Improving children’s affective decision making in the Children’s Gambling Task

Journal of Experimental Child Psychology 139 (2015) 18–34

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Improving children’s affective decision making in the Children’s Gambling Task Glenda Andrews ⇑, Jennifer Moussaumai School of Applied Psychology and Menzies Health Institute Queensland, Griffith University, Gold Coast Campus, Southport, Queensland 4222, Australia

a r t i c l e

i n f o

Article history: Received 27 March 2015 Revised 6 May 2015

Keywords: Affective decision making Children’s Gambling Task Cognitive complexity Awareness Relational complexity theory Cognitive development

a b s t r a c t Affective decision making was examined in 108 children (3-, 4-, and 5-year-olds) using the Children’s Gambling Task (CGT). Children completed the CGT and then responded to awareness questions. Children in the binary_experience and binary_experience+awareness (not control) conditions first completed two simpler versions. Children in the binary_experience+awareness condition also responded to questions about relational components of the simpler versions. Experience with simpler versions facilitated decision making in 4- and 5-year-olds, but 3-year-olds’ advantageous choices declined across trial blocks in the binary_experience and control conditions. Responding to questions about relational components further benefited the 4- and 5-year-olds. The 3-year-olds’ advantageous choices on the final block were at chance level in the binary_experience+awareness condition but were below chance level in the other conditions. Awareness following the CGT was strongly correlated with advantageous choices and with age. Awareness was demonstrated by 5-year-olds (all conditions) and 4-year-olds (binary-practice and binary_experience+awareness) but not by 3-year-olds. The findings demonstrate the importance of complexity and conscious awareness in cognitive development. Ó 2015 Elsevier Inc. All rights reserved.

⇑ Corresponding author. E-mail address: g.andrews@griffith.gu.edu.au (G. Andrews). http://dx.doi.org/10.1016/j.jecp.2015.05.005 0022-0965/Ó 2015 Elsevier Inc. All rights reserved.

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Introduction The capacity to make prudent decisions is a cognitive achievement whose importance in daily living is difficult to overstate. Decision making appears to have a protracted course of development, and even adults frequently make errors or succumb to biases (Kahnemann, 2011). Effective decision making usually involves conscious consideration and integration of potential costs and benefits in order to identify the best course of action. The complexity of this integration process has been identified as a source of difficulty for young children (Andrews, Bunch, & Tolliday, 2008; Bunch, Andrews, & Halford, 2007; Kerr & Zelazo, 2004). Another issue is the role of conscious awareness (Garon, Longard, Craig, & Kent, 2015; Garon & Moore, 2004, 2007). In the current research, we examined the roles of cognitive complexity and awareness in 3-, 4-, and 5-year-olds’ decision making on the Children’s Gambling Task (CGT; Kerr & Zelazo, 2004). The aim was to determine whether performance on the standard CGT is improved when less complex versions of the CGT are presented before the standard version and whether questioning children about the relational components of the tasks confers a further benefit. The CGT (Kerr & Zelazo, 2004) is a simplified version of the Iowa Gambling Task (IGT; Bechara, Damasio, Damasio, & Anderson, 1994) that is widely used to assess affective decision making in adults. In the IGT, adult participants are given an initial stake of play money and are instructed to win as much money as possible by choosing cards from four decks. The four decks have different gain–loss profiles. The cards in the two disadvantageous decks yield high gains but higher losses. Selection of cards from these decks results in a net loss over trials. The cards in the two advantageous decks yield smaller gains but minimal losses. Selection of cards from these decks results in a net gain over trials. Neurologically intact adults learn over trials to select cards from the advantageous decks and to avoid the disadvantageous decks. In contrast, patients with lesions to the ventromedial region of the prefrontal cortex continue to select from the disadvantageous decks (Bechara et al., 1994, 2001). The roles of conscious and nonconscious processes in advantageous responding on the IGT have been controversial (Bechara, Damasio, Tranel, & Damasio, 1997; Cui et al., 2015; Maia & McClelland, 2004). Proponents of the somatic marker hypothesis claim that conscious awareness emerges as the task progresses and that advantageous choices are made before conscious awareness of the advantageous decks is demonstrated. Others have questioned the latter point. Maia and McClelland’s (2004) research employed more sensitive measures of conscious knowledge than Bechara and colleagues’ research had done. Their findings suggest that advantageous choices were based on conscious knowledge. The roles of conscious awareness and complexity have been addressed in cognitive developmental research using the CGT. In the CGT (Kerr & Zelazo, 2004), there are two decks of cards rather than four. This version has been used with children from 3 years of age (Bunch et al., 2007; Gao, Wei, Bai, Lin, & Li, 2009; Garon & Moore, 2007; Mata, Sallum, Miranda, Bechara, & Malloy-Diniz, 2013). The cards display happy and sad faces indicating the numbers of rewards (e.g., sweets, stickers) won and lost, respectively. Kerr and Zelazo (2004) administered five 10-trial blocks. On later trial blocks, 4-year-olds made more choices from the advantageous deck than 3-year-olds, and 4-year-olds made significantly more advantageous choices than would be expected by chance on Blocks 3 and 5, whereas 3-year-olds made significantly fewer advantageous choices than would be expected by chance on Blocks 3 and 4. Kerr and Zelazo interpreted their findings in terms of cognitive complexity and control (CCC) theory (Zelazo & Frye, 1997; Zelazo, Müller, Frye, & Marcovitch, 2003), which proposes age-related increases in the maximum complexity of rules that children can use. From around 3 years of age, children can use a pair of arbitrary rules. At around 4 or 5 years of age, they can integrate two incompatible pairs of rules into a single rule system via a higher order rule (Zelazo, Jacques, Burack, & Frye, 2002). Older children are able to represent the higher order rule, and this allows them to appreciate net gains in the CGT. Representation of a higher order rule requires children to reflect on lower order rules. Without reflection, the full hierarchy in which lower order rules are embedded under higher order rules cannot be constructed (Zelazo, 2004). Thus, CCC theory specifies roles for cognitive complexity (lower order vs. higher order rules) and awareness (reflection on lower order rules) in the CGT and in cognitive development more generally.

