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7. Summary and issues

7.1 Survey overview

The 2004 AAP Mathematics Survey assessed pupil attainment within the outcomes of Information Handling, Number, Money & Measurement, Shape, Position & Movement and Problem Solving & Enquiry as detailed in the National Guidelines for Mathematics 5-14 ¹². Pupil performance in the core skills of communication (reading and writing) was explored through written tasks, each set within a mathematical context. Skills in using ICT and other core skills were explored through practical assessments. The survey also gathered pupils' views on their learning experiences, through a written questionnaire.

Schools were invited to provide information about the provision and resourcing of mathematics in schools, and to provide teachers' views about the quality of teaching and learning in practice. This information was gathered through questionnaires sent to about half of the schools involved in the survey, seeking responses from both school managers (head teachers of primary schools and principal teachers in secondary schools) and classroom teachers with responsibility for teaching mathematics in each of the P3, P5, P7 and S2 stages included in the survey.

The reported findings are based on the assessment results of pupils from 835 schools out of over 1000 invited to participate. School participation in the primary sector was higher than in the secondary sector, where there was only a 76% participation rate. This is a matter that may have to be strengthened as the Scottish Survey of Achievement ( SSA) assumes the main role of providing evidence of pupil progress across the stages within Scottish education.

7.2 Mathematics attainment in 2004

Almost 10,000 pupils participated in the written assessment of mathematics, with individual pupils attempting mixed-level booklets of items at two or three adjacent 5-14 levels: P3 at Levels A and B; P5 at Levels B, C and D; P7 at Levels C, D and E; and S2 at Levels D, E and F. For reporting purposes, throughout this section the 'expected level' refers to the broad criteria within the 1991 publication of guidelines for Mathematics 5-14, namely:

Level A should be attainable in the course of P1-P3 by almost all pupils.
Level B should be attainable by some pupils in P3 or even earlier, but certainly by most in P4.
Level C should be attainable in the course of P4-P6 by most pupils.
Level D should be attainable by some pupils in P5-P6 or even earlier, but certainly by most in P7
Level E should be attainable by some pupils in P7-S1 but certainly by most in S2

On the basis of assessment results in the survey, pupils achieving 80% or more of the marks were considered as having demonstrated 'considerable strengths' at the level concerned; pupils with at least 65% but fewer than 80% of the marks were considered as being 'secure' at the level; pupils achieving 50% or more of the marks but less than 65% were considered as having 'basic skills' at that level.

7.2.1 Pencil and paper written assessments

• Over 95% of the P3 pupils assessed in the survey were estimated to have shown at least basic skills at Level A, just under 90% were 'secure' or better at this level and almost 70% showed 'considerable strengths'. At Level B the corresponding proportions were over 60%, around one-third and just under 10%.
• At P5, 90% of the pupils were estimated to have demonstrated at least 'basic skills' at Level B, over 70% were at least 'secure' and just over 40% showed 'considerable strengths'. At Level C the corresponding proportions were 65%, 40% and 15%, respectively, and at Level D just over 25% demonstrated 'basic skills', 10% were 'secure' or better and 2% showed 'considerable strengths'.
• At P7, just under 90% of the pupils were estimated to have demonstrated at least 'basic skills' at Level C, almost 75% were 'secure' and over 40% showed 'considerable strengths'. At Level D the corresponding proportions were almost 70%, over 45% and over 15%, respectively, and at Level E almost 35% showed 'basic skills', almost 20% were 'secure' and just over 5% demonstrated 'considerable strengths'.
• At S2, 80% of the pupils were estimated to have basic skills at Level D, 60% were secure and 30% showed considerable strengths. At Level E the corresponding proportions were just under 60%, almost 40% and just under 20%, respectively, while at Level F the figures were over 15%, over 5% and 2%.

The proportion of pupils demonstrating 'secure' knowledge or 'considerable strengths' at the expected level for their stage progressively increased from 32% at P3 (Level B) through 40% at P5 (Level C) to 46% at P7 (Level D). At S2, where the expectation is Level E, the proportion of pupils achieving at least 'secure' status is only 37%. This is a concerning figure for S2, where as many as 41% are recorded as demonstrating less than 'basic' skills and understanding at Level E. This compares with roughly a third of the other stages that fall below 'basic' level of attainment for the expected level, achieving fewer than 50% of the available marks at Levels B, C and D.

