An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Saint Catherine’s Vocational School
Killybegs, County Donegal
Roll number: 71241W
Date of inspection: 21 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St Catherine’s Vocational School. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and makes recommendations for the further development of the teaching of this subject in the school. The evaluation was conducted over two days during which the inspector visited classrooms and observed teaching and learning. The inspector interacted with students and teachers, examined students’ work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachers’ written preparation. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal and subject teachers. The board of management of the school was given an opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.
St Catherine’s has a current enrolment of 272 students and offers the Junior Certificate programme, Transition Year (TY), established Leaving Certificate and Leaving Certificate Vocational (LCVP) programmes. Within each of these programmes, Mathematics is offered at all three levels – higher, ordinary and foundation. On the basis of the current weekly timetable, first, second and third-year classes are timetabled with fourteen periods of Mathematics between them, TY has three periods and fourth and fifth years have twelve periods between them. These time allocations are consistent with syllabus recommendations. The distribution of class periods has recently been changed in response to teacher requests and, this year, many year groups have one or more double periods of Mathematics. The result is that, for all year groups other than third year, Mathematics does not occur on each day of the school week. The effectiveness of this arrangement should be reviewed by the mathematics teaching team before the end of the current year and amendments, if deemed necessary, again requested of school management.
The concurrent timetabling of mathematics classes currently happens across all year groups and indicates a strong commitment to the subject. Such a structure is highly effective in allowing access for students to all levels and facilitating students in changing level during their programme of studies. In line with good practice, first-year classes are taught as mixed-ability groupings, allowing them a settling-in period prior to making choices regarding level of study to be taken for the Junior Certificate. Given that first year Mathematics is taught to stand-alone mixed ability groups for the duration of the year, the concurrent timetabling of lessons within this year group should not be necessary, and its removal would ease some restrictions on timetable preparation for the school.
Teachers are timetabled by school management, and the levels at which they teach Mathematics are agreed taking into account the need for continuity within programmes and the policy of rotation within the team. It is a healthy sign of teachers’ commitment and expertise that two-thirds of team members are involved in the rotation of the Leaving Certificate higher-level course.
Students with difficulties in the area of numeracy are initially identified while in sixth class through contact with feeder primary schools, through entrance assessment tests and from information provided by parents. On entering first year, feedback from teachers of first-year mathematics classes provides additional information. Supports offered to address such students’ numeracy needs include the formation of small class groups, at both junior cycle and senior cycle. Such classes allow for greater levels of individual attention and facilitate the delivery of the foundation level syllabus in Mathematics.
Students identified as having special educational needs (SEN) are offered supplementary small-group support in Mathematics and English during timetabled subjects from which they are exempt or no longer study. While acknowledging the worthwhile work being done, care needs to be taken to ensure that mathematics support is targeted at students specifically identified as needing additional support in this area.
Material resources to enhance the teaching and learning of Mathematics are normally acquired on request to school management and following discussion and agreement among team members. Resources currently available in the school include demonstration geometry sets, mathematical tables and computer hardware and software. Many of these materials are stored in the co-ordinator’s classroom, to which all team members have access.
Mathematics is further promoted in St Catherine’s through participation in co-curricular activities such as the first-year mathematics quiz and Team Maths competition organised by the Irish Mathematics Teachers’ Association (IMTA), and training sessions for the Irish Mathematical Olympiad. A notable feature at the school, and one which deserves commendation, is the assistance offered to parents who wish to re-familiarise themselves with the second-level curriculum. Valuable information and guidance are provided, thus enabling parents engage with their son or daughter regarding homework and other school assignments.
The mathematics department of six teachers is co-ordinated, on a voluntary basis, by one of the team. The agreed role for the co-ordinator includes calling and chairing meetings, recording and filing minutes, co-ordinating planning activities, and disseminating information gathered at in-service courses. Formal meetings, facilitated around staff meeting times, take place about once per term. It is also possible for teachers to occasionally request team meetings outside of these times. Informal meetings between subgroups of the full team, for example those teachers teaching within the same year group, take place on a regular basis. Minutes of formal meetings are recorded and those for past and current years, going back to September 2005, were made available for inspection. This excellent practice of the maintenance of long-term records gives clear evidence of collaborative planning and review among team members and indicates a wide range of relevant discussions taking place through the years.
Significant work has gone into the development of the mathematics department plan that includes assessment policy and practice, school homework policy, policy on calculators and long-term work programmes for each year group and level. The effectiveness of these work programmes would be increased if, following the next review, there was included, for each topic, a suggested teaching strategy or strategies and supporting resources. The TY plan contains an appropriate mix of content and, commendably makes clear links with other curricular areas. The inclusion of project assessment and fieldwork and a broader list of relevant resources would further enhance this plan and see it more accurately reflecting the reported classroom experience.
The next stage for mathematics department planning at St Catherine’s is for teachers to work together to agree consistent approaches to the teaching of certain core elements of the syllabus. The benefits for students are clear, particularly on changing from one class to another. Such approaches should be agreed, not only among the mathematics team, but, in the longer term, across other subjects such as Science, Business, Geography and the technological subjects where Mathematics plays a role.