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Complexity and awareness are also important in relational complexity (RC) theory (Halford, 1993; Halford, Wilson, Andrews, & Phillips, 2014; Halford, Wilson, & Phillips, 1998, 2010). In RC theory, higher cognitive processes, including reasoning and decision making, are characterized as requiring complex relational processing (Andrews, 2010; Andrews & Mihelic, 2014; Halford, Andrews, & Wilson, 2015). Relational complexity corresponds to the number of arguments related in a single decision. Unary relations have a single argument or slot as in class membership. For example, that Fido is a dog can be expressed as dog(Fido). Binary relations have two arguments or slots, as in larger than (elephant, mouse). Ternary relations such as arithmetic addition have three arguments, addition(5, 2, 3), whereas in quaternary relations such as proportion there are four arguments. Bunch and colleagues (2007) argued that identifying the advantageous deck in the CGT involves representing a ternary relation involving three variables: deck, magnitude of losses, and magnitude of gains. To test the complexity hypothesis, they designed two less complex binary-relational versions of the CGT in which the decks differed in either gains only or losses only, with the other variable held constant. These simpler versions were closely matched to the standard (ternary-relational) CGT in other respects. The 3-, 4-, and 5-year-olds reliably selected cards from the advantageous deck in the binary-relational versions, but only 5-year-olds did so in the ternary-relational CGT. These findings are consistent with complexity theories and with other empirical research showing that ternary-relational processing emerges at around 5 years of age, whereas binary-relational processing is observed from around 2 or 3 years of age (e.g., Andrews & Halford, 1998, 2002, 2011; Andrews, Halford, & Boyce, 2012; Andrews, Halford, Bunch, Bowden, & Jones, 2003; Bunch & Andrews, 2012; Halford & Andrews, 2014; Halford, Andrews, Dalton, Boag, & Zielinski, 2002a; Halford, Andrews, & Jensen, 2002b). RC theory specifies a role for awareness. One property of relational knowledge is that the components of relations are accessible to awareness and to other cognitive processes. Relational systems represent structure explicitly (Halford et al., 1998, 2010, 2014). In terms of the standard CGT, this means that relational representations would include three slots corresponding to deck, magnitude of gain, and magnitude of loss. The slots function as variables that can be filled in various ways. In a CGT problem where the reverse sides of cards in the advantageous deck have pink crosses and the reverse sides of cards in the disadvantageous deck have yellow stars, the three slots might be filled as follows: Yellow stars, Yellow stars, Pink crosses, Pink crosses,

2, 2, 1, 1,

4; 5; 0; 1.

If a relational representation is constructed during acquisition, its components will be accessible and available to conscious awareness (Halford et al., 1998, 2010, 2014). This would allow children to retrieve information about the deck, given the gain and loss values, to retrieve information about the gain values, given the deck and loss, and to retrieve information about the loss values, given the deck and gain. This exemplifies the omnidirectional access property of relational knowledge. The awareness questions used in the current research reflect this property. Existing empirical research (Garon & Moore, 2004, 2007; Garon et al., 2015) supports a role for awareness in children’s CGT performance. For example, Garon and Moore (2007) conducted two experiments using the CGT with 3- and 4-year-olds. Awareness was assessed by asking children to indicate which deck was better and which deck was worse and to explain their responses. In Experiment 1, these questions were asked after 40 card turns and again after 60 card turns. The 4-year-olds demonstrated greater awareness than the 3-year-olds, and awareness during the task was associated with better performance. In Experiment 2, children were assigned to one of three conditions. In all conditions, 60 card turns were required and the game was interrupted after 30 card turns. At this point, children in the question condition responded to awareness questions as in Experiment 1. Children in the question + symbol condition responded to awareness questions and placed pictures of a bear and a tiger next to the good and bad decks, respectively. Children in the control condition responded to unrelated questions. It was expected that explicitly labeling the decks in response to the awareness questions would facilitate subsequent CGT performance. This prediction

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was supported for the older children but not for the younger children. The findings confirmed previously observed age differences in CGT performance. They suggested that interventions designed to increase awareness are likely to improve children’s decision making but that such interventions might not be equally effective at different ages. As noted earlier, the CGT requires construction of a rule hierarchy in which lower order rules are embedded under a higher order rule according to CCC theory (Zelazo, 2004; Zelazo & Frye, 1997) or a ternary-relational representation according to RC theory (Bunch et al., 2007), and children younger than 4 or 5 years experience difficulty with tasks at this level of complexity (Andrews & Halford, 2002; Andrews et al., 2003, 2012; Bunch & Andrews, 2012; Frye, Zelazo, & Palfai, 1995; Halford et al., 2002a, 2002b; Kerr & Zelazo, 2004). Given evidence that younger children succeed on less complex versions of the CGT (Bunch et al., 2007) and that interventions designed to increase awareness can improve CGT performance (Garon & Moore, 2007), it seemed plausible that presenting the simpler CGT versions first and asking questions to alert children to the relational components in the simpler versions might help them to construct the more complex ternary relations required in the standard CGT. As noted above, the awareness questions used in the current research were designed to reflect the omnidirectional access property of relational representations (Halford et al., 1998, 2010, 2014). This means that if we were given all but one of the components of a relational instance, we can access (i.e., retrieve) the remaining component. Awareness of losses was assessed using questions such as the following: ‘‘When you picked up a card with purple triangles, you won 1 sticker. Sometimes stickers were taken away. How many were taken away—was it 1 or 5?’’ Comparable questions were devised to assess awareness of gains and awareness of decks. Thus, our method of assessing awareness differs from previous research by Garon and colleagues (Garon & Moore, 2004, 2007; Garon et al., 2015) in which awareness questions required children to identify the good and bad decks and to explain their responses. The current study extended previous research on the roles of complexity (Bunch et al., 2007; Kerr & Zelazo, 2004) and awareness (Garon & Moore, 2007) in children’s performance on the CGT. The aim was to determine whether children’s awareness and/or performance on the ternary-relational CGT could be improved by first presenting the simpler binary-gain and binary-loss versions developed by Bunch and colleagues (2007) and by asking questions about the relational components that these simpler versions entail. Children in each of three age groups (3, 4, and 5 years) participated in one of three conditions: control, binary_experience, or binary_experience+awareness. Children in all conditions completed the ternary-relational version of the CGT and then responded to questions assessing their awareness of the ternary-relational components. Children in the control condition did so with no prior experience with the binary-relational versions. Children in the binary_experience condition completed the two binary-relational versions prior to attempting the ternary-relational CGT. Children in the binary_experience+awareness condition also completed the two binary-relational versions. In addition, in an effort to increase awareness of the components in the ternary-relational CGT (deck, magnitude of gain, and magnitude of loss), children responded to questions after each of the simpler versions. These questions were similar to those presented after the ternary-relational CGT except that they related to two components (deck and either gains or losses) rather than three components. Thus, children in the binary_experience+awareness condition completed the binary-gain and binary-loss versions, each followed by questions, before progressing to the ternary-relational version of the CGT. The predictions for the ternary-relational CGT in the control condition were based on complexity theories (Halford et al., 2014; Zelazo, 2004; Zelazo & Frye, 1997) and previous empirical findings (Bunch et al., 2007; Garon & Moore, 2007; Kerr & Zelazo, 2004). We predicted that 5-year-olds would make advantageous choices on the ternary-relational version of the CGT but that younger children would experience difficulty. For 5-year-olds, card selections from the advantageous deck were expected to increase across successive trial blocks and to exceed chance level by Block 4. For 3-year-olds, advantageous choices were expected to decline across successive trial blocks and to be significantly below chance level by Block 4. The 4-year-olds were expected to perform at an intermediate level. Children of this age made advantageous choices at above chance level on Blocks 3 and 5 in Kerr and Zelazo’s (2004) study, but this group’s above-chance performance appears to have stemmed

