age on memory retrieval and its variance across children, we computed a 95% predictive interval for the linear slope, which turned out to be between −0.19 and 1.37, meaning that the random linear slopes of age among children were expected to lie between −0.19 and 1.37.² In Figure 1 we plotted the change in the measure of memory retrieval by age in which different linear slopes of age were used. As shown in this figure, regardless of the overall accelerating trend (i.e., the solid curve), there was still a small proportion of the children who might, in contrast, decrease or stay at the same level over time with respect to memory retrieval (i.e., other curves).

Figure 1. The Changes in Memory Retrieval Over Age.

The influence of stimulus set on memory retrieval and mental operations

Finally, adding stimulus set (M3) did not improve the model fit. While the linear and quadratic effects of age were considered, the effects of stimulus set on memory retrieval and mental operations were not significant, indicating that stimulus set had no influence on the process measures of children’s DT.

Control analyses on the testing effect

To examine whether a testing effect was present, the change in DT over the first, third, and fourth measurement waves were compared between children who were measured at the second measurement wave and children who were not (“group” variable). Results of multivariate models were similar for the product and the process measures, as presented in Table 5 and 6 respectively.

Table 5. Examining the Testing Effect in the Product Measures of Divergent Thinking (N = 106, with 287 units at the measurement level).

Model	Intercept-only model		Random slope model		The effect of group
Measure	Fluency	Originality	Fluency	Originality	Fluency	Originality
Fixed part	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)
Intercept	3.73 (0.12)***	1.69 (0.08)***	3.66 (0.12)***	1.63 (0.08)***	3.80 (0.16)***	1.64 (0.11)***
Age			1.02 (0.13)***	0.87 (0.09)***	1.04 (0.18)***	0.89 (0.12)***
Group					–0.30 (0.23)	–0.02 (0.15)
Age × Group					–0.07 (0.26)	–0.03 (0.18)
Random slope
σ^2age at child level			0.12 (0.29)	0.18 (0.13)	0.12 (0.29)	0.19 (0.13)
Random effect
σ^2child	0.56 (0.22)*	0.20 (0.09)*	0.73 (0.21)***	0.35 (0.09)**	0.71 (0.21)***	0.35 (0.09)**
σ^2wave	2.44 (0.26)***	1.13 (0.12)***	1.81 (0.24)***	0.66 (0.09)***	1.81 (0.24)***	0.66 (0.09)***
f ^2			0.18	0.32	0.19	0.32
Deviance (df)	1632.50 (8)		1499.35 (17)		1493.55 (21)
Δdeviance (Δdf)			133.15 (9)***, vs. M0		5.8 (13), vs. M1

In accordance with Lorah (2018), f ² indicates the proportion of variance explained in an outcome measure by a model with explanatory variables relative to the intercept-only model.

* p < .05. ** p < .01. *** p < .001.

Table 6. Examining the Testing Effect in the Process Measures of Divergent Thinking (N = 106, with 287 units at the measurement level).

Model	Intercept-only model		Random slope model		The effect of group
Measure	Memory retrieval	Mental operations	Memory retrieval	Mental operations	Memory retrieval	Mental operations
Fixed part	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)	Coeff. (s.e.)
Intercept	1.41 (0.06)***	0.34 (0.04)***	1.39 (0.06)***	0.31 (0.04)***	1.40 (0.09)***	0.29 (0.06)***
Age			0.49 (0.07)***	0.28 (0.05)***	0.54 (0.10)***	0.21 (0.07)**
Group					–0.02 (0.12)	0.06 (0.08)
Age × Group					–0.09 (0.14)	0.14 (0.10)
Random slope
σ^2age at child level			0.11 (0.08)	0.06 (0.04)	0.11 (0.08)	0.05 (0.04)
Random effect
σ^2child	0.15 (0.06)**	0.08 (0.03)**	0.24 (0.06)***	0.11 (0.03)**	0.24 (0.06)***	0.11 (0.03)**
σ^2wave	0.64 (0.07)***	0.24 (0.03)***	0.42 (0.06)***	0.20 (0.03)***	0.42 (0.06)***	0.20 (0.03)***
f ^2			0.20	0.03	0.20	0.03
Deviance (df)	1189.88 (8)		1068.02 (17)		1065.31 (21)
Δdeviance (Δdf)			121.86 (9)***, vs. M0		2.71 (13), vs. M1

In accordance with Lorah (2018), f ² indicates the proportion of variance explained in an outcome measure by a model with explanatory variables relative to the intercept-only model.

