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The purpose of this case study was to investigate and critically evaluate the typical learning experience of a child in primary school. To ensure anonymity, all names have been altered and allocated pseudonyms. The case study will review research into children's learning in school, with specific emphasis on counting in mathematics and reading in literacy, and discuss the finding from analysis in relation to the literature review.
The school in which the study was undertaken, Edburn Hill Primary, accommodates 173 pupils, 26 of which are in year 2. The 2011 Ofsted report awarded the school satisfactory and described it as smaller than average, with predominantly white British pupils whose first spoken language is primarily English. The school has higher than average proportions of pupils who receive free school meals and recently gained Healthy Schools Status (Ofsted, 2011). During the 5 weeks of the study, no pupils with special educational needs were situated in the focus class. Two focus pupils, Jack and Emily, were observed for the duration of the study before Emily was selected as the focus child for analysis. Emily was chosen for analysis on account of her interesting strategies for problem solving and willingness to discuss her methods, which provided more in-depth, rich data for analysis. Emily follows the heritage and first spoken language trend of the school, is not eligible for free school meals and was previously assessed by their teacher, Mrs Holmes, to be of average ability in all subject areas. Mrs Holmes, the class teacher, is an experienced teacher of 10 years who had access to 3 to 6 additional adults in the classroom during the 5 weeks of observation. The classroom itself contains an individual library, a rich variety of resources, and various topic and resource wall displays available to pupils.
Literature review (1,638)
The following literature review of theories and research into children's learning in primary school will focus on three main themes: Key educational psychologists, Mathematics (specifically counting) and Literacy (specifically reading).
Piaget (1896-1980) explains the development of children's cognitive processes and capabilities in four stages (Passer, Smith, Holt, Bremner, Sutherland & Vliek, 2009). The stages, assigned approximate age groupings, demonstrate that the cognitive processes of a child are not like that of an adult. They see the child move from interacting with their environment through senses and motor skills, to thinking logically and abstractly about ideas (Piaget, 1970). In the classroom, Piaget's theories have been influential in recognising children's stages of cognitive development, and the notion that until a child has reacted a certain level of mental maturity, they cannot learn particular concepts (Passer et al, 2009). Piaget's work has been criticised, however, by Vygotsky (1962) and Bruner (1965), the sociocultural psychologists. Bruner (1965) criticises Piaget's developmental stages, stating that pupils are denied educational experiences due to their assigned development stage. Vygotsky (1962) describes Piaget's stages as being unrealistic and oversimplified, challenging the constructivist view, stating that social interactions with others are key and cognitive development is continual rather than segmental. Vygotsky (1962) refers to the 'Zone of Proximal Development' (ZPD) which describes the difference between the child's current independent ability and that which they can perform in collaboration with a 'More Knowledgeable Other' (MKO). Vygotsky (1962) suggests that the role of the teacher in the child's cognitive development, is to offer modelling and scaffolding in tackling a new problem, and to teach within the child's ZPD.
Episodic Empiricism, described as containing no recall of prior knowledge, means the learner takes a randomised guess in hope of achieving the correct answer (Bruner, 1965). Cumulative Construction, on the other hand, is a much more considered approach; Bruner (1965) describes the learner as drawing upon previous knowledge to make a logical guess, resulting in a build of knowledge in a systematic way. Although the psychologists discussed disagree on many matters, they all agree on the notion that learning should be interactive and in the hands of the pupil. Dewey (1964) stresses the importance reflecting the pupil's interests in education. He states that the most enthusiastic and motivated learning occurs when the subject is focused on the pupil's curiosity, and the teacher develops problem-solving lessons around this (Dewey, 1964). Bruner (1965) also describes how the possibility of recall is much more likely if the child has organised their knowledge around their own interests and cognitive structures, known as Conservation of Memory.
Along with focusing learning on the pupil's interest, Whitebread and Basilio (2012) describe the importance of promoting meta-cognitive development: the ability to self-monitor. Whitebread and Basilio (2012) define the ability to self-regulate learning as an important factor, in the development of independent learning required to succeed in the educational context. Gardner (1983) defines success in education, in particular different subject areas, in terms of varying intelligence. He suggests that humans pose seven intelligences and the first two of these, linguistic and logical-mathematical, are traditionally related to the core subjects Mathematics and English. Although Brualdi (1998) argues intelligences are anatomically separate, Gardner (1983) maintains that the intelligences coincide and complement each other as the individual develops.
