Transformation of the incomplete figure in young children

Abstract

This study aims to examine the developmental changes in young children’s perception. A matching completion task consisting of three geometric figures and one bird-like figure were completed by children 3–5 years of age (N = 99). The rotation effect, in which the correct response decreased with orientation (45°, 90° 135°, and 180°), was confirmed, except in one of the geometric conditions. We found that two factors were needed for a child to perform the bird-like completion task: clarification of the reference to each stimulus and awareness of the turning orientation. These studies suggest that the children processed the contour and feature information individually, and that the contour information was processed earlier than the feature information. We derived three criteria for sensitive information to resolve the task, contact, contour, and left-right. Findings are discussed with regard to the reference action and the part-whole relationship.

Keywords

mental rotation part-whole perception preschoolers recognition

In their previous research on the part and whole, Differentiation from the whole (Gibson, 1969; Vurpillot, 1976; Werner, 1948; Wohlwill, 1962) is dominant in early childhood and perceptual tendencies from the whole to the part are recognized. Elkind (1978), who criticized the nativism of Gestalt psychology’s perceptual grouping and supported Piaget’s view, interpreted the part-whole as a semi-logical relationship between contour and area. Elkind studied figures with fruit, allowing neither a whole nor a part to be dominant, but rather having the children come to understand the relationship between part and whole during their development (Elkind, Koegler, & Go, 1964). This clearly shows that the division of things into whole and part begins in early childhood. Children do not unify the part-whole relationship until the age of 8–9 years (Aslin & Smith, 1988; Elkind et al., 1964).

Gibson (1969) proposed the idea of perceptual development in her differentiated theory that development involved improving the discrimination of innate features of stimulus, which is not the sequential constitution of representation. Distinctive features, invariant properties, and higher structures were learned. The perceptual learning of the stimulus-oriented studies showed that the children discriminated different stimulus features according to age (Gibson, Gibson, Pick, & Osser, 1962). Gibson et al.’s notion that an undifferentiated perception become analyze by an articulated attribution was succeeded by the classification studies with the development of integral-separable dimension (Shepp & Swartz, 1976). They showed that young children classify by an undifferentiated integral dimension, while older children classify by a differentiated separable one, and assumed that the cognitive process of the children not only extracts features or dimensions, but also ignore irrelevant features to abstract meaningful differences. Likewise, Evans & Smith (1988) confirmed that the shift from overall similarity to part identity classification appeared from 4–6-year-olds, and found that the 6-year-olds already classified the same way as adults did. A two-step process was assumed, in which children are first looking for similarity, then shift to the identity, thus motivating selective attention to single dimensions. Then it was suggested that an apparent increase in selective attention and knowing how children access the degree of similarity are important for development of perceptual classification (Smith, 1989).

Poirel, Meellet, Houde, and Pineau (2008) studied the part-whole relationship developmentally by the same-different judgment with Navon figures (Navon, 1977). They suggested that the shift from local preference in 4-year-olds to global preference in 9-year-olds as an adult’s strategy. Using the strategy of ignoring irrelevant dimensions, children learn to analyze the structural features. It is there confirmed that the global precedence effect appeared in 6-year-olds, who learned to ignore the irrelevant information as an adult (Poirel et al., 2008). Furthermore, not using Navon figures, Stiles, Delis, and Tada (1991) showed that children and adults can attend to both global and local attributes in the orientation judging task.

Sex differences

Sex differences in spatial tasks have interested many researchers, and developmental studies including adults were conducted (Linn & Petersen, 1985; Voyer, Voyer, & Bryden, 1995). As for the mental rotation test (MRT) (Vandenberg & Kuse, 1978), males performed better than females (Peters, 2005; Voyer et al., 1995), and Peters and colleagues (1995) showed that the performance of males who used the strategy of part rotation was significantly worse than for those who used entire rotation. Robert & Chevrier (2003) examined solving strategies about the update version of the MRT of Peters et al. (1995) with two visual and haptic conditions. The results showed that more females than males prefer to use the analytic strategies, and it was presumed that the preference of strategy was due to the sex differences. While the results of the haptic condition was worse than vision one, they supposed that the haptic exploratory procedure needs first to find the stimulus feature, then the encoding of partial properties, such an orientation or object contour, comes later.