* p < .05. ** p < .01. *** p < .001.

The results of the intercept-only models revealed that the ICCs were .19 for fluency, .15 for originality, .19 for memory retrieval, and .25 for mental operations. Next, adding the linear effect of age and allowing this effect to vary across children (i.e., the random slope models) significantly improved the model fit compared to the intercept-only models for both the product and process measures. The effect of age was significant on all measures, including fluency, originality, memory retrieval, and mental operations. Finally, adding the main effect of group and the interaction effect of age by group did not further improve the model fit, and neither were the main effect of group and the interaction effect of age by group significant for any outcome measures. Thus, whether or not children were tested at the second measurement wave did not influence children’s DT performance over time, indicating that a testing effect was absent. For conciseness, we did not report on results of the more complex models that also included the quadratic effect of age and the interaction effect of quadratic age by group, as also in those models, none of the Group-effects was significant.

Discussion

The present study investigated young children’s development of DT from the age of 4 to 6 years using a longitudinal design, from both a product and a process point of view. The results revealed that children’s levels of DT improved with age. A linear increase was found for the product measures fluency and originality and the process measure mental operations. The process measure memory retrieval showed non-linear growth; specifically, the increase in this measure accelerated with age. Moreover, this increase varied across children, showing that some children grew faster than others in this measure over time. Next, we found no evidence for significant effects on outcome measures of either using different AUT stimulus sets or repeatedly testing children with the AUT.

The finding that children’s fluency and originality scores increased over time between 4 and 6 years of age converge with findings of previous studies. These studies, employing product measures of DT such as fluency and originality, showed that DT increases with age during early childhood (Bijvoet-van & Hoicka, 2014; Krampen, 2012; c.f., Daugherty, 1993). In addition to this general trend, the results of the current study showed that the increases in fluency and originality were linear, which has not been previously investigated.

Next, the finding that children showed an increase with age in the reported application of two key DT processes, that is, memory retrieval and mental operations, also confirm our hypotheses. Past research has revealed that these DT processes were conducive to the generation of novel ideas in the AUT. For example, Gilhooly et al. (2007) found, in adults, that the overall frequency of occurrence of memory retrieval during the AUT predicted participants’ fluency and originality scores, and that the overall frequency of occurrence of mental operations predicted participants’ originality. Moreover, in Bai, Leseman, et al.’s (2021) study with 4-year-olds, the frequency of occurrence of memory retrieval was found to predict fluency, and the frequency of occurrence of mental operations was found to predict both fluency and originality. When these children grew older and were tested again at 6 years of age, the frequencies of occurrence of both memory retrieval and mental operations were positively associated with fluency and originality (Bai et al., 2021). The increasing application of these processes with age, especially alongside an increase in fluency and originality, lends further support to the idea that memory retrieval and mental operations underly the generation of novel ideas during the AUT. Thus, the use of such process indicators in the study of the development of DT in early childhood can inform us of why some children may generate more novel ideas than others.

A particular interesting finding regarding the process measures of DT was that memory retrieval developed rapidly, and the increase in this measure accelerated with age. In the current study, the process memory retrieval was coded when children explained a particular use generated for a stimulus object by referring to information from semantic or episodic memory (e.g., personal past experiences). In this regard, the accelerated development of children on the process measure of memory retrieval can be explained by children’s fast acquaintance of knowledge and experience and their fast-developing language skills (Hoff, 2009).