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from 7 of the 24 children in this age group. The 4-year-olds in other studies (Bunch & Andrews, 2012; Bunch et al., 2007) performed at chance level. The predictions for the binary-relational versions of the CGT in the binary_experience and binary_experience+awareness conditions were based on complexity theories (Halford et al., 2014; Zelazo, 2004) and previous empirical findings (Andrews et al., 2008; Bunch et al., 2007). The 3-, 4-, and 5-year-olds were expected to make advantageous choices on the simpler binary-relational versions that involve two variables (deck and magnitude of gain or deck and magnitude of loss). Advantageous choices should increase across successive trial blocks and exceed chance level by Block 4. If prior experience with the simpler binary-gain and binary-loss versions improves children’s performance in the ternary-relational CGT, then children in the binary_experience and binary_experience+awareness conditions should make more advantageous choices and demonstrate greater awareness than those in the control condition. If alerting children to the relational components of the CGT (via questions about the simpler versions) improves children’s performance in the ternary-relational CGT, then children in the binary_experience+awareness condition should make more advantageous choices and demonstrate greater awareness than those in the binary_experience condition. These effects of condition were examined as a function of age group.

Method Participants The sample consisted of 108 children who were recruited from five day-care centers and one school in the Gold Coast region of Queensland, Australia. There were 36 children (18 boys and 18 girls) in each of three age groups: 3-year-olds (M = 42.45 months, SD = 3.14, range = 36–47), 4-year-olds (M = 52 months, SD = 3.30, range = 48–59), and 5-year-olds (M = 65 months, SD = 3.14, range = 60–71). Approval to conduct the research was obtained from the human research ethics committee at Griffith University (approval number PSY/C2/12/HREC). Written parental consent was obtained for all children who participated in the research. Verbal assent was obtained from each child prior to commencing the session.

Materials There were three sets of laminated cards: one set for the binary-relational gain version, one set for the binary-relational loss version, and one set for the ternary-relational version. Each set contained two decks of 40 cards. The reverse sides of the cards had patterns that differentiated the disadvantageous and advantageous decks within each set (e.g., orange squares vs. purple triangles). The face sides of the cards were divided into upper and lower sections. Black line drawings of happy faces were depicted on a white background in the upper half. White line drawings of sad faces were depicted on a black background in the lower half. The happy and sad faces indicated the number of rewards that were gained and lost, respectively, by selecting that card. The bottom half of each card was covered with a yellow paper Post-It note. The sad faces were revealed when the Post-It note was lifted. The rewards were stickers depicting animals, stars, and other objects. Stickers were held in small transparent containers. The binary-relational gain and binary-relational loss versions were identical to those used in Bunch and colleagues (2007). The ternary-relational version was identical to that used in Bunch and colleagues (2007) and Kerr and Zelazo (2004). Table 1 shows the total number of rewards gained and lost and the net gains/losses over a 10-card sequence for each of the three versions. The questions used to assess children’s awareness of the ternary-relational structure are shown in Table 2. To assist comprehension, pictures depicting the loss values, gain values, and deck patterns were presented. These questions provided a measure of children’s awareness of the components of the ternary-relational structure of the CGT.

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Table 1 Gains and losses for each 10-card block in the advantageous and disadvantageous decks for the binary-relational gain, binaryrelational loss, and ternary-relational versions of the CGT. Version

Disadvantageous deck (per 10-card block)

Binary-relational gain Binary-relational loss Ternary-relational a

Advantageous deck (per 10-card block)

Gain

Loss

Neta

Gain

Loss

Neta

10 10 20

5 25 25

+5 15 5

20 10 10

5 5 5

+15 +5 +5

Plus sign (+) indicates gain; minus sign ( ) indicates loss.

Table 2 Questions used to assess awareness of the gain, loss, and deck components of the ternary-relational structure in the CGT. Question type

Awareness questions

Gain

When you picked up a card with yellow stars, 4, 5, or 6 stickers were sometimes taken away and you won some stickers. How many stickers did you win, 1 or 2? When you picked up a card with pink crosses, 1 sticker was sometimes taken away and you won some stickers. How many stickers did you win, 1 or 2? When you picked up a card with yellow stars, you won 2 stickers. Sometimes stickers were taken away. How many were taken away—was it just 1 or was it more than 1 (i.e., 4, 5, or 6)? When you picked up a card with pink crosses, you won 1 sticker. Sometimes stickers were taken away. How many were taken away—was it just 1 or was it more than 1 (i.e., 4, 5, or 6)? Sometimes you won 2 stickers and 4, 5, or 6 stickers were taken away. Did that happen when you picked up a card with yellow stars or pink crosses? Sometimes you won 1 sticker and 1 sticker was sometimes taken away. Did that happen when you picked up a card with yellow stars or pink crosses?

Loss

Deck

The questions administered following the binary-relational gain version in the binary_experience+awareness condition were similar to the gain and deck questions for the ternary-relational version except that there was no mention of losses. The questions administered following the binary-relational loss version in the binary_experience+awareness condition were similar to the loss and deck questions for the ternary-relational version except that there was no mention of gains.

