Accuracy of Children in Copying Angles - Lab Report Example

In the absence of children’s sufficient understanding of spatial coordinate systems, they tend to have a difficulty making angular figures,specifically, right angles and bisectors of right angles. This investigation looked into whether children are more accurate when making right angles, as represented by perpendicular lines, or right angle bisectors. Forty children aged four and five were tested on four types of figures: a) a baseline with another line at the middle at 90?; b) a baseline with another line at the end at 90? ; c) a baseline with another line at the middle at 45? / 135? ; and, d) a baseline with another line at the end at 45? / 135?. Results validate previous claims that due to cognitive underdevelopment and exposure to perpendicular real-world representations, children make more accurate representations of perpendicular lines rather than of lines representing 45? / 135? Introduction Background information The independent survival of a moving organism largely depends on its ability to represent and interpret the spatial coordinates of its surroundings. For example, in order to grasp an object such as food, one must know the location of that food, go to that location and grasp it. Essentially, spatial recognition is what gets organisms from point A to point B. Without the capability to properly represent space, a moving organism such as a human being will have a challenging existence. Based on ordinary observation, young children tend to be capable of imitating only spatial representations as they see it in their actual regular environment. Their capacity to make technical and analytical reinterpretations is not yet tapped at their young age. This translates to their lack of ability to make accurate location estimates, traverse unfamiliar places, and take shortcuts. As such, it would be important to find out and establish whether this observation is indeed valid and not a hasty generalization. This serves as the background for the investigation conducted in our 2213 class which looked into the capabilities of children aged four and five in terms of drawing perpendicular lines and lines that represented angles that measured 45? / 135?. This paper is the result of such an investigation, highlighting the impressionable points and findings made by the mentioned investigation. Review of relevant literature The first formal and valid investigation on the cognitive development of a child’s spatial capability was first conducted by Piaget and Inhelder in 1956 (Ibbotson & Bryant, 1976; Bremner & Taylor, 1982; Sandberg & Huttenlocher, 1996). They were able to conclude that young children find it challenging to draw horizontal and vertical lines given certain parameters (in Ibbotson & Bryant, 1976). Over the next decades, even more studies and investigations confirmed that spatial representation and recognition among very young children are still underdeveloped (Bremner, 1984). Bremner and Taylor (1982) have identified perpendicular error and bisection error as two possible causes of such spatial misrepresentations. They pointed out that the direction of the baseline figure also had an effect on the misrepresentations that occurred when children copied angles. That is, children made more errors when drawing angles from an oblique baseline rather than from a horizontal or vertical baseline (Bremner & Taylor, 1982). A study by Sandberg and Huttenlocher (1996) established that while adults are able to use two independent coordinates when representing the position of an object in a cartesian space, the same cannot be said for young children. Their study suggests that adults encode location on an intricate and categorical level whereas young children use the same coding skill on basic two-dimensional spatial representations. That is, they are not yet able to hierarchically and categorically code two-dimensional locations when given more a more complex set of parameters (Sandberg & Huttenlocher, 1996). On a similar note, Uttal (1996) looked into the capabilities of children to reconstruct and scale spatial configurations as this would also establish their cognitive capacities. Interestingly, his results seem to be of a different opinion as his experiments suggest that even young children are able to “represent and transform an entire configuration of objects” (Uttal, 1996). He does qualify, however, that while young children are able to perform simple configurations, the accuracy of such transformations are significantly lower compare to those made by older children and adults. Another study by Clements, Swaminathan, Hannibal and Sarama (1999) stressed the importance of investigating the spatial recognition capabilities of young children on the basis of the relevance of such an investigation to the eventual addressing of the development of children’s cognitive skills. They emphasized that the proper progression of spatial interpretation will be crucial in the development of children’s motor and internalized actions. Through their initial findings, they aimed to provide enough supporting evidence in establishing the need to make sure that children are cognitively prepared to interpret their spatial environment (Clements, Swaminathan, Hannibal, & Sarama, 1999). Rationale This investigation aims to serve its purpose by identifying the actual predominance in the spatial