First, with growing age and cumulating knowledge and experiences, children might simply have acquired more ideas and associations between ideas to support thinking of novel uses of stimulus objects. That is, their long-term semantic and episodic memories have expanded and become richer. Attending kindergarten from age 4 introduces children to a new physical, social, and educational context next to family life. In this new context, children are offered materials and opportunities for exploration and discovery, through which they can gain new experiences and knowledge about the world and enrich their memory (Lockman, 2000; Lockman & Kahrs, 2017; Oudgenoeg-Paz, Volman, & Leseman, 2016). This explanation is indirectly related to the finding that memory retrieval was not associated with the originality of mentioned uses at age 4 (Bai, Mulder, et al., 2021), while it was at age 6 (Bai, Leseman, et al., 2021). Perhaps, only a rich semantic and episodic memory can contribute to the generation of original ideas, but this conjecture is to be tested in future research.

Second, due to the progression in language development, children might have also improved in their ability to verbally express their memories and thoughts over time. The age range of 4 to 6 years is marked by rapid development of expressive vocabulary, grammatical knowledge, and pragmatic skills (Hoff, 2009). Research has shown that children’s rapidly growing expressive language skills help them to better express their inner thoughts when they are, as in the present study, supported with cues or interactive dialogs (Flavell, Green, & Flavell, 2000). In fact, typical kindergarten settings such as circle time were also found to promote children’s skills in reflecting upon and talking about their personal experiences (Fivush, 2011; Gathercole, 1998; Nelson & Fivush, 2004). This, in turn, could help children to structure their episodic memory and to develop encoding and retrieval strategies that promote retention and recall of richer details of experienced events. Maybe for these reasons, enrolling in kindergarten for some children may even boost their memory-based DT processes. As shown in the current study, children scoring low on memory retrieval at age 4 developed more rapidly than children scoring high at that age (see Figure 1).

There was also an increase in children’s references to mental operations with age, although the references to this process occurred less frequently overall, compared to memory retrieval at all measurement waves. For the development of children’s reported use of mental operations, three possible explanations can be considered.

First, attending kindergarten also increases children’s opportunities for learning about object properties in exploratory play within a well-furnished, stimulus-rich environment. This could provide children with the perception-action knowledge to manipulate and potentially also simulate disassembling, singling-out, rotating, and recombining object properties in novel ways (Lockman, 2000; Lockman & Kahrs, 2017; Oudgenoeg-Paz et al., 2016). Indeed, abundant evidence shows a relationship between exploration and spatial cognition (e.g., Newcombe, 2002; Oudgenoeg-Paz et al., 2015). Exploratory play is a predominant activity in Dutch kindergarten (SLO, 2020), which could have contributed to children’s development in applying mental operations on stimulus objects to come up with novel ideas in the current study.

Second, performing mental operations on a real or imagined stimulus object and its properties while resisting the common affordance structure of this object is effortful in nature. As has been argued in previous research, these processes require working memory involvement to hold a mental representation of the object or its properties in active memory in order to mentally operate (e.g., rotate) on this representation (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021; Gilhooly et al., 2007; Nusbaum & Silvia, 2011). Therefore, the development of the process of mental operations might also be associated with children’s gradually maturing visuo-spatial working memory in this age period (Cowan & Alloway, 2009; Diamond, 2013).

Third, like for memory retrieval, children’s growing expressive language skills enabled them to better reflect upon and report about their thinking, which could also explain part of the growth in the reported use of mental operations.

Strengths, limitations, and future research

The present study contributes to the current literature on DT in two ways. First, we confirmed that DT is already present in children as young as 4 years of age, and DT shows rapid development in the two years before children enroll in formal education. Second, to the best of our knowledge, the present study is the first to study the development of DT in young children from a process perspective, focusing on two types of DT processes that are conducive to creativity (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021; Gilhooly et al., 2007). In addition, the robustness and the generalizability of the reported findings were enhanced as we worked with different stimulus sets at consecutive measurement waves (to avoid testing effects) and used multivariate regression models to analyze theoretically related outcome measures in the same models (to reduce the probability of type I error).