Design and procedure Children in each age group were randomly assigned to one of three conditions. In the control condition, children received the ternary-relational version of the CGT, followed by six awareness questions. The questions were read aloud by the experimenter in a slow and clear manner as the relevant pictures were presented. Questions were repeated if necessary. Children were awarded 1 point for each correct response (maximum score = 6). Children in the binary_experience and binary_experience+awareness conditions received the binary-gain and binary-loss versions of the CGT in counterbalanced order before attempting the ternary-relational version and awareness questions. In the binary_experience+awareness condition, four questions (two deck and two gain) were presented following the binary-relational gain version and four questions (two deck and two loss) were presented following the binary-relational loss version. The purpose of these questions was to alert children to the relational components of these simpler versions. The gambling tasks and questions were administered to individual children in a quiet area of the day-care center or school. At the outset, the experimenter introduced herself and said, ‘‘We’re going to play a card game, and then I’ll ask you some questions about the game? Is that all right with you?’’ Each child received a sticker to motivate him or her to play and then received an initial stake of 10 stickers. The three versions were presented using comparable procedures and instructions. The experimenter demonstrated each version by selecting three cards consecutively from each deck.

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Explanations of rewards and losses were provided. For example, ‘‘Look, there are two happy faces; that means you win two stickers.’’ The two stickers were placed on the happy faces and then deposited into the child’s container. The experimenter then checked for losses: ‘‘Okay, now let’s see if there are any sad faces. Oh look, there are four sad faces; that means you lose four stickers.’’ The experimenter removed four stickers from the child’s container, placed them onto the sad faces, and then deposited them into the experimenter’s container. At this point, the experimenter commented, ‘‘We don’t like sad faces because we lose stickers, but we like happy faces because we win stickers, don’t we?’’ After the demonstration trials, the experimenter said, ‘‘Okay, we are ready to start playing the game. You’re allowed to pick whichever card you want to play with each time. You get to pick one card at a time and can pick as many cards from either the orange squares, the pink crosses, or both. The game will end when I say ‘STOP’. So remember, the aim of the game is to win as many stickers as possible! At the end of the game, you can take home the stickers you win, okay? Which card do you want to pick first?’’ The test trials were administered in the same manner as the demonstration trials. Four blocks of 10 trials were administered for each version. Children were unaware of the total number of trials. Card selections were recorded on specially prepared response sheets for each version. Children were not allowed to play with the stickers they had won until the end of the game. Testing duration in the control condition varied from approximately 15 min for the older children to 25 min for the younger children. Testing duration in the binary_experience and binary_experience+awareness conditions varied from approximately 45 min for the older children to 80 min for the younger children. Testing in the binary_experience and binary_experience+awareness conditions was completed during two sessions either at different times of the same day or over different days, depending on the class schedule.

Results Binary-relational versions The first set of analyses examined advantageous choices of children in the binary_experience and binary_experience+awareness conditions on the binary-relational gain and binary-relational loss versions. t-Tests for independent samples revealed no significant effect of presentation order on advantageous choices in the binary-relational gain version, t(70) = 1.07, p = .29, and in the binary-relational loss version, t(70) = 1.21, p = .23. There was also no significant gender difference, t(70) = 0.21, p = .84. These variables were not included in further analyses. Advantageous choices were subjected to a mixed 3 (Age)  2 (Condition)  2 (Version)  4 (Block) analysis of variance (ANOVA) in which version (gain or loss) and block (1, 2, 3, or 4) were within-participant variables and age and condition were between-group variables. The analysis yielded a significant effect of age, F(2, 66) = 20.72, p < .001, partial g2 = .386. Post hoc Scheffé tests showed that 5-year-olds (M = 7.77, SE = 0.07) made significantly more advantageous choices than both 4-year-olds (M = 7.46, SE = 0.07, p = .01) and 3-year-olds (M = 7.14, SE = 0.07, p < .001) and that 4-year-olds made more such choices than 3-year-olds (p = .007). There was a significant effect of block, F(3, 198) = 1129.58, p < .001, partial g2 = .95, which reflected an increase in advantageous choices across successive trial blocks. These effects were modified by a significant Age  Block interaction, F(6, 198) = 3.08, p = .007, partial g2 = .085. The simple effect of block was significant for 3-year-olds, F(3, 66) = 268.17, p < .001, partial g2 = .924, 4-year-olds, F(3, 66) = 537.76, p < .001, partial g2 = .961, and 5-year-olds, F(3, 66) = 391.71, p < .001, partial g2 = .947. Comparison of the effect sizes and the means in Table 3 suggest that the interaction reflects a slightly greater improvement across successive blocks for the 4-year-olds than for the other age groups. Single-sample t-tests showed that all means in Table 3 were significantly above chance level (5 of 10). The effects of condition, F(1, 66) = 3.02, p = .087, partial g2 = .044 (binary_experience: M = 7.40, SE = 0.057; binary_experience+awareness: M = 7.53, SE = 0.057), and version, F(1, 66) = 3.28, p = .075, partial g2 = .047 (gain: M = 7.40, SE = 0.058; loss: M = 7.51, SE = 0.042), did not reach significance. There were no other significant effects or interactions. Thus, children of all ages learned to make advantageous choices in the binary-relational versions.

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G. Andrews, J. Moussaumai / Journal of Experimental Child Psychology 139 (2015) 18–34 Table 3 Mean numbers of cards (and standard errors) selected from advantageous deck in binary-relational versions of the CGT. Trial block

3-year-olds 4-year-olds 5-year-olds

* ** ***

1

2

3

4

5.35* (0.11) 5.48** (0.11) 6.00*** (0.11)

6.79*** (0.08) 7.06*** (0.08) 7.46*** (0.08)

8.02*** (0.09) 8.27*** (0.09) 8.48*** (0.09)

8.40*** (0.09) 9.04*** (0.09) 9.15*** (0.09)

p < .05. p < .01. p < .001.

