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The estimation of length, surface area, and volume by blind and sighted children
International Congress Series 1282 (2005) 780 – 784
www.ics-elsevier.com
The estimation of length, surface area, and volume by blind and sighted children Yiannoula Andreoua,*, Konstantinos T. Kotsisb a
School of Education, University of Birmingham, Birmingham B13DB, UK b Department of Education, University of Ioannina, Greece
Abstract. In this article, we explore the ability of blind and sighted children to estimate and measure. We are mainly concerned with the estimation of length, surface area, and volume. The investigation was conducted through questionnaires given to blind and sighted children. The questions were multiple choices and, for each question, there were three or four possible answers. The sighted children were asked to mark the correct answer, while the children with visual impairment were asked to tell us which answer they considered to be correct. Generally, from our results, we can conclude that students with visual impairment conceive the estimation of length, surface area, and volume better in concrete concepts and concepts that are familiar to them, when compared to sighted students. This is because children with visual impairment use measurement in their everyday life in order to explore their surroundings and to increase the control they have over their lives and their environment. D 2005 Elsevier B.V. All rights reserved. Keywords: Estimation of dimensions; Blind students
1. Introduction Lack of sight, and measurably impaired vision, constitute special needs in educational terms. Many children with little or no sight may have a range of additional impairments, which might be physical, emotional, behavioural, and/or sensory in nature [1]. It is difficult to generalise about the impact of visual impairment on a child’s development. The needs of each child will vary, and factors such as personality, age, degree of visual loss, the
* Corresponding author. Apartment 51, Westgate Building, 10 Arthur Place, 6 Birmingham B13DB, UK. Tel.: +44 07830325997; fax: +44 0121 2330834. E-mail address: [email protected] (Y. Andreou). 0531-5131/ D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2005.05.027
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
781
presence or absence of additional disabilities, and cognitive ability will make each child unique [2]. Children who are blind cannot see other people performing a task and so are not motivated to develop a skill or explore different objects. They do not have a bmodelQ on which to base their physical actions. For their learning, children with visual impairment will be more reliant on information received through their other senses and they may have to work much harder than children who are fully sighted. Without a clear sight, most of the everyday tasks, which people who are fully sighted take for granted, become very difficult for children with severe visual impairment [3]. In order to form correct concepts of their body and their mental map of the world and their own position in it, children with visual impairment need to measure using their own body as a unit of measurement. As blind children move forward into a room, their perception of the room does not come from their own eyes but from their feet. Their interest is likely to be centred on the ground under the next step they take and, unlike sighted children, their bviewQ of the room will be partly based on the steps needed to cross it and on the floor’s surfaces [4]. Concepts, such as long distance or routes outside the school and in a wider environment, may be particularly difficult for them to grasp. That is why education must aim at giving blind children knowledge of the world around them and the confidence to cope with it. Since, for some of them, their experience of their environment may have been limited and their understanding of it may have been confused by visual impairment, practical opportunities such as moving and measuring, followed by discussion and interpretation, can clarify and strengthen their knowledge of the world [5]. Given the above, it is therefore highly relevant to investigate if blind and sighted children use estimation and measurement in their everyday life. The research project detailed below undertook this work. 2. The research The empirical research was held in Greece. 78 students, both blind and sighted, participated. Their ages ranged from 9 to 13 years old. The students were divided into two groups. The first group consisted of 23 blind students and students with severe visual impairments, without any additional disabilities. These students attend, in the mornings, mainstream schools and, during the afternoon, the Educational and Rehabilitation Centre in Athens (a school for children with severe visual impairments). The second group consisted of 55 sighted students from a primary school in Ioannina, Greece. The investigation was conducted through questionnaires given to both groups. The questions were multiple choices and, for each question, there were three or four possible answers. The sighted children were asked to mark the correct answer, while the children with visual impairment were asked to tell us which answer they considered to be correct.
3. Results The main aim of this research was to explore the ability of blind and sighted children to estimate and measure. We have analysed the results of the research, and state the major conclusions we have drawn.