The present study also has several limitations. One limitation is the psychometric quality of the AUT and the DT process measures in children this young. First, the distributions of some DT measures were skewed, particularly at the earlier measurement occasions and regarding the DT process mental operations. These results indicate that the AUT itself and the request to reflect upon thinking processes was difficult for children of 4 or 5 years of age. This was also reflected in the fact that, although being prompted, children did not give a clear and codable explanation for about 50% of the uses generated at each measurement wave. Second, the test procedures have put a heavy demand on children’s verbal skills. To keep the testing time short, we did not take separate measures of children’s language skills and therefore, could not test whether children’s language skills impacted the performance on the AUT . Yet, such impact is likely. In a recent study, Avila (2016) found that vocabulary knowledge was positively related to children’s performance on the AUT. Future research should investigate how the development of language skills influences the development of DT, for example by including concurrent longitudinal language measures in the analysis, or by applying the prompt-testing method to DT tasks that is less dependent on verbal ability (e.g., prompting object play with the Unusual Box Task designed by Hoicka et al., 2016).

Related to the use of prompting, two other limitations need to be considered. One limitation is that the use of prompts may have introduced, to some extent, subjectivity and experimenter-variance. Although the experimenters were instructed to prompt children to report on their thinking after each generated idea, in practice this was not possible because it tended to break children’s thinking flow and sometimes even upset children. Therefore, the experimenters had to decide in the field when and how many prompts were given to keep a balance between prompting children to give explanations and keeping them feel comfortable with the test. Next, specifically the prompts such as “Have you done that before?” could have primed the process memory retrieval and thus, increased the probability that children would refer to this process to explain how they came up with a particular idea. Given that we applied the same prompting procedure at all four measurement waves, we consider that our conclusions regarding the developmental trend of the DT process memory retrieval still stand. We recommend future research to adopt a more standardized procedure in giving verbal prompts during the testing of the AUT or other DT tasks for obtaining children’s thinking reports. In particular, whether and when to use prompts that may prime some types of thinking processes should be thoroughly thought through, and the effects of such prompts should be more rigorously examined. Next, in addition to analyzing children’s thinking reports, another complementary approach to understand the process of DT is to analyze children’s exploratory behaviors on action-based tasks. Some studies have shown that action-based DT tasks work well in capturing the full ability range of DT in children as young as 1 to 2 years (Hoicka et al., 2016; Hoicka, Powell, Knight, & Norwood, 2018).

There were also limitations regarding the design of the current study. First, to examine testing effects, we randomly excluded half of the participants for the AUT test at the second measurement wave. This was a simple and pragmatic approach given the limited resources that were available for the current study. For a more robust investigation of the effects of repeated testing, future research is recommended to include equivalent control groups at all measurement waves in which participants are only tested once. Second, when two equivalent sets of stimuli are used at different measurement waves, as was the case in the current study, the two stimulus sets should be counter-balanced across waves in future research. Third, the present study was not designed to detect possible fluctuations (e.g., temporary declines or spurts) in children’s DT ability on a more fine-grained time scale, nor to uncover the effects of major transitions, such as the transition from home to kindergarten and from kindergarten to primary school. To gain more insight in the dynamic aspects of DT development and the impact of transitions, it is recommended for future research to apply more frequent measurements and to schedule sufficient measurements before and after major transitions. This type of design could be used to test whether DT development indeed accelerates upon kindergarten enrollment and slows down after the transition to primary school, as has been suggested in past research (Gralewski et al., 2017; Krampen, 2012).

Finally, due to the limited sample size, we could not relate the developmental trajectories of the process measures memory retrieval and mental operations to the developmental trajectories of the product measures fluency and originality. Therefore, it remains uncertain to what extent growth in fluency and originality is possibly caused by growth in the DT processes. In our previous cross-sectional studies with the current sample at age 4 and age 6, we found significant predictive effects of the process measures on the product measures (Bai, Leseman, et al., 2021; Bai, Mulder, et al., 2021). Future research employing, for example, Latent Change Score modeling (combining growth modeling with cross-lag path analysis) in a larger sample would be needed to establish more firmly whether changes in the DT process measures can be regarded to be causally related to changes in the product measures (for an example of such an approach, see Verhagen, Boom, Mulder, De Bree, & Leseman, 2019).

