Equity and Social justice are important issues in mathematics teaching. This essay will explore the relevance of how mathematics education may be a necessary factor in determining the social justice of a child's upbringing, and consider how equity can be used in the classroom to ensure an education that is fair in its opportunities for all children to achieve progression in their learning.
Social Justice in Mathematics Education
Anne Watson believes that nearly all children are capable of learning 'significant mathematics given appropriate teaching'. (Watson, 2006, p. 2) She also believes there is a 'moral imperative' that children be educated well in mathematics in order 'realise the full potential of the human mind' and that it is a matter of 'social justice' to teach mathematics to all children as their achievement is judged throughout life, as well as a matter of empowerment when a child realises that he or she can enjoy mathematics learning. (Watson, 2006, p. 3) Grades achieved in mathematics exams can affect future studies and job prospects. For example, to enter university, usually a minimum of grade C GCSE Maths is required. In mathematics setting, the students in lower sets can only achieve a maximum of grade D. (Day, Sammons and Stobart, 2007, p. 165) This means these children will not be able go to university, or will have to take a maths GCSE again at a later stage, rendering their first grade D GCSE useless. This all seems unjust for the lower setted students, whose potential may not have been fully realised and who surely deserve the chance to achieve a higher grade if they are able.
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Every Child Matters is the government's initiative created with the aim of helping 'every child, whatever their background or their circumstances, to have the support they need' to be healthy, stay safe, enjoy and achieve, make a positive contribution, and achieve economic well-being. (website 2) It has to be asked if setting in mathematics classes really contributes towards that aim or, more likely, hinders it?
Setting by ability
Children can be taught in mixed ability classes, where all children learn together, or setted classes, where classes are separated in terms of ability level. The lower set children are taught more basic skills and higher set children more advanced skills. Children are then entered for exams appropriate to their level. There are many questions concerning the fairness of such an arrangement. The GCSE examination itself is rendered itself split into tiers, with only the higher set being allowed to attain 'good passes' of grades A-C. (Archer, Hutchings and Ross, 2003, p. 139) In mathematics setting, 'those in lower sets are less likely to be entered for higher tiers', (Day, Sammons and Stobart, 2007, p. 165) thus harming their future study and job opportunities. Also, some children can have a more advanced grasp of the subject due to an advantaged background, parents' help or private tuition. This could mean that setting is unfair as it is biased towards early developing children or those who have been given extra help outside the classroom.
Advantages of Setting by Ability
The main perceived advantage of separate ability grouping is that all students get the chance to learn at a pace suitable for them and they are not distracted from students of a different ability level with different educational needs. Setting means that children are only given the work that they are capable of completing. Some think that to do otherwise would be pointless and could harm the child's confidence and self-esteem levels, resulting in dissatisfaction and frustration for both pupils and teachers, class disruption and lower attendance levels. However, other people argue that mixed ability groups are more productive for all students. Indeed, in the many and varied studies in this area, 'there was evidence that all pupils gained socially from working in wide ability groups' this is because, it seems, 'such groupings allowed pupils from a wide variety of backgrounds, as well as abilities, to work together, strengthening social cohesion'. (Capel and Leask, 2005, p. 154-155)
Disadvantages of setting
There are some clear disadvantages to setting. For example, who is to decide on appropriate setting in the first place, and how? Although the setting system in schools is supposed to be purely for the ability level of the child, in reality, sometimes streaming could be decided upon for other reasons. For example, two areas of prejudice encountered can be social class and ethnic dimensions. (Capel and Leask, 2005, p. 155) Bartlett, Burton and Peim point out that often 'the lower class pupils were deemed to have a lower intellectual ability than middle class peers purely due to unrelated social issues such as accent or parents' jobs.' (Bartlett, Burton and Peim, 2002, p. 182) Sukhnandan and Lee (1998) also comment on the fact that the lower-ability classes often have a high number children from low social-class backgrounds, ethnic minorities, boys and children born in summer (thus, a younger age for their school year). (website 1)
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Harlen's study (1997) suggested that 'teachers with substantial experience of teaching mixed ability groups frequently used whole class methods inappropriate to mixed ability groupings and that teachers retained largely fixed views of ability and intelligence'. (Capel and Leask, 2005, p. 155) Another problem is that children do not get the chance to mix with other ability levels in the classroom environment, thus, giving them an unrealistic expectation of future life and general working environments. The problem of self-esteem is also an issue for the lower setted pupils, who feel disheartened that they are perceived as having weaker ability. Self-esteem is also an issue for higher setted children, who can be 'developmentally damaged' in a different way by their high set 'over inflating their self-esteem'. Sukhnandan and Lee believe that setting can in this way cause such 'social divisions'. (website 1)
Indeed, self-esteem is vitally important for children in learning mathematics. If a child has lowered self-esteem they could convince themselves that they are not bright enough to understand and so underachieve due to their defeatist attitude. Equally, a self-esteem too high in mathematics can make a child overly-relaxed about their learning and not try their hardest. Research has shown that the setting of pupils has 'a direct impact on the pupils' perceived mathematical competence' (Allen, 2004, p. 234) and that children can be affected psychologically about what they perceived they can or cannot do and learn. Also, a student who is setted is in some way 'branded' for the rest of their education and perhaps put in similar sets in other subjects. This branding can affect the students' perception of themselves and others perceptions of them.