The survey was administered in May and June, towards the end of the pupils' year. Given that timeframe, we can see that level B for P3 is potentially challenging, as this level should be attained by some pupils in P3 (or earlier), but by most pupils in P4. The AAP survey findings therefore present a positive picture for P3 with only 36% still to achieve this level over the following year. The challenge is to raise the proportion of pupils who can demonstrate the skills and understandings within this level in a 'secure' and confident manner, raising expectations for a strong foundation rather than any premature pushing on to Level C. It is good to note the very high proportion of pupils who demonstrate 'considerable strengths' at Level A whilst finishing P3.

Results for P5 pupils present a similar picture, with only 35% still to demonstrate 'basic skills' within Level C. Given there is another full year available for the expected level to be attained by most pupils, the current profile presents a positive position for study at Level C. As with the P3 cohort, it is good to note the consolidation that appears to have taken place with a very high proportion of pupils showing 'considerable strengths' and 'secure' performance at Level B as they finish P5.

The same cannot be said of the P7 stage. Although the proportion of pupils who were showing 'considerable strengths' and 'secure' status in the expected level continues the pattern from the earlier stages with a gradual increase across the stages there appears to be a bigger tail failing to meet the basic skill level expected. In P7, most pupils should be attaining Level D, so we might have anticipated a higher proportion demonstrating secure attainment at that level in the survey. A very similar proportion as witnessed in P3 and P5 are currently failing to demonstrate 'basic skills' for Level D, but there is not another year of study scheduled for those pupils. If the expected levels are adhered to, then more needs to be made of P6 and P7 to ensure Level D can be attained by most of the pupils. As with the P3 and P5 cohorts, it is good to note the consolidation that appears to have taken place at Level C, with a similarly high proportion of pupils showing 'secure' performance or even 'considerable strengths' at this level as they finish P7.

A similar picture is in evidence for the S2 stage. The expectation is for Level E to be attained by most pupils in S2. Although the proportion of pupils showing considerable strengths remains stable, the proportion showing secure attainment has noticeably reduced. Only 37% of the survey pupils were demonstrating 'secure' status or better at the end of S2 and a higher proportion (41%) were failing to demonstrate the 'basic skills' for Level E. This would suggest that in the first two years in secondary school able mathematicians are well catered for. Some pupils, however, are not able to build on their secure attainment at Level D as they work towards the next level; and some of those with only basic skills at Level D find themselves in considerable difficulty as they encounter the greater challenges of Level E work.

Given the limited proportion of S2 pupils who have progressed to secure status or better at Level D, after another two years of study, a question is raised over the underperformance in upper primary and lower secondary stages. Indeed, focusing on the lowest attaining pupils, one-fifth of the S2 pupils failed to demonstrate 'basic skills' at Level D, the level below their formal expected level. The pace of learning, and particularly approaches to consolidation of previous learning, rather than 'pushing on' to the next level, may both need to be reviewed for S1-S2.

There is no evidence of any real change in pupil performance over time. The last survey of mathematics in 2000 assessed pupils at P4, P7 and S2 so there is only a possibility of comparing performance over time at the P7 stage (Levels C, D & E) and S2 stage (Levels D, E & F). The small sample differences in attainment do not reach statistical significance. There is similarly no evidence in the survey data of any difference in the mathematics attainment of boys and girls.

The evidence from the survey highlights some issues in mathematics attainment in the P7 and S2 stages. The data show relatively low proportions achieving the expected level of attainment within these stages given the pattern of development evident in the earlier stages. Any of these concerns assume the validity of the expected level within the reported findings. One response might be that the expected levels, as determined in 1991, are in need of review. This is not the first AAP mathematics survey to highlight a shortfall in meeting the set levels, so there might be an expectation to review the targets in light of any year-on-year evidence. It is not, however, an across the board change that is highlighted, but rather a particular issue at the transition stage and early years of secondary provision.

The questionnaire evidence, gathered from a subset of the pupils and staff, highlights some interesting and pertinent points for consideration. Firstly, the majority of pupils at all stages considered mathematics to be important for later learning in other subjects and for future occupations, and they wanted to do well in the subject. Secondly, the majority of the pupils at all stages found mathematics an easy subject, were happy with the pace of work, were rarely left behind, and rarely found it difficult to catch up if they missed a lesson. Thirdly, the questionnaires acknowledged pupils were less positive about looking forward to lessons, with enthusiasm for mathematics learning decreasing with increasing age. These views will present further challenges for staff but it is reassuring to note the high regard and value pupils have for the subject and its importance for future options.

