An Investigation on How Children from Different Socioeconomic Status (SES) Classify Geometric Shapes

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An investigation on how children from different socioeconomic status (SES)

classify geometric shapes

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124 | PART B. SOCIAL SCIENCES AND HUMANITIES

D. Aslan, Yaşare A. Arnas, İ. Eti. An investigation on how children from different socioeconomic status (SES) classify geometric shapes. International Journal of Academic Research Part B; 2012; 4(6), 124-133.

DOI: 10.7813/2075-4124.2012/4-6/B.19

AN INVESTIGATION ON HOW CHILDREN FROM

DIFFERENT SOCIOECONOMIC STATUS (SES)

CLASSIFY GEOMETRIC SHAPES

Dr. Durmuş Aslan, Prof. Dr. Yaşare Aktaş Arnas, İnanç Eti

Çukurova University (TURKEY)

E-mails: asland@cu.edu.tr, yasare@cu.edu.tr, ieti@cu.edu.tr DOI: 10.7813/2075-4124.2012/4-6/B.19

ABSTACT

Geometric shapes are one of the main topics in early childhood mathematics education. The studies about the development of early mathematical knowledge reveal that there are some socioeconomic differences in mathematics subjects such as numbers and operations. This study has been carried out to find out whether there is a similar difference in geometry. In the study, four shape-classification tasks were developed by researchers and administered to the children. The sample of the study consisted of 105 children coming from low, middle and high socioeconomic families. The result of the study underlined the statistically significant difference among the SES groups in the rectangle, square and circle classification tasks. No statistically significant difference; however, was found in the triangle classification task. Besides, visual responses were mostly observed in the children’s responses but a decrease in the rate of visual answers and an increase in the number of property answers were observed in line with the transition from low to high socioeconomic class.

Key words: Preschool, Mathematics, Geometric Shapes, Socioeconomic Status 1. INTRODUCTION

Studies that have been carried out in the field of cognitive development for years have essentially changed the views about the development of mathematical thinking in the early years. While the traditional learning theorists advocated that children start to acquire the mathematical knowledge with the formal mathematical education in elementary schools, Piaget shifted the focus of the studies to the development of informal mathematical knowledge in the earlier years (Starkey, Klein & Wakeley, 2004).

The following studies in the field of cognitive development showed that in some respects, children have more extensive informal mathematical knowledge than the estimate of Piaget and this knowledge is occurred in an earlier period (Starkey, Klein, 2000; Starkey, Klein & Wakeley, 2004). The studies carried out on young children revealed that informal mathematical knowledge dimensions such as number, operation and geometry show significant improvement in the preschool period (Aslan & Aktas Arnas, 2007; Baroody, 1992; Beilin & Klein, 1982; Clements, Swaminathan, Hannibal & Sarama, 1999; Cooper, 1984; Hannibal & Clements, 2000; Satlow & Newcombe, 1988).

2. THEORETICAL FRAMEWORK

Recognition of Geometric Shapes in Preschool Children

Geometric shapes are the standards that a person uses to define the shape of an object. The shape, just like the size, separates an object from the other in the space. Geometric shapes have an important role in our recognition of the objects around us. How children learn the shape of an object and how their perception of geometric shapes become more consistent are the key issues of the studies about the developmental field (Leushina, 1991).

When the related literature is reviewed, it is seen that the theory of van Hiele about the development of geometrical thinking has been widely considered. According to van Hiele theory, the development of geometrical thinking consists of five stages. These stages are sequential like Piaget’s cognitive development stages and the success in one stage depends on the geometrical thinking property of the previous stage (Aktas Arnas, 2002). The first two of these stages cover the early childhood period. The first stage of van Hiele’s geometrical thinking development is the visual stage. According to van Hiele, children at this stage perceive the shapes by looking at their appearances and make judgement about them (van Hiele, 1999). The children at this stage can recognize the triangle, rectangle, square and circle. However, this does not show that the children are aware of the defining attributes of shape such as side and corner (Troutman & Lichtenberg, 1991). They perceive the shape as a whole and focus on the visual attributes of the shape. Although they know that a triangle is different from a square, they focus on the total shape of the triangle and square while explaining the difference and they do not become

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concerned in the defining attributes (Aktas Arnas, 2002). It has been accepted that most preschool children are at the visual stage (Kellough, Carin, Seefeldt, Barbour and Souviney, 1996; Seefeldt and Barbour, 1998). According to van Hiele theory, when a child starts to define a geometric shape depending on its defining attributes, his/her thinking is at the second level- the analysis level (van Hiele, 1986; Hannibal & Clements, 2000). Children generally reach this stage at the third or fourth grade of the elementary education (Altun, 1997).