Ternary-relational version A preliminary analysis revealed no significant gender difference, t(106) = 0.24, p = .81, so this variable was not included in further analyses. Advantageous choices were subjected to a mixed 3 (Age)  3 (Condition)  4 (Block) ANOVA in which block was the within-participant variable and age and condition were between-group variables. The analysis yielded significant effects of age, F(2, 99) = 276.51, p < .001, partial g2 = .848, condition, F(2, 99) = 45.48, p < .001, partial g2 = .479, and block, F(3, 297) = 55.35, p < .001, partial g2 = .359. There were three significant two-way interactions: Block  Age, F(6, 297) = 83.11, p < .001, partial g2 = .627, Block  Condition, F(6, 297) = 23.72, p < .001, partial g2 = .324, and Age  Condition, F(4, 99) = 7.64, p < .001, partial g2 = .236. These two-way interactions were modified by a significant three-way Block  Age  Condition interaction, F(12, 297) = 4.73, p < .001, partial g2 = .160, which is shown in Fig. 1. The three-way interaction was first partitioned according to condition. A mixed Age  Block ANOVA was conducted for each condition. In the control condition, the analysis yielded no significant effect of block, F(3, 99) = 0.06, p = .93, partial g2 = .002. There was a significant effect of age, F(2, 33) = 44.97, p < .001, partial g2 = .732, and a significant Age  Block interaction, F(6, 99) = 29.01, p < .001, partial g2 = .637 (upper panel of Fig. 1). For 3-year-olds, advantageous choices declined significantly across successive blocks, F(3, 33) = 26.78, p < .001, partial g2 = .709, and the means on Blocks 2, 3, and 4 were significantly below chance level. For 4-year-olds, advantageous choices did not change significantly across successive blocks, F(3, 33) = 0.83, p = .487, partial g2 = .07, and none of the means differed significantly from chance level. For 5-year-olds, advantageous choices increased significantly across blocks, F(3, 33) = 94.29, p < .001, partial g2 = .896, and the means on Blocks 2, 3, and 4 were significantly above chance level. In the binary_experience condition, there were significant effects of block, F(3, 99) = 11.68, p < .001, partial g2 = .261, and age, F(2, 33) = 268.88, p < .001, partial g2 = .942, and a significant Age  Block interaction, F(6, 99) = 37.32, p < .001, partial g2 = .693 (middle panel of Fig. 1). For 3-year-olds, advantageous choices declined significantly across blocks, F(3, 33) = 14.74, p < .001, partial g2 = .573, and the means on Blocks 2, 3, and 4 were significantly below chance level. For 4-year-olds, advantageous choices increased significantly across blocks, F(3, 33) = 35.47, p < .001, partial g2 = .763, and the means on Blocks 2, 3, and 4 were significantly above chance level. For 5-year-olds, advantageous choices increased significantly across blocks, F(3, 33) = 60.30, p < .001, partial g2 = .846, and the means for all four blocks were significantly above chance level. In the binary_experience+awareness condition, there were significant effects of block, F(3, 99) = 107.96, p < .001, partial g2 = .766, and age, F(2, 33) = 118.99, p < .001, partial g2 = .878, and a significant Age  Block interaction, F(6, 99) = 26.32, p < .001, partial g2 = .615 (lower panel of Fig. 1). For 3-year-olds, advantageous choices did not differ significantly across blocks (p = .77); the means on Blocks 2 and 3 were significantly below chance level, whereas the means on Blocks 1 and 4 did not differ from chance level. For 4-year-olds, advantageous choices increased significantly across

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Control condion Advantageous choices

10 8 6 4 2 0 1

2

3

4

Binary_experience condion

Advantageous choices

10 8 6 4 2 0 1

2

3

4

Binary_experience+awareness condion 10

Advantageous choices

9 8 7 6 5 4 3

3 years 4 years 5 years

2 1 0 1

2

Block

3

4

Fig. 1. Mean numbers of advantageous choices by 3-, 4-, and 5-year-olds on Blocks 1 to 4 of the CGT in the control condition (upper panel), binary_experience condition (middle panel), and binary_experience+awareness condition (lower panel). Error bars represent standard errors.

blocks, F(3, 33) = 116.89, p < .001, partial g2 = .914, and the means on Blocks 2, 3, and 4 were significantly above chance level. For 5-year-olds, advantageous choices increased significantly across blocks, F(3, 33) = 130.05, p < .001, partial g2 = .922, and the means for all four blocks were significantly above chance level. The three-way interaction was also partitioned by age. A mixed Block  Condition ANOVA was conducted for each age group. Changes across block were examined in the previous analyses, so our main interest here was the condition effect within each age and block. For 3-year-olds, there were significant effects of block, F(3, 99) = 24.48, p < .001, partial g2 = .426, and condition, F(2, 33) = 4.79, p = .015, partial g2 = .225, and a significant Block  Condition interaction, F(6, 99) = 6.55, p < .001, partial g2 = .284. The condition effect was not significant on Block 1, F(2, 33) = 1.38, p = .266, partial g2 = .077, or Block 2, F(2, 33) = 2.29, p = .117, partial g2 = .122, but it

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was significant on Block 3, F(2, 33) = 7.12, p = .003, partial g2 = .301, and Block 4, F(2, 33) = 8.22, p = .001, partial g2 = .333. On Block 3, Scheffé tests showed that there were significantly fewer advantageous choices in both the control condition (p = .013) and the binary_experience condition (p = .008) than in the binary_experience+awareness condition. Similarly, on Block 4, there were significantly fewer advantageous choices in both the control condition (p = .002) and the binary_experience condition (p = .015) than in the binary_experience+awareness condition. The control and binary_experience conditions did not differ significantly (p = .769). For 4-year-olds, there were significant effects of block, F(3, 99) = 37.63, p < .001, partial g2 = .533, and condition, F(2, 33) = 50.98, p < .001, partial g2 = .755, and a significant Block  Condition interaction, F(4, 66) = 20.34, p < .001, partial g2 = .552. The condition effect was not significant on Block 1, F(2, 33) = 1.04, p = .367, partial g2 = .059. The condition effect was significant on Block 2, F(2, 33) = 45.42, p < .001, partial g2 = .734, Block 3, F(2, 33) = 58.62, p < .001, partial g2 = .780, and Block 4, F(2, 33) = 40.19, p < .001, partial g2 = .709. Scheffé tests showed that on Block 2 there were significantly fewer advantageous choices in the control condition than in the binary_experience condition (p < .001) and the binary_experience+awareness condition (p < .001) and that there were significantly fewer advantageous choices in the binary_experience condition than in the binary_experience+awareness condition (p = .006). Similarly, on Block 3 there were significantly fewer advantageous choices in the control condition than in the binary_experience condition (p < .001) and the binary_experience+awareness condition (p < .001) and significantly fewer advantageous choices in the binary_experience condition than in the binary_experience+awareness condition (p = .002). In addition, on Block 4 there were significantly fewer advantageous choices in the control condition than in the binary_experience condition (p < .001) and the binary_experience+awareness condition (p < .001) and significantly fewer advantageous choices in the binary_experience condition than in the binary_experience+awareness condition (p = .005). For 5-year-olds, there were significant effects of block, F(3, 99) = 273.13, p < .001, partial g2 = .892, and condition, F(2, 33) = 8.35, p = .001, partial g2 = .336, and a significant Block  Condition interaction, F(6, 99) = 3.61, p = .003, partial g2 = .179. The condition effect was significant on Block 1, F(2, 33) = 5.47, p = .009, partial g2 = .249, Block 2, F(2, 33) = 7.33, p < .002, partial g2 = .308, Block 3, F(2, 33) = 4.66, p < .017, partial g2 = .22, and Block 4, F(2, 33) = 11.30, p < .001, partial g2 = .407. Scheffé tests showed that on Block 1 there were significantly fewer advantageous choices in the control condition than in the binary_experience condition (p = .015) and marginally fewer advantageous choices in the control condition than in the binary_experience+awareness condition (p = .052). On Block 2, there were significantly fewer advantageous choices in the control condition than in the binary_experience condition (p = .009) and the binary_experience+awareness condition (p = .009); the binary_experience and binary_experience+awareness conditions did not differ (p = 1.00). On Block 3, there were significantly fewer advantageous choices in the control condition than in the binary_experience+awareness condition (p = .02); the mean for the binary_experience condition did not differ significantly from that for the control condition (p = .135) or the binary_experience+awareness condition (p = .66). On Block 4, there were significantly fewer advantageous choices in the control condition than in the binary_experience+awareness condition (p < .001); the mean for the binary_experience condition was marginally higher than that for the control condition (p = .074) and marginally lower than that for the binary_experience+awareness condition (p = .074). To summarize, the effectiveness of our procedures for increasing advantageous choices on the CGT differed as a function of age. For 3-year-olds, providing prior experience with binary-relational versions combined with questioning children about the relational components produced a modest improvement from below chance level to at chance level advantageous responses by Block 4 of the CGT. For 4-year-olds, there was evidence that both prior experience with the simpler versions and questioning children about the relational components increased advantageous responding. There was a clear separation among the three conditions from Block 2 onward. For 5-year-olds, the differences among the three conditions did not always reach the conventional significance levels; however, the pattern on Blocks 3 and 4 paralleled those for 4-year-olds.