Anghileri (2006) suggests that those who find maths 'hard' seek a procedure to solve the problem rather than recognise and utilise number relations and patterns. Those with number sense, pose the ability to make mathematical judgments in a way that uses numbers and operations in a flexible manner, demonstrating understanding and the use of strategies. (Anghileri, 2006). This view is in line with Gardner (1983), who suggests linguistic and logical-mathematical intelligence can support one another. Anghileri (2006) suggests that teachers must focus on maths as a thinking process rather than rote learnt facts, and aid pupils in explaining and justifying their answers in order to develop number sense. Anghileri (2006) describes counting as important preparation for calculating, in which number sense is undeniably useful. Maclellan (2008) suggests that children progress from using concrete experiences to count, to abstract/ mental methods and finally to symbolic relations. Munn (2008) furthers this sequence by suggesting the motives for counting change from sequence counting to please adults (before school training), to understanding the mathematical concepts of numbers and counting to find out the total number (during school training).
Gallistel and Gelaman (1992) provide 3 principles that are required to be considered a successful counter: One-to-one correspondence, stable order and cardinality. In order to reach cardinality, the knowledge that the final number word represents the total number of matters, the child must first: recognise the correspondence between count words and matter; memorise those which have already to be counted and those left; identify that number words are assigned in the same order (Anghileri, 2006). Piaget (1965) stated that without cardinality, counting is of little use. Furthermore to Gallistel and Gelaman's (1992) 3 principles, it is also suggested to be successful, children must encompass the abstraction, order irrelevance and conservation principles (Anghileri, 2006). Hughes (1986) demonstrated how the use of real life situations aided children with these principles and abstract questions, providing support for Dewey's (1964) notion that education should reflect real life, society based situations.
Munn (2008) identifies three indications of deficits in children's early number logic: Inability to count objects in a randomised arrangement, the absence of number conservation and the deficiency of spontaneous counting without prompting. Threlfall (2008) discusses errors in terms of the strategies used: oral and enumeration. Bruce (2000) found that oral counting errors included: number omissions, repeating loops of numbers, repeating strings of numbers, and idiosyncratic continuation of a number string. Fuson (1988) described the development of enumeration from touching counted objects to eye fixation, as 'progressive internalisation'. Bruce (2000) suggested that children are keen to internalise enumeration in order to imitate the more advanced counters they observe. This however results in more errors such as: counting objects twice, omitting items and repeating patterns (Munn, 2008). If simply observed, these errors may appear insignificant, but with closer inspection and discussion with the child, they reveal a process of self-auditing, self-correction and analogical reasoning, providing support for Whitebread and Basilio (2012) theories on self-regulated learning. However Fuson (1988) argues that if a child has the skills to enumerate across a set of objects, it does not necessarily mean they poses cardinality. Sophian (1995) states that the 'how many' problem is a much less complex question in comparison to the 'give me x objects', which requires a deeper knowledge of the relationship between counting and cardinality.
The English language, due to its complexity and lack of relationship between spoken word and written representation, is a hard venture for children. Reading in particular requires a complex combination of evaluation, comprehension and interpretation, drawing upon the reader's previous knowledge, practice and imagination (Dombrey, 2009).
The Simple View of Reading (SVR), (Gough & Tunmer (1986), dominates the current educational view on literacy in school. The Ofsted paper 'Getting them ready early' (2011) explains that the model demonstrates two processes to reading: The recognition and understanding of the written words (decoding), and the development of an understanding of the language (comprehension). Gough and Tunmer (1986) define 'decoding' as the ability to recognise single words and 'comprehension' as linguistic comprehension. Rose (2006) clarifies that, to emphasise the importance of language recognition and comprehension at all levels of reading development, the SVR diagram is presented in a cross. The formula, RC= LC x D, represents the notion that Reading Comprehensions (RC) is the product of Listening Comprehension (LC) and Decoding (D) (Dombrey, 2009). However, the actual process of reading is a complex one and the SVR is only a simplified version for better understanding. That is, without one dimension of the formula, reading successfully is not possible. Neither dimension is sufficient on its own (Dombrey, 2009; Rose, 2006). Rose (2006) explains the top right hand corner of the SVR diagram as representing children who are good readers, meaning they have good word recognition and comprehension. The other three quadrants predict variations of poor reading. The bottom right represents good word recognition but poor comprehension, the bottom left represents poor word recognition and comprehension and the top left represents poor word recognition but good comprehension.
