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6. Teachers' reports on mathematics in the schools

6.1 The teacher questionnaires

Teacher questionnaire enquiries were incorporated into the survey at all stages. The questionnaires, which were designed to gather information about the provision and resourcing of mathematics in the schools, and to invite teachers' views about the quality of different aspects of pupils' mathematics experience in classrooms, were sent to a randomly selected half of the survey schools. One questionnaire was designed to be completed by school managers, i.e. primary school head teachers and S2 principal teachers, while the other was designed to be completed by class teachers at P3, P5 and P7 and by S2 mathematics teachers (both questionnaires are reproduced in Appendix F).

In the school managers' questionnaire, respondents were asked in what year their current mathematics programme was introduced, what were the bases for the course/programme, and whether it was currently under revision. Respondents were also asked to indicate on what basis the school reported pupil progress to parents, after which followed an invitation to rate the quality of various aspects of subject resourcing and related issues, and then to evaluate pupils' motivation for learning mathematics, teachers' expectations of pupils and teacher morale.

The class teacher questionnaire began with a set of demographic questions, followed by an enquiry into the nature of mathematics lessons at the stage concerned: respondents were asked how frequently their pupils engaged in different activities when studying mathematics, and how much use they themselves made of various kinds of resource materials in mathematics lessons.

6.2 Responses of primary head teachers and secondary principal teachers

6.2.1 The respondents

In the subsample of schools contacted, the school managers' questionnaire was completed by 303 head teachers/principal subject teachers: 245 primary head teachers (75 from schools in which P3 pupils were assessed, 76 from 'P5 schools' and 94 from 'P7 schools') and 58 secondary mathematics principal teachers. These figures translate to response rates of 65-70% in each sector.

6.2.2 Courses/programmes

In the primary schools where head teachers responded to the questionnaire, just over half (52%) the current mathematics programmes had been introduced in 2000 or later, compared with two-thirds of the S2 programmes in the responding secondary schools. Around 40% of the primary programmes, whether introduced prior to 2000 or later, were currently under revision. In the secondary schools, all the programmes introduced before 2000 were currently under revision, as were 80% of those introduced more recently.

Table 6.1 confirms that the most popular bases for mathematics programmes in both sectors were the national 5-14 guidelines (91% of the primary head teachers and 90% of the S2 principal teachers checked this option) and commercial textbooks and resource packs (89% in the primary sector and 95% at S2). The school's (or department's) own materials featured significantly more often among the S2 principal teachers' responses compared with the primary head teachers (42% of the primary head teachers indicating these compared with 57% of the S2 principal teachers), while local authority 5-14 guidelines were mentioned significantly less often by the S2 principal teachers than by the primary head teachers (54% of the primary programmes were based on this and other resources, compared with 26% of the S2 programmes). Other possible resources were used infrequently in either sector.

The following are a selection of comments offered on the question of programmes of work ( PHT - Primary head teacher, SPT - Secondary principal teacher):

We are looking at maths as an area of development for our HMI action plan and hope to augment materials during this time. [ PHT]

We have opted into proposals of developments in mathematics in Scottish Borders council in year 1, 2004-5. It is also a major part of our school improvement plan over the next two sessions. [ PHT]

Although our current maths programme has been in place for some time, components are updated, e.g. mental maths, problem solving, data handling on computer. [ PHT]

At present Scottish Heinemann is being phased into school at primary 1 and 2 stages August 04. … [ PHT]

This year, 2003/2004, we have introduced a new core scheme for learning/teaching mathematics. The scheme was evaluated in February 2004 and found to be very good for most pupils. High achieving pupils, however, require additional resources. We are currently reviewing extra resources for pupils who are gifted in mathematics. [ PHT]

Maths programme/scheme has been added to give breadth. However there is financial constraint on adopting the Scottish version of the scheme used as the core. [ PHT]

Modifications have been made to the maths programme each year since it was introduced in order to suit children's learning. [ PHT]

We have steadily been redeveloping the maths programme throughout the school. This development has included the introduction of formative assessment approaches. We are in the process of developing the programme for P6, having successfully introduced a similar approach across P1 to P5. Our P7 programme will be addressed in due course and will be formed in consultation with the high school. [ PHT]

We reviewed our maths curriculum at the beginning of the session. However, Edinburgh has introduced a new 10-14 curriculum for maths which will be implemented in August. [ PHT]