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Awareness Children in all three conditions responded to questions assessing their awareness following the ternary-relational version. Correct responses to the three question types were positively correlated (rs = .63, .64, and .69), so they were summed, and the total scores (out of 6) are reported in Table 4. A preliminary analysis revealed no significant gender difference, t(106) = –0.37, p = .72, so this variable was not included in further analyses. The 5-year-olds in the binary_experience+awareness condition performed at ceiling. This precluded the use of a 3 (Age)  3 (Condition) ANOVA. A one-way ANOVA revealed a significant age effect, F(2, 105) = 96.25, p < .001, partial g2 = .65. Post hoc Scheffé tests confirmed that 5-year-olds (M = 5.44, SE = 0.18) demonstrated significantly greater awareness than 4-year-olds (M = 4.28, SE = 0.18, p < .001) and 3-year-olds (M = 1.97, SE = 0.18, p < .001) and that 4-year-olds demonstrated significantly greater awareness than 3-year-olds (p < .001). For 3-year-olds, mean awareness scores did not exceed chance level (3 of 6 correct) in any condition. For 4-year-olds, mean awareness scores exceeded chance in the binary_experience and binary_ experience+awareness conditions but not in the control condition. For 5-year-olds, mean awareness scores exceeded chance level in all conditions. The effect of condition was examined within each age group using nonparametric Kruskal–Wallis tests. The mean ranks are also shown in Table 4. The effect of condition was significant for 3-year-olds, v2(2, N = 36) = 7.58, p = .023, 4-year-olds, v2(2, N = 36) = 25.97, p < .001, and 5-year-olds, v2(2, N = 36) = 17.45, p < .001. At all ages, awareness was highest in the binary_experience+awareness condition, followed by the binary_experience condition and then the control condition. To locate the source of these overall effects of condition, the analyses were repeated after excluding first the binary_experience+awareness condition and then the control condition. The effect of condition (control vs. binary_experience) was significant for 4-year-olds, v2(1, N = 24) = 8.72, p = .003, and 5-year-olds, v2(1, N = 24) = 6.59, p < .01, but was not significant for 3-year-olds (p = .623). After excluding the control condition, the effect of condition (binary_experience vs. binary_experience+awareness) was significant for 3-year-olds, v2(1, N = 24) = 5.46, p = .019, and 4-year-olds, v2(1, N = 24) = 14.25, p < .001, and it approached significance for 5-year-olds (p = .07). Awareness and CGT performance In the sample as a whole, awareness was significantly positively correlated with advantageous choices both before controlling for age, r(106) = .95, p < .001, and after controlling for age, r(105) = .89, p < .001. This was also the case within conditions: control condition, r(34) = .94, p < .001 and r(33) = .81, p < .001; binary_experience condition, r(34) = .94, p < .001 and r(33) = .83, p < .001; binary_experience+awareness condition, r(34) = .95, p < .001 and r(33) = .89, p < .001. Thus, greater awareness of the relational components and the number of advantageous choices were strongly related. Table 4 Mean correct responses to awareness questions following the CGT and mean ranks by age group and condition. Age group

Condition Control

Binary_experience

Binary_experience+awareness

3-year-olds Mean (SD) Mean rank

1.58 (0.10) 14.71

1.58 (0.67) 15.92

2.58 (1.08) 24.88

4-year-olds Mean (SD) Mean rank

3.00 (1.13) 8.54

4.25⁄ (0.62) 17.29

5.58⁄ (0.51) 29.67

5-year-olds Mean (SD) Mean rank

4.75⁄ (0.97) 10.08

5.58⁄ (0.91) 24.42

6.00⁄ (0.00) 25.00

Note: An asterisk (⁄) indicates that the mean is significantly above chance level (3 of 6 correct).

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Table 5 Correlations among age, condition, advantageous choices on the binary-gain, binary-loss, and ternary-relational CGT versions, and awareness following the CGT for children in the binary_experience and binary_experience+awareness conditions (N = 72).

1. 2. 3. 4. 5. 6. * ***

Age (months) Condition Advantageous choices binary-gain Advantageous choices binary-loss Advantageous choices ternary-relational Awareness following CGT

1

2

3

4

5

.06 .45*** .53*** .89*** .75***

.14 .14 .18 .26*

.49*** .52*** .52***

.64*** .63***

.94***

p < .05 (one-tailed). p < .001 (one-tailed).