Conclusion

The present study investigated the development of DT in children from the age of 4 to 6 years using both product and process measures. A linear increase in DT with age was found for the product measures of fluency and originality and for the process measure of mental operations. The development of the process measure memory retrieval showed an increase that accelerated with age. The present study provides a first glance at the development of the thinking processes involved in DT in young children. Future research is recommended to investigate the development of DT together with the development of other skills that are involved in DT, such as knowledge, working memory, and language skills, to unravel what drives DT development. Next, we also encourage researchers to examine DT development around major transitions in children’s lives alongside with measures of the environments to which these transitions pertain in the future. In this way, it is possible to identify environmental factors that affect the development of DT in young children. Finally, with larger samples, researchers could apply more advanced modeling to test the causal relationships between the development of DT processes and the development of DT product measures.

Models Used for Table 3: Product Measure of Divergent Thinking

M0: Intercept-only

In this model we do not include any predictor variables. The product measure of divergent thinking at wave $t$ in child $i$ is modeled as follows:

$produc{t}_{ti}={\beta }_{00}+u_{0i}+e_{ti}$

where the intercept ${\beta }_{00}$ is the mean score on the outcome across all waves and all children. The random effect $u_{0i}$ is child $i$’s deviation from the mean and $e_{ti}$ is the random effect at the wave level. These random effects are assumed to follow a normal distribution with mean 0 and variances ${\sigma }_{child}^2$ and ${\sigma }_{wave}^2$, respectively, and to be independent of each other.

M1: Linear and quadratic effects of age

We extend model M0 by allowing for growth over age using a linear and quadratic age trend. These growth trajectories are allowed to vary across children:

$produc{t}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{20}quadraticag{e}_{ti}+$

$u_{0i}+u_{1i}linearag{e}_{ti}+u_{2i}quadraticag{e}_{ti}+e_{ti}$

Age entered the model grand-mean centered. Thus, the intercept ${\beta }_{00}$ is now the mean outcome when grand-mean centered age is equal to zero and the random effect $u_{0i}$ is the deviation of child $i$ from this mean outcome. The regression coefficients ${\beta }_{10}$ and ${\beta }_{20}$ are the means of the linear and quadratic age effects and the random effect $u_{1i}$ and $u_{2i}$ are the corresponding deviations of child $i$. These random effects are assumed to follow a normal distribution with mean zero and variances ${\sigma }_{linearage}^2$ and ${\sigma }_{quadraticage}^2$, respectively. As in the previous model, $e_{ti}$ is the random effect at the wave level.

M2: Linear effect of age

It turned out that the quadratic effect of age, ${\beta }_{20}$, and the corresponding variance component, ${\sigma }_{quadraticage}^2$, in the previous model were insignificant. We therefore simplify the model by removing the quadratic age trend. The model thus becomes:

$produc{t}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

The interpretation of all model parameters is as in the previous model.

M3: Adding the stimulus set

The model with stimulus set added is

$produc{t}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{30}stimulusse{t}_{ti}+u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

The regression coefficient ${\beta }_{30}$ is the effect of the stimulus set. The interpretation of all other model parameters is as in model M1.

Models Used for Table 4: Process Measure of Divergent Thinking

M0: Intercept-only

In this model we do not include any predictor variables. The process measure of divergent thinking at wave $t$ in child $i$ is modeled as follows:

$proces{s}_{ti}={\beta }_{00}+u_{0i}+e_{ti}$

where the intercept ${\beta }_{00}$ is the mean score on the outcome across all waves and all children. The random effect $u_{0i}$ is child $i$’s deviation from the mean and is the random effect at the wave level. These random effects are assumed to follow a normal distribution with mean 0 and variances ${\sigma }_{child}^2$ and ${\sigma }_{wave}^2$, respectively, and to be independent of each other.

M1: Linear and quadratic effects of age

We extend model M0 by allowing for growth over age using a linear and quadratic age trend. These growth trajectories are allowed to vary across children:

$proces{s}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{20}quadraticag{e}_{ti}+$

$u_{0i}+u_{1i}linearag{e}_{ti}+u_{2i}quadraticag{e}_{ti}+e_{ti}$

Age entered the model grand-mean centered. Thus, the intercept ${\beta }_{00}$ is now the mean outcome when grand-mean centered age is equal to zero and the random effect $u_{0i}$ is the deviation of child $i$ from this mean outcome. The regression coefficients ${\beta }_{10}$ and ${\beta }_{20}$ are the means of the linear and quadratic age effects and the random effect $u_{1i}$ and $u_{2i}$ are the corresponding deviations of subject $i$. These random effects are assumed to follow a normal distribution with mean zero and variances and ${\sigma }_{quadraticage}^2$, respectively. As in the previous model, $e_{ti}$ is the random effect at the wave level.