Boaler points out that this setting of children by ability level can cause anxiety about exam performance among the more able pupils and underperformance, in particular, from girls. (Boaler, 1997) Boaler suggests this underperformance is due to crumbling under the pressure which affects girls more than boys because girls have 'a tendency to lack confidence'. (Noble, 2000, p. 125) Mike Ollerton supports the idea that setting by ability 'creates the conditions for under-achievement', (Ollerton, 2002, p. 264) a view also held by Boaler and William (2001). There is also the separate issue of children being streamed based on their achievements and not on their potential. This means that 'underperforming, very able pupils and pupils who are hardworking and perform well on tests can easily be placed in the same achievement group'. (Capel and Leask, 2005, p. 156) Indeed, an able pupil who is underachieving would be placed in a lower set than their ability should demand, whereas a student lower ability pupil who has a talent for performing well under pressure in exams could be placed in a higher set than their natural ability would normally allow.
In a similar way, boys often mess around in the classroom but perform well in exams. They could be placed in a lower set due to their bad behaviour and lack of attention, but their ability in maths could actually be worthy of a higher set. Indeed, for boys in particular, research shows that 'the set they were in reflected their behaviour more than their ability' (Allen, 2004, p. 208) There is also research to show that girls tend to do better in coursework compared to exams whereas boys do not do so well in coursework but perform well in exams. This is seen as being due to the fact that girls tend to do better in communicative tasks and enjoy writing more than boys who 'often don't enjoy "writing up" coursework'. (Noble, 2000, p. 123)
Modularisation in Mixed Ability Teaching
In a mixed ability class, the main concern is for the teacher in that they must decide what to teach and how to teach such a wide spread of abilities. Although this is still a concern in a setted class, this problem is much bigger in mixed ability classes. Sukhnandan and Lee (1998) comment that a more modular approach would benefit a mixed ability class. They suggest that schools should try to teach pupils' in relation to their individual needs rather than streaming by general ability, with this kind of equity in teaching more easily achieved 'through greater modularisation of the curriculum, an increased emphasis on independent learning and improved library and information technology resources'. (website 1)
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It seems that 'what goes on in the classroom, the pedagogic models and the teaching strategies used, is likely to have more impact on achievement than how pupils are grouped'. (Capel and Leask, 2005, p. 156) Indeed, a teacher's goal is to encourage learning progression in the classroom for all students. In order to achieve this, Ollerton suggests that this modular approach to teaching mathematics creates the feeling of having a fresh start to every section of learning, thus, helping self-esteem as everyone can 'embark upon a journey to learn, say trigonometry'. (Ollerton, 2002, p. 266) This progressive idea challenges the notion of the hierarchical structure of mathematical learning, (Ollerton, 2002, p. 266) with the effect being that everyone can start at the same level.
Differentiating Teaching Content
Tomlinson comments on the importance of differentiating content of a mathematics lesson in a mixed ability classroom. She points out that this includes adapting 'what we teach' and modifying 'how we give students access to what we want them to learn' (Tomlinson, 1995, p. 72) Giving different ability level students different tasks to complete appropriate to their ability is differentiating what they are learning. Tomlinson explains that giving higher ability level students time to read part of a text on their own while taking time to go through the text with the lower ability pupils separately. This differentiates their access to learning as they are learning the same thing in different ways, appropriate to their ability level. (Tomlinson, 1995, p. 72) Mathematics, it seems, would benefit from an approach that considers differentiation in what is taught rather than simply how it is taught. For example, some maths concepts would be too difficult for some children to understand, so the teacher must differentiate between the content suitable for the weaker students and the content suitable for stronger students: there is here a differentiation in what is taught. For example, 'trigonometry ... is usually only introduced to students in higher groups'. (Boaler, 2002, p. 7)
Equal Rights and Equity in Mathematics Education
The issue of equity is often confused with that of equality in the context of teaching. Zevenbergen points out that 'equity refers to the unequal treatment of students (or people more generally) in order to produce more equal outcomes'. This is in contrast to equality which means 'the equal treatment of students with the potential of unequal outcomes'. (Zevenbergen, 2001, p. 14) For example, students going to tertiary mathematical education but who have disadvantaged backgrounds could be offered extra help to catch up with their more advantaged peers' in order to hopefully achieve 'parity in the outcome for all students' (Zevenbergen, 2001, p. 14) The alternative method of equality, would mean that all students are given equal treatment and the same opportunities to succeed. However, some students would take more advantage of the opportunities than others and the results may be more disparate than with an equity programme. Indeed, equity programmes are 'designed to be more proactive and seek to redress differences in prior experiences', (Zevenbergen, 2001, p. 14) whereas equality programmes are more conservative in their approach and acknowledge that some students will achieve more than others. Justice in education can be achieved for children if they are taught in a way that meets these individual educational needs.