We would like to update our commercial resources. …Unfortunately, this is impossible given our financial circumstances. DSM budgets in the borders have been at a standstill for several years now and funding for such improvements is simply not there. [ PHT]

… I have been looking at condensing Maths in Action text books 1 and 2 into a first year course. I don't think there is enough to challenge the more able pupils. [S2]

This coming session we have bought many new resources to hopefully see a big improvement. [S2]

We have a 'creating time to learn' programme which is being phased in - it is basically a broad-banded approach with acceleration for the upper half. [S2]

With regard to methods of reporting pupil progress to parents, Table 6.2 shows very clearly that almost all the schools at both stages (98% primary, 95% secondary) reported to parents in terms of 5-14 levels, with high proportions also using teachers' own comments (89% primary, 93% secondary).

As far as other methods of reporting progress to parents are concerned, pupil progress at S2 was significantly more often reported in terms of marks or grades for effort (60% mentions by S2 principal teachers compared with 26% from primary head teachers), percentage marks in end of unit tests (17% compared with 3%) and percentage marks in end of year tests or exams (14% compared with just 1%). In contrast, comment banks were significantly more often used by the primary schools for reporting to parents than by the secondary schools (48% of primary head teachers checking this option compared with 31% of the S2 principal teachers). Among the 'other' possibilities mentioned by 21% of the S2 principal teachers were grades for quality of class work and of homework, a 1-5 scale covering the whole cohort, an average percentage relative to the class average, detailed comment on strengths and weaknesses, and an indication of progress into next levels.

6.2.3 Quality of resourcing and other issues

Using a four-point rating scale ('very good', 'generally good', 'fair' and 'unsatisfactory'), the school managers were invited to rate the quality of each of the following with respect to their pupils (P3, P5, P7 or S2, as appropriate): the availability of learning support, the availability of teaching/learning resources, the availability of computers for teachers and for pupils, internet access for teachers and for pupils, school/departmental accommodation, pupils' class attendance and behaviour, and parental support.

As there were no significant differences among the three groups of primary head teachers, with regard to pupils at P3, P5 and P7, Table 6.3 simply compares the responses of the primary head teachers, as a group, with those of the S2 principal teachers.

As Table 6.3 shows, among the primary head teachers the most positive ratings were given to computer and internet access for teachers and for pupils, and for pupil attendance at, and behaviour in, subject classes. The 'very good' proportions varied between 54% (internet access for teachers) and 37% (pupil access to computers). Differences in the rating patterns of primary head teachers and S2 principal teachers reached statistical significance for most aspects, including the availability of computers for teachers and for pupils, internet access for pupils, pupil attendance in classes and pupil behaviour in mathematics lessons. Interestingly, there was no difference in the rating patterns of the two sectors for teachers' in-school access to the internet. Parental support for their children's learning was less highly rated in both groups, as was the availability of learning support or enrichment for individual pupils in mathematics.

The following are some of the volunteered comments on resourcing and other issues covered here:

Due to a fire in school two years ago we do not have internet access for pupils readily available. We are in the midst of a rebuild and many classes are working out of hutted accommodation. [ PHT]

Internet access due to improve via broadband 2004-7. [ PHT]

Accommodation impacts on the ability to have computers. School is currently trying to develop its own ICT facility - self funded. [ PHT]

Internet access is a fairly new resource in school. [ PHT]

Our internet access has only been available for a few weeks. However it is now available in all classrooms. [ PHT]

Broadband/airport technology being introduced at present should ensure better access in future. [ PHT]

Parental support varies from stage to stage. However we have noted a marked lack of interest by parents in general at the early stages over the past few years. Home/school activity sheets are not well supported. [ PHT]

This school is the most socially deprived primary school in the authority and we experience the related difficulties of deprivation, such as poor attendance, parents/carers of limited skills in literacy & numeracy, and impoverished home environments. [ PHT]

6.2.4 Pupil motivation, teachers' expectations and teacher morale

The final enquiry in this questionnaire invited the respondents to evaluate the motivation of their pupils to learn mathematics, the expectations their teachers had of pupils to achieve in this subject, and the morale of teachers in their school or department. The results are shown in Table 6.4.

For teacher expectations of pupil achievement in mathematics, there was no significant difference in the rating distributions for the two groups: just under 60% of the respondents in each case evaluated this as 'very high'. But there were statistically significant differences between the groups in their evaluations of, particularly, pupil motivation to learn (with 94% of the primary head teachers rating this as 'very high' or 'moderately high' compared with 69% of the S2 principal teachers) and teacher morale (39% of the S2 principal teachers rating this 'fair' or 'low' compared with just 8% of primary head teachers).