However, if pupils find it easy to catch up having missed a lesson, are rarely left behind and find it all fairly easy, then this suggests scope for higher expectations and greater demands to be made of pupils who are keen to do so well. The evidence of progress at the level below the expected level highlights the need to consolidate learning and to maximise the number of pupils who demonstrate a 'secure' understanding or 'considerable strengths' at whatever level is being pursued; as currently witnessed in the P3, P5 and P7 stages. At S2 the survey findings indicate only 60% of the pupils were secure at Level D, with 30% demonstrating considerable strengths. This is well down on the pattern of progress in the other stages.

No comment can be made about S2 pupils' performance at Level C, as that level was not assessed in the survey. It would be interesting to note the level of security and strength demonstrated at Level C as pupils finish their studies in S2 - how far has this progressed from the comparable performance of 40% of P7 pupils showing considerable strengths at Level C? Have the lower levels of study been fully explored and truly understood in preparation for further study as the pupils follow their chosen national qualification courses in later years? It would be reassuring to acknowledge an ever-increasing proportion of pupils demonstrating considerable strengths in the lower level attainment outcomes.

7.2.2 Problem solving

The scale of the survey permitted an exploration of pupil performance in the different attainment outcomes, but in terms of averaged percentage item scores because individual pupils only attempted a few items from any one outcome. There was little variation in the performance between the outcomes covering Information Handling, Number, Money & Measurement and Shape, Position & Movement, but a marked difference was noted in the problem solving items at all stages and levels in the pencil and paper assessments. It is almost as if the development in problem solving is phased by one stage, with comparable item scores recorded at the later date. Performance in Problem Solving at each of P5, P7 and S2 is comparable to the performance in the other attainment outcomes at the expected level for the earlier stage. For example, the average percentage item score at Level C in P5 [53%, 73%, 60%], is close to the Problem Solving performance at the same level in P7 [60%]. There is a similar picture for both Level D and Level E in the later stages (see Table 2.7, page 17).

As an attainment outcome, Problem Solving is not detailed in the Guidelines by 5-14 level as each of the other outcomes is presented. It is therefore more difficult to be certain of the 'level', other than the fact that the items are more complex and usually involve more than one step. It is not unsurprising that problem solving performance is lower within each stage, replicating findings from earlier AAP mathematics surveys, but it is interesting to note this later development to an equivalent performance level, reflecting the increasing competence as other attainment outcomes are progressed to a higher level.

Problem solving items usually contain more words and may require comprehension and interpretive skills as well as mathematical ones. It is interesting to compare pupils' problem solving performance with performance in 'mathematics literacy' tasks administered by the field officers. At each stage, the data in Tables 2.7 and 2.9 (pages 17 and 19, respectively) illustrate some overlap with comparable 'average percentage item scores' in problem solving and maths literacy.

The lower problem solving performance could be explained by the pupils' restricted ability to interpret data, in combination with readability level and complexity of the tasks concerned. Pupils could benefit from more opportunities to develop literacy within mathematics. All teachers have a responsibility towards literacy within the initial teacher education Standards ¹³. Given the overlap between problem solving performance and performance in the maths literacy tasks, further opportunities to consider such contexts will ideally support problem solving and in turn potentially influence pupils' general mathematical attainment.

In comparison with earlier survey data it should be noted that problem solving has not improved over time. The average percentage item scores at the expected levels for P7 and S2 in the 2000 survey were each 49%. The survey data for the same stages in this survey at Levels D and E are 47% and 41%, respectively. The survey data confirms that problem solving is an area of mathematics that continues to need attention, particularly at the S2 stage.

7.2.3 Mental mathematics

There is a clear picture of difference between recorded performance on the 'pencil and paper' items and those items presented to pupils orally. Average item scores were generally 10-15 percentage points higher for the mental testing at each level (the small numbers of mental items attempted at each level by individual pupils preclude the reporting of percentages of pupils attaining levels). This is a very encouraging finding given the recent emphasis that has been placed on mental calculation strategies and mental approaches to mathematics.