M2: Linear and quadratic effect of age (with only a random effect for the linear age effect)

It turned out that the quadratic effect of age, ${\beta }_{20}$, was borderline significant but the corresponding variance component, ${\sigma }_{quadraticage}^2$, was insignificant in the previous model. We therefore simplify the model by removing the random effect of the quadratic age trend. The model becomes:

$proces{s}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{20}quadraticag{e}_{ti}+$

The interpretation of all model parameters is as in the previous model.

M3: Adding the stimulus set

The model with stimulus set added is

$proces{s}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{20}quadraticag{e}_{ti}+{\beta }_{30}stimulusse{t}_{ti}+$

$u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

The regression coefficient ${\beta }_{30}$ is the effect of the stimulus set. The interpretation of all other model parameters is as in model M1.

Models Used for Table 5: Product Measure of Divergent Thinking

Intercept-only model

In this model we do not include any predictor variables. The product measure of divergent thinking at wave $t$ in child $i$ is modeled as follows:

$produc{t}_{ti}={\beta }_{00}+u_{0i}+e_{ti}$

where the intercept ${\beta }_{00}$ is the mean score on the outcome across all waves and all children. The random effect $u_{0i}$ is child $i$’s deviation from the mean and $e_{ti}$ is the random effect at the wave level. These random effects are assumed to follow a normal distribution with mean 0 and variances ${\sigma }_{child}^2$ and ${\sigma }_{wave}^2$, respectively, and to be independent of each other.

Random slope model

We extend model M0 by allowing for growth over age using a linear age trend. These growth trajectories are allowed to vary across children:

$produc{t}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

Age entered the model grand-mean centered. Thus, the intercept ${\beta }_{00}$ is the mean outcome when grand-mean centered age is equal to zero and the random effect $u_{0i}$ is the deviation of child $i$ from this mean outcome. The regression coefficient ${\beta }_{10}$ is the mean of the linear age effects and the random effect $u_{1i}$ is the corresponding deviation of child $i$. This random effect is assumed to follow a normal distribution with mean zero and variances ${\sigma }_{linearage}^2$. As in the previous model, $e_{ti}$ is the random effect at the wave level.

The effect of group model

The model with group and the interaction effect of linear age by group added is

$produc{t}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{11}linearag{e}_{ti}\times grou{p}_i+{\beta }_{01}grou{p}_i+$

The regression coefficients ${\beta }_{11}$ and ${\beta }_{01}$ are the interaction effect of linear age by group and the main effect of group respectively. The interpretation of all other model parameters is as in the previous model.

Models Used for Table 6: Process Measure of Divergent Thinking

Intercept-only model

In this model we do not include any predictor variables. The process measure of divergent thinking at wave $t$ in child is modeled as follows:

$proces{s}_{ti}={\beta }_{00}+u_{0i}+e_{ti}$

where the intercept ${\beta }_{00}$ is the mean score on the outcome across all waves and all children. The random effect $u_{0i}$ is child $i$’s deviation from the mean and $e_{ti}$ is the random effect at the wave level. These random effects are assumed to follow a normal distribution with mean 0 and variances and ${\sigma }_{wave}^2$, respectively, and to be independent of each other.

Random slope model

We extend model M0 by allowing for growth over age using a linear age trend. These growth trajectories are allowed to vary across children:

$proces{s}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

Age entered the model grand-mean centered. Thus, the intercept ${\beta }_{00}$ is the mean outcome when grand-mean centered age is equal to zero and the random effect $u_{0i}$ is the deviation of child $i$ from this mean outcome. The regression coefficient ${\beta }_{10}$ is the mean of the linear age effects and the random effect $u_{1i}$ is the corresponding deviation of child $i$. This random effect is assumed to follow a normal distribution with mean zero and variances ${\sigma }_{linearage}^2$. As in the previous model, $e_{ti}$ is the random effect at the wave level.