Exploratory analyses Despite the facilitative effects of prior experience with the simpler versions and of responding to questions about relational components, age differences in advantageous choices in the CGT and awareness remained significant in the binary_experience and binary_experience+awareness conditions. There was also significant variation between and within the age groups on advantageous choices on the binary-relational gain and binary-relational loss versions. Correlational and regression analyses were conducted to determine the extent to which the number of advantageous choices on the simpler versions predicted advantageous choices and awareness on the ternary-relational CGT after controlling for age and the condition to which children were assigned. These analyses were based on the 72 children in the binary_experience and binary_experience+awareness conditions. The zero-order correlations in Table 5 show that advantageous choices on the binary-relational and ternary-relational versions were significantly positively correlated. A multiple regression analysis was conducted in which the criterion variable was total advantageous choices on the ternary-relational CGT. The analysis is summarized in Table 6. When age in months (continuous variable) and condition (a dummy variable reflecting whether children responded to questions about relational components after the simpler versions) were entered on Step 1, they accounted for significant variance in the advantageous choices. Both age and condition accounted for significant unique variance. When advantageous choices on the binary-gain and binary-loss versions were entered on Step 2, they accounted for a significant increase in variance. The unique contributions of age and condition remained significant. Advantageous choices on the binary-loss version also accounted for significant independent variance. The unique contribution of age was reduced from .77 at Step 1 to .36 at Step 2. This demonstrates that advantageous responding on the simpler binary-relational versions accounted for more than 50% of the age-related variance in advantageous choices on the ternary-relational CGT as well as accounting for unique variance. The multiple regression analysis was repeated with awareness scores as the criterion. Age and condition each accounted for unique variance on Step 1. Advantageous choices on the simpler versions accounted for significant additional variance when entered on Step 2. As in the previous analysis, advantageous choices on the binary-gain and binary-loss versions accounted for more than 50% of the age-related variance in awareness, and the beneficial effect of responding to questions following the simpler versions remained significant.

Discussion The primary aim was to determine whether young children’s affective decision making in the CGT is improved by prior experience with less complex versions of the task and by responding to questions intended to draw attention to the relational components of the CGT. The research was based on theories of cognitive development (Halford, 1993; Halford et al., 1998, 2014; Zelazo, 2004; Zelazo et al., 2003) in which the importance of complexity and conscious awareness is emphasized.

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Table 6 Multiple regression analyses with advantageous choices in CGT (upper) and awareness following CGT (lower) as criterion variables and age, condition, advantageous choices on the binary-gain and binary-loss versions as predictors (N = 72). b Advantageous choices on CGT Age (months) Condition Step 1 Age (months) Condition Binary-gain Binary-loss Step 2 Awareness of CGT Age (months) Condition Step 1 Age (months) Condition Binary-gain Binary-loss Step 2

.877 .2384 Multiple R2 = .80, F(2, 69) = 138.20, p < .001 .747 .194 .076 .179 Fchange(2, 67) = 6.46, p < .001 Multiple R2 = .83, F(4, 67) = 83.28, p < .001 .768 .302 Multiple R = .653, F(2, 69) = 64.79, p < .001 .592 .243 .110 .233 Fchange(2, 67) = 6.79, p = .002 Multiple R2 = .71, F(4, 67) = 41.22, p < .001

sr2

p

.766 .056

<.001 <.001

.364 .035 .004 .002

<.001 <.001 .21 .006

.586 .091

<.001 <.001

.228 .055 .008 .034

<.001 .001 .165 .006

2

The findings in the control condition where children attempted the CGT without first attempting the binary-relational versions were generally comparable to previous research (Bunch et al., 2007; Kerr & Zelazo, 2004) in that 5-year-olds chose advantageously, 3-year-olds chose disadvantageously, and 4-year-olds performed at an intermediate level that did not differ from chance. Awareness following the CGT increased with age as in Garon and Moore’s (2004, 2007) research. Only 5-year-olds demonstrated awareness in the control condition. These findings are consistent with complexity theories in which the capacity to deal with complex rules (Zelazo, 2004; Zelazo & Frye, 1997; Zelazo et al., 2003) or ternary relations (Andrews & Halford, 2011; Halford, 1993; Halford & Andrews, 2011; Halford et al., 1998, 2014) that are accessible to conscious awareness emerges at around 4.5 or 5 years of age. The experimental manipulations were effective in increasing advantageous choices and awareness in 4- and 5-year-olds. For 3-year-olds, prior experience with the binary-relational versions (alone) was not sufficient to improve performance or awareness of the ternary-relational components of the CGT. The 3-year-olds in the binary_experience and the control conditions responded similarly in that advantageous choices declined across trial blocks and there was no evidence of awareness following the CGT. Thus, experience with the simpler versions was not sufficient to overcome their preference for the disadvantageous deck. Experience with the binary-relational versions combined with responding to questions about the binary-relational components appears to have had a modest beneficial effect in arresting the decline to below chance performance that was observed on Block 4 in the control and binary_experience conditions. The procedures in the binary_experience+awareness condition were sufficient to overcome the preference for the disadvantageous deck. Indeed, 3-year-olds’ advantageous choices on Block 4 were comparable to those of 4-year-olds in the control condition (see Fig. 1). However there was no evidence of above chance advantageous choices on the CGT or of awareness of the ternary-relational components. It is possible that greater improvement in advantageous choices and awareness following the CGT would have been observed in 3-year-olds if additional trials had been presented on the binary-relational versions. Two findings are relevant here. First, 3-year-olds’ advantageous choices on Block 4 of the simpler versions were below ceiling level, indicating scope for further improvement. Second, advantageous choices on the simpler versions accounted for age-related and age-independent variance in advantageous choices and awareness on the ternary-relational CGT in the multiple regression analyses. These analyses suggest that additional trials in the binary-loss version might be especially beneficial. This version requires children to focus on losses that might be less salient than gains