On the other hand, the recent studies (Aslan and Aktas Arnas, 2007; Clements & Battista, 1992; Clements et al., 1999; Hannibal & Clements, 2000) claimed that the van Hiele theory is inadequate in explaining the geometrical thinking development in young children. While the van Hiele theory says that the children at visual stage recognize the shapes visually, the findings of this research reveal that the children at this stage can not distinguish a group of figures from others reliably, so a complete visual recognition can not be talked about. For example, while a great number of children recognize the typical triangle (equilateral triangle the base of which is horizontal and the vertex of which is in the center), it was found out that the children fail to recognize the atypical examples emerged when the non-defining attributes (such as orientation, aspect ratio, skewness) of the typical triangle are changed. Therefore, it is stated that these children's geometrical thinking level is not in line with the visual stage, so the lower stage, the pre-recognition level, is suitable for these children (Aslan and Aktas Arnas, 2007; Clements et al., 1999; Hannibal & Clements, 2000).

These studies that have been carried out lately (Aslan and Aktas Arnas, 2007; Clements et al., 1999; Hannibal and Clements, 2000) present that some important developments occur in the children’s skill of classifying the geometric shapes in the preschool period. For example, Clements et al. (1999) found out that children become more successful in recognizing the geometric shapes as they get older. Identically, Aslan and Aktas Arnas (2007) expressed that children’s skill of recognizing the geometric shapes increase in parallel with age. Furthermore, Aslan and Aktas Arnas determined that children tend to focus on defining attributes such as corner and side of the shapes instead of the visual attributes of the shape while they get older.

Socioeconomic Differences in Preschoolers’ Mathematics Achievement

Socioeconomic status has an important effect as well as the individual differences in children’s achievement in mathematics (Jordan, Huttenlocher, & Levine, 1992; Jordan, Kaplan, Locuniak, & Ramineni, 2007; Jordan, Kaplan, Ramineni, & Locuniak, 2009). The researchers discovered many social factors related with the differences in the children’s mathematical performances. These differences that are related to socioeconomic status in mathe-matical achievement emerge in the preschool period and continue to increase throughout the school life (Klein & Starkey, 2003; Starkey & Klein, 2008).

Many studies which have investigated the differences in socioeconomic status in early mathematical development found that there are developmental differences between the children from low-income families and the children from middle-income families in terms of informal mathematical knowledge they have (Starkey & Klein, 2000; Starkey, Klein, & Wakeley, 2004).

These studies show that the children from low-income families are confronted with the risk of failure; especially in mathematics. For example, Jordan et al. (Jordan, Kaplan, Olah & Locuniak., 2006; Jordan et al., 2007; Jordan, Kaplan, Ramineni & Locuniak., 2008) identified that the mathematical skills of the children from low-income families are lower than their peers from middle-income families. Jordan et al. investigated the performance and the development of number adequacy at the beginning of kindergarten in relation to the mathematical achievement. They found out that knowledge of counting, numerical relationships (e.g. recognizing the smaller number out of tow numbers) and numerical operations (e.g. making addition and subtraction with small numbers) of the children from low-income families were behind their peers from middle-income families in tasks on assessing number competence.

Ginsburg and Pappas (2004) investigated the possible differences in five-year-old children’s informal mathematical knowledge regarding socioeconomic status (SES). These researchers determined that the children in the high SES group achieved better in many mathematical problems than the children in the middle and low SES groups. In another study carried out with the children whose ages ranged between 2,5 and 4,5 years by Saxe, Guberman, & Gearhart (1987), it was found that four-year-old children from middle-income families showed greater competence than their peers from working-class in more complex numerical tasks. Even though the studies found a difference in the early mathematical knowledge according to socioeconomic status, most of them focused primarily on numerical skills such as counting or concrete addition and subtraction problems. Although this view is an appropriate point to start investigating, important fields of early mathematical knowledge such as spatial and geometrical judgement, pattern knowledge and measurement have not been investigated on preschool children from different socioeconomic groups, yet (Starkey, Klein & Wakeley, 2004).

In addition, the mathematical skills of children from low and middle socioeconomic status have been compared in these studies many of which have been carried out on matters except geometry (Ginsburg & Russell, 1981; Jordan, Huttenlocher & Levine, 1992; Sarama & Clements, 2009; Saxe, Guberman & Gearhart, 1987). The number of studies in which children from each three income groups were compared together is limited. Except for a few studies, there were not any large samples which included children from high-income group together with children from low and middle-income groups in any studies (Case & Okamoto, 1996; Ginsburg and Pappas, 2004).

Aim

This study aims to determine the effect of socioeconomic status on children’s geometric shape knowledge. For this purpose, this research is based on the following questions:

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126 | PART B. SOCIAL SCIENCES AND HUMANITIES

1. Do the children’s classification skills of the geometric shapes differ according to their

socioeconomic status?