782
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
Table 1 The answers of blind and sighted students on the length of their classroom Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Units in steps
Units in meters
Units in steps
Units in meters
Correct Wrong I do not know
90 10 0
39 19 42
65 28 7
26 63 11
In the first two questions (bHow many steps is the length of your classroom from its door to the opposite side?Q and bHow many meters is the length of your classroom from its door to the opposite side?Q), the correct answers depended on the size of each student’s classroom. We measured each classroom, and the answers were coded as dcorrect,T dwrong,T and dI don’t knowT. The results for the first and second questions of blind and sighted students regarding the length of their classroom, using firstly their steps and secondly meters as unit of measurement, are presented at Table 1. According to the above findings, it appears that the children with visual impairment conceive the process of measurement better than sighted children. They need to measure and compare sizes in their everyday life in order to have awareness of space and to understand their own position in it. In contrast to blind students, the process of measurement for sighted children is a concept that they have been taught in math or science. From the answers to the same question using meter as the unit of measurement, we can establish that that both sighed children and those with visual impairment have difficulties in using meter as a unit of measurement. However, they appear to have fewer problems measuring the length using their own steps as a unit of measurement. In questions (3) (bHow many steps is the width of your classroom’s door?Q) and (4) (bHow many meters is the width of your classroom’s door?Q), the majority of students, both blind and sighted, entered the correct answer. The results are presented in Table 2. According to the above findings, we can observe that the children with visual impairment entered a large percentage of correct answers. It seems that despite the fact that the sense of touch cannot give information to the brain about relationships between objects as easily as the sense of vision, and because of the fact that children with visual impairment will need to feel and identify the critical features of an object, in order to recognize it, they have to measure and classify objects, and keep in their memory features such as sizes, shape texture, etc. [2]. We conclude that this is the reason why they give more correct answers than the sighted children, especially when they use a unit of measurement well known to them (e.g., their own steps). In question (5), we ask the students to compare their bed at home and their desk at school, and tell us which one they think has a bigger surface area. The results are presented in Table 3. In question (6), we ask them to tell us if their seat at school or the front seat of their family car has a bigger surface area. The results are presented in Table 4.
Table 2 The answers of blind and sighted students on the width of their classroom’s door Answers
Correct Wrong I do not know
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Units in steps
Units in meters
Units in steps
Units in meters
81 19 0
73 4 23
63 34 3
61 28 11
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
783
Table 3 The answers of blind and sighted students to question (5), bWhich object has a bigger surface area: your bed at home or your desk at school?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
The bed The desk I do not know
86 14 0
94 6 0
According to the above, the majority of students, both blind and sighted, noted the correct answer. In question (5) (Table 3), a larger percentage (94%) of sighted students gave the correct answer, while in question (6) (Table 4), a larger percentage (95%) of blind children noted the correct answer. Children who are fully sighted learn to perceive objects in their entirely, and observe them in relation to their environment. They do not have to measure or keep in their memory critical features of an object in order to recognize it. Children with visual impairment cannot view objects in their entirety and move from parts to a whole. That is why it is more difficult for them to perceive the shape or volume of bigger objects (e.g., the bed). Measuring objects with a touch horizon (e.g., school/car seat) in the surrounding environment is easier for them to perceive and can help them to grasp the idea of a bwholeQ object [4]. In question (7), we ask the students, bHow many drinking glasses can 1 l of milk fill?Q The results are presented in Table 5. Volume is the measure of the amount of space that an object occupies. This is an important concept for students to understand because it is something that they use in their daily lives even though they never refer to it (e.g., they know in which cup to put their favourite drink, which ice ream is bigger, or which size of a storage container to use for some leftover food). In question (7) (estimation of volume), it is noticeable that the children with visual impairment entered a larger percentage of correct answers that the sighed children. The ability to estimate sizes, length, width, height, weight, or volume is vital for children who are visually impaired and is a process that they need to use in their everyday life in order to have an awareness of space. We conclude that this is the reason why the children with visual impairment entered a larger percentage of correct answers than sighted students.