The following comments relate in particular to these issues:

Although staff have high expectations of pupils many are not supported at home, e.g. tables not known, and late coming and absence also affect learning and teaching. … However there are groups of pupils who are motivated and supported. [ PHT]

Motivation of pupils tends very much to be influenced by individual members of staff. [ PHT]

Interactive teaching and learning is beginning to impact on children's motivation. However having children in class with SEBD has a detrimental effect on other children and the teachers' ability to deal with and focus on mathematical problems. [ PHT]

The skill of the teacher in motivating pupils is paramount in mathematics. A variety of strategies, i.e. interactive methods, opportunities to demonstrate learning to peer group, opportunities for independent learning, ensure that pupils are supported and challenged. [ PHT]

Self motivation of pupils a big problem. Very few possess a good work ethic. There is a lack of achievement due to lack of effort, parental support at parents' nights, and 40 percent (better for able pupils) pupils tend to give up when the going gets hard at lower end. Up to 40 pupils out of 150 are working at Level A/B. [ SPT]

We have a significant number of challenging pupils. Depending on the composition of the group behaviour varies from good to unsatisfactory. Difficulty in persuading children to purchase and bring calculators. Homework response is poor in most classes. School has been earmarked for closure. [ SPT]

6.3 Responses of P5 and P7 class teachers and S2 subject teachers

6.3.1 The respondents

In total, 293 class/subject teachers in 270 schools responded to the questionnaire: 70 P3 teachers in 67 schools, 73 P5 teachers in 70 schools, 90 P7 teachers in 86 schools, and 60 S2 mathematics teachers in 47 schools. These figures represent response rates on the part of schools of around 60%.

Among the primary class teachers, 93% were female, compared with 52% at S2. All the S2 teachers were teaching mathematics and 92% of them had mathematics degrees. Few of the primary class teachers held a degree qualification involving mathematics (2%).

6.3.2 Current teaching situations

The numbers of years respondents had been teaching and the numbers of years they had been in their current posts were positively correlated (0.6-0.7), with both variables ranging widely in both sectors, from one year to decades.

Class sizes varied very widely in both sectors, from one pupil to over 30 in primary schools, and from 9 pupils to a reported 33 pupils at S2. On average, class sizes were around 24 in the primary schools and 27 at S2. Class contact time was six hours per week on average in the primary schools and four hours at S2. Primary teachers reported their lesson preparation time to be four hours a week on average, whereas among the S2 teachers the weekly average was just two hours.

The respondents were asked how often they met with other subject teachers to talk about professional issues in mathematics. As Table 6.5 shows, there was a clear, and statistically significant, difference between the response profiles of the primary class teachers and the S2 mathematics teachers: over half the S2 mathematics teachers (55%) indicated that they met with colleagues once a week or more frequently to discuss mathematics education issues, compared with around one-third (34%) of the primary class teachers.

When asked how well motivated they thought their pupils were to learn mathematics, just over a quarter of the class teachers in both sectors (27%) responded 'very well'. However, a higher proportion of the S2 teachers than the primary teachers were negative in their perceptions of pupil motivation: the proportions checking 'not very well' or 'not at all' were 16% and 2%, respectively.

6.3.3 Learning activities in the classroom

The teachers were asked to rate 18 different learning activities, in terms of how often they estimated that their pupils were engaged in each. The findings are illustrated in Figure 6.1 and detailed in Appendix G.

Figure 6.1
Frequency of learning activities in lessons
(% teachers indicating each frequency among 233primary teachers and 60 S2 teachers)

The teachers' reports on lesson activities closely reflect those of their pupils (see Figure 5.1 in Chapter 5). According to the majority of the teachers in both sectors (83% at S2 and over 55% at P3/P5/P7), pupils are taught as a class for at least some of the time in most lessons. Group teaching, however, was significantly less prevalent at S2 than at P5/P7 (just 6% of the S2 teachers agreeing that pupils were taught as a group in most lessons, compared with over 70% of the primary teachers). At all the stages the majority of pupils spent at least some of the time in most maths lessons writing in their jotters and files (90% at S2 and just over 80% at P5/P7). Pupils also worked in pairs for at least some of the time in most lessons in around 60% of the S2 classes. In the S2 classes the evidence is that pupils more often used tools and instruments in investigations than did their younger peers, and they also used maps, drawings and diagrams more frequently. Use of computers in class was relatively rare in both sectors, but particularly at S2: around a third of the S2 teachers claimed that their pupils 'rarely' used computers in small group work and almost 60% reported the same for pupils working alone on a computer. Mathematics lessons were rarely carried out in the school grounds or outside the school, according to the teachers' responses.