2. Do the criteria that children use while distinguishing the geometric shapes from each other

change according to their socioeconomic status?

3. METHOD Participants

This study was carried out with 105 six-year-old children whose families differ in socioeconomic status (SES). The children were selected via random sampling method to have equal number of children in each socioeconomic status. 35 of the participants (range: 64 to 75 months; 15 girls and 20 boys) were attending a public preschool that served low-income families, 35 of the participants (range: 64 to 75 months; 15 girls and 20 boys) were attending a public preschool that served middle-income families and 35 of them (range:65 to 75 months; 16 girls and 19 boys) were attending a private preschool that served high-income families.

Most of the low-income parents were graduates of elementary schools. There were not university graduates among them. The majority of income mothers were not working in any jobs (housewives). Most of the low-income fathers were workers. In middle-low-income group, most of the parents graduated from high school. The majority of middle-income mothers were not working in any jobs (housewives) and the majority of middle-income fathers were tradesman and civil servants. Besides, most of the high-income parents had attained a BA or higher degree. The majority of high-income mothers had professional jobs such as doctor, manager and teacher. Indeed, most of the high-income fathers had proffesional jobs such as doctors, engineers and managers.

Materials

Four shape classification tasks (triangle, rectangle, square and circle) were used as the data collection tools in this study (See Appendix). Each classification task consisted of shapes that were drawn on an A4 sheet. The classification tasks were developed by the researchers in line with the previous studies (Aslan and Aktas Arnas, 2004, 2007; Clements et al., 1999; Hannibal and Clements, 2000; Satlow and Newcombe, 1998).

The past studies done on the children’s recognition of the geometric shapes (Aslan and Aktas Arnas, 2007; Clements et al., 1999; Hannibal and Clements, 2000) revealed that children focused on the non-defining attributes such as aspect ratio, skewness, orientation and size while classifying the geometric shapes and they made some classification mistakes because of this. In consequence, atypical examples that have non-defining attributes (orientation, aspect ratio, skewness, size) were included in addition to the typical examples into the each task while preparing the classification tasks (e.g. T1, T2, T3, T5, T6, T7 in triangle task). Moreover, some distractors were placed into each task so as to determine if children could distinguish the shapes belonging and not belonging to one shape group. Distractors were made up of two groups as the palpable and impalpable ones in each task. Palpable distractors consisted of typical samples belonging to groups of shapes out of the measured group of shape (e.g. TD2, TD3; RD3; SD2, SD3, SD6; CD2, CD3). Impalpable distractors were the figures that look like the tested group of shape, but did not belong to the tested group due to the corrosion of side or corner attributes (e.g. TD1, TD4, and TD6 in the task of triangle).

The KR 20 alpha value was calculated to determine the reliability of the geometric shape tasks. The results of the analysis showed that the KR 20 alpha value was.60 for the triangle task,.61 for the rectangle,.63 for the square and.78 for the circle.

Data Collection

Data was collected through individual interviews with each child in a quiet room of his/her school. First, the triangle task was given to the child, s/he was instructed to mark the triangles by asking "there are some shapes here and I want to classify these shapes. Could you put a cross (X) on triangles with a blue pen?". After the child had completed marking the triangles, s/he was told to put a cross (X) on the figures that were not a triangle with a red pen. If there were any unmarked shapes after the child finished marking, s/he was asked "I can see you did not mark this figure. Is it a triangle or not?" and wanted to mark according to his/her response. After all the shapes in the task had been marked, all shapes were shown to the child in a row and "You marked this figure as a triangle (or not a triangle), why do you think this is a triangle (or not a triangle)?" was asked to him/her. The child's responses were recorded in the explanation part of the interview record form. The same procedure was implemented for the other shape classification tasks every other day.

Data Analysis

The researcher coded incorrect responses with (0) and correct responses with (1) by checking the child's marking after the individual interview with the child had finished. Total scores that the children got from each test were calculated and Anova (variance) analysis was done in order to determine whether there was a significant difference among socioeconomic groups. When a significant difference was found, Tukey's Post Hoc analysis was done to specify the source of the difference.

Next, the child's reasons for classifying each figure were examined and his or her responses were classified. The child's response was accepted as "visual response" if it indicated the figure's visual attributes (fat, thin, big etc.) or another shape ("it looks like this shape") or object ("it looks like a door"). On the other side, the child's reponse was accepted as “property response" if it indicated the figure's defining attributes such as side and corner (e.g. "it has four equal sides", "it has three corners"). Thus, it was aimed to determine that the children focused on whether visual or property (defining) attitudes while classifiying the shapes.