4. Discussion As has already been showed, in this research, we tried to explore the ability of blind and sighed children to estimate and measure. We examined the nature of these concepts they acquired; we believed that further research is needed to learn more about the process of acquisition. According to the findings of this research, the following conclusions have been drawn. Table 4 The answers of blind and sighted students to question (6), bWhich object has a bigger surface area: the front seat of your family car or your seat at school?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
The car seat The seat at school I do not know
95 5 0
86 14 0
784
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
Table 5 The answers of students for the question, bHow many drinking glasses can 1 l of milk fill?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Correct Wrong I do not know
66 29 5
51 39 10
Children with visual impairment cannot view objects in their entirety. bStep by step, they will form in their minds a mental scheme by which the objects and phenomena in the external world enter into an ordered and comprehensible system of relationshipsQ [6]. It is important that a blind child has access to formal and informal learning experiences to develop basic skills such as classification, discrimination, measurement of sizes, comparisons between large and small, tall and short etc.—all these will help the child to move from concrete to abstract ideas. The ability to estimate length, width, height, or weight is vital for children who are visually impaired. The measurement of objects with a touch horizon (hand/steps), such as the desk surface, window length, or floor length, could help the children to grasp the idea of individual parts fitting together to make a bwholeQ object or surface. Sighted children, on the other hand, learn to perceive objects in their entirety. For them, the process of measurement is a skill that is taught at school—not something that they use in their everyday life. That is why it is more difficult for them to estimate or measure. Generally, we can support that students with visual impairment conceive the estimation of length, surface area, and volume better in concrete concepts and concepts that are familiar to them, when compared to sighted students. This is because children with visual impairment use some kind of measurement in their everyday life in order to explore the world. They need to remember details of the surrounding environment in order to have a good orientation and be able to move around without coming to any harm, and to increase the control they have over their lives and their environment. References [1] M. McLinden, S. McCall, Learning Through Touch, David Fulton Publishers, London, 2002. [2] D.H. Warren, Blindness and Children. An Individual Differences Approach, Cambridge University Press, Cambridge, 1994. [3] C. Arter, et al., Children with Visual Impairment in Mainstream Settings, David Fulton Publishers, London, 1999. [4] A.B. Best, Teaching Children with Visual Impairments, Open University Press, 1992. [5] V. Lewis, et al., New methods for studying blind children’s understanding of familiar space, British Journal of Visual Impairment 20 (1) (2002) 17 – 23. [6] A. Wexter, Experimental Science for the Blind. An Instruction Manual, Pergamon Press, Oxford, 1981.
www.ics-elsevier.com
The estimation of length, surface area, and volume by blind and sighted children Yiannoula Andreoua,*, Konstantinos T. Kotsisb a
School of Education, University of Birmingham, Birmingham B13DB, UK b Department of Education, University of Ioannina, Greece
Abstract. In this article, we explore the ability of blind and sighted children to estimate and measure. We are mainly concerned with the estimation of length, surface area, and volume. The investigation was conducted through questionnaires given to blind and sighted children. The questions were multiple choices and, for each question, there were three or four possible answers. The sighted children were asked to mark the correct answer, while the children with visual impairment were asked to tell us which answer they considered to be correct. Generally, from our results, we can conclude that students with visual impairment conceive the estimation of length, surface area, and volume better in concrete concepts and concepts that are familiar to them, when compared to sighted students. This is because children with visual impairment use measurement in their everyday life in order to explore their surroundings and to increase the control they have over their lives and their environment. D 2005 Elsevier B.V. All rights reserved. Keywords: Estimation of dimensions; Blind students
1. Introduction Lack of sight, and measurably impaired vision, constitute special needs in educational terms. Many children with little or no sight may have a range of additional impairments, which might be physical, emotional, behavioural, and/or sensory in nature [1]. It is difficult to generalise about the impact of visual impairment on a child’s development. The needs of each child will vary, and factors such as personality, age, degree of visual loss, the
* Corresponding author. Apartment 51, Westgate Building, 10 Arthur Place, 6 Birmingham B13DB, UK. Tel.: +44 07830325997; fax: +44 0121 2330834. E-mail address: [email protected] (Y. Andreou). 0531-5131/ D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2005.05.027
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
781