Perceptual factor as a part

The component of the stimulus is also important. The studies of Marmor (1975, 1977) showed that even 4- or 5-year-old children in the pre-operational stage could perform mental rotation and found that children use anticipatory kinetic imagery at an earlier stage than Piaget had thought. However, those studies did not discuss the role of the stimulus part, and other studies suggested that the strategies concerning the feature part of the stimulus is peculiar to young children (Foulkes & Hollifield, 1989; Kerr, Corbitt, & Jurkovic, 1980). After studying pre-operational stage children who spent considerable time examining a small angle of the rotational task, Kerr et al. (1980) demonstrated that children did not use coherent strategies of rotation, but instead utilized matching strategies, such as feature comparison.

In addition, Rosser and colleagues (Rosser, 1994; Rosser, Ensing, Glider, & Lane, 1984; Rosser, Stevens, Glider, Mazzeo, & Lane, 1989) suggested the importance of the feature of the stimulus at the rotation task. Rosser et al. (1984) showed that young children (4–5-year-olds) attended to the distinctive parts and used strategies that were different from whole rotation. Furthermore, Rosser et al. (1989) found that younger children (aged 5–7) judged with a unitary component of stimulus, while older children (aged 9–11) were able to treat multiple components simultaneously. Rosser (1994) showed that 5-year-olds tried to perform perceptual matching rather than mental rotation, and found that 8-year-olds still showed the tendency to depend on perceptual matching strategies, and therefore suggested that children have the ability to use either matching or rotation strategies approximately before the age of 11 years. As a result, Rosser supposed that the probability of using either strategy increased in relation to the task difficulty and the necessity to clarify the features of specific stimuli impeded the transition to the upper-level strategy.

Courbois and associates (Courbois, 2000; Courbois, Oross, & Clerc, 2007) examined feature salience, which impacts performance based on the idea that elongation and symmetry play an important role in deciding the frame of reference (Sekuler, 1996; Sekuler & Swimmer, 2000). Comparing 5- and 8-year old children with same-different judgment of inclined stimulus, some cognitive changes were assumed to occur from 5 to 8 years of age for sensitivity of salience (Courbois, 2000). For stimulus without salience, it was assumed to limit the derived reference system and lead to error on the transformation (Courbois et al., 2007). For the feature analysis of an object, the structural description theory was advocated (Bialystok, 1989; Olson & Bialystok, 1983). Bialystok (1989) proposed that mental rotation might be accomplished by calculating the relationship between the referred features and the structural features of an object. In this referent hypothesis, the missing part can be imagined even if the object was incomplete (e.g., a piece of a jigsaw puzzle). Therefore, as the features of this part become more distinct, the easier the part can be placed where it should be embedded.

Both the perceptual factor of an object itself and the relativeness of the object to the observer play an important role in defining the spatial position of the object (Corballis & Beale, 1976). Roberts and Aman (1993) suggested left-right confusion is caused by egocentric reference to the relationship between feature parts within the stimulus. They stated that the child could recognize the turning object correctly by alignment with self before judging left–right. If the alignment was inconsistent, inverted judgment of left–right resulted when the orientation exceeded 90°. Their results showed that children 7–8 years of age showed confusion while adults could comprehend the inconsistency.

Motor process

Important knowledge about physical relativeness to an object was provided from studies on motor imagery (Caeyenberghs, Tsoupas, Wilson, & Smith-Engelsman, 2009; Frick, Daum, Walser, & Mast, 2009; Funk, Brugger, & Wilkening, 2005; Noda, 2010; Wexler, Kosslyn, & Berthoz, 1998; Wiedenbauer & Jansen-Osmann, 2008; Wohlschläger & Wohlschläger, 1998). Funk et al. (2005) suggested that a 6-year-old’s motor imagery of an object was guided by the motor process with the results of manual posture leading to different response times in discriminating the turned objects. Wiedenbauer and Jansen-Osmann (2008) found improvement in mental rotation ability when children were first allowed to turn a picture by hand. Wexler, Kosslyn, and Berthoz (1998) supposed that intermodal transfer between motor and visual imagery was caused, as the motor rotation is compatible with mental rotation. Wohlschläger and Wohlschläger (1998) also confirmed interference between manual and mental rotation with adults and showed S-R compatibility to the direction of turning. When Frick, Daum, Walser, et al. (2009) examined developmental compatibility of motor and mental rotations, 5- and 8-year-olds confirmed the compatibility, but 11-year-olds and adults did not. Hence, they supposed that visual mental activity was dissociated from the motor process according to age, and the motor strategy of turning objects by hand to solve a task appeared in young children. In that sense, it is also suggested to visualize gesture made the profits for children than adults (Frick, Daum, Wilson, & Wilkening, 2009). In fact, 6–9-year-old children applied strategies, using not only their hand but also the inclination of their body (Noda, 2012).