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4. FINDINGS

Table 1. The results of variance analysis about the children’s scores in the

triangle task according to socioeconomic status

Source Sum of Squares df Mean Square F P

Between Groups 10,34 2 5,17 1,58 .209

Within Groups 332,28 102 3,25

Total 342,62 104

Table 1 shows the results of variance analysis about the scores that the children got from the triangle classification task according to socioeconomic status. It was found out that there was not a significant difference among the children’s scores in the triangle task according to socioeconomic status (F(2,102)=1,58, p>.05). The effect size for this analysis, calculated using eta squared, was small (d=.03).

Table 2. Distribution of the children’s responses about the reasons of their correct

classification in the triangle task according to socioeconomic status SES

Low SES Middle SES High SES Total

Type of Response f % f % f % f %

Visual 287 100 231 83 128 49 646 78

Property 0 0 26 9 135 51 161 19

IDK 0 0 23 8 0 0 23 3

Total 287 100 280 100 263 100 830 100

IDK: I don’t know

Responses given by children about the reasons of correct classification they made in the triangle task according to socioeconomic status can be seen in the table 2. The low SES children’s all responses and 83% of the middle SES children’s responses consisted of visual responses while 49% of the high SES children’s responses were visual. Even though the low SES children gave no property responses, 9% of the middle SES and 51% of the high SES children’s responses consisted of property responses.

Table 3. The results of variance analysis about the children’s scores in the

rectangle task according to socioeconomic status

Source Sum of Squares df Mean Square F p

Between Groups 136,93 2 68,46 24,13 .001

Total 426,24 104

Table 3 presents the results of the variance analysis about the scores that the children got from the rectangle classification task according to socioeconomic status. It was found out that there was a statistically significant difference among the children’s scores in the rectangle classification task according to socioeconomic status (F(2,102)=24,13, p=.001). The effect size for this analysis (d =.32) was found to exceed Cohen’s (1988) convention for a large effect (d =.14). As a result of the Tukey Post Hoc analysis done for finding the source of the difference, it was defined that there was a statistically significant difference among the children from the low, middle and high SES, against the children from the low SES.

classification in the rectangle task according to socioeconomic status SES

Visual 217 100 212 75 207 66 636 78

Property 0 0 52 19 108 34 160 20

IDK 0 0 17 6 0 0 17 2

Total 217 100 281 100 315 100 813 100

Table 4 points out the distribution of the responses that the children gave about the reasons of correct choice in the rectangle task according to socioeconomic status. When the children’s responses were analyzed, it was seen that the low SES children’s all responses and 75% of the middle SES children’s responses consisted of visual responses while 66% of the high SES children’s responses were visual. Although the children from the low SES did not give any property responses, 19% of the middle SES children’s responses and 34% of the high SES children’s responses consisted of property responses.

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128 | PART B. SOCIAL SCIENCES AND HUMANITIES

Table 5. The results of variance analysis about the children’s scores

in the square task according to socioeconomic status

Between Groups 102,7 2 51,35 23,9 .001

Total 321,84 104

Table 5 presents the results of the variance analysis about the children’s scores in the square task according to socioeconomic status. It was determined that there was a statistically significant difference among the children’s scores in square task according to socioeconomic status (F(2,102)=23,9, p=.001). The effect size for this analysis was high (d=.31). The results of Tukey analysis done in order to define the source of the difference expressed that there was a statistically significant difference among the low SES children and the middle and high SES children against the low SES children. Also, there was a statistically significant difference between middle SES children and high SES children in favour of the high SES children.

classification in the square task according to socioeconomic status SES

Visual 264 99 253 80 215 61 732 78

Property 2 1 52 16 136 38 190 20

IDK 0 0 13 4 0 0 13 2

Total 266 100 318 100 351 100 935 100

The distribution of the responses that the children gave about the reasons of correct choice in the square task according to socioeconomic status is given in Table 8. When the children’s responses were considered, it was seen that 99% of the low SES children’s responses, 80% of the middle SES children’s responses consisted of visual responses while 61% of the high SES children’s responses consisted of visual responses. On the other hand, 1% of the low SES children’s responses, 16% of the middle SES children’s responses and 38% of the high SES children’s responses were property responses.