The effect of group model

The model with group and the interaction effect of linear age by group added is

$proces{s}_{ti}={\beta }_{00}+{\beta }_{10}linearag{e}_{ti}+{\beta }_{11}linearag{e}_{ti}\times grou{p}_i+{\beta }_{01}grou{p}_i+$

$u_{0i}+u_{1i}linearag{e}_{ti}+e_{ti}$

The regression coefficients ${\beta }_{11}$ and ${\beta }_{01}$ are the interaction effect of linear age by group and the main effect of group respectively. The interpretation of all other model parameters is as in the previous model.

Acknowledgments

We are sincerely grateful to the teachers, parents, and children of the primary schools that have taken part in this study. We would also like to thank the bachelor’s and master’s students who have participated in the data collection. Additionally, our great appreciation goes to a fellow researcher Mare van Hooijdonk for her extensive support in recruiting participants.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by China Scholarship Council [201506870016]; Talent Introduction Program of Postdoctoral International Exchange Program (2021), China [301302].

Notes

1. The multilevel regression model can handle multiple outcome variables by placing these in a separate “variables” level, a level below the lowest level of the original data structure, and by using dummy variables to distinguish different outcome variables at this level in the model. Here we did not enter details regarding the full set-up of used multivariate multilevel models. Instead, following common standards in multilevel regression analysis, we elaborate on what effects were included in each of the models. In Appendix E, we included equations of multilevel regression models used in the current study to assist the interpretation of results presented in Table 3–6.

2. In accordance with Hox et al. (2017, p. 16), the varying regression slopes are assumed to follow a normal distribution with the mean equaling the estimated slope (i.e., 0.59 in this study) and the standard deviation equaling the square root of the estimated variances of the slopes (i.e., 0.39). Thus, in the current case, 95% (z = 2) of the random linear slopes of age among children was expected to lie between (0.59–0.39 × 2 =) – 0.19 and (0.59 + 0.39 × 2 =) 1.37.

Appendix A

Elaborations on the Dutch School System

In the Netherlands, right after their fourth birthday, children are eligible for free of charge full-day kindergarten for five days per week, and nearly 100% of an age cohort uses kindergarten from this age. From age five, kindergarten education becomes compulsory. Kindergarten education is part of the primary school system and comprises the first two of a total of eight grades. Primary schools are run by local boards of different religious denominations or by non-religious school boards. All primary schools are fully publicly funded.

Appendix B

Examples of Mentioned Action Types in Children’s Generated Uses

Table

Stimulus	Frequently mentioned action types	Unfrequently mentioned action types
Set-1 stimuli
Basket	To put something in (132/186) ^a To take something (54/186) For a picnic (44/186) For shopping (40/186) As a hat (21/186)	For swimming in there ^b For making a robot For drying something in there As a bridge To put on the head for against the bees
Brick	To build something (166/185) To beat something (35/185) To make a road (21/185) To put something on it (10/185) For sitting on it/as a stool (8/185)	For making the stand of a bed As a baby As a pillow for sleeping Make it soft and flat like dough and color it To make a door
Broom	To sweep (160/186) To clean something (66/186) For flying (as if you’re a witch) (17/186) To beat/break something (16/186) For horse riding (9/186)	As a racing track For making a lamp For against the wind For building the fence For the cats to bite on it
Fishnet	To fish (150/184) To catch something (113/184) To put something in (27/184) To take something out of water (19/184) To beat/break something (13/184)	For making a pen As a diving plank To stop the mills To shovel the sand As a mask
Hand towel	To clean somebody (157/183) To clean something (81/183) To play with (13/183) To put something in (10/183) To dry somebody (9/183)	As cloth material To put it in the hole to stop water leaking For painting As a diving boat As a baby diaper
Spoon	For eating (178/186) To shovel something (51/186) To stir something (26/186) To beat/break something (20/186) For drinking (19/186)	To make a fingernail As a magic stick To saw off a tree To prick something As pirate’s eye patch
Set-2 stimuli
Lunch box	To put food in/as a food box (122/151) To put something in/as a storage box (103/151) To put insect or animal in/as an insect box (39/151) For taking something with you (16/151) To put water or drink in (15/151)	For making a parking bord As something on which you can write or draw To put on the computer to prevent it from getting wet As a sliding door For making a drawer
Tire	For cars/to ride with (137/152) For making a swing (35/152) To play with (unspecified) (26/152) For sitting or lying on (24/152) To put something in (20/152)	For making a handle As a (giant) eye For making a mouth As a hanging stool To make you sit higher on a stool
Pencil	For drawing (116/152) For writing (97/152) To erase something (use the attached eraser) (70/152) For coloring (31/152) To poke something/to break something (19/152)	To saw it off and make a small car Put it in a rolled paper as if it’s a French fry As a chopstick For making a finger As a bridge
Umbrella	For raining/to protect you from the rain (146/152) As a boat (35 /152) As a sunshade/against the sun (20/152) To put something in (14/152) For fighting/as a sword (10/152)	For lying in it For doing magic, as a magic stick For hockey As WC As a vase
Shovel	To shovel/dig (144/152) To beat something or someone/to break something (36/152) To pick up or lift something (20/152) To put something on or in (17/152) To search for something (e.g., treasure) (15/152)	As a jumping stick For making a hat For cutting BBQ food As the steering wheel of a skateboard To make the stick of a broom
Toothbrush	To clean teeth (148/152) To clean something/as a cleaning brush (56/152) To clean someone (15/152) For painting or drawing (13/152) To brush hair/as a comb (12/152)	As a microphone For playing the witch game, as a witch stick As a walking stick For making a cross As a bookmark