Gough and Tunmer (1986) explain that recognition is not sufficient enough to assume understanding of the text; similarly children who cannot decode are fully prevented from appreciation. As the formula indicates, comprehension and decoding are both required for reading at all levels. Oakhill, Cain and Bryant (2003) provide some support for the notion different skills and knowledge underlie word recognition and reading comprehensions, through their study which found dissociation between predictors of comprehension and word recognition (Rose, 2006). Rumelhart (1976), however, argues that reading in fact involves both top down and bottom up processes, whereby semantic knowledge and the reader's expectations about meaning are also involved.
Similarly, Goodman, Watson and Burke (2005) have shown through miscue analysis that pupils make use of semantic and syntactic cues from surrounding texts to aid them in reading. Brown and Deavers (1999) have indicated that children learning to read English adopt strategies to complement the synthetic phonics, paying attention to syllables and whole word patterns. Furthermore Kirby and Savage (2008) suggest that illustrations aid comprehension in demanding texts. Although the simple view of reading in useful for explaining what is clearly a complex phenomenon, other situational and contextual cues must not be ignored. The Rose (2006) summarises in favour of the SVR, that context it utilised by poor and good readers for different purposes. The poor readers relied on context for word recognition and the good readers used context to construct an accurate representation of meaning, thus providing case for the separate dimensions of reading (Rose, 2006).
A case study was deemed the most appropriate methodology for this assignment as the aim of the study was not to generalise, but provide a more in-depth insight into the complex learning processes of the focus child in their everyday learning environment. The use of a case study allowed me to work closely with the focus children in order to gain a more realistic, genuine and holistic picture of their experiences within their learning environment. Furthermore, as the study was constrained by time, context and resources, the various methods and procedures of collecting data available through a case study was proven to be the most suitable (Thomas 2009; Sharp 2009).
Six Tasks, combining observation and assessment, were prescribed by the University of Leicester (2012) in order to collect the appropriate data. Four of these were used for analysis and were as follows:
A book, chosen by Emily, was shared. Notes were taken regarding the genre and difficulty of book chosen, phonic knowledge and comprehension reading behaviours and strategies to reading unfamiliar words.
Emily's counting was assessed. Notes were taken regarding strategies for counting, mistakes made and numerical range: All were discussed with the Emily after the assessment.
Emily's experience in English was observed over 3 consecutive school days. Notes were taken regarding participation during lessons, interaction with others, independent work produced, the use of phonics throughout the day, reading comprehension and strategies.
Emily's experience in Mathematics was observed over 3 consecutive school days. Notes were taken regarding participation during lessons, interaction with others, independent work produced, strategies and response to mathematical problems throughout the day.
Furthermore to the prescribed tasks, I heard Emily read her allocated reading book frequently, conducted a miscue reading analysis, copied the pupils work completed in class for analysis (including unaided assessments) and completed a tracking grid based on taught lessons. Whenever possible, I engaged in discussions with Emily about her strategies, thinking and opinions on the work I procured for analysis.
The aim of the present case study was to investigate and critically evaluate the typical learning experience of a child in primary school. In line with the literature review, this segment will be organised into two sections: mathematics (specially counting) and literacy (specifically reading), with the analysis of the Emily's performance in these areas being discussed in relation to existing research.