Table 7. The results of variance analysis about the children’s scores

in the circle task according to socioeconomic status

Between Groups 170,53 2 85,26 45,09 .001

Total 363,39 104

Table 7 shows the results of the variance analysis about the children’s scores in the circle classification task according to socioeconomic status. As seen in Table 9, there was a statistically significant difference among the children’s scores in the circle task according to socioeconomic status (F(2,102)=45,09, p=.001). The effect size for this analysis (d =.46) was found to exceed Cohen’s (1988) convention for a large effect (d =.14). As a result of the Tukey analysis which was done to find the source of the difference, it was defined that there was a significant difference among the low, middle and high SES children against the low SES children. Indeed, there was a significant difference between the middle and high SES children in favour of the high SES children.

classification in the circle task according to socioeconomic status SES

Visual 246 89 232 65 187 48 665 65

Property 32 11 117 33 205 52 354 34

IDK 0 0 7 2 0 0 7 1

Total 278 100 356 100 392 100 1026 100

Table 8 shows the distribution of the responses that the children gave about the reasons of classification in the circle classification task according to socioeconomic status. In Table 8, it was seen that 89% of the low SES children’s responses, 65% of the middle SES children’s responses and 48% of the high SES children’s responses consisted of visual responses. When the distribution of the property responses was examined, it was seen that 11% of the low SES children’s responses, 33% of the middle SES children’s responses and 52% of the high SES children’s responses consisted of property responses.

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5. DISCUSSION AND COMMENTS

In this study, we investigated the effect of socioeconomic status on the children’s classification of geometric shapes. We obtained two main findings about the children’s classification skills of geometric shapes from the results of this study.

The first main finding is that the children’s classification skills of geometric shapes differ according to their SES as it was found in the previous studies that presented the children’s numerical knowledge according to SES (Griffin, Case, & Siegler, 1995; Jordan, Huttenlocher, & Levine, l992; Starkey & Klein, l992; Starkey, Klein, & Wakeley, 2004). Our assessment showed that children’s scores in shape classification tasks increased in direct proportion to their socioeconomic status. However, this was not the same for the triangle task. While a significant difference in favour of the children from the middle and the high SES was found in the rectangle, square and circle tasks, there was not a significant difference in the triangle task. When the children’s classification scores in each item were examined in the triangle task, it was found that the high SES children were more successful than the low and middle SES children in impable distractors (TD1, TD4, TD5, TD6, TD7, TD8), while the low and middle SES children were more successful than the high SES children in atypical examples (T1, T2, T3, T5, T6, T7). It is believed that due to the failure of the high SES children in recognizing the atypical examples, there is not a significant difference among the SES groups in the triangle task. The failure of the high SES children in atypical examples might be causing from their teachers’ presenting the typical example of the triangle (T4) and neglecting the atypical examples while teaching the triangle. However, children need to see the atypical examples of a shape in addition to its typical examples in order to recognize a geometric shape completely and classify it correctly (Aslan & Aktas Arnas, 2007; Clements et al., 1999).

The second main finding is that the criteria children use while classifying the shapes differ according to their SES. The children from the low SES grounded on the visual attributes highly while classifying the shapes, they almost never used the defining attributes (e.g. side or corner attributes of the shape). This case may have been derived from the teachers’ focusing on visual attributes while teaching geometric shapes. In spite of grounding on the visual attributes mostly while classifying the shapes, the children from the middle and the high SES used the defining attributes, too. Besides, the visual responses decreased and the property responses increased together with the rise in SES. It was determined that similar situation has occurred among the preschoolers in line with age. Aslan and Aktas Arnas (2007) found that there was a decrease in the rate of visual answers and an increase in the number of property answers in line with age.

Both of these main findings show us that the low SES children’s mathematical knowledge about the geometric shapes is lower than the middle and high SES children’s mathematical knowledge about the geometric shapes. The findings obtained from this study were consistent with the ones obtained in the previous studies. When the literature is reviewed, it is reported that there are some differences in the mathematical knowledge resulting from the SES between the children coming from economically disadvantaged families and their peers coming from middle class families (Denton and West, 2002; Ginsburg, & Pappas, 2004; Ginsburg & Russell, 1981; Saxe, Guberman, & Gearhart, 1987; Jordan, Kaplan, Olah and Lociniak, 2006; Jordan, Huttenlocher and Levine,1992; Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006). For example; Jordan et all. (2006) found that the performances of the children coming from low-income families were lower than those of the children coming from middle-income families at the end of the kindergarten. In another study by Jordan, Huttenlocher and Levine (1992), it was found that although the children from the low and the middle-income families showed equal performances in non-verbal problems, the children from the middle-income families showed a significantly better performance than the children from the low-income families in verbal problems. This was seen in both addition and subtraction operations. In another study in which the mathematical knowledge of four-year-old children was assessed in detail at the beginning of the kindergarten, a difference causing from the SES was found. In the study, middle-income children got higher scores than low-income children in many fields of mathematics such as number order, number comparison, ordinal number terms, addition and subtraction with objects, shape naming, and reasoning about triangle transformations (Starkey, Klein and Wakeley, 2004). Polat Unutkan (2007) determined that the mathematical skills (attention-retention, recognizing numbers, the skills of addition-subtraction and sequencing) of low SES Children were lower than the mathematical skills of middle and high SES children and low SES children were not prepared enough for the elementary education in terms of mathematical skills. Moreover, Klibanoff, Levine, Huttenlocher, Vasilyeva and Hedges (2006) defined that there were distinct differences in the traditional mathematical knowledge of the children beginning from 4-year-old related with the socioeconomic status and the mathematical knowledge of the children from the low SES was lower than the mathematical knowledge of the children from the middle and the high SES.