Note. ^a Numbers that followed the action types indicated the number of children who mentioned this action type (i.e., 132 in this example) and the total number of children who had finished this stimulus item (i.e., 186 in this example). ^b For unfrequently mentioned action types, the chosen examples were all mentioned by only one child.

Appendix C

Details About the Reference Sample Used for Computing Originality Scores

Note that the categorization of uses (as implicated in the first step of computing originality scores) and the calculation of the originality of action types (as implicated in the second step of computing originality) were carried out for each object across waves. In other words, uses generated on the same set of stimuli but at different waves, that is, uses of the first and third measurement waves for the first stimulus set and uses of the second and fourth measurement waves for the second stimulus set respectively, were merged for the categorization of uses and the calculation of originality. This was done to allow comparison of the data of the first and third waves (1^st stimulus set) and of the second and fourth waves (2^nd stimulus set), respectively. In addition, participants at different measurement waves were seen as independent units in the calculation of the number of participants in relation to the equation for calculating the originality of an action type as given above. For example, a child who had generated the same use for an object at both the first and third measurement waves would contribute a count of two in calculating the number of participants who mentioned the related action type in the equation above for calculating the originality of a use. This rule also applied to the calculation of the total number of participants in the same equation.

Appendix D

Definitions and Examples of coded Divergent Thinking Processes in the Alternative Use Task (Bai et al., 2021).

Table

DT process category	Definition	Examples (C = child; T = experimenter)
1. Retrieval or recall of prior knowledge or experience (Memory retrieval)	There is clear evidence that the child refers to prior knowledge or prior experience while generating a use. The child may recall a specific memory of a real personal experience, or a memory related to here – say, a story, film or book that relates to the use; Or: the child gives an affirmative answer when asked by the experimenter if he or she had prior personal experience with the use (i.e., if he or she did/learned it before) or if the child knew about the use from others, stories, movies, or books.	1. C: “I always do that with my father.” 2a. T: “Have you done that before”? 2b. C: “Yes, I have done it once.”
2. Performing mental operations on the stimulus (Mental operations)	The child mentions or refers to a mental operation applied to the stimulus (e.g., disassembling, re-assembling, turning, distorting, folding, etc.) or the child proposes an (imagined) act of assembling, combining, or synthesizing the stimulus with other objects or materials, to obtain a functional change of the stimulus that enables the discovery of a use.	1. C: “If you take off these hairs (toothbrush) and then put such a brush on, and also paper on, then you can make a mouse.” 2. C: “If you attach a lot of balloons on it (basket), which keeps floating, a lot a lot, then you can sit in there just like a hot air balloon.”

Appendix E

Multilevel Regression Model Equations