presence or absence of additional disabilities, and cognitive ability will make each child unique [2]. Children who are blind cannot see other people performing a task and so are not motivated to develop a skill or explore different objects. They do not have a bmodelQ on which to base their physical actions. For their learning, children with visual impairment will be more reliant on information received through their other senses and they may have to work much harder than children who are fully sighted. Without a clear sight, most of the everyday tasks, which people who are fully sighted take for granted, become very difficult for children with severe visual impairment [3]. In order to form correct concepts of their body and their mental map of the world and their own position in it, children with visual impairment need to measure using their own body as a unit of measurement. As blind children move forward into a room, their perception of the room does not come from their own eyes but from their feet. Their interest is likely to be centred on the ground under the next step they take and, unlike sighted children, their bviewQ of the room will be partly based on the steps needed to cross it and on the floor’s surfaces [4]. Concepts, such as long distance or routes outside the school and in a wider environment, may be particularly difficult for them to grasp. That is why education must aim at giving blind children knowledge of the world around them and the confidence to cope with it. Since, for some of them, their experience of their environment may have been limited and their understanding of it may have been confused by visual impairment, practical opportunities such as moving and measuring, followed by discussion and interpretation, can clarify and strengthen their knowledge of the world [5]. Given the above, it is therefore highly relevant to investigate if blind and sighted children use estimation and measurement in their everyday life. The research project detailed below undertook this work. 2. The research The empirical research was held in Greece. 78 students, both blind and sighted, participated. Their ages ranged from 9 to 13 years old. The students were divided into two groups. The first group consisted of 23 blind students and students with severe visual impairments, without any additional disabilities. These students attend, in the mornings, mainstream schools and, during the afternoon, the Educational and Rehabilitation Centre in Athens (a school for children with severe visual impairments). The second group consisted of 55 sighted students from a primary school in Ioannina, Greece. The investigation was conducted through questionnaires given to both groups. The questions were multiple choices and, for each question, there were three or four possible answers. The sighted children were asked to mark the correct answer, while the children with visual impairment were asked to tell us which answer they considered to be correct.
3. Results The main aim of this research was to explore the ability of blind and sighted children to estimate and measure. We have analysed the results of the research, and state the major conclusions we have drawn.
782
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
Table 1 The answers of blind and sighted students on the length of their classroom Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Units in steps
Units in meters
Units in steps
Units in meters
Correct Wrong I do not know
90 10 0
39 19 42
65 28 7
26 63 11
In the first two questions (bHow many steps is the length of your classroom from its door to the opposite side?Q and bHow many meters is the length of your classroom from its door to the opposite side?Q), the correct answers depended on the size of each student’s classroom. We measured each classroom, and the answers were coded as dcorrect,T dwrong,T and dI don’t knowT. The results for the first and second questions of blind and sighted students regarding the length of their classroom, using firstly their steps and secondly meters as unit of measurement, are presented at Table 1. According to the above findings, it appears that the children with visual impairment conceive the process of measurement better than sighted children. They need to measure and compare sizes in their everyday life in order to have awareness of space and to understand their own position in it. In contrast to blind students, the process of measurement for sighted children is a concept that they have been taught in math or science. From the answers to the same question using meter as the unit of measurement, we can establish that that both sighed children and those with visual impairment have difficulties in using meter as a unit of measurement. However, they appear to have fewer problems measuring the length using their own steps as a unit of measurement. In questions (3) (bHow many steps is the width of your classroom’s door?Q) and (4) (bHow many meters is the width of your classroom’s door?Q), the majority of students, both blind and sighted, entered the correct answer. The results are presented in Table 2. According to the above findings, we can observe that the children with visual impairment entered a large percentage of correct answers. It seems that despite the fact that the sense of touch cannot give information to the brain about relationships between objects as easily as the sense of vision, and because of the fact that children with visual impairment will need to feel and identify the critical features of an object, in order to recognize it, they have to measure and classify objects, and keep in their memory features such as sizes, shape texture, etc. [2]. We conclude that this is the reason why they give more correct answers than the sighted children, especially when they use a unit of measurement well known to them (e.g., their own steps). In question (5), we ask the students to compare their bed at home and their desk at school, and tell us which one they think has a bigger surface area. The results are presented in Table 3. In question (6), we ask them to tell us if their seat at school or the front seat of their family car has a bigger surface area. The results are presented in Table 4.