The present study

Noda (2010) showed that 3–5-year-old children used various manipulative strategies to identify the turned objects. Even children who could mentally rotate needed some externalized movement of image rotation. This supplemental manipulative behavior in comparing objects is called Hikiutushi. Most observed manipulations superimposed the contour onto the other stimuli. This indicates that children attend to the contour and that their attention to the whole was dominant to the part in the preschool children. Noda (2008) examined 6–9-year-olds who performed the matching task of Flags (Thurstone & Jeffrey, 1956) and suggested the children processed the contour of the object and the feature within it separately until 8 or 9 years of age. Consequently, it is supposed that some action to bind the part with whole plays an important role in discriminating for identification, so we tried to explore how children synthesize the part-whole relationship developmentally using the contour and deficient part in this study for the function of reference in young children.

We presumed that the children’s task to make the incomplete stimulus the same as the standard stimulus by adding a piece reflects the requirement to complement the deficient part and rotate the whole imagery. Previous studies (Noda, 2008, 2010) asked children to make same-different judgments of stimuli not but of embedded incomplete stimuli as in this study. We presumed that an anticipatory imagery (Piaget & Inhelder, 1966/1971) would be required for the correct construction in this study.

First, we examined whether children’s part-whole strategies change according to development or sex difference. Secondly, we examined whether the abstract geometric or concrete bird-like figure was more efficient for manipulative of mental imagery. Finally, we examined what was the sensitive information for identification.

Method

Participants

Children (aged 3–6 years) were recruited from a kindergarten class in Tokyo, Japan to perform a matching completion task. All children came from lower to upper middle-class families. Socioeconomic status was based on parental occupation. None of the participants had any physical conditions that hindered them from completing the task. The 4-year-olds’ class included 10 boys and 17 girls (n = 27; mean age 3.8 years; range 3.3–4.2). The 4-year-olds’ class included 11 boys and 22 girls (n = 33; mean age 4.8 years; range 4.3–5.2). The 5-year-olds’ class included 23 boys and 16 girls (n = 39; mean age 5.7 years; range 5.3–6.3).

Materials

The task was to organize parts of the object stimulus so that it was the same as the standard stimulus. A test board and plates for the object stimuli were prepared. The 30 cm × 60 cm board was wooden, white-colored, and equipped with two objects. The first object was the standard stimulus placed on the left side of the board. The second object was a part of the standard stimulus and was placed on the right side of the board as the comparison stimulus. The completion plate was equipped with the comparison stimulus for conformation to the standard stimulus. The stimuli were presented on a circle base (φ 24 cm). The circle base for the comparison stimulus could be turned manually by 45°. The test board was inclined 45°–60° toward the participant. The stimuli were constructed from styrene foam and the stimuli patterns were printed on the surface of the stimuli. A magnet was set in the back of the plate so the participant could attach the plate to the circle base of the comparison stimulus.

We used two types of stimuli. The first included three geometric figures (4 cm × 6 cm) for Conditions 1, 2, and 3. The second consisted of a bird-like figure (3.3 cm × 7.5 cm) for Condition 4. We referred to Condition 4 as the bird-like completion task (BCT) because of its different appearance from the geometric ones. Therefore, we used two different reference clues that could be rotated to various angles: incomplete geometric figures and an incomplete bird-like figure with multiple referent clues of the bird’s beak and its body.

As indicated in Figure 1, each abstract stimulus showed a block pattern separated by four squares: three white and one yellow. The outline of the square was black. Conditions 1, 2, and 3 were assigned, as shown in Figure 1, with different connections among the three white squares and the yellow square. All the geometric shapes formed a dogleg by default, but were rotatable on the circle base. The bird-like standard stimulus consisted of a bird’s head with an eye, a beak, and a yellow arc-shaped body. The body part was used as the plate while the head was rotatable on the circle base for completion of Condition 4.

Figure 1.

Standard stimulus used for each condition.

For the initial test session, the standard and comparison stimuli were presented in an upright position (Figure 2) in which the head of Condition 4 faced left. The correct response was recognized when the child placed the completion plate on the comparison stimulus so that it was congruent with the standard stimulus, even if the comparison stimulus was inclined. A correct response was counted when the plate was placed at the appropriate position for Conditions 1, 2, and 3, but for Condition 4, a plate position within ±22.5° of the comparison stimulus was allowed.

Figure 2.

Completion task with the bird-like stimuli (bird-like completion task: BCT).