The picture of performance is very similar to that reported in 2000 for the expected levels at P7 and S2. In the 2000 AAP Mathematics survey it was noted that changes in classroom practice, such as the increased attention to mental approaches, might influence attainment in both mental calculation and possibly other areas of mathematics ¹⁴. This increased performance in mental mathematics has not as yet significantly affected other aspects of mathematics, as suggested in the 2000 survey report. However, the picture of attainment in mental mathematics is a positive one.

7.2.4 Practical mathematics

Four resource-based practical mathematics tasks were newly developed for this survey. Each task comprised a series of questions and activities, progressively moving from Level A to Level E, each designed to be completed in an interactive session with a field officer. This component of the survey provided a more in-depth exploration of particular topics. On this occasion, we have data on 'money', 'time and measure', 'fractions, percentages and ratio' and 'shape, angle and direction' .

Focusing on 'fractions, percentages and ratio' through this practical sequence of tasks was potentially the most interesting, because of the historic weaknesses that have been reported through AAP surveys on this aspect of mathematics. The inclusion of 'angle and direction' provided an insight into the 'Position and Movement' strand of Shape, Position & Movement, where turtle graphics are located.

• Success rates were generally higher at P7 and S2 than at P5, and higher at P5 than at P3, and success rates naturally fell as the level of the activity demand increased.

Money, Time and Measure

• At P5, P7 and S2, 90% or more of the pupils successfully carried out the various activities involving money. Performance was lower at P3, particularly when pupils were required to calculate and deliver change rather than simply to offer coins up to a given price. Discount problems were handled well by half to three-quarters of the S2 pupils.

High proportions of pupils were competent in all the money handling activities at Levels A to D. The exception to this rested with subtraction and calculating change. The context might well have assisted the completion, but the task that threw up anomalies was fairly straightforward: Calculate change for £3.75 from £5. More than half the P5 pupils were unable to do this with minimal support and nearly a third of P7 pupils were unable to complete this task. Surprisingly, a similar calculation requiring the change for £17.99 from £20 was more successfully completed, with over 50% of the P5 pupils and over 70% of the P7 pupils coping with minimal support. This may have as much to do with the emphasis placed on mental calculation discussed earlier than anything to do with the numbers themselves.

The other items that presented difficulty link in with percentage calculations:

'Find 50% of £120' 'Find 25% of £22'

Only half of the P7 pupils managed to find the first of these items and this reduced to a third who managed the second. The corresponding figures for the S2 pupils are 77% and 53%, respectively. Halves and quarters are not 'new' to the pupils, but percentages are only mentioned for the first time in Level D, the expected level for most of P7.

The picture of performance on time and measure was very positive at P7 and S2. The one difficulty that seems to be highlighted concerned the setting of an analogue display. The tasks of setting the analogue display to: "twenty five to one", "6:42" and "13:05" given digital displays, resulted in a decreasing proportion of P5 pupils responding correctly. The targets in the 'Time' strand of Number, Money & Measurement offer examples of what might be expected, but they are limited in nature. One possible reason behind such a poor response may be the level of interpretation being made within the Guidelines, where there is scope to be more inventive and extensive in challenging pupils to demonstrate 'secure' knowledge or indeed 'considerable strengths' rather than settling for a 'basic' level of understanding. The interpretation required in this strand is perhaps more obvious than elsewhere but the same principle of ensuring appropriate challenge to the pupils holds, as expressed in the section commenting on pencil and paper written assessments.

Fractions, Percentages and Ratio

• The fractions/percentages task revealed a steady attainment progression through the four stages, with particularly marked attainment gaps between P5 and P7 at Level D (percentages) and between P7 and S2 at Level E (ratio).

The proportion of pupils correctly responding to the tasks in this topic was generally lower than in the other practical activities. The majority of pupils in P7 and S2 pupils were familiar with halves and quarters and could 'work with' these fractions successfully. But when the actual tasks reported in Chapter 3 are looked at, it is interesting to note that difficulties begin to appear in reasonably straightforward situations. Particular tasks that caused difficulties included work with basic fractions (fifths, eighths, three-quarters), standard percentages (20%, 50%), as well as compound percentages that might involve multiple steps (15%, 60%), all presenting increasing difficulties, even for the upper stages in the survey. The major concerns lie within the performance from the P7 and S2 stages, where more might certainly be expected in handling such calculations. The interrelationships between fractions and percentages (and decimals) need to be strengthened through multiple-exposure to practical activities - interestingly, the use of 'square grids' as opposed to 'cubes' presented varied responses and difficulties, as illustrated in Table 3.3 (page 28).