6.3.4 Learning resources used in class

The teachers were asked how much use they made of 5-14 guidelines and various support materials in their lessons. The results are shown in Table 6.7, where we can see that among the S2 subject teachers the most frequently used resource was the department's own materials, half of the teachers reporting use of these 'in most lessons'. This compares with around a third of the primary teachers reporting similarly frequent use of their own school's materials, although another 40% used them every week.

The national 5-14 guidelines were less frequently used by S2 teachers than by primary teachers, just one-third of the former compared with half of the latter claiming to use these in most lessons; local authority 5-14 guidelines were used this frequently by 30-40% of the teachers in each group. Commercial textbooks and/or resource packs were used 'in most lessons' by over a third of the S2 teachers and just under half the primary teachers. Over a quarter of the teachers in both groups used materials they had developed themselves in most lessons, with another 30-40% using them most weeks.

Materials produced by a teachers' group or association, by other schools or by another education authority were the least used resources in both sectors.

6.4 Summary

The school managers' questionnaire was completed by 245 primary head teachers and 58 secondary mathematics principal teachers (a 65-70% response rate), and the class/subject teachers' questionnaire was completed by 233 primary teachers and 60 S2 mathematics teachers (a response rate of around 60% of the schools).

According to the head teachers and principal teachers who responded, just over half the current mathematics programmes in the primary schools had been introduced in 2000 or later, compared with two-thirds of the S2 programmes in the secondary schools. Around 40% of the primary programmes were currently under revision, along with the majority of the programmes at S2. The most popular bases for mathematics programmes in both sectors were the national 5-14 guidelines and commercial textbooks and resource packs. The school's (or department's) own materials featured significantly more often at S2 than in the primary school, with the reverse holding for local authority 5-14 guidelines. This was confirmed in the responses of the class/subject teachers with regard to the resources they used in their mathematics teaching: Other possible resources were used infrequently in either sector.

With regard to methods of reporting pupil progress to parents, almost all the schools in both sectors reported to parents in terms of 5-14 levels, with high proportions also using teachers' own comments. Compared with the situation in the primary sector, pupil progress at S2 was significantly more often reported in terms of test/exam results or marks/grades for effort. In contrast, comment banks were significantly more often used by the primary schools for reporting to parents than by the secondary schools.

When invited to rate the quality of various resources, differences in the rating patterns of primary head teachers and S2 principal teachers reached statistical significance for most aspects. Interestingly, there was no difference in the rating patterns of the two sectors for teachers' in-school access to the internet. Parental support for their children's learning was only moderately well rated in both groups, as was the availability of learning support or enrichment for individual pupils in mathematics. Among the primary head teachers the most positive quality ratings were given to computer and internet access for teachers and for pupils, and for pupil attendance at, and behaviour in, subject classes.

Most respondents in both sectors gave high ratings to teacher expectations of pupil achievement in mathematics. But for pupil motivation to learn and teacher morale, the primary head teachers gave significantly more positive ratings than the S2 principal teachers. When asked how well motivated they thought their pupils were to learn mathematics, just over a quarter of the class/subject teachers in both sectors responded 'very well'.

Class sizes varied very widely in both sectors, with an average of around 24 in the primary schools and 27 at S2. Class contact time was six hours per week on average in the primary schools and four hours at S2. Primary teachers reported their lesson preparation time to be four hours a week on average, whereas among the S2 teachers the weekly average was just two hours. Over half the S2 mathematics teachers indicated that they met with colleagues once a week or more frequently to discuss mathematics education issues, compared with around one-third of the primary class teachers.

According to the majority of the teachers in both sectors, pupils were taught as a class for at least some of the time in most lessons, while group teaching was significantly less prevalent at S2 than in the primary sector. Pupils also spent at least some of the time in most maths lessons writing in their jotters and files, and worked in pairs for at least some of the time in most lessons in the majority of the S2 classes. The evidence from the teachers' responses is that S2 pupils more often used tools and instruments in investigations than did their younger peers, and they also used maps, drawings and diagrams more frequently. Use of computers in class was relatively rare in both sectors, but particularly at S2, and mathematics lessons were rarely carried out in the school grounds or further afield.

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