During maths lessons and with problems posed throughout the day, Emily was a confident and eager student. It was clear from her willingness to please, that her motives are what Bruner (1965) describes as extrinsic. The external praise, attention and positive reinforcement Emily received for good behaviour, contribution and correct answers motivated and satisfied her. This was most clearly demonstrated in Emily's fear of failure, especially in maths. When asked to estimate length, weight or volume, regardless of what was considered by the adult to be a 'sensible guess', Emily would consistently, often in secret, alter her estimate to match the exact measurement. When asked why she altered her estimate, Emily informed that the estimate was incorrect. Even after the concept of an estimate and the task was reiterated, Emily still insisted on 'correcting' her estimate. Whitebread and Basilio (2012) would describe this self-correction and control over of her own work as positive meta-cognitive development. However in this instance, Emily's self-correction and egotistic unwillingness to be wrong was hindering her progress and understanding in that particular mathematical area. Based on Emily's egocentric behaviours and dominance of her own perception over her thinking, Piaget's (1970) theory would suggest she is in the pre-operational stage of development, considered correct for her age.
Emily's confidence, even when misplaced, was also observed in her own perceived counting abilities. When asked what the highest number she could count to was, Emily replied 99 million. When challenged to do so, she quickly changed her answer stating "probably 1000 actually but I have never tried". Dewey's (1964) theory that education should reflect society would suggest that as Emily in real life, has never had the need to count up to 1000 thus the notion that she should is unnecessary. When presented with the choice of oral counting being abstract or concrete with objects, in this case pumpkin seed, Emily chose to enumerate with concrete objects. Confidently, Emily counted the pumpkin seeds individually correctly from 1 to 100, only pausing for thought at the digits 40, 60 and 90. In opposition to Fuson's (1988) research, Emily, at the age of 6 in this circumstance, did not use progressive internalisation, but actively moved the pumpkin seeds to one side as she counted them. This may have been due to the sheer number of small objects she was subjected to counting; perhaps in an alternative concrete counting activity, using larger and fewer objects, Emily may have utilised eye fixation as a form of enumeration.
Emily's counting of the pumpkin seeds validated her recognition of 2 of the 3 principles of counting suggested by Gallistel and Gelman's (1992). By assigning one number word to each item and identifying numbers in the correct sequence, she demonstrated the one-to-one correspondence and stable order principles. When asked how many seeds there were, Emily confidently demonstrated cardinality by repeating the last number. As Sophian (1995) suggests however, repetition of the last number word does not necessarily suggest a relationship of understanding between counting and cardinality. To verify cardinality, I asked Emily to hand me 'x' number of seeds, which she did by counting the seeds to one side, again using enumeration, and handing me the exact number requested.
When presented with counting illustrated objects in a random formation, which could not be physically moved during counting, Emily adopted a different approach: circling the objects in twos. When asked why she counted illustrated objects in twos but physical objects individually, she stated that, she was usually expected to count more physical objects, thus counting singularly was easier so that she did not lose her place. When requested to count illustrations, Emily identified that there were usually fewer than 12 objects and as she could count in twos up to 12, she deemed this the more appropriate strategy. Although when counting illustrated objects in a random formation using this strategy, Emily would occasionally lose her starting point resulting in an incorrect final answer, the three principles of counting were still demonstrated as the error which Emily encountered was a simple spatial error. This justification of strategy use demonstrates development in executive functioning which Whitebread and Basilio (2012) would argue is essential in independent learning. Gardner's (1983) theory advocates that this logical reasoning displays development in Emily's logical-mathematical intelligence and shows the beginning of number sense development.
Although Emily was confident in her counting in signal digits to 100, and then accurately continuing the sequence to 120 without the need for modelling, she preceded from 120 to 200 with errors: repeating number string, omitting decades and adding idiosyncratic continuations of number strings. Whitebread and Basilio (2012) would suggest these 'clever' errors indicate analogical reasoning. When Emily was asked about her errors, her answer demonstrated what Bruner (1965) calls cumulative construction. Emily stated that she was unsure if the number strings were the same as the lower numbers, as 100 is clearly a much larger number: illustrating her use of previous knowledge to approach the problem. Vygotsky's (1962) theory would propose that the numbers above 120 are in Emily's ZPD, and she requires scaffolding from a MKO to tackle the problem.