Shape, Angle and Direction

• A variety of activities involving naming and drawing shapes and angles again revealed clear evidence of stage progression. Turtle programming was successfully achieved by 20-30% of the P3 pupils, 45-60% of the P5 pupils and 70% or more of the pupils at P7 and S2. Similar proportions of pupils at the different stages were successfully able to use a compass to identify direction.

One glaring discrepancy in this set of tasks came into Level C, where pupils were asked to "count the angles on the triangular prism" - not an unsurprising difficulty, given it is a rather unlikely and unusual activity for pupils to consider the number of angles in a 3D shape. Another cluster of tasks that highlighted a potential concern, focused on the 90-degree angle. A lot of emphasis is placed on this particular angle in the development of the angle strand at Level C, yet only 43% of the P5 pupils were able to correctly identify a 90-degree angle. A similarly low proportion of P5 pupils were correctly able to provide an alternative name for the angle (right-angle), or to identify and name an angle less than 90 degrees (acute). The proportion of P7 and S2 pupils able to do these tasks improved across the stages but the fact that the Level C task presented such difficulty for the P5 group remains a matter of concern.

7.3 Core skills attainment in 2004

The core skills of reading, writing and using ICT were assessed within a mathematics context in the 2004 survey.

7.3.1 Reading

The reading attainment of more than 5000 pupils in almost 800 schools was assessed using multi-item tasks based on texts set in mathematics contexts (e.g. featuring famous mathematicians). No prior mathematical knowledge was needed in order to show evidence of reading comprehension.

• Over 65% of the P3 pupils were estimated to be 'secure' or better at Level A (i.e. gaining at least 65% of the marks on their Level A task) and over half were also secure at Level B; over 80% of the P5 pupils were estimated to be secure at Level B and over half were also secure at Level C.
• Between P7 and S2 there is similarly clear evidence of continued stage progression, particularly at Levels D and E. At P7, 80% of the pupils were estimated to be secure at Level C, 60% at Level D and just over 15% at Level E. Corresponding proportions for S2 are 85%, just under 75% and just under 30%.
• There were significant gender differences in reading attainment at P3, P7 and S2, the girls generally outperforming the boys, and with strong evidence of topic effects.

A comparison with core skills reading in social subjects and science surveys (2002 and 2003 respectively) can be made, although any conclusions must be tentative because of statistical errors which may be high when task to task variation is properly taken into account. However the data suggest that, in comparison with previous surveys, where core skills in reading were assessed, pupils' performance has been stable across surveys for P3 at Level B. Slight improvement is noted, from that observed in the 2003 Science survey ¹⁵, for the P5 pupils at Levels B and C. For P7 pupils, slight improvements from the science survey at Levels C and D are reported, but for S2 a more mixed profile is observed with an improvement at Level D but a slight decline at Level E compared with the surveys in social subjects ¹⁶ and science (2002 and 2003 respectively).

7.3.2 Writing

Pupils attempting reading tasks were also invited to produce a piece of writing, with the reading task content as stimulus material. In total, over 3000 pieces of writing were evaluated using a 'best fit' scheme, the scripts having been drawn at random from a larger set. Three independent teacher-raters evaluated each script, with around 80% of the scripts classified in the same way by at least two raters. This process represents a significant improvement on previous surveys where results were based on single evaluators and as such has provided more reliable data. There was an expected stage progression evident in the resulting attainment decisions:

• The proportions of scripts judged to be at Level B or higher rose from almost 40% at P3 through around 75% at P5 and just over 85% at P7 to over 90% at S2. Around a quarter of the S2 pupils were judged to be at Level D and just fewer than 10% at Level E.
• There were significant gender differences in writing quality at all stages, with the girls tending to produce the better writing.

Minimal change has been noted over time in the core skill of writing. An improvement at P5 in Level B is noted; where figures of 57% and 56% were reported in the Science and Social Subjects surveys, but the three surveys all report a similar experience in S2 - not an encouraging situation with less than 10% of the cohort meeting the expected Level E over the period 2002-2004 in subject-based writing.

