Mathematics Assignment

The NNS (1999) advocates inclusion of all children in numeracy lessons, “The children in each class should, as far as possible, work together through the year’s programme… so that all children participate when a new unit of work starts… ” (sec. 1 p. 19). The NNS (1999) states that when classes are taught in this way all children make significant progress. Dewhurst (1996) identifies that before the NNS there seemed to be very little advice to teachers on how successful differentiation could be achieved (p. 12). However today the NNS identifies strategies, which can be used to ensure inclusion. Although this advice is now available Straker (1999) reflecting on the National Numeracy Project 1996 – 99, identifies the heavy demands placed on teachers implementing this ‘controlled differentiation’ (p. 45). This essay will discuss issues surrounding differentiation and inclusion relating them specifically to the teaching of properties of 3-D and 2-D shapes in year 4 and observations detailed in appendix A.

Having taught the above topic to a class of year 3 and 4 pupils I am aware of the importance and demands of differentiating whole class and group work while maintaining the inclusion of all the children, some with special education needs. The National Curriculum Council gives us the definition of differentiation as being, ‘the matching of work to the abilities of individual children, so that they are stretched but still achieve success’ (NCC, 1993).

The NNS (1999) states that pupils in year 4 should be taught to “describe and visualise 3-D and 2-D shapes and classify them according to their properties and make shapes and patterns with increasing accuracy” (sec. 6 p. 102 & 104). Within these statements are listed outcomes that children of that age/year group are expected to attain. However some children will not reach those expected outcomes and others will surpass them. Edwards (1998) states that when planning activities for children of different abilities, levels of expectation can be defined in terms of minimum, optimum and extension levels of performance (p. 10).

Appendix B shows an example of a lesson I taught with the work differentiated in a similar way as detailed by Edwards (1998). All the children’s expected outcomes were taken from the year 3 and 4 NNS strands, but the expectations for each group were matched to those children’s abilities. The pupils were grouped by ability for numeracy, however they were not kept within their separate year groups. The NNS (1999) accepts that if there are pupils in a class with a very wide-ranging ability the teacher/school might make the decision to set the pupils.

In my previous SE placement I was in a mixed year class, The teacher also ability grouped the children for numeracy, but the children were kept within their own year groups. I can see benefits to keeping year groups separate as it ensures they complete the NNS objectives in the correct year. The NNS (1999) advises teachers who mix year groups when setting to ensure that when the year 3 children move into year 4 they don’t repeat the previous year’s activities although they are in the same class (sec. p. 20). However, it has to be taken into account that although as Berger et al (2000) state the most able pupils may not be the oldest pupils (p. 16), and mixing children across year groups allows the most able to be in the highest ability group irrespective of their age. When planning to teach 2-D and 3-D shapes to the year 3/4 class, if found at times that I wasn’t aware of which year group the children were in.

As already mentioned this can cause problems in terms of children repeating work, but also year 3 children who were working in the most able group on year 4 NNS objectives could have gaps in their knowledge or misconceptions which haven’t been addressed by not covering the year 3 objectives. Berger et al (2000) also adds that these disadvantages of mixed year group setting have to be weighed against the benefits such as being able to stretch an able group and maintaining an appropriate pace at all times (p. 16).

Kelly (1974) criticises ability grouping within or across year groups, stating that it can lead to a kind of ‘self-fulfilling’ prophecy where pupils begin to work at the level of the group they find themselves in (p. 46). The success of setting depends on teacher expectations and as the NNS (1999) states that “lower expectations are not justified simply because pupils are in a ‘lower set'” (sec. 1 p. 20). In my last SE placement one year 4 boy was seen as exceptionally able and not sufficiently challenged enough, to be moved into the class above for numeracy.

As his and the class he moved into contained mixed year groups, he was a year 4 child working at year 6 standard. The teachers’ main concern was how they would stretch him for the next two years. Another concern was his level of maturity and ability to mix with the children in years 5 and 6. Fielker recognises this issue of maturity and states that although younger children may be brighter they do not mix easily with children who are physically, socially and emotionally more mature (p. 9).