Procedure

The test was performed individually in a small room to avoid interference from other children. The comparison stimulus was presented at 45°, 90°, 135°, and 180°. We then asked the children to make the comparison stimulus the same as the standard stimulus with the completion plate. The instructions were as follows:

1) Introduction

The instructor recorded the participant’s name and said to the child, “Let’s study with the board and plate”. The instructor then showed the child the test board with the standard stimulus, part of the standard stimulus of Condition 1, and the completion plate. Both stimuli were presented in the default upright position to make it the same as the sample.

2) Confirmation

The instructor placed the completion plate on the circle base of the comparison stimulus to show the child the identical standard stimulus. Then the instructor let the child confirm that both sides of the stimuli were identical. The instructor stated that the stimuli of Conditions 1–3 were figures while Condition 4 imitated a bird.

3) Practice

The instructor handed the completion plate to the child and told him or her to “make it the same” while pointing at the standard and comparison stimuli. The instructor then let the child complete Condition 1 of the task. The child was required to make the comparison stimulus the same as the standard stimulus by using the plate.

A practice trial for orientation of the comparison stimulus was conducted. If the child made an error, the child was allowed to go back to the previous correct trial and retry. When the instructor manually changed the orientation of the comparison stimulus, the child was told to close his or her eyes so as not to see the sequence change or the underside of the test board. At this phase, children who did not understand the task were not allowed to go onto the next session.

4) Test session

For the actual test, the child was handed the completion plate and asked to “make it the same as this one like a little while ago”. The order of the degrees was different from the practice session. Condition 1 was conducted in the order of 45°, 180°, 135°, and 90°. This was followed by Condition 2 (90°, 45°, 180°, and 135°), Condition 3 (135°, 90°, 45°, and 180°), and Condition 4 (180°, 135°, 90°, and 45°).

Results

Correct response for each condition

A response was considered correct when the constructed configurations were geometrically congruent with the standard stimulus, including front-back sides and orientations. Due to the task property of Condition 4, ±22.5° from the beak orientation was allowed for a correct response. A point was awarded for a correct response in each degree, so the score range was 0–1 for each stimulus condition. The mean and standard deviation of each age group, boy/girl, and conditions are summarized in Table 1. Data were analyzed for each age and sex as the between-subjects valuable, and conditions and orientation as the within-subjects valuables, using a mixed design analysis of variance (ANOVA). Significant differences were detected for all main effects; Age, F(2, 93) = 13.068, p <.01; Sex, F(1, 93) = 6.799, p <.05; Conditions, F(3, 279) = 35.064, p <.01; and Orientation, F(3, 279) = 41.278, p <.01. Post hoc analyses were conducted using Ryan’s multiple tests. Performances increased according to age (MSE = 0.144, p <.05), boys (M = 0.33) were better than girls (M = 0.22), and Conditions 1 and 3 were better than Conditions 2 and 4 (MSE = 0.162, p <.05). Though no differences were confirmed between 135 and 180 degrees, significant differences between other orientations were recognized (MSE = 0.144, p <.05). In addition, there was a significant interaction of age, sex and conditions, F(6, 279) = 2.789, p <.05, indicating boys were better than girls of 3-year-olds in Conditions 1, 2 and 3 (p <.05). Sex differences were not detected at the 4- and 5-year-old age categories or in Condition 4 (See Table 1). Furthermore, there was an interaction of age, conditions, and orientation, F(18, 837) = 3.496, p <.01, showing in Condition 1 that the performances increased with age and decreased according to orientations for 4- and 5-year-olds (p <.05) but not for the 3-year-olds (Figure 3a). For Condition 2, an orientation difference was detected only with the 5-year-olds, F(3, 116) = 4.237, p <.01, and the performance at 90 degrees was worse than at 45 and 180 degrees (p <.05), as shown in Figure 3b. For Condition 3, the performance of 45 degrees was better than 135,180 degrees among 5-year-olds, the 135 degrees was worse than 45 or 180 degrees among 4-year-olds, and performance decreased according to orientation among 3-year-olds (Figure 3c). For Condition 4, performances of the 4-and 5-year-olds increased according to orientation, but this was not detected among the 3-year-olds (Figure 3d).

Figure 3a.

Correct responses to Condition 1.

Figure 3b.

Correct responses to Condition 2.

Figure 3c.

Correct responses to Condition 3.

Figure 3d.

Correct responses to Condition 4.

Table 1.

Mean and standard deviation of each age groups for conditions.