representation skills of young children. Since spatial recognition is an integral part of one’s existence, it is but right to provide first-hand information based on sound scientific evidence and time-tested theories that tackle such concepts. Results of this investigation may shed some light on the appropriate techniques and strategies that ought to be crafted when developing a child’s cognate ability to represent and interpret spatial coordinates. Research Questions With these rationale in mind, this investigation aims to answer the following research questions: Are children more accurate when making representations of perpendicular lines than lines that form 45? / 135? angles? Moreover, Are younger children more accurate when making representations of perpendicular lines than lines that form 45? / 135? angles? Are older children more accurate when making representations of perpendicular lines than lines that form 45? / 135? angles? Are children more accurate when making representations of perpendicular lines than lines that form 45? / 135? angles from the end of the line? Are children more accurate when making representations of perpendicular lines than lines that form 45? / 135? angles from the middle of the line? Hypothesis The null hypothesis for this study is: H0: There is no difference in the accuracy of children when making representations of perpendicular lines and lines that form 45? / 135? angles. Consequently, this study alternatively hypothesizes that children make more accurate representations of perpendicular lines rather than lines that form 45? / 135? angles. Methods Participants In order to test the given hypothesis, a test was conducted on young children of the UWA Child Study Centre. For the indicated test, 22 four year olds and 18 five year olds were asked to respond to a given stimuli. Procedure The stimuli used for the study are Four A4 pages, each showing a complete figure (black oblique line, with smaller red line joining it) in the top half and a copy of the black oblique line, without the red line in the bottom half. The testing was conducted by the children’s teachers from the UWA Child Study Centre. Figure 1. Designs on the stimuli copied by participants. The teacher explained that Clara, the cow, has lots of energy and has finished all her drawings at the top of the pages. On the other hand, Dozy, the sleepy dog, started his drawings, but then got sleepy and is taking a nap. The children were asked to finish Dozy’s drawings so they would be the same as Clara’s. It should be noted that the order of completing the four sheets was counter-balanced across children. Figure 1 shows the designs that the children were required to copy as grouped by angle measure and line position. Research Design The investigation utilized a quasi-experimental design, which is the most appropriate type of research method when dealing with human behavioural considerations (Berg & Latin, 2008). The independent variable considered for this investigation is the measurement of the angle drawn by the child, either 90? or 45? / 135?. The dependent variable is represented by the errors made in drawing the required angle. This was measured by using a protractor to find the number of degrees that the drawn figure diverted from the required measure, within + 1?. For a richer extent of investigation, comparisons were also done based on Age grouping (Younger children vs Older children) and on Point of Intersection (Mid vs End). These scores were then tabulated on Microsoft Excel and analysed using the appropriate statistical techniques. For this particular investigation, t-test was used to determine if the errors committed by the participants were significantly different when they were drawing perpendicular lines compared to when they were drawing lines that represented 45? / 135? angles. The final data set used was the mean of the recordings from five randomly selected 2213 classes. Results Two participants were rated as representing outliers in terms of the required data and were thus removed from the investigation. After they were removed, there were a total of 38 participants, 20 of whom are female, and having an overall mean age of 59 months. Table 1. Mean errors (SD) for 90? and 135? end at middle positions in younger and older children.     Mean (SD)           90 135 t df Sig. Position Mid 7.90 (1.80) 29.94 (3.98) 7.26 37 0.000 End 10.68 (3.25) 15.86 (3.65) 1.94 37 0.060 Age Younger 10.7 (3.45) 27.77 (4.18) no data available   Older 7.55 (1.93) 16.88 (5.0) no data available Overall 9.29 (2.13) 22.9 (3.62) 6.45 37 0.000 T test results from Table 1 reveal that children made more errors in drawing 45? / 135? angles (Mean = 22.9, SD = 3.62) as compared to drawing 90? angles (Mean = 9.29, SD = 2.13), t(37)=6.45, p < .001. This same trend is reflected when participants are divided into the Younger children group and Older children group. Younger children made more errors in drawing 45? / 135? angles (Mean = 27.77, SD = 4.18) as compared to drawing 90? angles (Mean = 10.7, SD = 3.45), no t test data available. In the same manner, older children also made more errors in drawing 45? / 135? angles (Mean = 16.88, SD = 5.0) as compared to drawing 90? angles (Mean = 7.55, SD = 1.93), no t test data available. In addition, 45? / 135? angles drawn from the middle of the line (Mean = 29.94, SD = 3.98) generated more errors that 90? angles drawn