These differences causing from the SES can derive from two main environments, the environment of home and school, which can support the early mathematical developments of the children. There are some studies which investigated the home and school environment of the children in the related literature. These studies showed that the socioeconomic status of the parents affect the existence of experience support for the children at home (Gersten and Chard, 1999) and the mathematical support around the home is lower in families from low socioeconomic status (Blevins-Knabe and Musun-Miller, 1996; Clements & Sarama, 2007; Holloway, Rambaud, Fuller & Eggers-Pierola 1999; Saxe et al., 1987; Starkey, Klein, Chang, Dong, Pang, & Zhou, 1999; Starkey et al., 2004; İvrendi & Wakefield, 2009; Aslan, Aktas Arnas & Hayta, 2012). For example; Blevins-Knabe and Musin-Miller (1996) determined that the parents with low-income provide not only fewer but also low-level of mathematical activities compared to the parents with middle-income. Similarly, Starkey et al. (1999) revealed that American parents with middle-income do a broader distribution of mathematical activities more frequently than the parents with low-income. Ivrendi and Wakefield (2009) found that the parents with a higher education degree play with their

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children rather than accompanying them use the language of mathematics more and participate in the verbal language activities more. Melhuishet et al. (2008) determined in their study that the familial factors such as parents’ educational and socioeconomic status are important and home learning activities cause a big and independent effect in child’s education. The socioeconomic status differences in the support which the parents give for their children’s mathematical development might be deriving from various reasons. Reasons such as the limited educational level of the parents, the pressure of inadequate financial resources, unfulfilled spiritual needs, discomfort about the parents’ own mathematical skills and the lack of awareness about the importance of early mathematical development of the children can result from socioeconomic status differences (Clements and Sarama, 2007; Cross,Woods, & Schweingruber, 2009).

6. CONCLUSION

The results of the research show the significant difference among the SES groups against the low SES children in the rectangle, square and circle classification tasks. Such a difference can not be mentioned in the triangle task. Furthermore, the children from the low SES ground on the visual attributes mostly while classifying the shapes. On the other hand, it was determined that the children ground on the visual attributes less and focus on the property attributes more in parallel with the increase in SES.

Past studies showed that there were differences in the children’s mathematical knowledge related with the SES in early childhood period. Economically disadvantaged children get less support about mathematics both in school and at home. Consequently, the children who have different socioeconomic background start the elementary school with various readiness levels about mathematics. An approach for making up this difference is the improvement and application of the curricula at schools to which economically disadvantaged children attend. Klein, Starkey, Clements, Sarama, & Iyer, (2008) confirmed in their study the mathematical implementations before starting to school make up the difference in the children’s early mathematical knowledge. Similarly, Starkey, P. & Klein, A. (2000) expressed in their study that the parents with low-income were more willing to support the mathematical development field of their children after a training had been provided for them and they managed to implement those activities. This support which the parents provided for their children via this application was found clearly effective in increasing the development of the children’s informal mathematical knowledge. The parents with low-income should be trained and supported about their younger children’s mathematical developments for the readiness at school.

Besides, it can also be recommended to arrange better and richer educational environments in order to reduce the deficiency resulting from the home environment at schools to which children from disadvantaged families attend.

REFERENCES

1. A. Ivrendi and A. Wakefield. Mothers’ and fathers’ participation in mathematical activities of their young children. 5th international balkan education and science congress proceedings. Edirne, Turkey, 2009, pp. 50–54.

2. A.J. Baroody. The development of preschoolers’ counting skills and principles. In Pathways to Number, J. Bideau, C. Meljac and J. P. Fischer, Eds.,Hillsdale, NJ: Erlbaum, 1992, pp. 99–126. 3. A. Klein and P. Starkey. Fostering preschool children’s mathematical knowledge: Findings from the

Berkeley Math Readiness Project. In Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education, D. H. Clements & J. Sarama, Eds. Lawrence Erlbaum Associates, Mahwah, NJ, 2003, pp 343-360

4. A. Klein, P. Starkey, D.H. Clements, J. Sarama and R. Iyer. Effects of a pre-kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1, 155–178, (2008). http://dx.doi.org/10.1080/19345740802114533.

5. A. Leushina. The development of elementary mathematical concepts in preschool children. In Soviet Studies in Mathematics Education, L. Steffe, Ed. Vol. 4. NCTM, Reston, VA, 1991.