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in the CGT. The additional trials are likely to be more effective if children also respond to questions about the binary-relational components, as in the binary_experience+awareness condition of the current study where 3-year-olds’ preference for the disadvantageous deck was eliminated on Block 4. To the extent that age differences persist even after this modification or other modifications, they might reflect a maturation-based limit in the capacity to represent rule hierarchies and ternary relations that are accessible to conscious awareness. Further development of this capacity might require maturation of prefrontal regions of the brain, which have been implicated in relational processing (e.g., Andrews, Halford, Chappell, Maujean, & Shum, 2014; Andrews et al., 2013; Bunge & Zelazo, 2006; Crone et al., 2009; Kroger et al., 2002). For 4-year-olds, prior experience with the binary-relational versions was sufficient to produce advantageous responding on the ternary-relational CGT. Unlike same-age children in the control condition, 4-year-olds in the binary_experience condition made advantageous choices at above chance level on Blocks 2, 3, and 4, and they demonstrated awareness at above chance level. Responding to questions about the binary-relational components in the binary_experience+awareness condition resulted in a further increase in 4-year-olds’ advantageous choices. The 4-year-olds in this condition made advantageous choices at a level that was midway between that of 5-year-olds in the control and the binary_experience conditions. Moreover, their awareness was comparable to that of 5-year-olds in the binary_experience condition. The greater improvements observed in 4-year-olds is consistent with previous research suggesting that this is a transitional period (Andrews & Halford, 2002; Andrews et al., 2003) during which they might benefit greatly from relevant experience. The 5-year-olds also benefited from prior experience with the binary-relational versions. Advantageous choices and awareness were higher in the binary_experience condition than in the control condition. Responding to questions about the binary-relational components in the binary_experience+awareness condition conferred a further benefit. The 5-year-olds’ advantageous choices were close to ceiling by Block 4 of the CGT, and correct responses to the awareness questions reached ceiling level. In the current research, advantageous responding and awareness on the CGT were closely linked. The two variables were strongly correlated (before and after controlling for age) in the sample as a whole and within conditions. Moreover, advantageous choices on Block 4 and correct responses to the awareness questions exceeded chance levels in five of the nine cells of the 3 (Conditions)  3 (Age) design. These were the binary_experience and binary_experience+awareness conditions for 4-year-olds and the control, binary_experience, and binary_experience+awareness conditions for 5-year-olds. In the remaining four cells, neither advantageous choices nor correct responses to awareness questions exceeded chance level. The strong associations between advantageous responding and awareness are consistent with complexity theories. In CCC theory, construction of higher order rules requires reflection on and conscious awareness of lower order rules (Zelazo, 2004). In RC theory, omnidirectional access to components is a property of relational structures (Halford et al., 1998, 2010, 2014). Thus, the finding that advantageous choices were observed at the same ages and in the same conditions as awareness was demonstrated is consistent with the view that the CGT involves higher order rules or complex ternary relations. Given that our procedures were effective in increasing children’s advantageous responding and their conscious awareness of the relational components of the CGT, it is appropriate to consider potential mechanisms. In RC theory, the processing loads imposed by cognitive tasks increase with complexity. The ternary-relational CGT would impose a higher load on cognitive resources than the binary-relational versions. Although the precise nature of the cognitive resource is unclear (Andrews & Halford, 2011), potential candidates include working memory and controlled attention. The observed improvements might have occurred because our binary-relational versions and the subsequent questions helped children to make better use of their limited resources by directing them to the most relevant aspects of the task (i.e., magnitude of gains, magnitude of losses, and decks). Given that attentional processes are involved in cognitive performance and conscious awareness, more efficient use of available attentional resources would provide a parsimonious explanation of the improvement we observed. The involvement of controlled attentional processes is consistent with complexity approaches to cognitive development.

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Another potential explanation for the improvements associated with questioning in the binary_experience+awareness condition relates to the so-called hot–cool distinction (Zelazo & Müller, 2011). The CGT is often conceptualized as a test of hot executive function because of the motivational aspects involved in winning stickers or candies. Responding to questions after the binary-relational versions might have prompted children to focus on the more abstract relational aspects of the task. This could be interpreted as a cool strategy. Thus, the observed improvement might reflect movement away from reliance on a (hot) motivational strategy toward a (cooler) more cognitive strategy. RC theory (Bunch & Andrews, 2012) and CCC theory (Frye et al., 1995; Kerr & Zelazo, 2004) have been applied to tasks in hot and cool domains. Although previous research (e.g., Andrews & Halford, 2002; Bunch & Andrews, 2012) has demonstrated that ternary-relational processing in many different content domains emerges at a median age of 5 years, far fewer studies have examined whether relational processing can be improved or whether age differences can be reduced. One exception is a recent study (Andrews et al., 2012) in which most 5-year-olds did not employ ternary-relational processing when a conditional discrimination learning task was presented alone. However, after prior experience with a simpler binary-relational reversal learning task, followed by awareness questions, the majority of 5-year-olds used ternary-relational processing on the conditional discrimination task. The current study extended this line of research to the CGT. It showed that similar manipulations in the binary_experience+awareness condition boosted ternary-relational processing of 4-year-olds to a level that was at least comparable to 5-year-olds in the control condition. Significant improvement was also observed for 5-year-olds. The findings have implications for education because many of the concepts that children encounter during the early years of school are ternary-relational (Andrews & Halford, 2011; Halford & Andrews, 2006). These include numerical concepts such as cardinal value (Andrews & Halford, 2002), arithmetic operations such as addition and subtraction (Knox, Andrews, & Hood, 2010), scientific concepts such as mechanical equilibrium (Andrews, Halford, Murphy, & Knox, 2009; Halford et al., 2002a), taxonomic relations (Halford et al., 2002b), and the ability to consider situations from different perspectives (Andrews et al., 2003; Halford and Andrews, 2014). Cross-task correspondences in performance are typically observed (Andrews and Halford, 2002; Bunch and Andrews, 2012), and this raises the possibility that improvements in ternary-relational processing in one task might transfer to other tasks. If so, children’s cognitive development would be greatly enhanced. Based on our findings, we suggest that attempts to improve ternary-relational processing in young children are most likely to be effective if they focus on providing experience at the less complex binary-relational level where younger children are likely to succeed. We also recommend that efforts be made to encourage children to reflect and become consciously aware of how they performed the task, which factors influenced their decision, and whether their decision was optimal. The questions in Table 2 illustrate how this was achieved in the current research, but other methods might also be effective in some situations. Introduction of the more complex ternary-relational tasks would occur after success at the binary-relational level has been demonstrated. Returning to the simpler level would remain an option if children found the ternary-relational tasks to be too challenging. References Andrews, G. (2010). Belief-based and analytic processing in transitive inference depends on premise integration difficulty. Memory & Cognition, 38, 928–940. Andrews, G., & Halford, G. S. (2011). Recent advances in relational complexity theory and its application to cognitive development. In P. Barrouillet & V. Gaillard (Eds.), Cognitive development and working memory: A dialogue between neoPiagetian and cognitive approaches (pp. 47–68). Hove, UK: Psychology Press. Andrews, G., Bunch, K. M., & Tolliday, E. (2008). Young children’s difficulty on the Children’s Gambling Task: Complexity or variability of losses? In M. J. Esposito (Ed.), Psychology of gambling (pp. 111–129). New York: Nova Science. 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