from the middle of the line (Mean = 7.90, SD = 1.80), t(37) = 7.26, p < .001. The same trend, though in this case non-significant, applied to 45? / 135? angles drawn from the end of the line (Mean = 15.86, SD = 3.65) which generated more errors that 90? angles drawn from the end of the line (Mean = 10.68, SD = 3.25), t(37) = 1.94, n. s. Discussion This investigation aimed to find out if children made more accurate representations of perpendicular lines rather of lines representing 45? / 135? angles. The results obtained validate the findings made by Ibbotson and Bryant (1976) which showed that children generally had an easier time and produced more accurate results when copying perpendicular lines compared to when they were making oblique angles. Moreover, children tended to draw angles that represented the perpendicular, a phenomenon labeled as the “perpendicular error” (Ibbotson & Bryant, 1976). This error is further attributed by Ibbotson and Bryant (1976) to the fact that the immediate environment that the young child is exposed to consists more of perpendicular lines rather than of oblique angles. Such an exposure most likely impacts the spatial cognition of a young child. The findings of this investigation likewise bear similarities to the results of Sandberg and Huttenlocher (1996) which emphasizes that due to the cognitive load that is required in making oblique angles as opposed to right angles, young children are not able to manage such at a task with the same ease as older children and adults do. Highly cognitive tasks such as reconstruction and scaling are challenging to young children who have not yet developed their capacities in the cognate category. It should be noted that these findings do not go along with findings made in the study of Uttal (1996) which highlighted the apparent capacities of young children to represent and transform an entire configuration of objects. Perhaps it would be more prudent to point out that while children are able to approximate the representation and transformation of a number of basic geometric objects, such approximations are not very accurate. As pointed out in his research, the transformations and representations made by younger children (represented by preschoolers in his study) were on a smaller or larger scale and in an irregular manner compared to those made by older children and adults. This phenomenon clearly indicates that younger children are not cognitively as prepared when dealing with the spatial coordinates of the objects around them. With these results, this study supports the research of Clements, et al. (1999) which points to the general manner by which children distinguish spatial markers, that is, by visual matching. However, younger children have still not developed enough in terms of their cognate skills which results to a discrepancy in the matches that they have made visually and the corresponding representations that they make on paper. Adults that assist in the cognitive development of a child should constantly encourage the child to accurately depict the spatial representations in the objects around him or her in order to hasten the child’s accuracy when making visual matchings. Recommendations As the importance of spatial recognition is greatly highlighted over the years, more and more research are being conducted to further the knowledge on the said field. Based on the findings of this investigation, it is recommended that more inquiries of the sort should be done, specially those that factor in more variables of interest. One particular area of interest may be on the effect of the child’s sex on his or her spatial recognition capacities. As male children are known to cognitively develop at a much later stage compared to female children, it would be noteworthy to investigate whether their spatial recognition capabilities likewise develop at a later stage. Another area of interest that may be explored is the impact of culture and real-world exposure on a child’s spatial development. Would a child who was socially exposed earlier on make more accurate spatial decisions and representations than a child who was reared at a more seclusive manner? Such an investigation may likewise merit notable additions to the annals of cognitive development science. References Berg, K., & Latin, R. (2008). Essentials of research methods in health, physical education, exercise science and recreation, (3rd ed.). Baltimore, MD: Lippincott Williams & Williams. Bremner, J. G. (1984). Errors towards the perpendicular in children’s copies of angular figures: a test of the bisection interpretation. Perception , 13, 117-128. Bremner, J. G., & Taylor, A. J. (1982). Children’s errors in copying angles: perpendicular error or bisection error? Perception , 11, 163-171. Clements, D., Swaminathan, S., Hannibal, M. A., & Sarama, J. (1999). Young children's concepts of shapes. Journal for Research in Mathematics Education , 30 (2), 192-212. Ibbotson, A., & Bryant, E. P. (1976). The perpendicular error and the vertical effect in children’s drawings. Perception , 5, 319-326. Sandberg, E. H., & Huttenlocher, J. (1996). The development of hierarchical representation of two-dimensional space. Child Development , 67 (3), 721-739. Uttal, D. (1996). Angles and distances: Children's and adults' reconstruction and scaling in spatial configurations. Child Development , 67, 2763-2779. Read More