		3 years old				4 years old				5 years old
		boy		girl		boy		girl		boy		girl
	Orientation	M	SD	M	SD	M	SD	M	SD	M	SD	M	SD
Condition 1	45	0.40	0.49	0.12	0.32	1.00	0.00	0.64	0.48	0.87	0.34	0.94	0.24
	90	0.40	0.49	0.06	0.24	0.55	0.50	0.27	0.45	0.52	0.5	0.44	0.50
	135	0.20	0.40	0.00	0.00	0.36	0.48	0.32	0.47	0.39	0.49	0.19	0.39
	180	0.20	0.40	0.00	0.00	0.09	0.29	0.14	0.34	0.3	0.46	0.44	0.50
Condition 2	45	0.40	0.49	0.00	0.00	0.09	0.29	0.27	0.45	0.35	0.48	0.25	0.43
	90	0.30	0.46	0.00	0.00	0.00	0.00	0.05	0.21	0.13	0.34	0.00	0.00
	135	0.00	0.00	0.00	0.00	0.00	0.00	0.23	0.42	0.3	0.46	0.19	0.39
	180	0.00	0.00	0.00	0.00	0.19	0.39	0.23	0.42	0.52	0.5	0.25	0.43
Condition 3	45	0.70	0.46	0.35	0.48	0.46	0.50	0.46	0.50	0.61	0.49	0.56	0.50
	90	0.70	0.46	0.12	0.32	0.27	0.45	0.46	0.50	0.48	0.5	0.56	0.50
	135	0.30	0.46	0.06	0.24	0.09	0.29	0.18	0.39	0.39	0.49	0.31	0.46
	180	0.10	0.30	0.00	0.00	0.64	0.48	0.32	0.47	0.3	0.46	0.44	0.50
Condition 4	45	0.20	0.40	0.06	0.24	0.55	0.50	0.41	0.49	0.48	0.5	0.44	0.50
	90	0.00	0.00	0.06	0.24	0.18	0.39	0.14	0.34	0.35	0.48	0.19	0.39
	135	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.13	0.34	0.62	0.24
	180	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.13	0.34	0.13	0.33

Analysis of geometric figure error responses

Almost all incorrect responses showed left-right reversed symmetric construction. The symmetric construction was shaped based on the object axes in a different orientation from the original. It had the same contour but the front and back were reversed as “b” and “d.” We named that specific incorrect response the Re response (Noda, 2008). Few young children made a quarter turn to put the plate at the corner of stimulus or placed the plate apart from the comparison stimulus. We scored one point for the Re response, and ANOVAs for orientation for each condition were conducted. There were significant differences for Condition 1, F(3, 392) = 4.934, p <.01, Condition 2, F(3, 392) = 12.504, p <.001, and Condition 3, F(3, 392) = 5.811, p <.01. Re response increased according to orientation for Conditions 1 and 3, but most frequently dropped at 90° compared with adjacent orientations for Condition 2.

Analysis of bird-like figure error responses

We categorized correct answers and errors into the four specific responses based on the referent hypothesis and the simple error response (E). Table 2 shows the diagram for correct and categorized error responses in each orientation. The contour information and the turning distance from the standard to comparison stimulus are also displayed in Table 2. We used two reference systems for the hypothesis. The first system was referred to as the whole based on the contour orientation of the beak and body part of the bird-like figure. It contains the correct response (A) and the mirror response (M), which was defined as a mirror image of the correct answer. The other reference was based on the body part of the standard stimulus. It was assumed that the children would place the plate parallel to the body of the standard stimulus or align the plate horizontally regardless of the beak orientation. We categorized the specific responses by the second reference as the grand response (G). Placing the plate horizontally but at the opposite side of the body part was categorized as the grand reverse response (GR). Since the position at 180° of M was identical to that of GR, GR was tentatively represented in the diagram. Likewise, the upright position of G was identical to A and thus represented as A (Table 2). E was when the body part was placed apart from the head or the belly side of the body part was attached to the head.

Table 2.

Diagram for response categories of Condition 4 (bird-like completion task: BCT).