Table 2 The answers of blind and sighted students on the width of their classroom’s door Answers
Correct Wrong I do not know
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Units in steps
Units in meters
Units in steps
Units in meters
81 19 0
73 4 23
63 34 3
61 28 11
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
783
Table 3 The answers of blind and sighted students to question (5), bWhich object has a bigger surface area: your bed at home or your desk at school?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
The bed The desk I do not know
86 14 0
94 6 0
According to the above, the majority of students, both blind and sighted, noted the correct answer. In question (5) (Table 3), a larger percentage (94%) of sighted students gave the correct answer, while in question (6) (Table 4), a larger percentage (95%) of blind children noted the correct answer. Children who are fully sighted learn to perceive objects in their entirely, and observe them in relation to their environment. They do not have to measure or keep in their memory critical features of an object in order to recognize it. Children with visual impairment cannot view objects in their entirety and move from parts to a whole. That is why it is more difficult for them to perceive the shape or volume of bigger objects (e.g., the bed). Measuring objects with a touch horizon (e.g., school/car seat) in the surrounding environment is easier for them to perceive and can help them to grasp the idea of a bwholeQ object [4]. In question (7), we ask the students, bHow many drinking glasses can 1 l of milk fill?Q The results are presented in Table 5. Volume is the measure of the amount of space that an object occupies. This is an important concept for students to understand because it is something that they use in their daily lives even though they never refer to it (e.g., they know in which cup to put their favourite drink, which ice ream is bigger, or which size of a storage container to use for some leftover food). In question (7) (estimation of volume), it is noticeable that the children with visual impairment entered a larger percentage of correct answers that the sighed children. The ability to estimate sizes, length, width, height, weight, or volume is vital for children who are visually impaired and is a process that they need to use in their everyday life in order to have an awareness of space. We conclude that this is the reason why the children with visual impairment entered a larger percentage of correct answers than sighted students.
4. Discussion As has already been showed, in this research, we tried to explore the ability of blind and sighed children to estimate and measure. We examined the nature of these concepts they acquired; we believed that further research is needed to learn more about the process of acquisition. According to the findings of this research, the following conclusions have been drawn. Table 4 The answers of blind and sighted students to question (6), bWhich object has a bigger surface area: the front seat of your family car or your seat at school?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
The car seat The seat at school I do not know
95 5 0
86 14 0
784
Y. Andreou, K.T. Kotsis / International Congress Series 1282 (2005) 780–784
Table 5 The answers of students for the question, bHow many drinking glasses can 1 l of milk fill?Q Answers
Blind students (n = 23) (%)
Sighted students (n = 55) (%)
Correct Wrong I do not know
66 29 5
51 39 10
Children with visual impairment cannot view objects in their entirety. bStep by step, they will form in their minds a mental scheme by which the objects and phenomena in the external world enter into an ordered and comprehensible system of relationshipsQ [6]. It is important that a blind child has access to formal and informal learning experiences to develop basic skills such as classification, discrimination, measurement of sizes, comparisons between large and small, tall and short etc.—all these will help the child to move from concrete to abstract ideas. The ability to estimate length, width, height, or weight is vital for children who are visually impaired. The measurement of objects with a touch horizon (hand/steps), such as the desk surface, window length, or floor length, could help the children to grasp the idea of individual parts fitting together to make a bwholeQ object or surface. Sighted children, on the other hand, learn to perceive objects in their entirety. For them, the process of measurement is a skill that is taught at school—not something that they use in their everyday life. That is why it is more difficult for them to estimate or measure. Generally, we can support that students with visual impairment conceive the estimation of length, surface area, and volume better in concrete concepts and concepts that are familiar to them, when compared to sighted students. This is because children with visual impairment use some kind of measurement in their everyday life in order to explore the world. They need to remember details of the surrounding environment in order to have a good orientation and be able to move around without coming to any harm, and to increase the control they have over their lives and their environment. References [1] M. McLinden, S. McCall, Learning Through Touch, David Fulton Publishers, London, 2002. [2] D.H. Warren, Blindness and Children. An Individual Differences Approach, Cambridge University Press, Cambridge, 1994. [3] C. Arter, et al., Children with Visual Impairment in Mainstream Settings, David Fulton Publishers, London, 1999. [4] A.B. Best, Teaching Children with Visual Impairments, Open University Press, 1992. [5] V. Lewis, et al., New methods for studying blind children’s understanding of familiar space, British Journal of Visual Impairment 20 (1) (2002) 17 – 23. [6] A. Wexter, Experimental Science for the Blind. An Instruction Manual, Pergamon Press, Oxford, 1981.