When posed with a simple calculation using the concrete apparatus, Emily counted the seeds in twos using enumeration and stated her answer confidently. When the seeds were moved into a different formation and the same question was asked, Emily, without hesitation or counting, stated her answer. When asked how she knew, she specified that the number of seeds had not changed, I had 'just moved them about'. Emily's answer indicated her acceptance of order irrelevance and conservation, which Piaget (1965) suggests is an attribute of the concrete operational stage. Emily's display of attributes from two of Piaget's stages, advocate that perhaps as Bruner (1965) and Vygotsky (1962) suggest, development is continual rather than a stage process as Piaget (1965) advises. Although Emily appeared confident with sequential forms of counting, her ability to manipulate the number sequence and recognise number relations involved in order to answer questions is not yet developed. When asked what number precedes 90, Emily stated she would have to count from the beginning, suggesting that without scaffolding, she does not yet poses the number sense needed to logically calculate the answer. When encountering calculations, Emily demonstrated further her need for concrete apparatus. During a lesson based on counting money, in which the class were being encouraged to calculate the total amount abstractly, Emily produced a number of errors in line with her inability to yet manipulate number sequences abstractly. In support of Hughes (1986) Emily's understanding, self-correction and number of correct answers drastically improved when the problem was given a meaningful context, coin apparatus and a number line was provided to work with. Reiterating further Emily's need of concrete aids in her current development stage, during group work with peers who were working abstractly, Emily chose to count on her fingers, however under the table out of sight. Bruce (2006) explains such behaviour as a desire to appear to be enumerating internally, like those more advanced peers or adults in proximity.
During multiplication and subtraction calculations, Emily demonstrated errors which Anghileri's (2006) theory attributes to seeking a procedure to solve the problem rather than recognising the number relations involved. Frequently during calculations, Emily would revert to addition rather than employing the required action demanded by the specific symbol. The reasons for this are unclear, and could be attributed to Emily's lack of understanding of the abstract symbols or her preference for 'safer' more familiar strategy. Threlfall (2008) suggests that if a child is insecure of their ability or ridiculed for making mistakes, they are more likely to adopt a safer strategy that has provided them with approval in the past. Moyles (2007) and Threlfall (2008) both suggest that play and exploration of number in a risk free environment, is essential for good early number development and development of investigation. Over the course of the five weeks, I observed very little time allocated to play and exploration in any subject due to time and curriculum constraints, which may explain some of Emily's behaviours regarding her fear of failure and lack of development in number sense. Emily's absence in understanding of operations and flexibility in mathematical judgment was most clearly demonstrated in her work on the inverse rule. Many of Emily's number sentences based on the inverse were clearly rote learnt or, in some cases, based on no previous knowledge resulting in a random formation of the digits involved. Bruner (1965) describes this form of response as episodic empiricism. Vygotsky's (1962) theory would suggest that the inverse is out of Emily's ZPD, for which she needs more scaffolding and modelling from a MKO.
As with numeracy, Emily is confident in her own ability and appears to read for extrinsic motives as opposed to pleasure (Bruner, 1965). During guided reading sessions, she frequently reads ahead, shouting out to answer questions which were not directed at her and offered help to peers. Although the helping of others in the form of answering their questions may seem like a selfless act, it was quite obviously egotistical behaviour, as Piaget (1965) would suggest, as without fail Emily would then direct her attention to the adult for approval or praise.
When permitted to choose a book to read from the class library (containing a range of literature suitable for the reading levels of the pupils in year 2), Emily made her choice based on her own interest, experiences and the illustrations, rather than the level of difficulty of text. While favouring books with more illustrations and context in which she could relate, Emily would often convey stories of own experiences in relation to the storyline of the literature. Dewey (1964) has suggested that the students own interests should be embraced in order for the child to recognise the usefulness of the task, and Bruner (1965) confirms that recall and conservation of memory is much more likely if the student has organised the new knowledge around their own interests.
Emily's comprehension of the chosen text was demonstrated through her commentary, relating the context to her own experiences and asking questions about the story. Dewey (1964) and Bruner (1965) may argue that this ability to comprehend was due, somewhat, to the text being chosen by Emily herself and the content lying within her own interests. Although Emily stated that her choice was based upon subject and illustration, the exertion of the text may still have had an influence on her choice. As Emily is a pupils who is eager to impress and receive praise, it would be logical to assume that the chosen book, containing language well with in Emily's attainment or ZPD as Vygotsky (1962) would suggest, was also the influence of extrinsic motives (Bruner, 1965). It would appear that Emily's choice of book was an egocentric one, in line with her cognitive developmental stage (Piaget, 1965).