6. A.P. Troutman and K.B. Lichtenberg. Mathematics a Good Beginning. Strategies for Teaching Children. California: Brooks / Cole Pub, 1991.

7. B. Blevins-Knabe and L. Musun-Miller. Number use at home by children and their parents and its relationship to early mathematical performance. Early Development and Parenting, 5(1): 35-45, (1996). http://dx.doi.org/10.1002/(SICI)1099-0917(199603)5:1<35::AID-EDP113>3.0.CO;2-0.

8. C. Seefeldt and N. Barbour. Early Childhood Education (4th edn). Merrill, Upper Saddle River, NJ, 1998.

9. C.T. Cross, T.A. Woods and H.A. Schweingruber (eds.); Committee on Early Childhood Mathematics; National Research Council. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. National Academies Press, Washington, DC, 2009.

10. D. Aslan and Y. Aktas Arnas. 3–6 yas grubu cocuklarda geometrik dusuncenin gelisimi [The development of geometrical thinking in three-to six-year-old children’s group]. 1st International Pre-School Education Conference, Istanbul, Turkey, June 30 – July 3, 2004.

11. D. Aslan and Y. Aktas Arnas. Three- to six-year-old children’s recognition of geometric shapes. International Journal of Early Years Education, 15(1), 83–104, (2007). http://dx.doi.org/10.1080/0966 9760601106646.

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Baku, Azerbaijan| 131

12. D. Aslan, Y. Aktas Arnas and Hayta, B. Parents' math activities with their children according to SES.

3rd International Congress of Early Childhood Education, Adana, Turkey, 12-15 September, 2012. 13. D.H. Clements and M.T. Battista. Geometry and spatial reasoning. In Handbook of Research on

Mathematics Teaching and Learning, D. A. Grouws,ed. Macmillan, New York, 1992, pp. 420–464. 14. D.H. Clements and J. Samara. Early childhood mathematics learning. In Second Handbook on

Mathematics Teaching and Learning, F.K. Lester, Ed. Information Age, Charlotte, NC, 2007, pp.461-555.

15. D.H. Clements, S. Swaminathan, M.A. Hannibal and J. Sarama. Young children’s concepts of shape. Journal for Research in Mathematics Education, 30, 192-212, (1999). http://dx.doi.org/10.2307/ 749610.

16. E.C. Melhuish, M.B. Phan, K. Sylva, P. Sammons, I. Siraj-Blatchford and B. Taggart. Effects of the home learning environment and preschool center experience upon literacy and numeracy development in early primary school. Journal of Social Issues, 64(1), 95-114, (2008). http://dx.doi.org/10.1111/j.1540-4560.2008.00550.x.

17. E. Satlow and N. Newcombe. When is a triangle not a triangle? Young children’s conceptions of geometric shapes, Cognitive Development, 13, 547–559, 1998. http://dx.doi.org/10.1016/S0885-2014(98)90006-5.

18. G.B. Saxe, S.R. Guberman and M. Gearhart. Social processes in early number development. Monographs of the Society for Research in Child Development, 52(2–3, Whole No. 216), (1987). 19. H. Beilin and A. Klein. Strategies and structures in understanding geometry. (Grant No. SED 79

12809). Washington, DC: National Science Foundation, (1982).

20. H.P. Ginsburg and R.L. Russell. Social class and racial influences on early mathematical thinking. Monographs of the Society for Research in Child Development, 46 (6, Serial No. 193), (1981). 21. H.P. Ginsburg, S. Pappas. SES, ethnic, and gender differences in young children’s informal addition

and subtraction: A clinical interview investigation. Journal of Applied Developmental Psychology, 25:171–192, (2004). http://dx.doi.org/10.1016/j.appdev.2004.02.003.

22. J. Sarama and D.H. Clements. Early Childhood Mathematics Education Research: Learning Trajectories for Young Children. New York: Routledge, 2009.

23. K. Denton and J. West. Children's reading and mathematics achievement in kindergarten and first grade. National Center for Education Statistics. Available: http://nces.ed.gov/pubsearch/ pubsinfo.asp? pubid=2002125, 2002. May 2010.

24. M. Altun. Egitim Fakülteleri ve Sinif Ogretmenleri icin Matematik Ogretimi. [Mathematics Education for School of Education and Elementary Teachers]. Erkam Matbaacilik, Bursa, 1997.

25. M.A.Z. Hannibal and D.H. Clements. Young children’s understanding of basic geometric shapes. Arlington, VA, National Science Foundation. Grant no. ESI-8954644., 2000.

26. N.C. Jordan, D. Kaplan, C. Ramineni and M.N. Locuniak. Development of number combination skill in the early school years: When do fingers help? Developmental Science, 11:662–668, (2008). http://dx.doi.org/10.1111/j.1467-7687.2008.00715.x.