Standard stimulus			Completed comparison stimulus at each orientation
			0°	45°	90°	135°	180°
(bird-like stimulus)	Correct response	A
	Mirror response	M					GR
	Ground response	G	A
	Ground reverse response	GR
	Simple error	E
Contour information

We calculated the ratio of each categories for every orientations of the three age groups with Freedman’s test (Table 3). M increased according to age, χ²(2, N = 9) = 6.000, p <.05, and decreased according to the orientations, χ²(2, N = 9) = 6.00, p <.05, except for 180° because of the duplication of GR. The results of G showed no difference with age, but there was a significant tendency for orientations, χ²(3, N = 12) = 6.10, p =.09. G decreased according to the orientations for 5-year-olds, but increased at 180° for 3- and 4-year-olds. This might have been caused by the width range of individual variance. The results of GR showed that the response decreased according to age, χ²(2, N = 9) = 6.00, p <.05, and increased according to the orientation, χ²(2, N = 9) = 5.01, p =.08. GR at 180° orientation was omitted because of its duplication to G.

Table 3.

Frequencies of each category for age groups by orientation at Condition 4 (BCT).

		3 year olds		4 year olds		5 year olds
		(N = 27)		(N = 33)		(N = 39)
Categories	Orientation (°)	n	%	n	%	n	%
Correct response (A)	45	3	11.1	15	45.5	18	46.2
	90	1	3.7	5	15.2	11	28.2
	135	0	0.0	0	0.0	4	10.3
	180	0	0.0	0	0.0	5	12.8
Mirror response (M)	45	0	0.0	2	6.1	3	7.7
	90	1	3.7	5	15.2	16	41.0
	135	7	25.9	14	42.4	22	56.4
Ground response (G)	45	8	29.6	10	30.3	13	33.3
	90	5	18.5	2	6.1	6	15.4
	135	4	14.8	2	6.1	3	7.7
	180	7	25.9	5	15.2	2	5.1
Ground reverse response (GR)	45	6	22.2	3	9.1	3	7.7
	90	11	40.7	10	30.3	3	7.7
	135	13	48.1	10	30.3	6	15.4
Simple error (E)	45	6	22.2	2	6.1	2	5.1
	90	9	33.3	11	33.3	3	7.7
	135	2	7.4	4	12.1	3	7.7
	180	3	11.1	1	3.0	0	0.0

Response categories for Condition 4

To clarify the relationship among the response categories for Condition 4, we used Hayashi Quantification Method Type III, which is similar to the correspondence analysis, and sorted responses based on the similarity between categories. Categories were re-sorted into four groups: A, M, the pooled ground response set (G and GR), and E. Although G and GR were different in terms of the left-right arrangement, we thought that common strategies were used in those two categories. Thus, we tried to analyze G and GR as one category. It was scored 1 point in every response category for 45°, 90°, and 135°; however, the response at 180° was not applied to this test because of duplication. Hence, we calculated similarity with all children’s (N = 99) responses with 12 variables (three orientations and four categories).

The eigenvalue of the first axis was 0.690, the contribution ratio was 22.2%, and the coefficient of correlation was 0.83. The eigenvalue of the second axis was 0.651, with a contribution ratio of 21.0% and a coefficient of correlation of 0.81. The eigenvalues of both axes showed high and cumulative contribution rations summed to 43.3%, which explained almost half the variations. Category quantification for each axis of each response category is depicted in Figure 4. The results were divided into three clusters. The clusters to the left of the second axis represented A and M, while the cluster to the right of the second axis was the pooled set G and GR. The upper side of the first axis was E. As the Type III Method utilizes how categories react to identical participants to raise their similarity, it implies that there were children who react to G and GR or A and M simultaneously, and there were few children who reacted to E with other categories.

Figure 4.

Scatter diagram of categories for Condition 4 using the Hayashi Quantification Method Type III. We calculated 12 valuables for three orientation of 45°, 90°, and 135° × four categories of the correct response (A), mirror response (M), ground response set (G, GR), and the simple error (E). The first axis represented a shift of reference factor, which leads to the link between the head and the body part, while the second axis represented an awareness of the turning (Estes, 1998), which leads to the sequential understanding of rotation.

Discussion

Correct response

The performance of boys was better than that of girls at age 3 years, but sex differences were not found at ages 4 and 5 years. Geometric stimuli were confirmed but the specific bird-like Condition 4 was not. Although many spatial tasks show a sex difference (Linn & Petersen, 1985; Voyer et al., 1995), the difference disappears among older children owing to the increasing performance of girls compared with boys. Seeing that the task required not only manipulative elaboration but also familiarity, it may be the young boys accepted the geometric stimulus freely.