7.3.3 ICT skills

Over 1300 pupils in over 340 schools participated in the assessment of ICT skills: 250-400 pupils per stage. Pupils undertook their tasks individually, using a laptop computer supplied by an observing field officer. The findings show clear evidence of age-related progression, with the majority of P7 and S2 pupils competent in most aspects.

• High proportions of the pupils at all stages (typically 90%+) claimed familiarity with use of keyboard and mouse. Familiarity was also high for P7 and S2 with respect to the operating system ( PC/Windows) used for the assessments, but markedly lower at P5 and P3.
• High proportions of P7 and S2 pupils were also familiar with Word, proportions dropping to a third for P3 pupils
• Familiarity with Excel was much lower, from over half the S2 pupils to almost none of those at P3.
• The majority of pupils at P7 and S2 were competent when using the technology (opening a folder, scrolling a file, saving text under a new name, etc), the proportions being lower for P5 and lower still for P3, with variation depending on the specific task.
• Text handling and graphic manipulation ('creating and presenting') were also well done in general by most pupils at P7 and S2. Justifying text, creating two or more columns of text, bulleting and wrapping text were the most challenging tasks.
• Table handling ('collecting and analysing') proved more difficult than text handling and graphic manipulation in general, but again there was very clear evidence of skills development with age.

The use of a spreadsheet is an explicit target from Level D onwards, so the fact that spreadsheets were less well developed is a matter of concern. Indeed, there is not much of a progression across the stages as can be seen from the specific tasks reported in Table 4.17 (page 46).

The ability to interpret a chart is stronger than the other aspects assessed. This is probably not to do with the use of ICTper se, but more a consequence of this type of activity being explored through conventional texts and other resources.

The quality of resources and availability of ICT is high, but this does not appear to have had a direct impact on pupils' opportunities or performance in using spreadsheets.

When invited to rate the quality of various resources, differences in the rating patterns of primary head teachers and S2 principal teachers frequently reached statistical significance, with primary head teachers being the more positive. School managers certainly report a positive picture of ICT resources (internet and computer access) being available for staff, with 90% of primary teachers and nearly 70% of secondary teachers having 'Good' or 'Very good' quality of provision. Pupil access is less favourable, according to their questionnaire responses, but nearly 80% of primary pupils and over 60% of secondary pupils are nevertheless well placed to access ICT resources in their learning.

Comparing this provision of ICT with actual use, as reported by class teachers and pupils, it is evident that pupils rarely work at the computer on their own or with a partner. In S2 this accounts for 50-60% of the pupils, with a further 30% gaining termly access. For the primary stages, the picture is slightly stronger with about 50% of the pupils having weekly access and a further 40-45% having termly access. It must be assumed that specific mathematical development using spreadsheets does not feature highly in the time devoted to ICT.

It was interesting to note the way pupils' responses did not seem to be adversely affected by the fact they completed the tasks on a PC base when they were used to working on a Macintosh system. One of the most frequent criticisms from field officers was the fact that pupils were often using unfamiliar equipment and software. This highlights the pupils' ability to be very adaptable when it comes to technology, with a brief laptop familiarisation being sufficient introduction before successfully completing the various tasks. Home resources will also play a part in this confident use of ICT, with 65-80% of the pupils reporting computer access at home.

Given such familiarity and confidence in the pupils' use of ICT, staff could exploit the wealth of ICT resources to greater effect. The survey reports up to 74% of the S2 pupils not usually or never having access to a computer to do their work during mathematics lessons. Slightly fewer pupils in P7 and P5 registered such limitations, with 67% and 70%, respectively, falling into the same category. There are likely to be staff development issues here in raising staff confidence to use the available technology to best effect. Recent research has indicated that many teachers lack the confidence to take the risk of using technology in their subject areas, although they have reasonable facilities at school and they use computers at home. As staff use increases, it might be reasonable to expect this will filter through to enhance pupils' opportunity to access ICT.

