This section draws together HMI judgements about four major aspects of learning and teaching. Each is covered by a separate published performance indicator.
The quality of learning and teaching
From S1 to S6 the quality of learning was very good in 5% of departments. It showed more strengths than weaknesses in 55% and some important weaknesses in 40%. There was very little variation between stages in the quality of learning.
From S1 to S6, the quality of teaching was very good in 10% of departments. It showed more strengths than weaknesses in 75% and some important weaknesses in 15%. Mathematics teachers generally displayed strengths in explaining concepts and methods and questioning individuals and groups. The key features of very good learning and teaching in mathematics are shown in Box 9.
In S1/S2, less effective teaching often resulted from over-emphasis on individualised learning, resulting in slow overall progress. Some pupils were allowed to work slowly through the materials without fully comprehending or recalling what they had learned. Where homework came at the end of a topic the slowest workers were often not set tasks. At the other extreme, over-use of explanations to the whole class, followed by individual routine examples, resulted in pupils losing motivation. Teachers need to ensure that pupils are actively involved in their learning and have opportunities to talk about mathematics, discuss problems and develop independent thinking.
9Where the quality of learning and teaching was very good, teachers:
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Less effective teaching from S3 to S6 often resulted from:
Some departments made good use of graphics calculators, particularly in S5/S6 Higher and CSYS classes, to support pupils' understanding in key areas such as calculus and trigonometry. However, there is scope for much more use of this technology to improve pupils' learning of mathematics. All teachers of mathematics should take note of the advice contained in Advanced Calculators in Mathematics Education. Mathematics teachers should also consider how wider use of ICT including computers, CD ROMs and the Internet could enrich their teaching and make the subject more stimulating and attractive to pupils.
Meeting pupils' needs
In S1/S2, pupils' needs were well met or very well met in 50% of departments but in the rest there were important weaknesses. These were often related to the structure of the course. Where the course was not matched to 5-14 levels, or took insufficient account of attainment information from primary school, tasks were often inappropriate for pupils. Higher attaining pupils were frequently under-challenged, particularly in S1. In departments where mixed ability classes operated in S2, few courses met pupils' needs well. Teachers generally found it easier to match tasks to pupils' abilities more effectively where broad-banding or setting arrangements had been made. These arrangements also allowed for efficient deployment of learning support staff. Input from learning support staff was most effective where there was close collaboration between the mathematics and learning support departments to produce individual programmes for the pupils concerned.
From S3 to S6, departments were more successful in meeting pupils' needs. In S3/S4, almost 75% of departments were judged to be very good or having more strengths than weaknesses and, in S5/S6, 80% of departments achieved this level. This was largely due to well planned setting of pupils and greater clarity in teaching objectives, as defined in terms of the external certification.
In S5/S6, many mathematics departments offered a wide range of courses which covered a range of pupil needs. The new Higher Still courses being introduced in 1999 will allow schools to maintain or improve this breadth of provision.
Assessment as part of teaching
Assessment as part of teaching was very good in 15% of cases and had more strengths than weaknesses in 45%. There were important weaknesses in 40% of departments with a small number being unsatisfactory. Weaknesses were mainly related to assessment in S1/S2. The strengths and weaknesses of assessment as part of teaching are shown in boxes 10 and 11.
10Where assessment as part of teaching was very good its strengths were:
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11Where assessment as part of teaching was poor, its weaknesses were:
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Many teachers had procedures which allowed them to monitor S1/S2 pupils' coursework and give them good feedback on their progress. However, some teachers did not examine classwork often enough and relied too much on self-correction by pupils. This often led to the repetition of errors. Almost all departments used formal tests to assess pupils' progress and recorded results systematically. However, these arrangements were not always well matched to 5-14 levels.
The proportion of departments using national tests to confirm their judgement of pupils' attainment increased from 40% in 1996/97 to 80% in 1998/99. However, the tests were not always used according to national guidance. Sometimes pupils were given tests before they were ready, usually at the end of a session. Some teachers entered pupils for national tests before the teacher had assessment evidence that the pupils had completed the programme of study for the level and were performing consistently and confidently across the level in their classwork. Where this happened, pupils sometimes passed the test but had gaps in their attainment in aspects not included in the test. For example, many departments had very little evidence of pupils' performance in mental calculation. In practice, the pupils might have difficulties in this aspect or with other key topics.
Most departments had inadequate evidence to provide reports to parents which conformed with national guidance.
From S3 to S6, internal assessment complemented SCE examinations well and provided pupils with good information on their progress. The new Higher Still assessment arrangements due to come into operation in 1999 will assist departments in further improving the links between internal and external assessment.