The NNS (1999) recognises the need for some children to work with others who are working at a similar level, but in a years time the boy will have no one else in the school working at his level. It could be at this point that an individualised scheme is provided for him. Fielker (1997) recognises the benefits of work that is set for a particular pupil’s capabilities, but states that the teacher can find it difficult to occupy a role other than managing the child within the class, instead of actually teaching him/her (p. 15).

During the teaching of 2-D and 3-D shapes my main method of differentiation was by task. Referring to the statement made in the NNS (1999) that differentiation should be manageable and Straker’s (1999) assertion that the aims of the NNS place heavy demands on teachers, open-ended tasks relieve some of the pressure of differentiating for all children in the class which is corroborated by Edwards (1998) who identifies that “the design of open-ended tasks is less time-consuming for a teacher to prepare than worksheets” (p. 210).

One practical open-ended task I used with children (shown in appendix C) was to create shape riddles in mixed ability pairs, each child invented 3 statements to describe a 2-D then 3-D shape and their pair had to guess the shape. The design of this task allowed children to support and be supported by each other and to create statements at their level of knowledge of a shape’s properties. Proctor et al (2001) talk of the risks children have to take in learning and how paired work can minimize the vulnerability they feel, they may be more inclined to ‘have a go’ in a pair or a group as they gain confidence from ‘braver’ classmates (p. 4). Edwards (1998) advises that “closed tasks allow for no differentiation apart form the different rates children work through activities” (p. 209). Having personally used published schemes, which generally present closed tasks, to set work for children in school it has been an important part of my planning to alter the questions and provide extension opportunities to ensure that children are not restricted by the set parameters these schemes can impose upon children’s learning.

Open-ended tasks however provide the opportunity for each child to work at his/her level, allowing all children to succeed at the task. Edwards (1998) states that “open ended tasks allow children to have success at all levels” (p. 210). Koshy (2001) agrees that particularly for the able child open-ended mathematical-enquiries provide opportunities for in-depth exploration of mathematical ideas and allow children to pursue individual lines of enquiry (p. 75). Another aspect to consider when differentiating by task is the content to include.

The NNS (1999) framework can be followed forward a year for the most able and tracked back a year for the least able, however if doing this to differentiate it is essential to ensure that all children are focussing on common content, In my last SE when planning a weeks work on 3-D shape, my teacher-tutor suggested that the lowest ability group should not move onto 3-D shapes, but spend the week consolidating their work on 2-D shapes, reflecting back on this I feel that this decision was not in line with the NNS (1999) which states that “differentiation is centred round work common to all children in the class” (sec. p. 5) the lowest ability group should still have had the opportunity to work with 3-D shapes along with the rest of the class. In order to achieve this I differentiated the resources I gave to different groups, allowing the lowest ability group to use multilink to create a variety of 3-D shapes. From my observation and assessments this kinaesthetic approach to learning increased their interest and ability to access the concepts of 3-D shapes.

Diorio (29/05/03) states that some children learn kinaesthetically and processes information primarily through touching and movement. Kelly (1974) criticises this approach to all children studying the same content, his views, which are pre the National Curriculum on mixed-ability classes, are that the content does not have to be the same as long as the objectives are common (p. 10). In practice this can cause difficulties in terms of planning and managing sessions, specifically if a variety of resources are needed, when children are not working on similar tasks.

An alternative method of differentiation is by questioning, while differentiation by task relates specifically to pupil activities within the numeracy lesson, questioning is a technique which can be employed throughout the session. The NNS (1999) places a strong emphasis on differentiation during whole-class oral work and questioning plays a main part in this session. The NNS (1999) states that a variety of questions should be used including planning some questions to target particular children.

Open questions, like open-ended tasks allow all children to participate, as they can give an answer appropriate to their level of ability/knowledge. For example while teaching the properties of shape I regularly asked the children to name any properties of a particular shape, allowing the least able to give the number of sides and stretching the most able who might say the shape is a type of prism. As identified in Kyriacou although (1998) “open questions are more stimulating” (p. 35), there are a range of purposes when closed questions are deemed to be appropriate.