As pointed out in Insight 20 (2005) ¹⁷, reporting on the impact of ICT in Scottish schools, availability of hardware and software is not of itself enough to progress the use of technology in classrooms. There is a lot more to integrating ICT into the educational experience of pupils than ensuring there are networked machines and that the recommended ratio of computers to pupils is met. Staff development is a high priority in this core skill, making high demands on time - time for staff to learn new skills, to find out about resources and technologies, to plan and try out new approaches to teaching and learning, and to reflect upon and consolidate their experiences. It is unlikely that the ICT initiatives can be sustained through individual enthusiasts alone. The profession needs to move forward together, in a suitably supported manner to ensure that pupils experience a level of ICT they are becoming accustomed to in other areas, in particular the home environment that for many is of a higher quality than that currently experienced in schools. The use of word processing packages is currently good, but there is scope for further development of spreadsheets within the mathematics activities. There was no indication in the performance data of any difference in the ICT skills of boys and girls.

7.4 Key issues for consideration

The findings from the survey highlight a number of issues relevant to future developments in learning and teaching mathematics in primary and lower secondary school. There are clearly positive messages to be taken from this survey but it also raises issues for staff development and review of provision within the 5-14 stages.

• The current review of the curriculum could usefully reconsider levels and expectations, based on experiences over multiple AAP surveys and other evidence that might guide such a review, so that realistic expectations are made of pupils at each of the key stages. The reference group acknowledged the need to strive for 'secure' knowledge and 'considerable strengths', favouring depth of treatment in the earlier stages over any pushing on prematurely. This calls for teachers at all stages to interpret the 5-14 guidelines in the fullest way to challenge the pupils in their care.
• The pace of pupils' learning needs to be reviewed and consolidation of study is required to ensure that 'secure' knowledge and understanding or 'considerable strengths' can be demonstrated across the different attainment outcomes at each stage.
• Pupils' enthusiasm for mathematics learning decreases with increasing age, yet the majority of pupils across all stages considered mathematics to be important and they wanted to do well.
• Problem solving is an area that continues to need attention, particularly at the S2 stage.
• The picture of attainment in mental mathematics is a positive one, although this has not as yet significantly affected other aspects of mathematics as suggested in the report on the 2000 AAP mathematics survey.
• There are significant gender differences in reading attainment and in the quality of writing across most stages, with girls tending to outperform boys.
• Core skills of reading and writing are the only aspects that have shown a gender difference in favour of girls. As all teachers have a responsibility to promote literacy, perhaps the model explored in the core skills part of this survey could be pursued more widely in mathematics classrooms. Books 'about mathematics' are not widely accessed by pupils, or strongly identified as a positive motivator, but they could provide a link with literacy, something that is currently missing. Such activity might close the gender gap through more regular exposure to mathematical texts with the opportunity to write about them within a supported framework. Pupils have not reported a lot of interesting topics or investigations in their study of mathematics and it is clear that problem solving continues to be a matter for concern. It is worth considering what scope there is for broadening pupils' experiences within the level of study, embracing more problem solving, mathematical literacy tasks and generally consolidating knowledge, skills and understanding to gain secure status and considerable strengths in preference to any premature acceleration, that may be a factor in the declining standards evidenced in the S2 profiles.
• Mathematics literacy tasks provide contexts that potentially support problem solving and in turn pupils' general mathematical attainment.
• High quality ICT provision is under-utilised. Class teachers and pupils report limited use of ICT in mathematics classes yet home access is good, suggesting scope for fuller use within subject teaching. Use of spreadsheets seems to be particularly limited.
• Pupils' appreciation of the importance of mathematics and their enthusiasm for learning needs to be capitalised upon to ensure they remain motivated as they move through the stages. Given the high quality of ICT reported as being in schools, it is important to fully utilise these resources with pupils in the classroom. Pupils appear to be confident in their use of ICT, increasingly gaining access at home, so it clearly makes sense to capitalise on this ever-expanding learning resource in a more formal capacity.
• There is scope for more inventive and extensive interpretation of the guidelines when it comes to reviewing 'examples' within any strand e.g. Time, Fractions & Percentages. The aim should be for 'secure' knowledge and understanding or 'considerable strengths' to be demonstrated within strands and attainment outcomes.
• Staff development opportunities will need to be supported - an aspect that appears to be worthy of support is an unpacking of what 'consolidation' might entail to ensure staff are comfortable with their interpretation of the guidelines, going beyond the stated targets but working within the level of study and resisting the temptation to accelerate towards the higher levels. Another staff development opportunity would be within the ICT domain, providing support for staff to extend their personal knowledge (subject and pedagogical) and confidence with their use of ICT to maximise the classroom use of the resources that are now reported to be in schools.

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