Abstract
Pupils with severe learning difficulties (SLD) have in the past often been provided with restricted opportunities for learning about mathematics, reflecting the low level of priority assigned to this area of learning by teachers and other staff (Porter 1996; 1999).
Indeed it is not surprising that this is an area in which pupils included within mainstream have been found to have greater gains (Casey et al 1986). This paper will present the results of a small scale exploratory study investigating the achievements pupils with SLD in the area of numeracy during the academic year in which for the first time pupils will receive a daily lesson of mathematics.
Assessment is based around a tool previously developed to compare group differences in school mathematical achievement (Ginsburg et al 1997). The game element of this tool has been extended to cater for pupils who are achieving at early levels, and includes an additional measure designed to test children's understanding of the principles of counting. In this paper the author will examine the types of progress made by pupils. For example, do pupils make most gains with respect to recognising and using numerals and production of the number string- areas which researchers have previously described as rote learning?
In the past pupils with severe learning difficulties (SLD) have often been provided with restricted opportunities for learning about mathematics, reflecting the low level of priority assigned to this area of learning by teachers and other staff (Porter 1996;1999). Indeed it is not surprising that this is an area in which at least one group of pupils included within mainstream have been found to make greater gains (Casey et al 1988). The introduction of the numeracy strategy for all pupils has raised the profile of mathematics and the expectations of what pupils may be able to achieve given regular and frequent mathematical learning experiences. The numeracy strategy puts particular emphasis on oral methods, on increasing the range of strategies that children use for mental calculation as well as delaying the teaching of sums. The evaluation of the literacy and numeracy strategies by Earle et al (2000) points to the unique approach of trying to achieve country wide change in the approach to teaching mathematics. The report concludes however that there is "at best uneven evidence" to support the methods employed by the numeracy (and literacy) strategies. It is therefore particularly important to ask whether this approach will raise standards in the pupils who may experience the greatest difficulties in this subject area, and furthermore are there any early lessons to be learnt about its implementation.
This paper reports in brief an exploratory study, carried out in an SLD school, investigating the gains made by a group of pupils who spanned the range of age and attainment level of pupils in an SLD school. It builds on the findings of previous studies (Porter 1998; 1999a; 1999b) of the mathematical attainments of pupils with severe learning difficulties which indicated that:
The aim of this study was to investigate the skills and understanding acquired by pupils over a period of a year. The pupils were in their second year of the numeracy strategy as the school had taken part in the national pilot. There was in place a clearly defined approach of 5-10 minutes whole group work on the topic, 40 minutes with two rotating small group activities and individual IEP work, followed by 10 minutes whole group plenary. A topic was followed for a week and returned to twice more in a term with an average of 4 topics a term.
Method
10 pupils attending a special school for primary aged pupils with severe learning difficulties, ranging in age from 5-10 years old (mean 8.3 years) were selected by the teachers because they were concerned whether provision was fully meeting these pupils' needs. One pupil was subsequently dropped from the sample due to ill health. Of the remaining 9 pupils, four scored on the British Picture Vocabulary Scale (Dunn et al 1982) ranging from 2 years 6 months to 4 years 5 months (mean 3 years 4 months) and five failed to score. One of the sample was described by their class teacher as having profound and multiple learning difficulties.
Children were assessed on two or more occasions towards the beginning of the academic school year and again at the end, using the "Birthday Party Game" a test of informal early mathematical thinking devised by Ginsburg et al (1997). Imbedded in the game are 10 tasks, each of which include demonstration and a practice. It was chosen in part for its motivational properties, its wide use across cultures and the opportunities for non-verbal responses. Results were validated through checking pupil responses with the class teacher at the end of the school year.
Results and Discussion
All of the children were making some progress, although there was great variation in the extent of this. In some instances the scale was not sufficiently sensitive to fully indicate this and in one instance the pupil was at the ceiling level of performance. For these pupils assessment was based on tasks to directly validate class records and teacher reports, and in the case of pupils at the earliest levels of understanding downward extension activities.
Most significantly, testing did reveal that three pupils had succeeded in making the cardinal count transition in the course of the year. The link between counting and cardinality was revealed in their ability to make small sets from a larger set of 10, a task that they failed at the beginning of the year by "giving all". Two of these children also developed skills of addition. This development can be viewed as an important milestone in that it suggests pupils understanding of the cardinal principle an important basis for future conceptual understanding (Rittle-Johnson & Siegler 1998).
The progress of the most able pupil was not well measured by the scale. One of his attainments was to learn the two times table. This was not purely achieved as a rote memory exercise. Whilst his mental strategy was not clear the pause between question and response suggested some form of mental strategy for adding on, rather than mental reciting of the table.
Progress was most difficult to measure in three pupils at the earliest stages who failed all items on the test. This however should not be taken as indicative of no knowledge or understanding. Assessment procedures were developed to extend perceptual items on the test to elicit their awareness of numerosity, building on research findings with typically developing infants (Wynn 1992; 1998). Starting from children's interest for particular items it was possible to devise individualised games which elicited differentiated responses to numerosity. A continuum of responses from awareness to simple actions to problem solving behaviour was demonstrated (Porter and Ashdown in preparation).
Two pupils gained skills of finger production and reciting the number string. Both of these attainments benefit from the repetition that can be part of the numeracy strategy. In one pupil the finger production gains were also reflected in a growing ability to differentiate between visual arrays. Whilst these two pupils made gains in these skill areas however, others lost in precisely the same areas. This indicates how unstable learning can be and the need to monitor previous learning as well as the achievement of new targets. The loss of particular skills could be attributed to a number of factors. Memory of rote skills is dependent on repetition and practise. To retain these skills over time there needs to be salient cues which will act as triggers for their recall. The linking of skills to understanding is an important way of achieving this. We need therefore to ensure that the numeracy hour provides learning opportunities where rote skills are meaningfully presented and there is repetition and practice.
Conclusion
The inclusion of pupils with severe learning difficulties in the numeracy strategy is to be welcomed. This exploratory study has provided good evidence that even those pupils about whom teachers express most concern are making gains in mathematics over the course of a year. There is a need however to develop sensitive measures for those at the very earliest stages of acquisition. The assessment procedures used here indicated the need for teaching contexts to be individually devised, building on the particular interests of the pupil. The study also indicates the importance of ensuring monitoring of previous learning and providing opportunities to consolidate learning. The structure of the numeracy strategy with respect to introducing and developing topics may well need further consideration for some pupils.
References
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