Children who have English as a Foreign Language
Pupils who speak English as a second language often underachieve in mathematics due to issues of language competency. Students must work within the language of instruction in order to read text books and understand verbal instructions. Educational progress is enhanced or impeded depending on whether a student's first language is that of their instruction or not. (Zevenbergen, 2001, p. 15) Indeed, mathematics has many words particular to the subject, for example, 'integral, differentiate, matrix, volume and mass'. This can be confusing for non-native English students, as they have to learn new meanings in the context of mathematics. (Zevenbergen, 2001, p. 16) The same word can be interpreted in different ways by non-native English students, a misunderstanding which can affects learning. This lack of common language background can make a maths class very difficult for a teacher to teach. For example the words 'times' normally is related to the time on a clock, not to multiplication; the words 'hole' and 'whole' sound the same but have different meanings, in maths meaning a whole number. (Gates, p. 44)
If a non-native English student has trouble with language, they may work more slowly or misunderstand questions and thus be perceived as weak at maths. This can affect which set the child is placed in, causing a non-native English student to be setted at a lower level in maths due to their lack of skills in English, which is clearly unfair.
Children with Special Educational Needs (SEN)
Children with special educational needs also require special differentiation in teaching methodology. Learning disabilities which need to be considered in the maths classroom include dyscalculia, where the child cannot grasp the meaning of number, poor numeracy skills, problems such as Aspergers syndrome and autism, or physical disabilities and sensory impairments. (Cowan, 2006, p. 202-203) In a mixed ability class with special needs, the teacher needs to be aware of using simple and precise instructive language, a clear method of presentation and, perhaps, modified content difficulty and reduced quantity of work. (Cowan, 2006, p. 203)
How Equity can mean Social Justice for all Learners
It is clear that 'the tiering of mathematics papers is likely to have an important impact' on student development and pupils often 'make more progress if taught in a higher set rather than a lower set'. (Day, p. 165) This means that in mathematics teaching, the same topic should be address in a mixed class of varying educational needs, whether including different ability levels, special needs children or non-native English speaking children. Tasks can be organised according to needs level. Key stage 3 and the National Numeracy Strategy (NNS) advises planning a lesson using three stages: the pre-active phase, where the necessary prior knowledge is identified and presentation planned; the interactive phase, where the teaching takes place and tasks are worked through, including a plenary at the end of the lesson where there is a recap and learning outcomes are discussed; thirdly, the evaluative phase, where the teacher reflects on the lesson and on learning successes or difficulties. (Cowan, 2006, p. 59)
In sum, then, 'by using a range of tasks comprising different levels of difficulty but addressing the same topic or theme within the one class, the three stage lesson advocated by the NNS and KS3 Strategy can be maintained'. (Cowan, 2006, p. 212) By following a structured lesson plan, equity can be achieved for all students, whatever their ability level or special need and in this way social justice is maintained for all students in mathematics teaching and learning.
The government's Every Child Matters initiative supports the view that equal rights for all children means equal opportunities for all children. It seems that in order to achieve this kind of social justice, every child needs to be given the chance to take an examination paper that allows them to achieve an A grade. In doing this, each child will have an opportunity to go on to further study should their ability and interests allow. Setting by ability not only makes this difficult, but actually increases problems in the classroom, such as damaged self-esteem and under-achievement and can even encourage some prejudice regarding race and class. A Setted class is not necessarily easier for teachers to teach either, as they will still need to differentiate content for different class members. It therefore seems that a strong lesson structure incorporating modularisation and appropriate differentiation in teaching content will provide a more effective environment in which equity can be used to maintain social justice in the teaching of children in a mixed ability classroom.