27. N.C. Jordan, D. Kaplan, C. Ramineni and M.N. Locuniak. Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850-867, (2009). http://dx.doi.org/10.1037/a0014939.

28. N.C. Jordan, D. Kaplan, L.N. Olah and M.N. Locuniak. Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153– 175, (2006). http://dx.doi.org/10.1111/j.1467-8624.2006.00862.x.

29. N.C. Jordan, D. Kaplan, M.N. Locuniak and C. Ramineni. Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research and Practice, 22(1), 36–46, (2007). http://dx.doi.org/10.1111/j.1540-5826.2007.00229.x.

30. N.C. Jordan, J. Huttenlocher and S.C. Levine. Differential calculation abilities in young children from middle- and low-income families. Developmental Psychology, 28(4), 644-653, (1992). http://dx.doi.org/10.1037/0012-1649.28.4.644.

31. Ö. Polat Unutkan. Okul öncesi dönem cocuklarının matematik becerileri asısından ilkogretime hazır bulunuslugunun incelenmesi. [A study of pre-school children’s school readiness related to skills of mathematics]. Hacettepe University Journal of Ecucation, 32: 243-254, 2007.

32. P.M. van Hiele. Structure and Insight: A Theory of Mathematics Education. Orlando, FL: Academic Press, 1986.

33. P.M. van Hiele. Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310–316, (1999).

34. P. Starkey and A. Klein. Economic and cultural influence on early mathematical development. In New Directions in Child and Family Research: Shaping Head Start in the 90s, F. L. Parker, R. Robinson, S. Sombrano, C. Piotrowski, J. Hagen, S. Randoph and A. Baker, Eds. National Council of Jewish Women; New York, 1992, pp.440.

35. P. Starkey and A. Klein. Fostering parental support for children's mathematical development: An intervention with Head Start families. Early Education and Development., 11: 659–680, (2000). http://dx.doi.org/10.1207/s15566935eed1105_7.

36. P. Starkey and A. Klein. Sociocultural influences on young children’s mathematical knowledge. In, Contemporary Perspectives on Mathematics in Early Childhood Education, O. N. Saracho and B. Spodek, eds. IAP, INC, Baltimore. MD, 2008, pp. 45-66.

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132 | PART B. SOCIAL SCIENCES AND HUMANITIES

37. P. Starkey, A. Klein and A. Wakeley. Enhancing young children's mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19: 99– 120, (2004). http://dx.doi.org/10.1016/j.ecresq.2004.01.002.

38. P. Starkey, A. Klein, I. Chang, Q, Dong, L. Pang and Y. Zhou. Environmental supports for young children’s mathematical development in China and the United States. Paper presented at the meeting of the Society for Research in Child Development, Albuquerque, New Mexico, 1999.

39. R. Case and Y. Okamoto. The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development, 61, 1–265 (Serial No. 246, Nos. 1–2), (1996).

40. R.D. Kellough, A.A. Carin, C. Seefeldt, N. Barbour and R.J. Souviney. Integrating Mathematics and Science for kindergarten and Primary Children. Merrill, Columbus, OH, 1996.

41. R.G. Cooper. Early number development: Discovering number space with addition and subtraction. In The Origins of Cognitive Skills, C. Sophian, Ed.: Erlbaum, Hillsdale, NJ, 1984, pp. 157–192. 42. R. Gersten and D. Chard. Number sense: Rethinking arithmetic instruction for students with

mathematical disabilities. The Journal of Special Education, 33, 18−28, (1999). http://dx.doi.org/ 10.1177/002246699903300102.

43. R.S. Klibanoff, S.C. Levine, J. Huttenlocher, M. Vasilyeva and L. V. Hedges. Preschool children’s mathematical knowledge: The effect of teacher “math talk”. Developmental Psychology, 42(1), 59– 69, (2006). http://dx.doi.org/10.1037/0012-1649.42.1.59.

44. S.D. Holloway, M.F. Rambaud, B. Fuller and C. Eggers-Pierola. What is “appropriate practice” at home and in child care? Low-income mothers’ views on preparing their children for school. Early Childhood Research Quarterly, 10(4), 451-473, (1995). http://dx.doi.org/10.1016/0885-2006(95) 90016-0.

45. S. Griffin, R. Case and R. S. Siegler. Rightstart: Providing the central conceptual prerequisites for first formal learning in arithmetic to students at risk for school failure. In Classroom Lessons: Integrating Cognitive Theory and Classroom Practice, K. McGilly, Ed. MA: MIT Pres, Cambridge, 1995.

46. Y. Aktas Arnas. Okul Oncesi Donemde Matematik Egitimi. [Mathematics Education in Preschool]. Nobel Tip Kitapevi, Adana, 2002, 77-94.

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APPENDIX

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