As discussed by the NNS (1999) closed questions can be opened up by discussing the methods used. This enables higher ability children to suggest a variety of methods and explaining the reasoning behind their answers and allows lower ability children to understand how to ‘work out’ a question that they might not have previously been able to. Koshy (2001) identifies that for the able child specifically “the teachers ingenuity of questioning will determine the positioning of the child’s experience within the spectrum of possibilities of the daily mathematics lesson” (p. 4). Providing the support of the teacher or an additional adult in the classroom is another method of differentiation, this provision may be aimed at a group or maybe one particular child who has SEN. The NNS (1999) states that children with SEN or IEPs should be included fully in the numeracy lesson. Support staff can aid in this inclusion by enabling these children to access the curriculum. The NNS (1999) accepts however that if problems are complex and severe children can work on an individualised programme in the main part of the lesson.

In my last SE during an observation in the year5/6 class I watched a particularly successful partnership between an albino boy with limited vision and his LSA, this was substantiated by a SEN inspector who commented on the success of the provision the boy was receiving, without him being removed from the classroom. However Thomas et al. (1998) urged schools to give careful consideration to the ways in which they use additional classroom support: the allocation of additional staffing to named individuals, far from encouraging inclusion, may create dependency in the pupil and emphasise the ‘differentness’ of the individual with SEN.

Headteachers were asked, in a study on the conditions of inclusion by Rose (2001), to comment on the implications for greater inclusion, all interviewees mentioned the importance of classroom support and nine of the teachers regarded the provision of additional staffing as a critical factor in enabling inclusion to succeed. If it’s a small class with good levels of support, classroom support and teaching support, then it is possible that it could be beneficial to the child.

I also have a concern for all the other children in the class as well, because if a teacher is having to spend so much time with one child, it can be at the expense of other children. (Headteacher 3) Recently EMTAG teachers have been placed in classrooms with a high proportion of EAL children or children who belong to traveller communities. They plan along side the classroom teachers giving their expertise in how these children can be specifically differentiated for.

The NNS (1999) states that numeracy has a strong visual element, which can be capitalised upon when working with children who have EAL (sec1. p. 22). EMTAG teachers spend time working with children on their use of mathematical vocabulary to enable them to begin to present their work orally. However Tope (2003) identifies that “EAL is not always an additional need/barrier”. Headington (1997) identifies the importance of supporting and briefing teaching assistants in order to use them to the best advantage (p. 59).

Planning for and supporting assistants can be a time-consuming process, however a report by Ofsted (2002) confirmed that when managed well, teaching assistants bring considerable benefits into the classroom. During my last SE I had two teaching assistants, one who specifically sat with 3 boys who had IEPs during the whole numeracy lesson. Having her there throughout the whole session meant that she listened to my teaching input and was aware of the lesson’s objectives and could provide help by ensuring the boys used specific resources such as small whiteboards/number cards.

The NNS (1999) stresses the importance of having support staff positioned near any children who have specific needs (sec. 1 p. 25). Her specific knowledge of the boys’ targets on their IEPs also enabled her to work on these with them, alongside their group/individual work. The report by Ofsted (2002) did however note that despite the benefits of teaching assistants there were some key issues schools needed to consider, for example “ensuring the assistants had the knowledge and skills to work effectively with the pupils” (p. ). The report also raised the issue that not all newly qualified teachers are trained to work with teaching assistants. In my first SE I did not have a teaching assistant and therefore in my second SE placement I undertook a steep learning curve in how to plan for and maximise the use of the two extra adults I had in the classroom. Various methods of differentiating have been discussed in this essay and there are more, which could be considered. It can be said that there are benefits and disadvantages to all.

The NNS (1999) makes the statement that differentiation should be manageable and yet centred round work common to all the pupils and offers guidance in how to effect this within the classroom. During my SE placemats and observations carried out in other classes I have seen many methods used, what is important is that all the teachers I have questioned have justified their reasoning behind their differentiation in that it is suitable for those children within that classroom.