The performance increased with age, and the older children showed the performance on the rotation effect that decreased according to orientation. Condition 2 was shown different patterns from others. Seeing the low-performance of the young children, it is likely that children did not detect the difference of orientation in the first place. Young children could not distinguish the orientation sufficiently but the results of specific difficulty for orientations at the 4- or 5-year-olds can be interpreted as the appearance of some distinctive features (Gibson, 1969). Though the 3-year-olds showed the rotation effect on Condition 3, it might be caused by the specific stimulus structure which allowed the sensitivity to the orientation. Indeed, as the performance for Condition 3 was better than for Conditions 2 and 4, the construction of Condition 3 might have contained some familiarity or simplicity. While Condition 2 had a dropping profile at 90°, it was assumed that the structural information of the stimulus figure reflected the perceptual difficulty of identification. To account for the involvement of the contour information of the object, we tried to depict the diagram of the contour information and turning distance about Condition 2 to analyze the task structure of the stimuli. Table 4 displayed the correct, Re response and the contour pattern for each orientation. The figure’s contour in Condition 2 formed point symmetry; as indicated in Table 4, an isomorphism was formed between the contour of 0° and 180°. That is, the contours of the point symmetry figure come to congruence by turning it 180° in either direction. Hence, the farthest distance from the standard stimulus was 90°, and the relative distance decreased from the boundary of the 90°. That specificity with point symmetry may account for the drop at 90° compared to the other geometric conditions. It appeared that the process on the contour occurred particularly with 5-year-olds, but not with 3- and 4-year-olds. The younger children might have processed only part or a feature of the stimulus (Elkind et al., 1964) and could not recognize the multiple components simultaneously (Evans & Smith, 1988; Rosser, 1994; Rosser et al., 1984, 1989; Shepp & Swartz, 1976; Smith, 1989). However, there is the possibility that the 5-year-olds focused their attention excessively on the contour and did not integrate the parts into the whole yet on the Condition 2.

Table 4.

Task structural information of Condition 2 using the stimulus as point symmetry.

Standard stimulus		Inclination of completed comparison stimulus
		0°	45°	90°	135°	180°
	Correct
	Re response
Contour information
Turning distance of clockwise		0	+45	+90	+135	+180
Real turning distance		0	+45	±90	−45	0

Note. Although the clockwise turning distance increased linearly, based on the standard stimulus, the real distance increased and decreased, based on 90°. From the point of serial pattern of the contour information, 0° and 180° were isomorphic forms of each other, with the contour of 90° located at the halfway point.

Re response

Almost all errors on the geometric figures were Re responses; the results of each orientation showed reverse with the correct response. This was considered that the error of the spatial location for the marker as a feature or a part increased according to the difficulties maintain isomorphism as a whole contour. The correct information of feature location required mental rotation (Marmor, 1975, 1977), and not only an organized whole but also strategies of comparison to the discriminative parts were predictable in young children (Courbois, 2000; Foulkes & Hollifield, 1989; Kerr et al., 1980; Roberts & Aman, 1993; Rosser, 1994; Rosser et al., 1984, 1989). The young children focused on contour information without attending to information of both contour and feature, which leads to difficulties of perceptual identification, so it may be said that the Re occurred because the orientation made it impossible to integrate feature properly with contour. Alternatively, for the possibility of the left-right error, Roberts and Aman (1993) suggested that a child would be more likely to make a mistake when the object’s orientation was more than ±90° beyond the child’s body midline. Though a distinct change of profile was not found at the boundary of 90° except in Condition 2, much left-right error occurred at 135° and 180°. We can interpret the completion level has changed from 90° according to orientation in the specific case of the point symmetry.

Bird-like figure caused various errors which support multi-reference

From the response patterns of Condition 4, it was supposed that the correct response (A) and the mirror response (M), along with the ground response (G), and the ground reverse response (GR), formed a close relationship with each other. This agreed with the three categorical groups of Hayashi’s Quantification Method Type III (equivalence to correspondent analysis, Figure 4). Those four categories (A, M, G, GR) appeared as a result of reference action to congruent orientation, not simply contact part to part as the simple error (E). It can be said that selective attention (Smith, 1989) as the reference action to the part might be caused. It was supposed that the first axis reflected the action of the referent object going from a positive to negative direction.