The department plan includes data on the Junior Certificate and Leaving Certificate examinations from 2005 to 2008 and there is a good level of awareness of the school’s standing in achievement levels and take-up rates. There is also clear evidence that analysis of these data contributes to planning and review activities.
Almost all teachers made personal planning and preparation materials available for inspection. Student handouts, worksheets, extensive supplies of test papers, prepared acetates and ‘real-life’ documentation for use in class provided evidence of good planning for resources. In addition, teacher notes and records of work covered in class, along with some personal evaluations of progress made in class were indicative of thorough preparation by a number of teachers.
Six lessons were observed during the inspection and in all cases teachers were well-prepared for their teaching. Pre-written acetates for use with the overhead projector, copies of detailed notes for students, a photocopied cut-out from a newspaper, worksheets and the raw materials for a simple student activity all served to either support teachers in their teaching or students in their learning. In most classes, the lesson objective was explicitly shared with students and, in line with good practice, linked with prior learning. In one instance, a lively and relevant guided discussion was used as a means of achieving the lesson objective and it also provided excellent links with ‘real life’ and the students’ own experiences.
The pace of lessons was generally sufficient to maintain students’ interest and provide an appropriate challenge. However, there were some occasions when an unnecessary amount of time was spent correcting homework or repeating examples. It is recommended that teachers look out for opportunities when differentiated teaching would be more appropriate, allowing some students work on alternative tasks to the class as a whole, in line with their competencies in the area.
In all lessons observed, teachers made appropriate and natural use of mathematical terminology. While there were instances where this could also be said of students, generally teachers need to encourage more active participation in class by students and support them in communicating using the correct subject-specific vocabulary. This can be done most simply through asking students to explain their workings to questions, to suggest next steps in examples or to accurately identify the nature of errors made in homework. In some lessons observed there were repeated references made to the chief examiner’s report on Leaving Certificate Mathematics, thus appropriately preparing students for certificate examinations and encouraging learning from the noted strengths and weaknesses of others.
All mathematics lessons observed were predominantly structured around the teacher presenting work at the board followed by the assigning of exercises for student practice. While recognising that this approach will always have relevance for mathematics teaching, it is recommended that teachers explore ways in which to include alternative student activities into class work. There was one example observed of a student survey conducted in class and the enthusiasm and energy created by this exercise clearly enhanced the learning experience.
At all times, the class atmosphere created was supportive and affirming for students and in a number of classrooms the physical environment was enhanced through the display of posters and graphs. Attitudes and behaviours indicated a strong sense of mutual respect between teachers and students. Overall, teachers had high but realistic expectations of students’ abilities and work and students responded appropriately.
Teachers monitor students’ progress by assigning and marking homework and class work and by tracking achievement in topic tests and in end-of-term examinations. There is widespread use within the mathematics team of common tests marked according to a common scheme, a practice that supports students in deciding on the level at which they will study the subject. The frequent use of such tests has led to the development of a substantial bank of question papers on all topics and at all levels. To build on this good practice, teachers are encouraged to investigate other possible assessment strategies in Mathematics. These might include the grading of project work, practical work, or participation in classroom activities.
A random sample of students’ copy books was examined during the inspection. Work contained therein was relevant to syllabus and level, was generally well-presented by students and was being monitored regularly by teachers.
Members of the mathematics department are very proud of achievements of students in co-curricular activities, as indicated by reference in department minutes to the school coming first in the Donegal IMTA first-year mathematics quiz.
Progress in Mathematics is reported to parents at parent-teacher meetings held once in the year for each year group, and through twice-yearly written reports. The student journal and school homework report are other means of communication between the school and individual students and their parents.
The following are the main strengths identified in the evaluation:
· The time allocations for Mathematics are consistent with syllabus recommendations. The concurrent timetabling of mathematics classes across all year groups is highly effective in allowing
access for students to all levels of the subject and facilitating change of level.
· The school offers assistance to parents to support their involvement in their child’s homework and other school assignments.
· The mathematics department maintains records of team meetings from current and previous years giving clear evidence of collaborative planning and review.
· Significant work has gone into the development of the mathematics department plan. In addition, there is clear evidence that the analysis of results and take-up rates in certificate examinations
contributes to planning and review activities.
· In most classes observed by the inspector, the lesson objective was explicitly shared with students and linked with prior learning.
· At all times, the classroom atmosphere was supportive and affirming for students. Attitudes and behaviours indicated a strong sense of mutual respect and students responded to
teachers’ high expectations.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· In the mathematics department plan, the effectiveness of work programmes should be increased with the inclusion of suggested teaching strategies and supporting resources.
· Teachers, both in Mathematics and in other curricular areas, should work together to develop consistent approaches to the teaching of certain core elements of the syllabus.
· Teachers should be alert to opportunities for differentiated teaching, when having students working on different tasks would present the most effective use of class time.
· To expand on the traditional approach to mathematics teaching, ways in which to include alternative student activities into class work should be explored.
A post-evaluation meeting was held with the teachers of Mathematics and the principal at the conclusion of the evaluation, when the draft findings and recommendations of the evaluation were presented and discussed.
Published June 2009