In comparison to the SVR (Gough & Tunmer, 1986), I would place Emily in the top right hand corner of the diagram, suggesting that she was capable of good word recognition through decoding and language comprehension when provided texts within or just above her current attainment level. The use of miscue analyses (employing books from the Oxford Reading Scheme) performed at Emily's present and preceding reading levels produced interesting results. At Emily's current reading level, few errors were produced. However, the errors which were present were all substitutions. Emily utilised semantic and syntactic cues to substitute words successfully, suggesting that she was able to use meaning from the passage and language of the sentence when selecting an alternative word (Brown, Goodman & Marek, 1996). Only when the substitution did not make semantic or syntactic sense, such as when phonographic cues were used, did Emily self-correct without prompting. Such was Emily's ability to use syntactic cues; she applied contraction to written words, reading the word aloud as if internal letters had been omitted. Whitebread and Basilio's (2012) theory praises this detection of inaccurate word use and self-correction as advances in meta-cognitive development. Emily's use of semantic cues for substitution may provide support for Rumelhart (1976) theory of top down and bottom up processes.
In comparison to the miscue analysis performed within Emily's current reading attainment, the results produced from the material considered her to be two reading levels above. This suggests that with harder reading material, Emily's attention to syntactic cues decreased as she concentrated on decoding, using phonics and the more difficult words. This was demonstrated through repetition of words and sentences, which was not observed with the lower level text. Although all the errors produced were substitutions, as with the first reading analysis, the number of comparable mistakes drastically increased due to phonographic cues. However, substitutions that did not make semantic or syntactic sense were not self-corrected as reliably in the second analysis. As no omissions were observed in either analysis, it can be suggested that Emily is capable of strong visual tracking (Brown et al, 1996).
Emily's use of phonics to decode difficult and unfamiliar words and use of semantic and contextual cues provides support for the SVR's two strand approach and Goodman et al's (2005) research. Without the ability to decode or comprehend, Emily would not be able to read the texts (Rose, 2006). However, in support of Kirby and Savage (2008), whilst decoding unfamiliar words, Emily would frequently announce that she had used the illustrations to help her. Rose (2006) would suggest that Emily's use of illustrations and context to aid meaning provides a support for the different dimensions of reading.
The findings from this case study conclude that Emily is a confident and able child, whose extrinsic motives and egotistical nature place her in the correct cognitive developmental stage for her age, the pre-operational stage (Piaget, 1965).
In summary, Emily demonstrated in various situations her grasp of the mathematical principles: one-to-one correspondence, stable order, cardinality, abstraction, order-irrelevance and conservation. Although Emily's abstract mathematical ability is not yet reliable, it is apparent through discussion with her that she has begun to develop some simple strategic thinking processes. Suggesting that although she has not yet developed internal enumeration or number sense, she has begun to recognise relationships between numbers. Given mathematical problems with contextual meaning and the correct concrete apparatus, Emily's ability to manipulate and self-regulate improved drastically. Emily's word recognition and language comprehension was strong. This was shown through her ability to decode new words and use semantic and syntactic cues to replace words appropriately. The majority of reading errors produced by Emily were substitutions. However, these errors the majority of the time, were semantically and syntactically appropriate alternatives. As long as the text was at the appropriate reading level, Emily self-monitored and corrected the substitutions when it was not semantically or syntactically correct.
The case study has attributed to the consideration of my own practise in terms of children's stages of development and scaffolding in the core subjects. I am conscious of the effect moving pupils on to quickly or removing the apparatus and resources too soon, can have on development and understanding of future concepts. Seeing the direct benefits that interactive learning, learning with a purpose and real life context can have, I am eager to adopt these strategies into my own practise.
The naturalistic nature of the case study methodology allowed for the rich, holistic insight into, what was considered to be, the average primary school child. Although the chosen methodology meant no generalisation could be applied on the basis of an individual case, it was concluded that the quality of data collected and theories observed in practise, could not have been matched within a controlled study. Although it was not possible to spend more one-on-one time with Emily, it is advised that in replication more discussions are undertaken. Possible future investigations may include: The effect of social interactions with others on the fear of failure, and the use of real life contents in learning.