Prominent features or salience (Courbois, 2000; Rosser, 1994; Rosser et al., 1984, 1989), such as the beak, might assist the perceptual resolution, but the young children could not yet utilize it and were confused perceptually. It may be that the salience is an interference for young children; but, by noticing that it is irrelevant information (Shepp & Swartz, 1976; Poirel et al., 2008), children finally come to the stage of multi-reference to the beak and imaged body. Probably, recognition of the orientation seemed to define the extent of difficulties to synthesize the part and whole. We can consequently interpret the developmental shift of reference action from simple part to multiple parts was reflected the progression of the G set to the A or M response on the second axis by awareness to the turning orientation (Figure 4). Alternatively, though it seems that the opposite result from local to global was found in the study that used Navon figures (Poirel et al., 2008), because the Navon stimuli have hierarchically structured patterns in which every single part is compatible with the entire constitution, the results of this study is not contradictory. That is to say, children firstly attend to a part in terms of the single dimension, which could not be recognized comprehensively, but then they come to recognize the total connection with multiple-reference. Therefore it seemed that some activity (Estes, 1998; Piaget & Inhelder, 1966/1971; Smith, 1989) was needed to form an image of the connected end-product of parts and whole. If we presume that the multiple-reference action to synthesize part with whole is an indication of relativeness to the object, different synthesizing to make isomorphism will be required in the various orientations.

The cause of error and action

Both the geometric and the bird-like figure actually showed various specific patterns, hence we tried to show the common source of error for the referent to consider the perceptual activity (Table 5). Since various errors might result from the difficulty to recognize two more components at a time (Rosser, 1994; Rosser et al., 1984, 1989; Shepp & Swartz, 1972; Smith, 1989), we assumed three noteworthy criteria. The first was “contact,” whether the part made contact with another part (e.g., it was not detached from the side of geometry or the bird’s beak part) which could result in beginning to refer to a single dimension. The second was “contour,” whether the end product had the same contour as the standard stimulus (Noda, 2010) to maintain isomorphism. The third was the location of “left-right,” whether the completion was on the same side as the standard one (e.g., the plate was not placed symmetrically, in other words not inside out). These criteria were supposed to assess the child's attention to the connection between the parts (Evans & Smith, 1988; Smith, 1989), and the child’s use of imagery to perceive the object’s contour as an invariable whole (Elkind, 1978; Elkind et al., 1964; Piaget & Inhelder, 1966/1971) without adhering to the wrong parts as in the Re response or the G set (G or GR response), M response. Specifically, the child was required to ignore irrelevant information of the standard part (Gibson, 1969; Poirel et al., 2008; Shepp & Swartz, 1976) and imagined substitute position. Lastly, it was supposed that the space relations of attach-detach for contact, isomorphism for contour, and relative relation of orientation which define left-right were attained according to development (Table 5).

Table 5.

Sensitive information and factor to resolve the tasks in this study.

categories		criteria			factor
Condition 1∼3	Condition 4	contact	contour	left-right	factor
Correct response	Correct response (A)	✓	✓	✓	correct reference and awareness of turning
Re response	Mirror response (M)	✓	✓	—	left-right confusion, and preference to the symmetry
Re response	Ground response set (G,GR)	✓	—	—	referent error
other error	Simple error (E)	—	—	—	ignore the relationship of pars

As for the movement component, we supposed that the referent action to replace the plate repeatedly is not only a simple movement to regulate the placement of stimulus itself but that it also involved manipulative properties to coordinate the body-stimulus relationship (Noda, 2010). There is also a possibility that the manipulative subtle movements were compatible with the orientation of inner rotation, and the compatibility promoted the resolution of the rotation task (Frick, Daum, et al., 2009; Wiedenbauer & Jansen-Osmann, 2008). Though sex differences were not found with holistic and analytic strategies (Robert & Chevrier, 2003), there were two types of children who tried to place repeatedly and who placed with no hesitation. These types of children seem to reflect the differences of representational level that the former children refer to a single dimension, while the latter children have already attained comprehensive imagery to synthesize each constituent. These differences seemed to be caused by the preliminary simulation with dissociation of action and representation according to the age. In this respect, we can foresee that the manipulative movement through simulation organizes the part-whole representation closely.

In summary, though young children attend to a dimensional part, children aged from 3 years old to 4 or 5 years old begin to also attend to the contour and they can refer to multiple dimensions. But various errors were caused because of the insufficiency of the synthesized imagery. Given that the manipulative behavior as a referent action binds with each constituent, it was supposed that preliminary imagery would synthesis part and whole properly. Consequently, it was assumed that the behaviors toward the object, which consisted both of perceptual and body-movement play important roles to image an incomplete part. Further studies are needed to clarify the fundamental function at the object-body relationship in the context of resolving the object’s transformation.

Footnotes

Funding

This research was partly supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 25560119.

Acknowledgments

The author is most grateful to the late Professor Emeritus Dr. Hiroshi Motoaki. The author also thanks the children and staff of Katsushika Shirayuri Kindergarten, Tokyo, Japan.

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