During the term of school placement, I was placed at School X where I taught a variety of topics to two year 7 classes, a year 8 class and a year 10 class. I taught these classes continuously from half-term until my placement at School X ended. School X adopts a policy of grouping mathematics pupils according to their ability. For the purpose of this assignment, I will focus on my experiences with the “bottom set” of Year 7.
Features of the Class The class consisted of 26 pupils aged 11 and 12. These pupils are from differing backgrounds and have vastly differing personalities, as highlighted by Denvir: “Low attainers……… will not form a homogenous group. Their only common characteristic may be low attainment in mathematics.” (Denvir et al, 1982, page 17). While the class was deemed to have low mathematical ability, I was surprised to find such a wide range of ability within the set. This is confirmed by the findings of Kyriacou: “Even in classes composed of pupils selected as being of relatively similar ability, there exists a marked range of ability.” (Kyriacou, 1986, page 82)
To familiarize myself with the pupils of the class, and their individual characteristics, I compiled a “characteristic cloud” (see appendix 1) for each of the pupils. These provided valuable information that I used to plan lessons and arrange classroom activities. Whilst composing this information, I was very mindful of ensuring that I didn’t fall into the trap of “teacher labeling” identified by Kyriacou (1986). There was a general lack of confidence and many of the pupils labeled themselves as poor mathematicians. To avoid apathy, I was keen to demonstrate that the pupils were capable of learning and enjoying mathematics.
“Pupils who see themselves as unable to learn usually cease to take school seriously.” (Black ; Wiliam, 2001, page 4) Out of the class of 26, 15 were identified as have Special Educational Needs. I was made aware of two pupils who were on medication, and the effects this had on their classroom behaviour. Differentiation of Ability Even though it was “ability grouped” the class had a wide range of ability. Several of the pupils experienced far more difficulties than the rest of the class.
This was never more evident than when I was teaching the topic of Time. Whilst talking about the differences between a 12-hour clock and a 24-hour clock. I noticed that Pupil Z was uncomfortable. While the class was working, I approached Pupil Z to offer supplemental explanation. She then confessed that she “could not tell the time.” To overcome this, I arranged for Pupil Z to attend Maths Club2 where I taught her how to tell the time using a children’s wooden analogue clock. (See appendix 2). Using a different approach to teach Pupil Z responds positively to the statement made by Cockcroft:
“It is very important to realize that within any mathematics set there will still be marked differences in the mathematical attainment of pupils. It is therefore essential that the teaching takes account of these differences and is responsive to the needs of individual pupils. It should not be assumed that the same teaching approach will be necessarily suited to all in the group.” (Cockcroft, 1982, page 27).
Generally, I was able to overcome ability differentiation by giving the more able pupils work which they found challenging, without confusing the majority, by giving supplementary exercises to the more able pupils. These were obtained from the textbooks that the school used. Also, I was able to prepare worksheets with progressively more difficult questions incorporating at least one “stopper” question. Typically, the more challenging questions would require the pupils to apply the concept being taught to real-life applications. E.g. when covering shapes, one of the challenging questions was to think of real life applications of the shapes cube, cuboid, prism and pyramid and then to think why this shape was the most appropriate for that particular application. This would allow pupils to think about problems on a deeper level and “discover mathematics” as Backhouse suggests:
“If learners discover some mathematics, they are less likely to forget it. This is partly because of the satisfaction that this achievement will give them.” (Backhouse et al, 1992, page 72) Examples of worksheets can be found in appendix 3. Another method I employed was to make tasks open-ended. One example of this was to require pupils to draw a symmetrical shape or pattern on squared paper. More imaginative pupils incorporated colour and more complicated shapes into their patterns. (See Appendix 4).